Analytical solution for the convectively-mixed atmospheric boundary layer
Ouwersloot, H.G.; Vilà-Guerau de Arellano, J.
2013-01-01
Based on the prognostic equations of mixed-layer theory assuming a zeroth order jump at the entrainment zone, analytical solutions for the boundary-layer height evolution are derived with different degrees of accuracy. First, an exact implicit expression for the boundary-layer height for a situation
Analytical Solutions for Beams Passing Apertures with Sharp Boundaries
Luz, Eitam; Malomed, Boris A
2016-01-01
An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the condition that the thickness of its edges is much smaller than any other length scale in the beam's initial profile. The approximation can be easily generalized for any beam whose initial profile has several sharp features. Therefore, this method can be used as a tool to investigate the diffraction of beams on complex obstacles. The analytical results are compared to numerical solutions and experimental findings, which demonstrates high accuracy of the approximation. For an initially uniform field confined by sharp boundaries, this solution becomes exact for any propagation distance and any sharpness of the edges. Thus, it can be used as an efficient tool to represent the beams, produced by series of slits with a complex structure, by a simple but exact analytical solution.
Ouwersloot, H.G.; Arellano, de J.V.G.
2013-01-01
In Ouwersloot and Vila-Guerau de Arellano (Boundary-Layer Meteorol. doi: 10. 1007/s10546-013-9816-z, 2013, this issue), the analytical solutions for the boundary-layer height and scalar evolutions are derived for the convective boundary layer, based on the prognostic equations of mixed-layer slab
An analytical solution for the Marangoni mixed convection boundary layer flow
DEFF Research Database (Denmark)
Moghimi, M. A.; Kimiaeifar, Amin; Rahimpour, M.
2010-01-01
In this article, an analytical solution for a Marangoni mixed convection boundary layer flow is presented. A similarity transform reduces the Navier-Stokes equations to a set of nonlinear ordinary differential equations, which are solved analytically by means of the homotopy analysis method (HAM...... the convergence of the solution. The numerical solution of the similarity equations is developed and the results are in good agreement with the analytical results based on the HAM....
Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan
2016-01-01
Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.
Analytical solution of the transpiration on the boundary layer flow ...
African Journals Online (AJOL)
An analysis is carried out to study the effects that blowing/injection and suction on the steady mixed convection or combined forced and free convection boundary layer flows over a vertical slender cylinder with a mainstream velocity and a wall surface temperature proportional to the axial distance along the surface of the ...
Ding, Xiao-Li; Nieto, Juan J.
2017-11-01
In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.
Wijnant, Ysbrand H.; Spiering, R.M.E.J.; Blijderveen, M.; de Boer, Andries
2006-01-01
Previous research has shown that viscothermal wave propagation in narrow gaps can efficiently be described by means of the low reduced frequency model. For simple geometries and boundary conditions, analytical solutions are available. For example, Beltman [4] gives the acoustic pressure in the gap
Latyshev, A. V.; Yushkanov, A. A.
2013-03-01
The second Stokes problem concerning the behavior of a rarefied gas in the half-space bounded over a plate undergoing harmonic in-plane oscillations is solved analytically using the Bhat-nagar-Gross-Krook equation with Cercignani boundary conditions for gas molecules reflecting from the wall. The distribution function of the gas molecules is constructed. The gas velocity in the half-space and near the wall, the drag force exerted by the gas on the boundary, and the energy dissipation rate per unit area of the oscillating plate are found.
The system of governing equations of a simplified slab model of the uniformly-mixed, purely convective, diurnal atmospheric boundary layer (ABL) is shown to allow immediate solutions for the potential temperature and specific humidity as functions of the ABL height and net radiation when expressed i...
Analytical solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subj...
Analytical solutions for tomato peeling with combined heat flux and convective boundary conditions
Cuccurullo, G.; Giordano, L.; Metallo, A.
2017-11-01
Peeling of tomatoes by radiative heating is a valid alternative to steam or lye, which are expensive and pollutant methods. Suitable energy densities are required in order to realize short time operations, thus involving only a thin layer under the tomato surface. This paper aims to predict the temperature field in rotating tomatoes exposed to the source irradiation. Therefore, a 1D unsteady analytical model is presented, which involves a semi-infinite slab subjected to time dependent heating while convective heat transfer takes place on the exposed surface. In order to account for the tomato rotation, the heat source is described as the positive half-wave of a sinusoidal function. The problem being linear, the solution is derived following the Laplace Transform Method. In addition, an easy-to-handle solution for the problem at hand is presented, which assumes a differentiable function for approximating the source while neglecting convective cooling, the latter contribution turning out to be negligible for the context at hand. A satisfying agreement between the two analytical solutions is found, therefore, an easy procedure for a proper design of the dry heating system can be set up avoiding the use of numerical simulations.
Luce, Charles H.; Tonina, Daniele; Applebee, Ralph; DeWeese, Timothy
2017-11-01
Two common refrains about using the one-dimensional advection diffusion equation to estimate fluid fluxes and thermal conductivity from temperature time series in streambeds are that the solution assumes that (1) the surface boundary condition is a sine wave or nearly so, and (2) there is no gradient in mean temperature with depth. Although the mathematical posing of the problem in the original solution to the problem might lead one to believe these constraints exist, the perception that they are a source of error is a fallacy. Here we develop a mathematical proof demonstrating the equivalence of the solution as developed based on an arbitrary (Fourier integral) surface temperature forcing when evaluated at a single given frequency versus that derived considering a single frequency from the beginning. The implication is that any single frequency can be used in the frequency-domain solutions to estimate thermal diffusivity and 1-D fluid flux in streambeds, even if the forcing has multiple frequencies. This means that diurnal variations with asymmetric shapes or gradients in the mean temperature with depth are not actually assumptions, and deviations from them should not cause errors in estimates. Given this clarification, we further explore the potential for using information at multiple frequencies to augment the information derived from time series of temperature.
Marshall, J. S.
2016-12-01
We analytically construct solutions for the mean first-passage time and splitting probabilities for the escape problem of a particle moving with continuous Brownian motion in a confining planar disc with an arbitrary distribution (i.e., of any number, size and spacing) of exit holes/absorbing sections along its boundary. The governing equations for these quantities are Poisson's equation with a (non-zero) constant forcing term and Laplace's equation, respectively, and both are subject to a mixture of homogeneous Neumann and Dirichlet boundary conditions. Our solutions are expressed as explicit closed formulae written in terms of a parameterising variable via a conformal map, using special transcendental functions that are defined in terms of an associated Schottky group. They are derived by exploiting recent results for a related problem of fluid mechanics that describes a unidirectional flow over "no-slip/no-shear" surfaces, as well as results from potential theory, all of which were themselves derived using the same theory of Schottky groups. They are exact up to the determination of a finite set of mapping parameters, which is performed numerically. Their evaluation also requires the numerical inversion of the parameterising conformal map. Computations for a series of illustrative examples are also presented.
Analytical Solution of Forced-Convective Boundary-Layer Flow over a Flat Plate
DEFF Research Database (Denmark)
Mirgolbabaei, H.; Barari, Amin; Ibsen, Lars Bo
2010-01-01
In this letter, the problem of forced convection heat transfer over a horizontal flat plate is investigated by employing the Adomian Decomposition Method (ADM). The series solution of the nonlinear differential equations governing on the problem is developed. Comparison between results obtained a...... and those of numerical solution shows excellent agreement, illustrating the effectiveness of the method. The solution obtained by ADM gives an explicit expression of temperature distribution and velocity distribution over a flat plate....
Directory of Open Access Journals (Sweden)
G. H. Gudmundsson
2008-07-01
Full Text Available New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow-ice-sheet approximation, and with solutions of the full Stokes equations. The shallow-ice-stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow-ice-sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow-ice-stream approximation overestimates the effects of bed topography perturbations on surface profile for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow-ice-stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow-ice-stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow-ice-sheet approximation. In particular, in contrast to the shallow-ice-sheet approximation, the shallow-ice-stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed given by solving a linearised version of the full Stokes system. In accordance with the full Stokes solutions, the shallow-ice-sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses.
Energy Technology Data Exchange (ETDEWEB)
Yokoi, T. [Building Research Institute, Tokyo (Japan); Sanchez-Sesma, F. [Universidad National Autonoma de Mexico, (Mexico). Institute de Ingenieria
1997-05-27
Formulation is introduced for discretizing a boundary integral equation into an indirect boundary element method for the solution of 3-dimensional topographic problems. Yokoi and Takenaka propose an analytical solution-capable reference solution (solution for the half space elastic body with flat free surface) to problems of topographic response to seismic motion in a 2-dimensional in-plane field. That is to say, they propose a boundary integral equation capable of effectively suppressing the non-physical waves that emerge in the result of computation in the wake of the truncation of the discretized ground surface making use of the wave field in a semi-infinite elastic body with flat free surface. They apply the proposed boundary integral equation discretized into the indirect boundary element method to solve some examples, and succeed in proving its validity. In this report, the equation is expanded to deal with 3-dimensional topographic problems. A problem of a P-wave vertically landing on a flat and free surface is solved by the conventional boundary integral equation and the proposed boundary integral equation, and the solutions are compared with each other. It is found that the new method, different from the conventional one, can delete non-physical waves from the analytical result. 4 figs.
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Alsaedi Ahmed
2009-01-01
Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.
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Te-Wen Tu
2015-01-01
Full Text Available An analytical solution for the heat transfer in hollow cylinders with time-dependent boundary condition and time-dependent heat transfer coefficient at different surfaces is developed for the first time. The methodology is an extension of the shifting function method. By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. The transformed system is thus solved by series expansion theorem. Limiting cases of the solution are studied and numerical results are compared with those in the literature. The convergence rate of the present solution is fast and the analytical solution is simple and accurate. Also, the influence of physical parameters on the temperature distribution of a hollow cylinder along the radial direction is investigated.
Energy Technology Data Exchange (ETDEWEB)
Goncalez, Tifani T. [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Segatto, Cynthia F.; Vilhena, Marco Tullio, E-mail: csegatto@pq.cnpq.b, E-mail: vilhena@pq.cnpq.b [Universidade Federal do Rio Grande do Sul (DMPA/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada
2011-07-01
In this work, we report an analytical solution for the set of S{sub N} equations for the angular flux, in a rectangle, using the double Laplace transform technique. Its main idea comprehends the steps: application of the Laplace transform in one space variable, solution of the resulting equation by the LTS{sub N} method and reconstruction of the double Laplace transformed angular flux using the inversion theorem of the Laplace transform. We must emphasize that we perform the Laplace inversion by the LTS{sub N} method in the x direction, meanwhile we evaluate the inversion in the y direction performing the calculation of the corresponding line integral solution by the Stefest method. We have also to figure out that the application of Laplace transform to this type of boundary value problem introduces additional unknown functions associated to the partial derivatives of the angular flux at boundary. Based on the good results attained by the nodal LTS{sub N} method, we assume that the angular flux at boundary is also approximated by an exponential function. By analytical we mean that no approximation is done along the solution derivation except for the exponential hypothesis for the exiting angular flux at boundary. For sake of completeness, we report numerical comparisons of the obtained results against the ones of the literature. (author)
Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Baleanu, Dumitru; Lorenzini, Giulio
2017-03-01
In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.
Directory of Open Access Journals (Sweden)
Muhammad Awais
Full Text Available Analysis has been done to investigate the heat generation/absorption effects in a steady flow of non-Newtonian nanofluid over a surface which is stretching linearly in its own plane. An upper convected Maxwell model (UCM has been utilized as the non-Newtonian fluid model in view of the fact that it can predict relaxation time phenomenon which the Newtonian model cannot. Behavior of the relaxations phenomenon has been presented in terms of Deborah number. Transport phenomenon with convective cooling process has been analyzed. Brownian motion "Db" and thermophoresis effects "Dt" occur in the transport equations. The momentum, energy and nanoparticle concentration profiles are examined with respect to the involved rheological parameters namely the Deborah number, source/sink parameter, the Brownian motion parameters, thermophoresis parameter and Biot number. Both numerical and analytic solutions are presented and found in nice agreement. Comparison with the published data is also made to ensure the validity. Stream lines for Maxwell and Newtonian fluid models are presented in the analysis.
Energy Technology Data Exchange (ETDEWEB)
Xie, Wei; Lei, Wei-Hua; Wang, Ding-Xiong, E-mail: leiwh@hust.edu.cn [School of Physics, Huazhong University of Science and Technology, Wuhan 430074 (China)
2016-12-20
A stellar-mass black hole (BH) surrounded by a neutrino-dominated accretion flow (NDAF) has been discussed in a number of works as the central engine of gamma-ray bursts (GRBs). It is widely believed that NDAF cannot liberate enough energy for bright GRBs. However, these works have been based on the assumption of a “no torque” boundary condition, which is invalid when the disk is magnetized. In this paper, we present both numerical and analytical solutions for NDAFs with non-zero boundary stresses and reexamine their properties. We find that an NDAF with such a boundary torque can be powerful enough to account for those bright short GRBs, energetic long GRBs, and ultra-long GRBs. The disk becomes viscously unstable, which makes it possible to interpret the variability of GRB prompt emission and the steep decay phase in the early X-ray afterglow. Finally, we study the gravitational waves radiated from a processing BH-NDAF. We find that the effects of the boundary torque on the strength of the gravitational waves can be ignored.
Directory of Open Access Journals (Sweden)
Hamid Khan
2012-01-01
Full Text Available We investigate squeezing flow between two large parallel plates by transforming the basic governing equations of the first grade fluid to an ordinary nonlinear differential equation using the stream functions ur(r,z,t=(1/r(∂ψ/∂z and uz(r,z,t=−(1/r(∂ψ/∂r and a transformation ψ(r,z=r2F(z. The velocity profiles are investigated through various analytical techniques like Adomian decomposition method, new iterative method, homotopy perturbation, optimal homotopy asymptotic method, and differential transform method.
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.
On Continuation of Solutions to Boundary Problems
DEFF Research Database (Denmark)
Modern investigation of the real-analytic continuability of solutions to boundary problems involves elements of complex and microlocal analysis, as well as the theory of pseudodifferential operators. Apart from its purely mathematical interest, this investigation can lead to significant improvement...... of numerical methods used in, e.g., acoustic and electromagnetic scattering. In this talk, I shall take as the starting point the desire to improve one such numerical method, namely the so-called Method of Auxiliary Sources (MAS). The latter is a promising numerical scheme, with the potential of replacing...... the traditional boundary layer formulations in the numerical solution of scattering problems. To address the convergence issues inherent to the MAS, I shall introduce a relevant general real-analytic continuation problem and describe how it can be reformulated in terms of an analytic Cauchy problem in the complex...
Directory of Open Access Journals (Sweden)
M.J. Uddin
2016-03-01
Full Text Available This paper deals with an analytical solution of free convective flow of dilatant nanofluid past a vertical cone/plate. A two-phase mixture model is used for nanofluid in which the Brownian motion and thermophoretic diffusivities are the important slip mechanisms between solid and liquid phases. The governing transport equations along with physically realistic thermal and mass convective boundary conditions are reduced to similarity equations using relevant similarity transformations before being solved by homotopy analysis method. The effects of the governing parameters (Brownian motion, thermophoresis, convection–conduction, convection–diffusion, Lewis number, buoyancy ratio, and power-law on the dimensionless velocity, temperature and nanoparticle volume fraction, friction and heat transfer rates are plotted and discussed. It is found that friction factor decreases with the increase in Le and Nr for both vertical plate and cone. The local Nusselt number decreases with the increase in the thermophoresis and Brownian motion parameters for both the plate and cone. The local Sherwood number increases with the Brownian motion parameter and decreases for thermophoresis parameter. The results have been compared with the published ones and an excellent agreement has been noticed.
Asgharzadeh, Hafez; Borazjani, Iman
2017-02-15
The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the
Boundary Value Problems and Approximate Solutions ...
African Journals Online (AJOL)
In this paper, we discuss about some basic things of boundary value problems. Secondly, we study boundary conditions involving derivatives and obtain finite difference approximations of partial derivatives of boundary value problems. The last section is devoted to determine an approximate solution for boundary value ...
Boundary Value Problems and Approximate Solutions
African Journals Online (AJOL)
Tadesse
2. METHODOLOGY. The finite difference method for the solution of a two point boundary value problem consists in replacing the derivatives present in the differential equation and the boundary conditions with the help of finite difference approximations and then solving the resulting linear system of equations by a standard ...
Analytic solution of an oscillatory migratory α2 stellar dynamo
Brandenburg, A.
2017-02-01
Context. Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant α effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant α. Aims: We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant α, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two boundaries. Methods: We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions. Results: The solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The field always migrates away from the perfect conductor boundary toward the vacuum boundary, independently of the sign of α. Conclusions: The obtained solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory migratory dynamos are possible with constant α.
A combined analytic-numeric approach for some boundary-value problems
Directory of Open Access Journals (Sweden)
Mustafa Turkyilmazoglu
2016-02-01
Full Text Available A combined analytic-numeric approach is undertaken in the present work for the solution of boundary-value problems in the finite or semi-infinite domains. Equations to be treated arise specifically from the boundary layer analysis of some two and three-dimensional flows in fluid mechanics. The purpose is to find quick but accurate enough solutions. Taylor expansions at either boundary conditions are computed which are next matched to the other asymptotic or exact boundary conditions. The technique is applied to the well-known Blasius as well as Karman flows. Solutions obtained in terms of series compare favorably with the existing ones in the literature.
Zou, Li; Liang, Songxin; Li, Yawei; Jeffrey, David J.
2017-03-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Energy Technology Data Exchange (ETDEWEB)
Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics
2017-06-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Fuzzy Weighted Average: Analytical Solution
van den Broek, P.M.; Noppen, J.A.R.
2009-01-01
An algorithm is presented for the computation of analytical expressions for the extremal values of the α-cuts of the fuzzy weighted average, for triangular or trapeizoidal weights and attributes. Also, an algorithm for the computation of the inverses of these expressions is given, providing exact
The boundary value problem for discrete analytic functions
Skopenkov, Mikhail
2013-06-01
This paper is on further development of discrete complex analysis introduced by R.Isaacs, J.Ferrand, R.Duffin, and C.Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is called discrete analytic, if for each face the difference quotients along the two diagonals are equal.We prove that the Dirichlet boundary value problem for the real part of a discrete analytic function has a unique solution. In the case when each face has orthogonal diagonals we prove that this solution uniformly converges to a harmonic function in the scaling limit. This solves a problem of S.Smirnov from 2010. This was proved earlier by R.Courant-K.Friedrichs-H.Lewy and L.Lusternik for square lattices, by D.Chelkak-S.Smirnov and implicitly by P.G.Ciarlet-P.-A.Raviart for rhombic lattices.In particular, our result implies uniform convergence of the finite element method on Delaunay triangulations. This solves a problem of A.Bobenko from 2011. The methodology is based on energy estimates inspired by alternating-current network theory. © 2013 Elsevier Ltd.
Analytical solution of one dimensional temporally dependent ...
African Journals Online (AJOL)
... chemically non-reactive. The first order decay term which is inversely proportional to the dispersion coefficient is also considered. Initially the porous domain is considered solute free. Analytical solutions are obtained by using Laplace transform technique for continuous uniform and increasing input source concentration.
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.
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.
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...
Analytical Solution for the Time-Fractional Telegraph Equation
Directory of Open Access Journals (Sweden)
F. Huang
2009-01-01
Full Text Available We discuss and derive the analytical solution for three basic problems of the so-called time-fractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variable t and x, respectively. the appropriate structures and negative prosperities for their Green functions are provided. The boundary problem in a bounded space domain is also solved by the spatial Sine transform and temporal Laplace transform, whose solution is given in the form of a series.
Analytical solution of population balance equation involving ...
Indian Academy of Sciences (India)
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 ... 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 ...
ANALYTICAL BENDING SOLUTION OF ALL CLAMPED ISOTROPIC ...
African Journals Online (AJOL)
ANALYTICAL BENDING SOLUTION OF ALL CLAMPED ISOTROPIC RECTANGULAR PLATE ON WINKLERâ€™S FOUNDATION USING CHARACTERISTIC ... The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).
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.
Manufactured analytical solutions for isothermal full-Stokes ice sheet models
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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.
Solute transport with multiprocess nonequilibrium: a semi-analytical solution approach
Neville, Christopher J.; Ibaraki, Motomu; Sudicky, Edward A.
2000-07-01
A semi-analytical solution for the simulation of one-dimensional subsurface solute transport incorporating multiple nonequilibrium processes is presented. The solution is based on the theory developed by Brusseau et al. (1992) [Brusseau, M.L., Jessup, R.E., Rao, P.S.C., 1992. Modeling solute transport influenced by multiprocess nonequilibrium and transformation reactions. Water Resources Research 28 (1), 175-182.] which is a generalized combination of two-site and two-region model. In addition to developing a semi-analytical complement to their numerical solution, we extend the range of boundary and initial conditions considered. The semi-analytical solution can represent domains of both finite and semi-infinite extent and accommodates nonzero initial concentrations. The solution is derived in Laplace space and final results are obtained using an accurate and robust numerical inversion algorithm. The solution is particularly well suited for interpreting experimental results obtained under controlled laboratory conditions. Identification of the input parameters for the solution is examined by simulating a column experiment by van Genuchten (1974) [van Genuchten, M., 1974. Mass Transfer Studies in Sorbing Porous Media. PhD thesis, New Mexico State University, Las Cruces, NM.].
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.
Analytic, High-beta Solutions of the Helical Grad-Shafranov Equation
Energy Technology Data Exchange (ETDEWEB)
D.R. Smith; A.H. Reiman
2004-05-19
We present analytic, high-beta ({beta} {approx} O(1)), helical equilibrium solutions for a class of helical axis configurations having large helical aspect ratio, with the helix assumed to be tightly wound. The solutions develop a narrow boundary layer of strongly compressed flux, similar to that previously found in high beta tokamak equilibrium solutions. The boundary layer is associated with a strong localized current which prevents the equilibrium from having zero net current.
Analytic theory of curvature effects for wave problems with general boundary conditions
DEFF Research Database (Denmark)
Willatzen, Morten; Gravesen, Jens; Voon, L. C. Lew Yan
2010-01-01
A formalism based on a combination of differential geometry and perturbation theory is used to obtain analytic expressions for confined eigenmode changes due to general curvature effects. In cases of circular-shaped and helix-shaped structures, where alternative analytic solutions can be found......, the perturbative solution is shown to yield the same result. The present technique allows the generalization of earlier results to arbitrary boundary conditions. The power of the method is illustrated using examples based on Maxwell’s and Schrödinger’s equations for applications in photonics and nanoelectronics....
Directory of Open Access Journals (Sweden)
Rai Nath Kabindra Rajeev
2009-01-01
Full Text Available In this paper, the solution of the one dimensional moving boundary problem with periodic boundary conditions is obtained with the help of variational iterational method. By using initial and boundary values, the explicit solutions of the equations have been derived, which accelerate the rapid convergence of the series solution. The method performs extremely well in terms of efficiency and simplicity. The temperature distribution and the position of moving boundary are evaluated and numerical results are presented graphically.
Boundary and analytic attitude: reflections on a summer holiday break.
Wright, Susanna
2016-06-01
The effect of a boundary in analytic work at the summer holiday break is discussed in relation to archetypal experiences of exclusion, loss and limitation. Some attempts by patients to mitigate an analyst's act of separation are reviewed as enactments, and in particular the meanings of a gift made by one patient. Analytic attitude towards enactment from within different schools of practice is sketched, with reference to the effect on the analyst of departing from the received practice of their own allegiance. A theory is adumbrated that the discomfort of 'contravening the rules' has a useful effect in sparking the analyst into consciousness, with greater attention to salient features in an individual case. Interpretation as an enactment is briefly considered, along with the possible effects of containing the discomfort of a patient's enactment in contrast to confronting it with interpretation. © 2016, The Society of Analytical Psychology.
Stationary solutions and Neumann boundary conditions in the Sivashinsky equation.
Denet, Bruno
2006-09-01
New stationary solutions of the (Michelson) Sivashinsky equation of premixed flames are obtained numerically in this paper. Some of these solutions, of the bicoalescent type recently described by Guidi and Marchetti, are stable with Neumann boundary conditions. With these boundary conditions, the time evolution of the Sivashinsky equation in the presence of a moderate white noise is controlled by jumps between stationary solutions.
Applying the method of fundamental solutions to harmonic problems with singular boundary conditions
Valtchev, Svilen S.; Alves, Carlos J. S.
2017-07-01
The method of fundamental solutions (MFS) is known to produce highly accurate numerical results for elliptic boundary value problems (BVP) with smooth boundary conditions, posed in analytic domains. However, due to the analyticity of the shape functions in its approximation basis, the MFS is usually disregarded when the boundary functions possess singularities. In this work we present a modification of the classical MFS which can be applied for the numerical solution of the Laplace BVP with Dirichlet boundary conditions exhibiting jump discontinuities. In particular, a set of harmonic functions with discontinuous boundary traces is added to the MFS basis. The accuracy of the proposed method is compared with the results form the classical MFS.
Boundary properties of solutions of equations of minimal surface kind
Miklyukov, V. M.
2001-10-01
Generalized solutions of equations of minimal-surface type are studied. It is shown that a solution makes at most countably many jumps at the boundary. In particular, a solution defined in the exterior of a disc extends by continuity to the boundary circle everywhere outside a countable point set. An estimate of the sum of certain non-local characteristics of the jumps of a solution at the boundary is presented. A result similar to Fatou's theorem on angular boundary values is proved.
Analytical solutions for the recovery tests after constant-discharge ...
African Journals Online (AJOL)
A new analytical solution for residual drawdown during the recovery period after a constant rate pumping test is described. A comparison between the proposed solution, existing solutions and experimental data from field observation are presented. The proposed analytical solution is in perfect agreement with the ...
Directory of Open Access Journals (Sweden)
Hammad Khalil
2016-01-01
Full Text Available The paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions, m^-point nonlocal boundary conditions and mixed derivative boundary conditions. We develop some new operational matrices. These matrices are used along with some previously derived results to convert the problem under consideration into a system of easily solvable matrix equations. The convergence of the developed scheme is studied analytically and is conformed by solving some test problems.
Analytical Solution for Reactive Solute Transport Considering Incomplete Mixing
Bellin, A.; Chiogna, G.
2013-12-01
The laboratory experiments of Gramling et al. (2002) showed that incomplete mixing at the pore scale exerts a significant impact on transport of reactive solutes and that assuming complete mixing leads to overestimation of product concentration in bimolecular reactions. We consider here the family of equilibrium reactions for which the concentration of the reactants and the product can be expressed as a function of the mixing ratio, the concentration of a fictitious non reactive solute. For this type of reactions we propose, in agreement with previous studies, to model the effect of incomplete mixing at scales smaller than the Darcy scale assuming that the mixing ratio is distributed within an REV according to a Beta distribution. We compute the parameters of the Beta model by imposing that the mean concentration is equal to the value that the concentration assumes at the continuum Darcy scale, while the variance decays with time as a power law. We show that our model reproduces the concentration profiles of the reaction product measured in the Gramling et al. (2002) experiments using the transport parameters obtained from conservative experiments and an instantaneous reaction kinetic. The results are obtained applying analytical solutions both for conservative and for reactive solute transport, thereby providing a method to handle the effect of incomplete mixing on multispecies reactive solute transport, which is simpler than other previously developed methods. Gramling, C. M., C. F. Harvey, and L. C. Meigs (2002), Reactive transport in porous media: A comparison of model prediction with laboratory visualization, Environ. Sci. Technol., 36(11), 2508-2514.
Spline solutions for nonlinear two point boundary value problems
Directory of Open Access Journals (Sweden)
Riaz A. Usmani
1980-01-01
Full Text Available Necessary formulas are developed for obtaining cubic, quartic, quintic, and sextic spline solutions of nonlinear boundary value problems. These methods enable us to approximate the solution of the boundary value problems, as well as their successive derivatives smoothly. Numerical evidence is included to demonstrate the relative performance of these four techniques.
Influence of boundary conditions on the solution of a hyperbolic thermoelasticity problem
Vitokhin, Evgeniy Yu.; Babenkov, Mikhail B.
2017-03-01
We consider a series of problems with a short laser impact on a thin metal layer accounting various boundary conditions of the first and second kind. The behavior of the material is modeled by the hyperbolic thermoelasticity of Lord-Shulman type. We obtain analytical solutions of the problems in the semi-coupled formulation and numerical solutions in the coupled formulation. Numerical solutions are compared with the analytical ones. The analytical solutions of the semi-coupled problems and numerical solutions of the coupled problems show qualitative match. The solutions of hyperbolic thermoelasticity problems are compared with those obtained in the frame of the classical thermoelasticity. It was determined that the most prominent difference between the classical and hyperbolic solutions arises in the problem with fixed boundaries and constant temperature on them. The smallest differences were observed in the problem with unconstrained, thermally insulated edges. It was shown that a cooling zone is observed if the boundary conditions of the first kind are given for the temperature. Analytical expressions for the velocities of the quasiacoustic and quasithermal fronts as well as the critical value for the attenuation coefficient of the excitation impulse are verified numerically.
Global solution branches of two point boundary value problems
Schaaf, Renate
1990-01-01
The book deals with parameter dependent problems of the form u"+*f(u)=0 on an interval with homogeneous Dirichlet or Neuman boundary conditions. These problems have a family of solution curves in the (u,*)-space. By examining the so-called time maps of the problem the shape of these curves is obtained which in turn leads to information about the number of solutions, the dimension of their unstable manifolds (regarded as stationary solutions of the corresponding parabolic prob- lem) as well as possible orbit connections between them. The methods used also yield results for the period map of certain Hamiltonian systems in the plane. The book will be of interest to researchers working in ordinary differential equations, partial differential equations and various fields of applications. By virtue of the elementary nature of the analytical tools used it can also be used as a text for undergraduate and graduate students with a good background in the theory of ordinary differential equations.
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.
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.
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)
Wexler, Eliezer J.
1992-01-01
Analytical solutions to the advective-dispersive solute-transport equation are useful in predicting the fate of solutes in ground water. Analytical solutions compiled from available literature or derived by the author are presented for a variety of boundary condition types and solute-source configurations in one-, two-, and three-dimensional systems having uniform ground-water flow. A set of user-oriented computer programs was created to evaluate these solutions and to display the results in tabular and computer-graphics format. These programs incorporate many features that enhance their accuracy, ease of use, and versatility. Documentation for the programs describes their operation and required input data, and presents the results of sample problems. Derivations of selected solutions, source codes for the computer programs, and samples of program input and output also are included.
Solutions of boundary-value problems in discretized volumes
Directory of Open Access Journals (Sweden)
Mihaly Makai
2002-01-01
Full Text Available The solution of a boundary-value problem in a volume discretized by finitely many copies of a tile is obtained via a Green's function. The algorithm for constructing the solution exploits results from graph and group theory. This technique produces integral equations on the internal and external boundaries of the volume and demonstrates that two permutation matrices characterize the symmetries of the volume. We determine the number of linearly independent solutions required over the tile and the conditions needed for two boundary-value problems to be isospectral. Our method applies group theoretical considerations to asymmetric volumes.
Finite element solution theory for three-dimensional boundary flows
Baker, A. J.
1974-01-01
A finite element algorithm is derived for the numerical solution of a three-dimensional flow field described by a system of initial-valued, elliptic boundary value partial differential equations. The familiar three-dimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.
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.
Analytic solutions for groundwater whirls in box-shaped, layered anisotropic aquifers.
Bakker, M.; Hemker, C.J.
2004-01-01
Analytic solutions are derived for flow through an elongated box-shaped aquifer that is bounded on the left, right, top and bottom sides by impermeable boundaries; the head gradient normal to the ends of the box is specified to be constant. The aquifer consists of a number of horizontal layers, each
Numerical solutions of fifth order boundary value problems using ...
African Journals Online (AJOL)
Mamadu-Njoseh polynomials are polynomials constructed in the interval [-1,1] with respect to the weight function () = 2 + 1. This paper aims at applying these polynomials, as trial functions satisfying the boundary conditions, in a numerical approach for the solution of fifth order boundary value problems. For this, these ...
Positive solutions for higher order singular p-Laplacian boundary ...
Indian Academy of Sciences (India)
This paper investigates 2 m − t h ( m ≥ 2 ) order singular -Laplacian boundary value problems, and obtains the necessary and sufficient conditions for existence of positive solutions for sublinear 2-th order singular -Laplacian BVPs on closed interval.
Chen, Jui-Sheng; Li, Loretta Y.; Lai, Keng-Hsin; Liang, Ching-Ping
2017-11-01
A novel solution method is presented which leads to an analytical model for the advective-dispersive transport in a semi-infinite domain involving a wide spectrum of boundary inputs, initial distributions, and zero-order productions. The novel solution method applies the Laplace transform in combination with the generalized integral transform technique (GITT) to obtain the generalized analytical solution. Based on this generalized analytical expression, we derive a comprehensive set of special-case solutions for some time-dependent boundary distributions and zero-order productions, described by the Dirac delta, constant, Heaviside, exponentially-decaying, or periodically sinusoidal functions as well as some position-dependent initial conditions and zero-order productions specified by the Dirac delta, constant, Heaviside, or exponentially-decaying functions. The developed solutions are tested against an analytical solution from the literature. The excellent agreement between the analytical solutions confirms that the new model can serve as an effective tool for investigating transport behaviors under different scenarios. Several examples of applications, are given to explore transport behaviors which are rarely noted in the literature. The results show that the concentration waves resulting from the periodically sinusoidal input are sensitive to dispersion coefficient. The implication of this new finding is that a tracer test with a periodic input may provide additional information when for identifying the dispersion coefficients. Moreover, the solution strategy presented in this study can be extended to derive analytical models for handling more complicated problems of solute transport in multi-dimensional media subjected to sequential decay chain reactions, for which analytical solutions are not currently available.
RETRACTED ARTICLE: The Effect of Solute Atoms on Grain Boundary Migration: A Solute Pinning Approach
Hersent, Emmanuel; Marthinsen, Knut; Nes, Erik
2012-12-01
The effect of solute atoms on grain boundary migration has been modeled on the basis of the idea that solute atoms will locally perturb the collective rearrangements of solvent atoms associated with boundary migration. The consequence of such perturbations is the cusping of the boundary and corresponding stress concentrations on the solute atoms which will promote thermal activation of these atoms out of the boundary. This thermal activation is considered to be the rate-controlling mechanism in boundary migration. It is demonstrated that the present statistical approach is capable of explaining, in phenomenological terms, the known effects of solute atoms on boundary migration. The experimental results on the effect of copper on boundary migration in aluminum, due to Gordon and Vandermeer, have been well accounted for.
Directory of Open Access Journals (Sweden)
Mark A Lau
2016-09-01
Full Text Available This paper presents the implementation of numerical and analytical solutions of some of the classical partial differential equations using Excel spreadsheets. In particular, the heat equation, wave equation, and Laplace’s equation are presented herein since these equations have well known analytical solutions. The numerical solutions can be easily obtained once the differential equations are discretized via finite differences and then using cell formulas to implement the resulting recursive algorithms and other iterative methods such as the successive over-relaxation (SOR method. The graphing capabilities of spreadsheets can be exploited to enhance the visualization of the solutions to these equations. Furthermore, using Visual Basic for Applications (VBA can greatly facilitate the implementation of the analytical solutions to these equations, and in the process, one obtains Fourier series approximations to functions governing initial and/or boundary conditions.
Analyticity of solutions of singular fractional differential equations
Kangro, Urve
2016-06-01
We study singular fractional differential equations in spaces of analytic functions. We reformulate the equation as a cordial Volterra integral equation of the second kind and use results from the theory of cordial Volterra integral equations. This enables us to obtain conditions under which the equation has a unique analytic solution. Note that the smooth solution in this case is unique without any initial conditions; in fact, giving initial conditions usually results in nonsmooth solution. We also consider approximate solution of these equations and prove exponential convergence of approximate solutions to the exact solution.
SOLUTION TO THE PROBLEM OF THERMOELASTIC VIBRATION OF A PLATE IN SPECIAL BOUNDARY CONDITIONS
Directory of Open Access Journals (Sweden)
Egorychev Oleg Aleksandrovich
2012-10-01
Full Text Available Operating conditions of uneven non-stationary heating can cause changes in physical and mechanical properties of materials. The awareness of the value and nature of thermal stresses is needed to perform a comprehensive analysis of structural strength. The authors provide their solution to the problem of identification of natural frequencies of vibrations of rectangular plates, whenever a thermal factor is taken into account. In the introductory section of the paper, the authors provide the equation describing the thermoelastic vibration of a plate and set the initial and boundary conditions. Furthermore, the authors provide a frequency equation derivation for the problem that has an analytical solution available (if all edges are simply supported at zero temperature. The equation derived by the authors has no analytical solution and can be solved only numerically. In the middle of the paper, the authors describe a method of frequency equation derivation for plates exposed to special boundary conditions, if the two opposite edges are simply supported at zero temperature, while the two other edges have arbitrary types of fixation and arbitrary thermal modes. For this boundary condition derived as a general solution, varying fixation of the two edges makes it possible to obtain transcendental trigonometric equations reducible to algebraic frequency equations by using expending in series. Thus, the obtaining frequency equations different from the general solution becomes possible for different types of boundary conditions. The final section of the paper covers the practical testing of the described method for the problem that has an analytical solution (all edges are simply supported at zero temperature as solved above. An approximate equation provided in the research leads to the analytical solution that is already available.
Directory of Open Access Journals (Sweden)
John Graef
2013-09-01
Full Text Available The authors consider a nonlinear fractional boundary value problem with the Dirichlet boundary condition. An associated Green's function is constructed as a series of functions by applying spectral theory. Criteria for the existence and uniqueness of solutions are obtained based on it.
Positive solutions for higher order singular p-Laplacian boundary ...
Indian Academy of Sciences (India)
of positive solutions for sublinear 2m-th order singular p-Laplacian BVPs on closed interval. Keywords. Positive solution; singular BVPs; sufficient and necessary conditions; p-Laplacian equations. 1. Introduction. In this paper, we are concerned with higher order singular p-Laplacian boundary value problems. ⎧. ⎨. ⎩.
A numerical solution of a singular boundary value problem arising in boundary layer theory.
Hu, Jiancheng
2016-01-01
In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.
Analytical solution for soil water redistribution during evaporation process.
Teng, Jidong; Yasufuku, Noriyuki; Liu, Qiang; Liu, Shiyu
2013-01-01
Simulating the dynamics of soil water content and modeling soil water evaporation are critical for many environmental and agricultural strategies. The present study aims to develop an analytical solution to simulate soil water redistribution during the evaporation process. This analytical solution was derived utilizing an exponential function to describe the relation of hydraulic conductivity and water content on pressure head. The solution was obtained based on the initial condition of saturation and an exponential function to model the change of surface water content. Also, the evaporation experiments were conducted under a climate control apparatus to validate the theoretical development. Comparisons between the proposed analytical solution and experimental result are presented from the aspects of soil water redistribution, evaporative rate and cumulative evaporation. Their good agreement indicates that this analytical solution provides a reliable way to investigate the interaction of evaporation and soil water profile.
Analytic solutions in nonlinear massive gravity.
Koyama, Kazuya; Niz, Gustavo; Tasinato, Gianmassimo
2011-09-23
We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free nonlinear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism, recovering general relativity below a Vainshtein radius given by (r(g)m(2))(1/3), where m is the graviton mass and r(g) is the Schwarzschild radius of a matter source. Another branch of exact solutions exists, corresponding to de Sitter-Schwarzschild spacetimes where the curvature scale of de Sitter space is proportional to the mass squared of the graviton.
Analytical solutions of one-dimensional advection–diffusion ...
Indian Academy of Sciences (India)
Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal ﬁnite initially solute free domain,for two dispersion problems.In the ﬁrst one,temporally dependent solute dispersion along uniform ﬂow in homogeneous domain is studied.In the second problem the ...
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 travelling wave solutions and parameter analysis for the ...
Indian Academy of Sciences (India)
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 ...
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 population balance equation involving ...
Indian Academy of Sciences (India)
Laplace transform obtained from literature. ... used in the literature. Keywords. Population balance; aggregation; breakage; auxiliary equation method; Laplace transform. PACS Nos 02.70.−c; 02.30.Mv; 02.30.Jr. 1. ...... assumptions proposed earlier, a more realistic representation of the solutions is obtained compared to the ...
Analytical Solutions To Describe Juxtaposed Sands | Adeniji ...
African Journals Online (AJOL)
... face flow rate, but can be extended, using convolution integral that can be deconvolved by Laplace transformation, to correct for storage capacity of the well bore and near well bore complexities. These solutions can improve design and analysis of interference testing. Type curves are presented to characterize flow regime ...
Analytical construction of peaked solutions for the nonlinear ...
African Journals Online (AJOL)
We obtain analytical solutions, by way of the homotopy analysis method, to a nonlinear wave equation describing the nonlinear evolution of a vector potential of an electromagnetic pulse propagating in an arbitrary pair plasma with temperature asymmetry. As the method is analytical, we are able to construct peaked ...
Numerical solutions of telegraph equations with the Dirichlet boundary condition
Ashyralyev, Allaberen; Turkcan, Kadriye Tuba; Koksal, Mehmet Emir
2016-08-01
In this study, the Cauchy problem for telegraph equations in a Hilbert space is considered. Stability estimates for the solution of this problem are presented. The third order of accuracy difference scheme is constructed for approximate solutions of the problem. Stability estimates for the solution of this difference scheme are established. As a test problem to support theoretical results, one-dimensional telegraph equation with the Dirichlet boundary condition is considered. Numerical solutions of this equation are obtained by first, second and third order of accuracy difference schemes.
Second-order analytic solutions for re-entry trajectories
Kim, Eun-Kyou
1993-01-01
With the development of aeroassist technology, either for near-earth orbital transfer with or without a plane change or for planetary aerocapture, it is of interest to have accurate analytic solutions for reentry trajectories in an explicit form. Starting with the equations of motion of a non-thrusting aerodynamic vehicle entering a non-rotating spherical planetary atmosphere, a normalization technique is used to transform the equations into a form suitable for an analytic integration. Then, depending on the type of planar entry modes with a constant angle-of-attack, namely, ballistic fly-through, lifting skip, and equilibrium glide trajectories, the first-order solutions are obtained with the appropriate simplification. By analytic continuation, the second-order solutions for the altitude, speed, and flight path angle are derived. The closed form solutions lead to explicit forms for the physical quantities of interest, such as the deceleration and aerodynamic heating rates. The analytic solutions for the planar case are extended to three-dimensional skip trajectories with a constant bank angle. The approximate solutions for the heading and latitude are developed to the second order. In each type of trajectory examined, explicit relations among the principal variables are in a form suitable for guidance and navigation purposes. The analytic solutions have excellent agreement with the numerical integrations. They also provide some new results which were not reported in the existing classical theory.
High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities
2015-03-31
elliptic equations . In Proceedings of the Soviet-American Conference on Partial Differential Equations , pages 303–304, Novosibirsk, Moscow, Russia, 1963...193, 2012. [19] L. Fox and R. Sankar. Boundary singularities in linear elliptic differential equations . J. Inst. Math. Appl., 5:340–350, 1969. [20] D.S...57] R.S. Lehman. Developments at an analytic corner of solutions of elliptic partial differential equations . J. Math. Mech., 8:727–760, 1959. [58
Directory of Open Access Journals (Sweden)
Hussein A. H. Salem
2013-01-01
Full Text Available The object of this paper is to investigate the existence of a class of solutions for some boundary value problems of fractional order with integral boundary conditions. The considered problems are very interesting and important from an application point of view. They include two, three, multipoint, and nonlocal boundary value problems as special cases. We stress on single and multivalued problems for which the nonlinear term is assumed only to be Pettis integrable and depends on the fractional derivative of an unknown function. Some investigations on fractional Pettis integrability for functions and multifunctions are also presented. An example illustrating the main result is given.
Multiple Solutions for a Class of Fractional Boundary Value Problems
Directory of Open Access Journals (Sweden)
Ge Bin
2012-01-01
Full Text Available We study the multiplicity of solutions for the following fractional boundary value problem: where and are the left and right Riemann-Liouville fractional integrals of order , respectively, is a real number, is a given function, and is the gradient of at . The approach used in this paper is the variational method. More precisely, the Weierstrass theorem and mountain pass theorem are used to prove the existence of at least two nontrivial solutions.
Rugate filter design: An analytical approach using uniform WKB solutions
Perelman, N.; Averbukh, I.
1996-03-01
An analytical approach to the design of rugate filters with a smooth amplitude modulation of the sine-wave index is developed. The approach is based on the uniform WKB solutions (asymptotic expansions) of the coupled-wave equations. A closed-form solution for the inverse problem (finding the refractive index profile for a given reflectance shape inside the stop band) is found.
Analytical solutions for one-dimensional advection–dispersion ...
Indian Academy of Sciences (India)
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.
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.
Multiplicity of solutions for elliptic boundary value problems
Directory of Open Access Journals (Sweden)
Yiwei Ye
2014-06-01
Full Text Available In this article, we study the existence of infinitely many solutions for the semilinear elliptic equation $-\\Delta u+a(xu=f(x,u$ in a bounded domain of $\\mathbb{R}^N$ $(N\\geq 3$ with the Dirichlet boundary conditions, where the primitive of the nonlinearity $f$ is either superquadratic at infinity or subquadratic at zero.
Periodic solutions of a certain nonlinear boundary value problem ...
African Journals Online (AJOL)
... differential equation formed the basis for a theorem for existence of periodic solutions for the nonlinear boundary value problem of a fourth order differential equation. The proof of the theorem is by the Leray-Schauder fixed point technique with the use of integrated equation as the mode for estimating the a priori bounds.
Existence of solutions for fractional differential inclusions with boundary conditions
Directory of Open Access Journals (Sweden)
Dandan Yang
2010-07-01
Full Text Available This article concerns the existence of solutions for fractional-order differential inclusions with boundary-value conditions. The main tools are based on fixed point theorems due to Bohnerblust-Karlin and Leray-Schauder together with a continuous selection theorem for upper semi-continuous multi-valued maps.
Positive Solutions for Some Beam Equation Boundary Value Problems
Directory of Open Access Journals (Sweden)
Xu Weiya
2009-01-01
Full Text Available A new fixed point theorem in a cone is applied to obtain the existence of positive solutions of some fourth-order beam equation boundary value problems with dependence on the first-order derivative where is continuous.
Transmission Line Adapted Analytical Power Charts Solution
Sakala, Japhet D.; Daka, James S. J.; Setlhaolo, Ditiro; Malichi, Alec Pulu
2017-08-01
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.
A comprehensive analytical solution of the nonlinear pendulum
Energy Technology Data Exchange (ETDEWEB)
Ochs, Karlheinz, E-mail: ochs@ieee.org [Chair of Communications, Department of Electrical Engineering and Information Technology, Ruhr-University Bochum (Germany)
2011-03-15
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 and starts with the solution of a pendulum that swings over. Due to a meticulous sign correction term, this solution is also valid if the pendulum does not swing over.
On analytic continuability of the missing Cauchy datum for Helmholtz boundary problems
DEFF Research Database (Denmark)
Karamehmedovic, Mirza
2015-01-01
We relate the domains of analytic continuation of Dirichlet and Neumann boundary data for Helmholtz problems in two or more independent variables. The domains are related à priori, locally and explicitly in terms of complex polyrectangular neighbourhoods of planar pieces of the boundary. To this ......We relate the domains of analytic continuation of Dirichlet and Neumann boundary data for Helmholtz problems in two or more independent variables. The domains are related à priori, locally and explicitly in terms of complex polyrectangular neighbourhoods of planar pieces of the boundary...
Analytical investigation of boundary layer growth and swirl intensity decay rate in a pipe
Energy Technology Data Exchange (ETDEWEB)
Maddahian, Reza; Kebriaee, Azadeh; Farhanieh, Bijan; Firoozabadi, Bahar [Sharif University of Technology, School of Mechanical Engineering, Tehran (Iran, Islamic Republic of)
2011-04-15
In this research, the developing turbulent swirling flow in the entrance region of a pipe is investigated analytically by using the boundary layer integral method. The governing equations are integrated through the boundary layer and obtained differential equations are solved with forth-order Adams predictor-corrector method. The general tangential velocity is applied at the inlet region to consider both free and forced vortex velocity profiles. The comparison between present model and available experimental data demonstrates the capability of the model in predicting boundary layer parameters (e.g. boundary layer growth, shear rate and swirl intensity decay rate). Analytical results showed that the free vortex velocity profile can better predict the boundary layer parameters in the entrance region than in the forced one. Also, effects of pressure gradient inside the boundary layer is investigated and showed that if pressure gradient is ignored inside the boundary layer, results deviate greatly from the experimental data. (orig.)
A hybrid ICT-solution for smart meter data analytics
DEFF Research Database (Denmark)
Liu, Xiufeng; Nielsen, Per Sieverts
2016-01-01
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......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...
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...
A Hybrid Analytical-Numerical Solution to the Laminar Flow inside Biconical Ducts
Directory of Open Access Journals (Sweden)
Thiago Antonini Alves
2015-10-01
Full Text Available In this work was presented a hybrid analytical-numerical solution to hydrodynamic problem of fully developed Newtonian laminar flow inside biconical ducts employing the Generalized Integral Transform Technique (GITT. In order to facilitate the analytical treatment and the application of the boundary conditions, a Conformal Transform was used to change the domain into a more suitable coordinate system. Thereafter, the GITT was applied on the momentum equation to obtain the velocity field. Numerical results were obtained for quantities of practical interest, such as maximum and minimum velocity, Fanning friction factor, Poiseuille number, Hagenbach factor and hydrodynamic entry length.
Analytical solutions of basic models in quantum optics
Braak, Daniel
2015-01-01
The recent progress in the analytical solution of models invented to describe theoretically the interaction of matter with light on an atomic scale is reviewed. The methods employ the classical theory of linear differential equations in the complex domain (Fuchsian equations). The linking concept is provided by the Bargmann Hilbert space of analytic functions, which is isomorphic to $L^2(\\mathbb{R})$, the standard Hilbert space for a single continuous degree of freedom in quantum mechanics. I...
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 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.
Multi-analyte validation in heterogeneous solution by ELISA.
Lakshmipriya, Thangavel; Gopinath, Subash C B; Hashim, Uda; Murugaiyah, Vikneswaran
2017-12-01
Enzyme Linked Immunosorbent Assay (ELISA) is a standard assay that has been used widely to validate the presence of analyte in the solution. With the advancement of ELISA, different strategies have shown and became a suitable immunoassay for a wide range of analytes. Herein, we attempted to provide additional evidence with ELISA, to show its suitability for multi-analyte detection. To demonstrate, three clinically relevant targets have been chosen, which include 16kDa protein from Mycobacterium tuberculosis, human blood clotting Factor IXa and a tumour marker Squamous Cell Carcinoma antigen. Indeed, we adapted the routine steps from the conventional ELISA to validate the occurrence of analytes both in homogeneous and heterogeneous solutions. With the homogeneous and heterogeneous solutions, we could attain the sensitivity of 2, 8 and 1nM for the targets 16kDa protein, FIXa and SSC antigen, respectively. Further, the specific multi-analyte validations were evidenced with the similar sensitivities in the presence of human serum. ELISA assay in this study has proven its applicability for the genuine multiple target validation in the heterogeneous solution, can be followed for other target validations. Copyright © 2017 Elsevier B.V. All rights reserved.
Analytical solution of groundwater waves in unconfined aquifers with ...
Indian Academy of Sciences (India)
Selva Balaji Munusamy
2017-07-29
Jul 29, 2017 ... vertical beach face. However, in natural systems the beach face is normally sloped. Nielsen [2] used a linearized. Boussinesq equation to provide solutions for a coastal aquifer with sloping beach face. Nielsen [2] assumed a fixed location boundary condition and the perturbation parameter included.
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.
Analytical solutions for systems of partial differential-algebraic equations.
Benhammouda, Brahim; Vazquez-Leal, Hector
2014-01-01
This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.
On the Analytic Solution for a Steady Magnetohydrodynamic Equation
Soltanalizadeh, Babak; Ghehsareh, Hadi Roohani; Yıldırım, Ahmet; Abbasbandy, Saeid
2013-07-01
The purpose of this study is to apply the Laplace-Adomian Decomposition Method (LADM) for obtaining the analytical and numerical solutions of a nonlinear differential equation that describes a magnetohydrodynamic (MHD) flow near the forward stagnation point of two-dimensional and axisymmetric bodies. By using this method, the similarity solutions of the problem are obtained for some typical values of the model parameters. For getting computational solutions, we combined the obtained series solutions by LADM with the Padé approximation. The method is easy to apply and gives high accurate results. The presented results through tables and figures show the efficiency and accuracy of the proposed technique.
Solution of Boundary-Value Problems using Kantorovich Method
Directory of Open Access Journals (Sweden)
Gusev A.A.
2016-01-01
Full Text Available We propose a computational scheme for solving the eigenvalue problem for an elliptic differential equation in a two-dimensional domain with Dirichlet boundary conditions. The solution is sought in the form of Kantorovich expansion over the basis functions of one of the independent variables with the second variable treated as a parameter. The basis functions are calculated as solutions of the parametric eigenvalue problem for an ordinary second-order differential equation. As a result, the initial problem is reduced to a boundary-value problem for a set of self-adjoint second-order differential equations for functions of the second independent variable. The discrete formulation of the problem is implemented using the finite element method with Hermite interpolation polynomials. The effciency of the calculation scheme is shown by benchmark calculations for a square membrane with a degenerate spectrum.
Analytic solution to variance optimization with no short positions
Kondor, Imre; Papp, Gábor; Caccioli, Fabio
2017-12-01
We consider the variance portfolio optimization problem with a ban on short selling. We provide an analytical solution by means of the replica method for the case of a portfolio of independent, but not identically distributed, assets. We study the behavior of the solution as a function of the ratio r between the number N of assets and the length T of the time series of returns used to estimate risk. The no-short-selling constraint acts as an asymmetric \
Surface integrals approach to solution of some free boundary problems
Directory of Open Access Journals (Sweden)
Igor Malyshev
1988-01-01
Full Text Available Inverse problems in which it is required to determine the coefficients of an equation belong to the important class of ill-posed problems. Among these, of increasing significance, are problems with free boundaries. They can be found in a wide range of disciplines including medicine, materials engineering, control theory, etc. We apply the integral equations techniques, typical for parabolic inverse problems, to the solution of a generalized Stefan problem. The regularization of the corresponding system of nonlinear integral Volterra equations, as well as local existence, uniqueness, continuation of its solution, and several numerical experiments are discussed.
Solution of higher order boundary value problems by spline methods
Chaurasia, Anju; Srivastava, P. C.; Gupta, Yogesh
2017-10-01
Spline solution of Boundary Value Problems has received much attention in recent years. It has proven to be a powerful tool due to the ease of use and quality of results. This paper concerns with the survey of methods that try to approximate the solution of higher order BVPs using various spline functions. The purpose of this article is to thrash out the problems as well as conclusions, reached by the numerous authors in the related field. We critically assess many important relevant papers, published in reputed journals during last six years.
Suk, Heejun
2017-11-01
A one-dimensional semi-analytical solution of land-derived solute transport, subject to tidal fluctuation in a coastal confined aquifer, was derived using the generalized integral-transform technique (GITT). To investigate the plume migration of land-derived contaminants within a tidally influenced aquifer, both spatially and temporally varying expressions of the Darcy velocity and dispersion coefficients obtained from the analytical solution of the groundwater head response, which were subject to sinusoidal boundary conditions due to tidal fluctuation, were considered. This new semi-analytical solution was verified against a numerical solution, as well as the peak location trajectory obtained using the Predictor-Corrector method. Sensitivity analyses of tidal amplitude, hydraulic conductivity, and storage coefficient using the proposed solution were performed to understand plume behavior with regard to plume shape, plume spatial moments, and macrodispersion coefficients to gain a better understanding of the transport mechanisms. As the tidal amplitude, hydraulic conductivity, and storage coefficient were increased, the peaks were travelled faster, and peak concentrations were decreased. In addition, an increase in tidal amplitude, hydraulic conductivity, and storage coefficient caused an increase in variance as well as the macrodispersion coefficient. It was observed that negative macrodispersion appeared when the storage coefficient was largest, as well as when the difference between landward-directed advective velocity at the leading and trailing edges of the plume was greatest. This newly developed semi-analytical solution provides a useful mathematical tool for validating numerical models and understanding the physical mechanism of the migration of plume discharge to the sea or estuaries within a tidally influenced aquifer.
Analytic solutions for tachyon condensation with general projectors
Energy Technology Data Exchange (ETDEWEB)
Okawa, Y. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Rastelli, L. [C.N. Yang Institute for Theoretical Physics, Stony Brook, NY (United States); Zwiebach, B. [Massachusetts Inst. of Tech., Cambridge, MA (United States). Center for Theoretical Physics
2006-11-15
The tachyon vacuum solution of Schnabl is based on the wedge states, which close under the star product and interpolate between the identity state and the sliver projector. We use reparameterizations to solve the long-standing problem of finding an analogous family of states for arbitrary projectors and to construct analytic solutions based on them. The solutions simplify for special projectors and allow explicit calculations in the level expansion. We test the solutions in detail for a one-parameter family of special projectors that includes the sliver and the butterfly. Reparameterizations further allow a one-parameter deformation of the solution for a given projector, and in a certain limit the solution takes the form of an operator insertion on the projector. We discuss implications of our work for vacuum string field theory. (orig.)
Analytical Solution Of Complete Schwarzschild\\'s Planetary Equation
African Journals Online (AJOL)
It is well known how to solve the Einstein\\'s planetary equation of motion by the method of successive approximation for the corresponding orbit solution. In this paper, we solve the complete schwarzschild\\'s planetary equation of motion by an exact analytical method. The result reveals that there are actually eight exact ...
An Analytical Method For The Solution Of Reactor Dynamic Equations
African Journals Online (AJOL)
In this paper, an analytical method for the solution of nuclear reactor dynamic equations is presented. The method is applied to a linearised high-order deterministic model of a pressurised water reactor plant driven by step-reactivity insertion. A comparison of this method with two other techniques (the matrix exponential and ...
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
An analytical solution of compressible charged porous media
Malakpoor, K.; Huyghe, J.M.
2009-01-01
A one-dimensional analytical solution is derived for saturated charged compressible porous media. The equations describe infinitesimal deformation of charged porous media saturated with a fluid with dissolved cations and anions. In the one-dimensional case the governing equations reduce to a coupled
Analytical solutions of coupled-mode equations for microring ...
Indian Academy of Sciences (India)
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 × 4 linearly distributed coupler is also obtained. This paper may be of interest to optical physics and integrated photonics ...
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.
New Approximate Analytical Solutions of the Falkner-Skan Equation
Directory of Open Access Journals (Sweden)
Beong In Yun
2012-01-01
Full Text Available We propose an iterative method for solving the Falkner-Skan equation. The method provides approximate analytical solutions which consist of coefficients of the previous iterate solution. By some examples, we show that the presented method with a small number of iterations is competitive with the existing method such as Adomian decomposition method. Furthermore, to improve the accuracy of the proposed method, we suggest an efficient correction method. In practice, for some examples one can observe that the correction method results in highly improved approximate solutions.
Energy Technology Data Exchange (ETDEWEB)
Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)
1997-12-31
This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)
Analytic solution for tachyon condensation in open string field theory
Schnabl, M
2006-01-01
We propose a new basis in Witten's open string field theory, in which the star product simplifies considerably. For a convenient choice of gauge the classical string field equation of motion yields straightforwardly an exact analytic solution that represents the nonperturbative tachyon vacuum. The solution is given in terms of Bernoulli numbers and the equation of motion can be viewed as novel Euler--Ramanujan-type identity. It turns out that the solution is the Euler--Maclaurin asymptotic expansion of a sum over wedge states with certain insertions. This new form is fully regular from the point of view of level truncation. By computing the energy difference between the perturbative and nonperturbative vacua, we prove analytically Sen's first conjecture.
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.
On numerical-analytic techniques for boundary value problems
Czech Academy of Sciences Publication Activity Database
Rontó, András; Rontó, M.; Shchobak, N.
2012-01-01
Roč. 12, č. 3 (2012), s. 5-10 ISSN 1335-8243 Institutional support: RVO:67985840 Keywords : numerical-analytic method * periodic successive approximations * Lyapunov-Schmidt method Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/aeei.2012.12.issue-3/v10198-012-0035-1/v10198-012-0035-1. xml ?format=INT
An analytic solution of the static problem of inclined risers conveying fluid
Alfosail, Feras
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
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.
Horses for courses: analytical tools to explore planetary boundaries
van Vuuren, Detlef P.; Lucas, Paul L.; Häyhä, Tiina; Cornell, Sarah E.; Stafford-Smith, Mark
2016-03-01
There is a need for more integrated research on sustainable development and global environmental change. In this paper, we focus on the planetary boundaries framework to provide a systematic categorization of key research questions in relation to avoiding severe global environmental degradation. The four categories of key questions are those that relate to (1) the underlying processes and selection of key indicators for planetary boundaries, (2) understanding the impacts of environmental pressure and connections between different types of impacts, (3) better understanding of different response strategies to avoid further degradation, and (4) the available instruments to implement such strategies. Clearly, different categories of scientific disciplines and associated model types exist that can accommodate answering these questions. We identify the strength and weaknesses of different research areas in relation to the question categories, focusing specifically on different types of models. We discuss that more interdisciplinary research is need to increase our understanding by better linking human drivers and social and biophysical impacts. This requires better collaboration between relevant disciplines (associated with the model types), either by exchanging information or by fully linking or integrating them. As fully integrated models can become too complex, the appropriate type of model (the racehorse) should be applied for answering the target research question (the race course).
Analytical Determination of the Boundaries of Transition Natural Zones (Ecotones
Directory of Open Access Journals (Sweden)
Rulev Aleksandr Sergeevich
2015-04-01
Full Text Available The morphological units that are part of the catena, are recognized in accordance with the response to the geomorphological and soil processes. The spatial relationship is the main unit between them. In this regard, the landscape patterns acquire a cascade type, and their main link becomes the zonal catena, which has specific stable features, reflecting the dependence of the complex of natural conditions and processes of latitude. However, clear-cut boundaries do not exist – they have spatial and temporal displacement, associated with the cyclical nature of the global climatic processes. The landscapes in these transition zones (ecotones a priori can be considered unstable. The detection of ecotones boundaries provides the opportunity to divide natural zones to potentially stable and potentially unstable parts for planning measures on preventing the degradation of landscapes localized in them. The latitude of the ecotones localization can be determined through the connection of the radiation heat flux on land (R with the normalized geographical latitude of the subboreal belt (x, which is described by the equation of the energy balance, expressed in the logistic function R = А / [1 + 0,72 exp(4,25 – Bx] + C.
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.
Analytic solutions of integral moving least squares for polygon soups.
Park, Taejung; Lee, Sung-Ho; Kim, Chang-Hun
2012-10-01
This paper presents analytic solutions to the integral moving least squares (MLS) equations originally proposed by Shen et al. by choosing another specific weighting function that renders the numerator in the MLS equation unitless. In addition, we analyze the original method to show that their approximation surfaces (i.e., enveloping surfaces with nonzero values in the weighting function) often form zero isosurfaces near concavities behind the triangle-soup models. This paper also presents error terms for the integral MLS formulations against signed distance fields. Based on our analytic solutions, we show that our method provides both interpolation and approximation surfaces faster and more efficiently. Because our method computes solutions for integral MLS equations directly, it does not rely on numerical steps that might have numerical-accuracy issues. In particular, unlike the original method that deals with incorrect approximation surfaces by iteratively adjusting parameters, this paper proposes faster and more efficient approximations to surfaces without needing iterative routines. We also present computational efficiency comparisons, in which our method is 15-fold faster in computing integrations, even with conservative assumptions. Finally, we show that the surface normal vectors on the implicit surfaces formed by our analytic solutions are identical to the angle-weighted pseudonormal vectors.
Analytical solution for viscous incompressible Stokes flow in a spherical shell
Thieulot, Cedric
2017-11-01
I present a new family of analytical flow solutions to the incompressible Stokes equation in a spherical shell. The velocity is tangential to both inner and outer boundaries, the viscosity is radial and of the power-law type, and the solution has been designed so that the expressions for velocity, pressure, and body force are simple polynomials and therefore simple to implement in (geodynamics) codes. Various flow average values, e.g., the root mean square velocity, are analytically computed. This forms the basis of a numerical benchmark for convection codes and I have implemented it in two finite-element codes: ASPECT and ELEFANT. I report error convergence rates for velocity and pressure.
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...
Approximate Analytical Solutions to the Relativistic Isothermal Gas Spheres
Saad, A. S.; Nouh, M. I.; Shaker, A. A.; Kamel, T. M.
2017-10-01
In this paper we introduce a novel analytical solution to Tolman-Oppenheimer-Volkoff (TOV) equation, which is ultimately a hydrostatic equilibrium equation derived from general relativity in the framework of relativistic isothermal spheres. To improve the convergence radii of the obtained series solutions, a combination of an Euler-Abel transformation and a Padé approximation has been done. The solutions are given in the ξ-θ and ξ-ν phase planes taking into account the general relativistic effects σ=0.1, 0.2 and 0.3. A comparison between the results obtained by the suggested approach and the numerical one indicates a good agreement, with a maximum relative error of order 10-3, which establishes the validity and accuracy of the method. The proposed procedure accelerated the power series solution about ten times that of the traditional one. An application to a neutron star is presented.
Analytic solutions of a class of nonlinear partial differential equations
Directory of Open Access Journals (Sweden)
Eugenia N. Petropoulou
2015-08-01
Full Text Available We study a class of nonlinear partial differential equations, which can be connected with wave-type equations and Laplace-type equations, by using a functional-analytic technique. We establish primarily the existence and uniqueness of bounded solutions in the two-dimensional Hardy-Lebesque space of analytic functions with independent variables lying in the open unit disc. However these results can be modified to expand the domain of definition. The proofs have a constructive character enabling the determination of concrete and easily verifiable conditions, and the determination of the coefficients appearing in the power series solution. Illustrative examples are given related to the sine-Gordon equation, the Klein-Gordon equation, and to equations with nonlinear terms of algebraic, exponential and logistic type.
Solution Matching for a Second Order Boundary Value Problem on Time Scales
Directory of Open Access Journals (Sweden)
Aprillya Lanz
2012-01-01
Full Text Available Let be a time scale such that <;,∈. We will show the existence and uniqueness of solutions for the second-order boundary value problem ΔΔ(=(,(,Δ(,∈[,],(=,(=, by matching a solution of the first equation satisfying boundary conditions on [,] with a solution of the first equation satisfying boundary conditions on [,], where ∈(,.
Boundary value problems for third order differential equations by solution matching
Directory of Open Access Journals (Sweden)
Johnny Henderson
2009-10-01
Full Text Available For the ordinary differential equation, $y''' = f(x,y,y',$ $y'',$ solutions of 3-point boundary value problems on $[a,b]$ are matched with solutions of 3-point boundary value problems on $[b,c]$ to obtain solutions satisfying 5-point boundary conditions on $[a,c]$.
Analytic solution of the Starobinsky model for inflation
Energy Technology Data Exchange (ETDEWEB)
Paliathanasis, Andronikos [Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Durban University of Technology, Institute of Systems Science, Durban (South Africa)
2017-07-15
We prove that the field equations of the Starobinsky model for inflation in a Friedmann-Lemaitre-Robertson-Walker metric constitute an integrable system. The analytical solution in terms of a Painleve series for the Starobinsky model is presented for the case of zero and nonzero spatial curvature. In both cases the leading-order term describes the radiation era provided by the corresponding higher-order theory. (orig.)
Boundary element method solution for large scale cathodic protection problems
Rodopoulos, D. C.; Gortsas, T. V.; Tsinopoulos, S. V.; Polyzos, D.
2017-12-01
Cathodic protection techniques are widely used for avoiding corrosion sequences in offshore structures. The Boundary Element Method (BEM) is an ideal method for solving such problems because requires only the meshing of the boundary and not the whole domain of the electrolyte as the Finite Element Method does. This advantage becomes more pronounced in cathodic protection systems since electrochemical reactions occur mainly on the surface of the metallic structure. The present work aims to solve numerically a sacrificial cathodic protection problem for a large offshore platform. The solution of that large-scale problem is accomplished by means of “PITHIA Software” a BEM package enhanced by Hierarchical Matrices (HM) and Adaptive Cross Approximation (ACA) techniques that accelerate drastically the computations and reduce memory requirements. The nonlinear polarization curves for steel and aluminium in seawater are employed as boundary condition for the under protection metallic surfaces and aluminium anodes, respectively. The potential as well as the current density at all the surface of the platform are effectively evaluated and presented.
Development of CAD implementing the algorithm of boundary elements’ numerical analytical method
Directory of Open Access Journals (Sweden)
Yulia V. Korniyenko
2015-03-01
Full Text Available Up to recent days the algorithms for numerical-analytical boundary elements method had been implemented with programs written in MATLAB environment language. Each program had a local character, i.e. used to solve a particular problem: calculation of beam, frame, arch, etc. Constructing matrices in these programs was carried out “manually” therefore being time-consuming. The research was purposed onto a reasoned choice of programming language for new CAD development, allows to implement algorithm of numerical analytical boundary elements method and to create visualization tools for initial objects and calculation results. Research conducted shows that among wide variety of programming languages the most efficient one for CAD development, employing the numerical analytical boundary elements method algorithm, is the Java language. This language provides tools not only for development of calculating CAD part, but also to build the graphic interface for geometrical models construction and calculated results interpretation.
A full analytic solution of SO(10)-inspired leptogenesis
Di Bari, Pasquale; Fiorentin, Michele Re
2017-10-01
Recent encouraging experimental results on neutrino mixing parameters prompt further investigation on SO(10)-inspired leptogenesis and on the associated strong thermal solution that has correctly predicted a non-vanishing reactor mixing angle, it further predicts sin δ ≲ 0, now supported by recent results at ˜ 95% C.L., normally ordered neutrino masses and atmospheric mixing angle in the first octant, best fit results in latest global analyses. Extending a recent analytical procedure, we account for the mismatch between the Yukawa basis and the weak basis, that in SO(10)-inspired models is described by a CKM-like unitary transformation V L , obtaining a full analytical solution that provides useful insight and reproduces accurately all numerical results, paving the way for future inclusion of different sources of theoretical uncertainties and for a statistical analysis of the constraints. We show how muon-dominated solutions appear for large values of the lightest neutrino mass in the range (0 .01-1) eV but also how they necessarily require a mild fine tuning in the seesaw relation. For the dominant (and untuned) tauon-dominated solutions we show analytically how, turning on V L ≃ V CKM, some of the constraints on the low energy neutrino parameters get significantly relaxed. In particular we show how the upper bound on the atmospheric neutrino mixing angle in the strong thermal solution gets relaxed from θ 23 ≲ 41° to θ 23 ≲ 44°, an important effect in the light of the most recent NO νA, T2K and IceCube results.
A Meshless Solution Method for Unsteady Flow with Moving Boundary
Directory of Open Access Journals (Sweden)
Jun Zhang
2014-02-01
Full Text Available Using the concept of overlapping mesh method for reference, a new method called as Overlapping Clouds of Points Method (OCPM is firstly proposed to simulate unsteady flow with moving boundary problems based on meshless method. Firstly, a set of static background discrete points is generated in the whole calculation zone. Secondly, moving discrete points are created around moving body. According to the initial position of moving object in the flow field, the two sets of discrete points can be overlapped. With the motion of moving objects in the calculation field, moving discrete points around the moving body will inherently move. The exchange of flow field information between static points and moving points is realized by the solution of the clouds of points made up of static and moving discrete points using weighted meshless method nearby overlapping boundary. Four cases including piston problem, NACA0012 airfoil vibration flow around a moving sphere in supersonic and multibody separation are given to verify accuracy and practicability of OCPM. The numerical results agree well with exact solution and experimental results, which shows that the proposed OCPM can be applied to the simulation of unsteady flow problem.
Analytical solutions for the radial Scarf II potential
Lévai, G.; Baran, Á.; Salamon, P.; Vertse, T.
2017-06-01
The real Scarf II potential is discussed as a radial problem. This potential has been studied extensively as a one-dimensional problem, and now these results are used to construct its bound and resonance solutions for l = 0 by setting the origin at some arbitrary value of the coordinate. The solutions with appropriate boundary conditions are composed as the linear combination of the two independent solutions of the Schrödinger equation. The asymptotic expression of these solutions is used to construct the S0 (k)s-wave S-matrix, the poles of which supply the k values corresponding to the bound, resonance and anti-bound solutions. The location of the discrete energy eigenvalues is analyzed, and the relation of the solutions of the radial and one-dimensional Scarf II potentials is discussed. It is shown that the generalized Woods-Saxon potential can be generated from the Rosen-Morse II potential in the same way as the radial Scarf II potential is obtained from its one-dimensional correspondent. Based on this analogy, possible applications are also pointed out.
An Analytical Solution of Partially Penetrating Hydraulic Fractures in a Box-Shaped Reservoir
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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.
An analytic solution to a driven interface problem
Energy Technology Data Exchange (ETDEWEB)
Hammerberg, J.E.; Pepin, J. [Los Alamos National Lab., NM (United States). Applied Theoretical and Computational Physics Div.
1997-10-01
The frictional properties of sliding metal interfaces at high velocities are not well known from either an experimental or theoretical point of view. The constitutive properties and macroscopic laws of frictional dynamics at high velocities necessary for materials continuum codes have only a qualitative validity and it is of interest to have analytic problems for sliding interfaces to enable separation of model from numerical effects. The authors present an exact solution for the space and time dependence of the plastic strain near a sliding interface in a planar semi-finite geometry. This solution is based on a particular form for the strain rate dependence of the flow stress and results in a hyperbolic telegrapher equation for the plastic strain. The form of the solutions and wave structure will be discussed.
An analytic solution to a driven interface problem
Energy Technology Data Exchange (ETDEWEB)
Hammerberg, J.E.; Pepin, J. [Applied Theoretical and Computational Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
1998-07-01
The frictional properties of sliding metal interfaces at high velocities are not well known either from an experimental or theoretical point of view. The constitutive properties and macroscopic laws of frictional dynamics at high velocities necessary for materials continuum codes have only a qualitative validity and it is of interest to have analytic problems for sliding interfaces to enable separation of model from numerical effects. We present an exact solution for the space and time dependence of the plastic strain near a sliding interface in a planar semi-infinite geometry. This solution is based on a particular form for the strain rate dependence of the flow stress and results in a hyperbolic telegrapher equation for the plastic strain. The form of the solutions and wave structure are discussed. {copyright} {ital 1998 American Institute of Physics.}
Electromagnetic wave theory for boundary-value problems an advanced course on analytical methods
Eom, Hyo J
2004-01-01
Electromagnetic wave theory is based on Maxwell's equations, and electromagnetic boundary-value problems must be solved to understand electromagnetic scattering, propagation, and radiation. Electromagnetic theory finds practical applications in wireless telecommunications and microwave engineering. This book is written as a text for a two-semester graduate course on electromagnetic wave theory. As such, Electromagnetic Wave Theory for Boundary-Value Problems is intended to help students enhance analytic skills by solving pertinent boundary-value problems. In particular, the techniques of Fourier transform, mode matching, and residue calculus are utilized to solve some canonical scattering and radiation problems.
Analytical solutions of laminar swirl decay in a straight pipe
Yao, Shanshan; Fang, Tiegang
2012-08-01
In this work, the laminar swirl flow in a straight pipe is revisited and solved analytically by using prescribed axial flow velocity profiles. Based on two axial velocity profiles, namely a slug flow and a developed parabolic velocity profiles, the swirl velocity equation is solved by the separation of variable technique for a rather general inlet swirl velocity distribution, which includes a forced vortex in the core and a free vortex near the wall. The solutions are expressed by the Bessel function for the slug flow and by the generalized Laguerre function for the developed parabolic velocity. Numerical examples are calculated and plotted for different combinations of influential parameters. The effects of the Reynolds number, the pipe axial distance, and the inlet swirl profiles on the swirl velocity distribution and the swirl decay are analyzed. The current results offer analytical equations to estimate the decay rate and the outlet swirl intensity and velocity distribution for the design of swirl flow devices.
Analytical solutions of transport problems in anisotropic media
Energy Technology Data Exchange (ETDEWEB)
Lapenta, G.; Ravetto, P.; Rostagno, M.M.
2000-07-01
Recently, the problem of neutron transport in anisotropic media has received new attention in connection with safety studies of water reactors and design of gas-cooled systems. In situations presenting large voided regions, as the axial streaming is dominating with respect to the transverse one, the average properties of the homogenized material should physically account for such macroscopic anisotropy. Hence, it is suggested that cell calculations produce anisotropic average cross sections, e.g., axial ({sigma}{sub A}) and transverse ({sigma}{sub T}) values. Since material anisotropy is due to leakage, as a first-step approximation, the medium can be considered isotropic with respect to scattering phenomena. Transport codes are currently being adapted to include anisotropic cross sections. An important aspect of code development is the validation of algorithms by analytical benchmarks. For that purpose, the present work is devoted to the fully analytical solution of transport problems in slab geometry.
Analytic solution of neural network with disordered lateral inhibition
Hamaguchi, Kosuke; Hatchett, J. P. L.; Okada, Masato
2006-05-01
The replica method has played a key role in analyzing systems with disorder, e.g., the Sherrington-Kirkpatrick (SK) model, and associative neural networks. Here we study the influence of disorder in the lateral inhibition type interactions on the cooperative and uncooperative behavior of recurrent neural networks by using the replica method. Although the interaction between neurons has a dependency on distance, our model can be solved analytically. Bifurcation analysis identifies the boundaries between paramagnetic, ferromagnetic, spin-glass, and localized phases. In the localized phase, the network shows a bump like activity, which is often used as a model of spatial working memory or columnar activity in the visual cortex. Simulation results show that disordered interactions can stabilize the drift the of bump position, which is commonly observed in conventional lateral inhibition type neural networks.
Existence of solutions to boundary value problem of fractional differential equations with impulsive
Directory of Open Access Journals (Sweden)
Weihua JIANG
2016-12-01
Full Text Available In order to solve the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line, the existence of solutions to the boundary problem is specifically studied. By defining suitable Banach spaces, norms and operators, using the properties of fractional calculus and applying the contraction mapping principle and Krasnoselskii's fixed point theorem, the existence of solutions for the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line is proved, and examples are given to illustrate the existence of solutions to this kind of equation boundary value problems.
Directory of Open Access Journals (Sweden)
Anastasia S. Lermontova
2012-01-01
Full Text Available The article describes a method yielding approximate analytical solutions under the theory of elasticity for a set of interacting arbitrarily spaced shear fractures. Accurate analytical solutions of this problem are now available only for the simplest individual cases, such as a single fracture or two collinear fractures. A large amount of computation is required to yield a numerical solution for a case considering arbitrary numbers and locations of fractures, while this problem has important practical applications, such as assessment of the state of stress in seismically active regions, forecasts of secondary destruction impacts near systems of large faults, studies of reservoir properties of the territories comprising oil and gas provinces.In this study, an approximate estimation is obtained with the following simplification assumptions: (1 functions showing shear of fractures’ borders are determined similar to the shear function for a single fracture, and (2 boundary conditions for the fractures are specified in the integrated form as mean values along each fracture. Upon simplification, the solution is obtained through the system of linear algebraic equations for unknown values of tangential stress drop. With this approach, the accuracy of approximate solutions is consistent with the accuracy of the available data on real fractures.The reviewed examples of estimations show that the resultant stress field is dependent on the number, size and location of fractures and the sequence of displacements of the fractures’ borders.
Off-shell amplitudes as boundary integrals of analytically continued Wilson line slope
Energy Technology Data Exchange (ETDEWEB)
Kotko, P. [Department of Physics, The Pennsylvania State University,University Park, PA 16802 (United States); Serino, M. [The Henryk Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences,Radzikowskiego 152, 31-342, Kraków (Poland); Staśto, A.M. [Department of Physics, The Pennsylvania State University,University Park, PA 16802 (United States)
2016-08-03
One of the methods to calculate tree-level multi-gluon scattering amplitudes is to use the Berends-Giele recursion relation involving off-shell currents or off-shell amplitudes, if working in the light cone gauge. As shown in recent works using the light-front perturbation theory, solutions to these recursions naturally collapse into gauge invariant and gauge-dependent components, at least for some helicity configurations. In this work, we show that such structure is helicity independent and emerges from analytic properties of matrix elements of Wilson line operators, where the slope of the straight gauge path is shifted in a certain complex direction. This is similar to the procedure leading to the Britto-Cachazo-Feng-Witten (BCFW) recursion, however we apply a complex shift to the Wilson line slope instead of the external momenta. While in the original BCFW procedure the boundary integrals over the complex shift vanish for certain deformations, here they are non-zero and are equal to the off-shell amplitudes. The main result can thus be summarized as follows: we derive a decomposition of a helicity-fixed off-shell current into gauge invariant component given by a matrix element of a straight Wilson line plus a reminder given by a sum of products of gauge invariant and gauge dependent quantities. We give several examples realizing this relation, including the five-point next-to-MHV helicity configuration.
Analytical solution for irradiance due to inhomogeneous Lambertian polygonal emitters.
Chen, Min; Arvo, James
2003-05-01
We present an analytic solution for the irradiance at a point due to a polygonal Lambertian emitter with radiant exitance that varies with position according to a polynomial of arbitrary degree. This is a basic problem that arises naturally in radiative transfer and more specifically in global illumination, a subfield of computer graphics. Our solution is closed form except for a single nonalgebraic special function known as the Clausen integral. We begin by deriving several useful formulas for high-order tensor analogs of irradiance, which are natural generalizations of the radiation pressure tensor. We apply the resulting tensor formulas to linearly varying emitters, obtaining a solution that exhibits the general structure of higher-degree cases, including the dependence on the Clausen integral. We then generalize to higher-degree polynomials with a recurrence formula that combines solutions for lower-degree polynomials; the result is a generalization of Lambert's formula for homogeneous diffuse emitters, a well-known formula with many applications in radiative transfer and computer graphics. Similar techniques have been used previously to derive closed-form solutions for the irradiance due to homogeneous polygonal emitters with directionally varying radiance. The present work extends this previous result to include inhomogeneous emitters, which proves to be significantly more challenging to solve in closed form. We verify our theoretical results with numerical approximations and briefly discuss their potential applications.
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...
Fayolle, Guy; Malyshev, Vadim
2017-01-01
This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum Physics. This second edition consists of two parts. Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using Complex Function Theory, Boundary Value Problems, Riemann Surfaces, and Galois Theory, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the Transient Behavior of the walks, as well as to find explicit solutions to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems. Part II borrows spec...
Directory of Open Access Journals (Sweden)
Nahed S. Hussein
2014-01-01
Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.
Decision exploration lab: a visual analytics solution for decision management.
Broeksema, Bertjan; Baudel, Thomas; Telea, Arthur G; Crisafulli, Paolo
2013-12-01
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 goals. In our work, we consider decision models (executable models of the business domain) as ontologies that describe the business domain, and production rules that describe the business logic of decisions to be made over this ontology. Executing a decision model produces an accumulation of decisions made over time for individual cases. We are interested, first, to get insight in the decision logic and the accumulated facts by themselves. Secondly and more importantly, we want to see how the accumulated facts reveal potential divergences between the reality as captured by the decision model, and the reality as captured by the executed decisions. We illustrate the motivation, added value for visual analytics, and our proposed solution and tooling through a business case from the car insurance industry.
Wu, Junde; Zhou, Fujun
2017-05-01
In this paper we study a free boundary problem modeling the growth of solid tumor spheroid. It consists of two elliptic equations describing nutrient diffusion and pressure distribution within tumor, respectively. The new feature is that nutrient concentration on the boundary is less than external supply due to a Gibbs-Thomson relation and the problem has two radial stationary solutions, which differs from widely studied tumor spheroid model with surface tension effect. We first establish local well-posedness by using a functional approach based on Fourier multiplier method and analytic semigroup theory. Then we investigate stability of each radial stationary solution. By employing a generalized principle of linearized stability, we prove that the radial stationary solution with a smaller radius is always unstable, and there exists a positive threshold value γ* of cell-to-cell adhesiveness γ, such that the radial stationary solution with a larger radius is asymptotically stable for γ >γ*, and unstable for 0 < γ <γ*.
Zuo, Chao; Chen, Qian; Asundi, Anand
2014-04-21
The transport of intensity equation (TIE) is a two-dimensional second order elliptic partial differential equation that must be solved under appropriate boundary conditions. However, the boundary conditions are difficult to obtain in practice. The fast Fourier transform (FFT) based TIE solutions are widely adopted for its speed and simplicity. However, it implies periodic boundary conditions, which lead to significant boundary artifacts when the imposed assumption is violated. In this work, TIE phase retrieval is considered as an inhomogeneous Neumann boundary value problem with the boundary values experimentally measurable around a hard-edged aperture, without any assumption or prior knowledge about the test object and the setup. The analytic integral solution via Green's function is given, as well as a fast numerical implementation for a rectangular region using the discrete cosine transform. This approach is applicable for the case of non-uniform intensity distribution with no extra effort to extract the boundary values from the intensity derivative signals. Its efficiency and robustness have been verified by several numerical simulations even when the objects are complex and the intensity measurements are noisy. This method promises to be an effective fast TIE solver for quantitative phase imaging applications.
A walkthrough solution to the boundary overlap problem
Mark J. Ducey; Jeffrey H. Gove; Harry T. Valentine
2004-01-01
Existing methods for eliminating bias due to boundary overlap suffer some disadvantages in practical use, including the need to work outside the tract, restrictions on the kinds of boundaries to which they are applicable, and the possibility of significantly increased variance as a price for unbiasedness. We propose a new walkthrough method for reducing boundary...
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
Grain boundary structure and solute segregation in titanium-doped sapphire bicrystals
Energy Technology Data Exchange (ETDEWEB)
Taylor, Seth Thomas [Univ. of California, Berkeley, CA (United States)
2002-01-01
Solute segregation to ceramic grain boundaries governs material processing and microstructure evolution, and can strongly influence material properties critical to engineering performance. Understanding the evolution and implications of grain boundary chemistry is a vital component in the greater effort to engineer ceramics with controlled microstructures. This study examines solute segregation to engineered grain boundaries in titanium-doped sapphire (Al_{2}O_{3}) bicrystals, and explores relationships between grain boundary structure and chemistry at the nanometer scale using spectroscopic and imaging techniques in the transmission electron microscope (TEM). Results demonstrate dramatic changes in solute segregation stemming from small fluctuations in grain boundary plane and structure. Titanium and silicon solute species exhibit strong tendencies to segregate to non-basal and basal grain boundary planes, respectively. Evidence suggests that grain boundary faceting occurs in low-angle twis t boundaries to accommodate nonequilibrium solute segregation related to slow specimen cooling rates, while faceting of tilt grain boundaries often occurs to expose special planes of the coincidence site lattice (CSL). Moreover, quantitative analysis of grain boundary chemistry indicates preferential segregation of charged defects to grain boundary dislocations. These results offer direct proof that static dislocations in ionic materials can assume a net charge, and emphasize the importance of interactions between charged point, line, and planar defects in ionic materials. Efforts to understand grain boundary chemistry in terms of space charge theory, elastic misfit and nonequilibrium segregation are discussed for the Al_{2}O_{3} system.
Approximate explicit analytic solution of the Elenbaas-Heller equation
Liao, Meng-Ran; Li, Hui; Xia, Wei-Dong
2016-08-01
The Elenbaas-Heller equation describing the temperature field of a cylindrically symmetrical non-radiative electric arc has been solved, and approximate explicit analytic solutions are obtained. The radial distributions of the heat-flux potential and the electrical conductivity have been figured out briefly by using some special simplification techniques. The relations between both the core heat-flux potential and the electric field with the total arc current have also been given in several easy explicit formulas. Besides, the special voltage-ampere characteristic of electric arcs is explained intuitionally by a simple expression involving the Lambert W-function. The analyses also provide a preliminary estimation of the Joule heating per unit length, which has been verified in previous investigations. Helium arc is used to examine the theories, and the results agree well with the numerical computations.
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.
Directory of Open Access Journals (Sweden)
Dina V. Lazareva
2015-06-01
Full Text Available A new mathematical model of asymmetric support structure frame type is built on the basis of numerical-analytical boundary elements method (BEM. To describe the design scheme used is the graph theory. Building the model taken into account is the effect of frame members restrained torsion, which presence is due to the fact that these elements are thin-walled. The built model represents a real object as a two-axle semi-trailer platform. To implement the BEM algorithm obtained are analytical expressions of the fundamental functions and vector load components. The effected calculations are based on the semi-trailer two different models, using finite elements and boundary elements methods. The analysis showed that the error between the results obtained on the basis of two numerical methods and experimental data is about 4%, that indicates the adequacy of the proposed mathematical model.
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I. Yu. Popov
2014-06-01
Full Text Available Geodynamic modeling is often related with challenging computations involving solution of the Stokes and continuity equations under the condition of highly variable viscosity. Based on a new analytical approach we have developed particular analytical solutions for 2-D and 3-D incompressible Stokes flows with both linearly and exponentially variable viscosity. We demonstrate how these particular solutions can be converted into 2-D and 3-D test problems suitable for benchmarking numerical codes aimed at modeling various mantle convection and lithospheric dynamics problems. The Main advantage of this new generalized approach is that a large variety of benchmark solutions can be generated, including relatively complex cases with open model boundaries, non-vertical gravity and variable gradients of the viscosity and density fields, which are not parallel to the Cartesian axes. Examples of respective 2-D and 3-D MatLab codes are provided with this paper.
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Hytham. A. Alkresheh
2016-02-01
Full Text Available In this paper, an algorithm based on a new modification, developed by Duan and Rach, for the Adomian decomposition method (ADM is generalized to find positive solutions for boundary value problems involving nonlinear fractional ordinary differential equations. In the proposed algorithm the boundary conditions are used to convert the nonlinear fractional differential equations to an equivalent integral equation and then a recursion scheme is used to obtain the analytical solution components without the use of undetermined coefficients. Hence, there is no requirement to solve a nonlinear equation or a system of nonlinear equations of undetermined coefficients at each stage of approximation solution as per in the standard ADM. The fractional derivative is described in the Caputo sense. Numerical examples are provided to demonstrate the feasibility of the proposed algorithm.
Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Diabate Nabongo
2008-01-01
Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.
Positive solutions for second-order boundary-value problems with sign changing Green's functions
Directory of Open Access Journals (Sweden)
Alberto Cabada
2017-10-01
Full Text Available In this article we analyze some possibilities of finding positive solutions for second-order boundary-value problems with the Dirichlet and periodic boundary conditions, for which the corresponding Green's functions change sign. The obtained results can also be adapted to Neumann and mixed boundary conditions.
Solution of Moving Boundary Space-Time Fractional Burger’s Equation
Directory of Open Access Journals (Sweden)
E. A.-B. Abdel-Salam
2014-01-01
Full Text Available The fractional Riccati expansion method is used to solve fractional differential equations with variable coefficients. To illustrate the effectiveness of the method, the moving boundary space-time fractional Burger’s equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time. The linear and periodic moving boundaries for the kink solution of the Burger’s equation are presented graphically and discussed.
He, Cairong; Wang, Tongke; Zhao, Zhixue; Hao, Yonghong; Yeh, Tian-Chyi J.; Zhan, Hongbin
2017-11-01
Submarine groundwater discharge (SGD) has been recognized as a major pathway of groundwater flow to coastal oceanic environments. It could affect water quality and marine ecosystems due to pollutants and trace elements transported through groundwater. Relations between different characteristics of aquifers and SGD have been investigated extensively before, but the role of fractures in SGD still remains unknown. In order to better understand the mechanism of groundwater flow and solute transport through fractures in SGD, one-dimensional analytical solutions of groundwater hydraulic head and velocity through a synthetic horizontal fracture with periodic boundary conditions were derived using a Laplace transform technique. Then, numerical solutions of solute transport associated with the given groundwater velocity were developed using a finite-difference method. The results indicated that SGD associated with groundwater flow and solute transport was mainly controlled by sea level periodic fluctuations, which altered the hydraulic head and the hydraulic head gradient in the fracture. As a result, the velocity of groundwater flow associated with SGD also fluctuated periodically. We found that the pollutant concentration associated with SGD oscillated around a constant value, and could not reach a steady state. This was particularly true at locations close to the seashore. This finding of the role of fracture in SGD will assist pollution remediation and marine conservation in coastal regions.
He, Cairong; Wang, Tongke; Zhao, Zhixue; Hao, Yonghong; Yeh, Tian-Chyi J; Zhan, Hongbin
2017-11-01
Submarine groundwater discharge (SGD) has been recognized as a major pathway of groundwater flow to coastal oceanic environments. It could affect water quality and marine ecosystems due to pollutants and trace elements transported through groundwater. Relations between different characteristics of aquifers and SGD have been investigated extensively before, but the role of fractures in SGD still remains unknown. In order to better understand the mechanism of groundwater flow and solute transport through fractures in SGD, one-dimensional analytical solutions of groundwater hydraulic head and velocity through a synthetic horizontal fracture with periodic boundary conditions were derived using a Laplace transform technique. Then, numerical solutions of solute transport associated with the given groundwater velocity were developed using a finite-difference method. The results indicated that SGD associated with groundwater flow and solute transport was mainly controlled by sea level periodic fluctuations, which altered the hydraulic head and the hydraulic head gradient in the fracture. As a result, the velocity of groundwater flow associated with SGD also fluctuated periodically. We found that the pollutant concentration associated with SGD oscillated around a constant value, and could not reach a steady state. This was particularly true at locations close to the seashore. This finding of the role of fracture in SGD will assist pollution remediation and marine conservation in coastal regions. Copyright © 2017 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Liu Yuji
2008-01-01
Full Text Available Abstract This paper deals with the existence of solutions of the periodic boundary value problem of the impulsive Duffing equations: . Sufficient conditions are established for the existence of at least one solution of above-mentioned boundary value problem. Our method is based upon Schaeffer's fixed-point theorem. Examples are presented to illustrate the efficiency of the obtained results.
A New Iterative Scheme for the Solution of Tenth Order Boundary ...
African Journals Online (AJOL)
A new iterative scheme for the solution of tenth order boundary value problems has been implemented using first-kind Chebychev polynomials as trial functions. The method involves transforming tenth order boundary value problems into a system of ordinary differential equations (ODEs). The trial solution is introduced into ...
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.
Positive solutions for singular three-point boundary-value problems
Directory of Open Access Journals (Sweden)
Zengqin Zhao
2007-11-01
Full Text Available In this paper, we present the Green's functions for a second-order linear differential equation with three-point boundary conditions. We give exact expressions of the solutions for the linear three-point boundary problems by the Green's functions. As applications, we study uniqueness and iteration of the solutions for a nonlinear singular second-order three-point boundary value problem.
Energy Technology Data Exchange (ETDEWEB)
Anezaki, S. [Taisei Corp., Tokyo (Japan)
1998-03-01
Sea/fresh-water boundary caused by density and concentration balance of sea-water and fresh-water is an important item for groundwater flow evaluation in deep underground near the coast. Also, in order to evaluate groundwater quality, it is important to understand the characteristics of sea/fresh-water boundary, for example boundary shape, salt distribution. In order to establish the evaluation and analytical methods for groundwater flow with considering sea/fresh-water boundary, we investigated the following items in this study. (1) Literature survey and data collection. (2) Investigation of analytical methods. (3) Planning of further study. (author). 78 refs.
Analytical solutions of heat transfer for laminar flow in rectangular channels
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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.
Steady-State Thermoelastic Analytical Solutions for Insulated Pipelines
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M. Fraldi
2016-01-01
Full Text Available A steady-state thermoelastic analytical solution for a multilayer hollow cylinder, composed of an arbitrary number of phases and subject to both radial pressure and temperature gradient, is presented. By assuming each phase to be homogeneous and thermally isotropic and by varying the mechanical and thermal constitutive parameters, a sensitivity analysis has been performed with the aim of finally applying the study to the mechanical behaviour of an industrial pipeline composed of three phases (steel, insulating coating, and polyethylene under the action of the above-mentioned load conditions. By making reference to a classical Hencky-von Mises criterion, the stress profiles along the thickness of the layers have been carried out, also localizing the onset of plasticity as a function of the temperature variations, material properties, and geometrical features characterizing the composite structure of interest. At the end, some numerical results of practical interest in the engineering applications have been specialized to three different insulated coating materials (expanded polyurethane, laminate glass, and syntactic foam, to highlight the cases in which thermal properties and loads can significantly interfere with the mechanical response in pipes, in terms of stresses, in this way suggesting possible strategies for avoiding unexpected failure and supporting the optimal structural design of these systems.
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Qunying Zhang
2016-10-01
Full Text Available This article concerns with the solution to a heat equation with a free boundary in n-dimensional space. By applying the energy inequality to the solutions that depend not only on the initial value but also on the dimension of space, we derive the sufficient conditions under which solutions blow up at finite time. We then explore the long-time behavior of global solutions. Results show that the solution is global and fast when initial value is small, and the solution is global but slow for suitable initial value. Numerical simulations are also given to illustrate the effect of the initial value on the free boundary.
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
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......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...
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Salomatov Vladimir
2016-01-01
Full Text Available This work is dedicated to the search for the exact analytical dependences of microwave heating due to absorption of a plane electromagnetic wave by coal layer with asymmetric and non-uniform heat dissipation conditions I and III kind. Some of simplifications have been made, such as one-dimensional problem, uniformity and isotropic coal material, and the constancy of the electrical properties of thermal coal during heating of microwave radiation. This has led to the fact that the Maxwell’s task is solved separately from the Fourier’s task, and a heat source generated in the carbon layer is subject to Bouguer law. For the system of equations of heat transfer has been found a new dependent variable, which is to simplify the search for a final solution. All this has given the possibility of finding rigorous analytical solution of the problem of microwave heating of the coal layer in the presence of asymmetric and inhomogeneous boundary conditions I and III kind.
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Kulish Vladimir V.
2004-01-01
Full Text Available This paper presents an integral solution of the generalized one-dimensional equation of energy transport with the convective term.The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of noninteger orders. Confluent hypergeometric functions, known as Whittaker's functions, appear in the course of the solution procedure upon applying the Laplace transform to the original transport equation.The analytical solution of the problem is written in the integral form and provides a relationship between the local values of the transported property (e.g., temperature, mass, momentum, etc. and its flux.The solution is valid everywhere within the domain, including the domain boundary.
Transient Analytic Element Solutions for Flexible Aquifer Test Analyses
Kuhlman, K. L.; Neuman, S. P.
2007-12-01
We present three extensions to the 2D Laplace transform analytic element method (LT-AEM), introduced by Furman and Neuman (2003), which exemplify the types of problems that are easily solved using the LT-AEM, and are useful for performing flexible aquifer test analyses. First, we give the equation for a simplified leaky aquifer- aquitard LT-AEM system, similar to that used by Hantush (1960); in this example the source term is proportional to the drawdown in the aquifer (dual-domain flow is another example). Secondly, we present an approximate unconfined integrodifferential equation, as initially proposed by Boulton (1954) and generalized by Herrera, et al (1978). This solution illustrates how problems defined by convolution integrals are easily handled using LT-AEM (leaky systems can also be represented using convolution integrals). Finally, we present a damped-wave generalization of the diffusion equation that arises from considering a more general form of Darcy's law. The effects of inertia in the aquifer can be considered and may be important near sources in very course materials (e.g., gravel packed envelopes surrounding pumping wells). This final example shows how higher-order time derivatives may be handled in a simple and elegant fashion using LT-AEM techniques; solving the wave equation is as straightforward as solving the diffusion equation in Laplace space. Each of the LT-AEM problems presented here can be solved using any developed LT-AEM element (e.g., point, line, or area sources) or any combination of them, with little modification to the method used to solve the standard diffusion equation.
Energy Technology Data Exchange (ETDEWEB)
Petracca, S. [Salerno Univ. (Italy)
1996-08-01
Debye potentials, the Lorentz reciprocity theorem, and (extended) Leontovich boundary conditions can be used to obtain simple and accurate analytic estimates of the longitudinal and transverse coupling impedances of (piecewise longitudinally uniform) multi-layered pipes with non simple transverse geometry and/or (spatially inhomogeneous) boundary conditions. (author)
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 $r=2M$. ...
Numerical solution of fuzzy boundary value problems using Galerkin ...
Indian Academy of Sciences (India)
Abstract. This paper proposes a new technique based on Galerkin method for solving nth order fuzzy boundary value problem. The proposed method has been illustrated by considering three different cases depending upon the sign of coefficients with benchmark example problems. To show the applicability of the.
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)
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
Schöpfer, Martin; Lehner, Florian; Grasemann, Bernhard; Kaserer, Klemens; Hinsch, Ralph
2017-04-01
analytical solution is derived for the critical fracture spacing, i.e. the spacing below which the maximum tensile stress cannot reach the layer strength. The model results are consistent with an approximate analytical solution, and illustrate that the spacing of bending-induced fractures is proportional to layer thickness and a square root function of the ratio of layer tensile strength to confining pressure. Although highly idealised, models and analysis presented in this study offer an explanation for fracture saturation during folding and point towards certain key factors that may control fracture spacing in natural systems.
Approximate solution to a singular perturbed boundary value problem of thermal shielding
Latypov, I. I.
2017-11-01
The paper aims to investigate the problem of distribution of a non-regular, non-steady-state thermal field in the porous thermal shield material irradiated by a high flow of energy. A mathematical model of the original problem is stated in the form of a singular perturbed boundary value problem of a thermal conductivity equation with the nonlinear boundary conditions on moving boundaries. Its solution is obtained as asymptotic Poincare-type expansions in powers of small parameters.
Solution to the one-dimensional telegrapher's equation subject to a backreaction boundary condition
Prüstel, Thorsten; Meier-Schellersheim, Martin
2013-01-01
We discuss solutions of the one-dimensional telegrapher's equation in the presence of boundary conditions. We revisit the case of a radiation boundary condition and obtain an alternative expression for the already known Green's function. Furthermore, we formulate a backreaction boundary condition, which has been widely used in the context of diffusion-controlled reversible reactions, for a one-dimensional telegrapher's equation and derive the corresponding Green's function.
Alexandrov, Dmitri V.; Ivanov, Alexander A.; Alexandrova, Irina V.
2018-01-01
The processes of particle nucleation and their evolution in a moving metastable layer of phase transition (supercooled liquid or supersaturated solution) are studied analytically. The transient integro-differential model for the density distribution function and metastability level is solved for the kinetic and diffusionally controlled regimes of crystal growth. The Weber-Volmer-Frenkel-Zel'dovich and Meirs mechanisms for nucleation kinetics are used. We demonstrate that the phase transition boundary lying between the mushy and pure liquid layers evolves with time according to the following power dynamic law: http://www.w3.org/1999/xlink" xlink:href="RSTA20170217IM1"/>, where Z1(t)=βt7/2 and Z1(t)=βt2 in cases of kinetic and diffusionally controlled scenarios. The growth rate parameters α, β and ε are determined analytically. We show that the phase transition interface in the presence of crystal nucleation and evolution propagates slower than in the absence of their nucleation. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.
Hydrodynamics of Highly Viscous Flow past a Compound Particle: Analytical Solution
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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.
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Yumei Zou
2017-01-01
Full Text Available This paper deals with the integral boundary value problems of fractional differential equations at resonance. By Mawhin’s coincidence degree theory, we present some new results on the existence of solutions for a class of differential equations of fractional order with integral boundary conditions at resonance. An example is also included to illustrate the main results.
Existence of Solutions for Nonlinear Four-Point -Laplacian Boundary Value Problems on Time Scales
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Topal SGulsan
2009-01-01
Full Text Available We are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a -Laplacian operator on time scales. The proofs are based on the fixed point theorems concerning cones in a Banach space. Existence result for -Laplacian boundary value problem is also given by the monotone method.
Existence of Three Positive Solutions to Some p-Laplacian Boundary Value Problems
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Moulay Rchid Sidi Ammi
2013-01-01
Full Text Available We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some p-Laplacian boundary value problems on time scales.
Existence of arbitrarily smooth solutions of the LLG equation in 3D with natural boundary conditions
Feischl, Michael; Tran, Thanh
2016-01-01
We prove that the Landau-Lifshitz-Gilbert equation in three space dimensions with homogeneous Neumann boundary conditions admits arbitrarily smooth solutions, given that the initial data is sufficiently close to a constant function.
Existence of positive solutions for a system of semipositone fractional boundary value problems
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Johnny Henderson
2016-05-01
Full Text Available We investigate the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to coupled integral boundary conditions.
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Johnny Henderson
2016-01-01
Full Text Available We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.
Existence and uniqueness of solutions for a Neumann boundary-value problem
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Safia Benmansour
2011-09-01
Full Text Available In this article, we show the existence and uniqueness of positive solutions for perturbed Neumann boundary-value problems of second-order differential equations. We use a fixed point theorem for general $alpha$-concave operators.
Exact solution for the fractional cable equation with nonlocal boundary conditions
Bazhlekova, Emilia; Dimovski, Ivan
2013-10-01
The fractional cable equation is studied on a bounded space domain. One of the prescribed boundary conditions is of Dirichlet type, the other is of a general form, which includes the case of nonlocal boundary conditions. In real problems nonlocal boundary conditions are prescribed when the data on the boundary can not be measured directly. We apply spectral projection operators to convert the problem to a system of integral equations in any generalized eigenspace. In this way we prove uniqueness of the solution and give an algorithm for constructing the solution in the form of an expansion in terms of the generalized eigenfunctions and three-parameter Mittag-Leffler functions. Explicit representation of the solution is given for the case of double eigenvalues. We consider some examples and as a particular case we recover a recent result. The asymptotic behavior of the solution is also studied.
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
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
In this article, a variety of solitary wave solutions are found for some nonlinear equations. In mathematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study travelling wave solutions, we used ...
Povstenko, Y.
2013-09-01
The axisymmetric time-fractional diffusion-wave equation with the Caputo derivative of the order 0 function and the values of its normal derivative at the boundary. The fundamental solutions to the Cauchy, source, and boundary problems are investigated. The Laplace transform with respect to time and finite Hankel transform with respect to the radial coordinate are used. The solutions are obtained in terms of Mittag-Leffler functions. The numerical results are illustrated graphically.
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R. T. Al-Khairy
2009-01-01
source, whose capacity is given by (,=((1−− while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discussion of solutions for different time characteristics of heat sources capacity (constant, instantaneous, and exponential is presented. The effect of absorption coefficients on the temperature profiles is examined in detail. It is found that the closed form solution derived from the present study reduces to the previously obtained analytical solution when the medium velocity is set to zero in the closed form solution.
On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation
Mohammed Guedda; Abdelilah Gmira; Mohammed Benlahsen
2007-01-01
This paper concerns the singular solutions of the equation $$ f''' +kappa ff''-eta {f'}^2 = 0, $$ where $eta < 0$ and $kappa = 0$ or 1. This equation arises when modelling heat transfer past a vertical flat plate embedded in a saturated porous medium with an applied magnetic field. After suitable normalization, $f'$ represents the velocity parallel to the surface or the non-dimensional fluid temperature. Our interest is in solutions which develop a singularity at some point (t...
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M. T. Mustafa
2014-01-01
Full Text Available A new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented. It is based on an effective combination of Lie symmetry method, homotopy perturbation method, finite element method, and simulation based error reduction techniques. Implementation of the proposed approach is demonstrated by applying it to determine approximate analytic solutions of real life problems consisting of transient nonlinear heat conduction in semi-infinite bars made of stainless steel AISI 304 and mild steel. The results from the approximate analytical solutions and the numerical solution are compared indicating good agreement.
Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach
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Panos K. Palamides
2012-01-01
Full Text Available We investigate the existence of positive or a negative solution of several classes of four-point boundary-value problems for fourth-order ordinary differential equations. Although these problems do not always admit a (positive Green's function, the obtained solution is still of definite sign. Furthermore, we prove the existence of an entire continuum of solutions. Our technique relies on the continuum property (connectedness and compactness of the solutions funnel (Kneser's Theorem, combined with the corresponding vector field.
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Zhang Jing
2011-01-01
Full Text Available Abstract We discuss Neumann and Robin problems driven by the -Laplacian with jumping nonlinearities. Using sub-sup solution method, Fucík spectrum, mountain pass theorem, degree theorem together with suitable truncation techniques, we show that the Neumann problem has infinitely many nonconstant solutions and the Robin problem has at least four nontrivial solutions. Furthermore, we study oscillating equations with Robin boundary and obtain infinitely many nontrivial solutions.
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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.
Energy Technology Data Exchange (ETDEWEB)
Messaris, Gerasimos A. T., E-mail: messaris@upatras.gr [Department of Physics, Division of Theoretical Physics, University of Patras, GR 265 04 Rion (Greece); School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras (Greece); Hadjinicolaou, Maria [School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras (Greece); Karahalios, George T. [Department of Physics, Division of Theoretical Physics, University of Patras, GR 265 04 Rion (Greece)
2016-08-15
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 < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall 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
A new analytical solution to the diffusion problem: Fourier series ...
African Journals Online (AJOL)
This paper reviews briefly the origin of Fourier Series Method. The paper then gives a vivid description of how the method can be applied to solve a diffusion problem, subject to some boundary conditions. The result obtained is quite appealing as it can be used to solve similar examples of diffusion equations. JONAMP Vol.
Large time behavior of solutions to parabolic equations with Neumann boundary conditions
da Lio, Francesca
2008-03-01
In this paper we are interested in the large time behavior as t-->+[infinity] of the viscosity solutions of parabolic equations with nonlinear Neumann type boundary conditions in connection with ergodic boundary problems which have been recently studied by Barles and the author in [G. Barles, F. Da Lio, On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions, Ann. Inst. H. Poincaré Anal. Non Linèaire 22 (5) (2005) 521-541].
Analytical solution for two-phase flow in a wellbore using the drift-flux model
Energy Technology Data Exchange (ETDEWEB)
Pan, L.; Webb, S.W.; Oldenburg, C.M.
2011-11-01
This paper presents analytical solutions for steady-state, compressible two-phase flow through a wellbore under isothermal conditions using the drift flux conceptual model. Although only applicable to highly idealized systems, the analytical solutions are useful for verifying numerical simulation capabilities that can handle much more complicated systems, and can be used in their own right for gaining insight about two-phase flow processes in wells. The analytical solutions are obtained by solving the mixture momentum equation of steady-state, two-phase flow with an assumption that the two phases are immiscible. These analytical solutions describe the steady-state behavior of two-phase flow in the wellbore, including profiles of phase saturation, phase velocities, and pressure gradients, as affected by the total mass flow rate, phase mass fraction, and drift velocity (i.e., the slip between two phases). Close matching between the analytical solutions and numerical solutions for a hypothetical CO{sub 2} leakage problem as well as to field data from a CO{sub 2} production well indicates that the analytical solution is capable of capturing the major features of steady-state two-phase flow through an open wellbore, and that the related assumptions and simplifications are justified for many actual systems. In addition, we demonstrate the utility of the analytical solution to evaluate how the bottomhole pressure in a well in which CO{sub 2} is leaking upward responds to the mass flow rate of CO{sub 2}-water mixture.
Directory of Open Access Journals (Sweden)
Asterios Pantokratoras
2008-01-01
Full Text Available Exact analytical solutions of boundary layer flows along a vertical porous plate with uniform suction are derived and presented in this paper. The solutions concern the Blasius, Sakiadis, and Blasius-Sakiadis flows with buoyancy forces combined with either MHD Lorentz or EMHD Lorentz forces. In addition, some exact solutions are presented specifically for water in the temperature range of 0∘C≤≤8∘C, where water density is nearly parabolic. Except for their use as benchmarking means for testing the numerical solution of the Navier-Stokes equations, the presented exact solutions with EMHD forces have use in flow separation control in aeronautics and hydronautics, whereas the MHD results have applications in process metallurgy and fusion technology. These analytical solutions are valid for flows with strong suction.
Directory of Open Access Journals (Sweden)
Nelly S. Khapilova
2015-10-01
Full Text Available We present the analytical solution of the axisymmetric mixed problem for the isotropic half-space with the surface fixed elastically outside the circular area of the application of a distributed load. In the solution of the problem, the transition procedure from a distributed load to the concentrated force has been justified. A compact form of the exact analytical solution of the problem on the concentrated force applied to the half-space with the surface fixed elastically was obtained. In the specific case when the proportionality factor of normal stresses and displacements vanishing under the condition of the elastic fixing of the boundary, the constructed analytical solution was shown to coincide with the well-known Boussinesq formulae.
On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation
Directory of Open Access Journals (Sweden)
Mohammed Guedda
2007-05-01
Full Text Available This paper concerns the singular solutions of the equation $$ f''' +kappa ff''-eta {f'}^2 = 0, $$ where $eta < 0$ and $kappa = 0$ or 1. This equation arises when modelling heat transfer past a vertical flat plate embedded in a saturated porous medium with an applied magnetic field. After suitable normalization, $f'$ represents the velocity parallel to the surface or the non-dimensional fluid temperature. Our interest is in solutions which develop a singularity at some point (the blow-up point. In particular, we shall examine in detail the behavior of $f$ near the blow-up point.
numerical solutions of fifth order boundary value problems using ...
African Journals Online (AJOL)
Dr A.B.Ahmed
solving these problems by employing polynomials as trial functions in the ... numerical solution of Volterra integral equations by Galerkin method. Caglar et .... and continuous on [0,1], i α ,. 2,1,0. = i and i β ,. ,1,0. = i are finite real constants. Transforming (10) – (11) to systems of ordinary differential equations, we have. 1 yy. =.
Analytical solutions of time–space fractional, advection–dispersion ...
Indian Academy of Sciences (India)
The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional ... Department of Mathematics, School of Science and Engineering, Lahore University of Management Sciences, Lahore Cantt 54792, Pakistan; Department of ...
Analytic Solutions of the Space-Time Fractional Combined KdV-mKdV Equation
Directory of Open Access Journals (Sweden)
Emad A.-B. Abdel-Salam
2015-01-01
Full Text Available The fractional mapping method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional combined KdV-mKdV equation. Many types of exact analytical solutions are obtained. The solutions include generalized trigonometric and hyperbolic functions solutions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time.
Directory of Open Access Journals (Sweden)
Jiqiang Jiang
2012-01-01
Full Text Available We consider the existence of positive solutions for a class of nonlinear integral boundary value problems for fractional differential equations. By using some fixed point theorems, the existence and multiplicity results of positive solutions are obtained. The results obtained in this paper improve and generalize some well-known results.
Directory of Open Access Journals (Sweden)
Charyyar Ashyralyyev
2015-07-01
Full Text Available This article studies the numerical solution of inverse problems for the multidimensional elliptic equation with Dirichlet-Neumann boundary conditions and Neumann type overdetermination. We present first and second order accuracy difference schemes. The stability and almost coercive stability inequalities for the solution are obtained. Numerical examples with explanation on the implementation illustrate the theoretical results.
Three symmetric positive solutions of fourth-order singular nonlocal boundary value problems
Directory of Open Access Journals (Sweden)
Fuyi Xu
2011-12-01
Full Text Available In this paper, we study the existence of three positive solutions of fourth-order singular nonlocal boundary value problems. We show that there exist triple symmetric positive solutions by using Leggett-Williams fixed-point theorem. The conclusions in this paper essentially extend and improve some known results.
Numerical solutions of a three-point boundary value problem with an ...
African Journals Online (AJOL)
Numerical solutions of a three-point boundary value problem with an integral condition for a third-order partial differential equation by using Laplace transform method Solutions numeriques d'un probleme pour une classe d'equations differentielles d'ordr.
Positive solutions of second-order singular boundary value problem with a Laplace-like operator
Directory of Open Access Journals (Sweden)
Ge Weigao
2005-01-01
Full Text Available By use of the concavity of solution for an associate boundary value problem, existence criteria of positive solutions are given for the Dirichlet BVP , , , where is odd and continuous with , , and may change sign and be singular along a curve in .
Positive Solutions of a Nonlinear Fourth-order Integral Boundary Value Problem
Directory of Open Access Journals (Sweden)
Benaicha Slimane
2016-07-01
Full Text Available In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii’s fixed point theorem on cones, sufficient conditions for the existence of at least one positive solutions are obtained.
Directory of Open Access Journals (Sweden)
Mohammad Zamani Nejad
2014-01-01
Full Text Available Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT. These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM is also presented and good agreement was found.
Analytical Reduced Models for the Non-stationary Diabatic Atmospheric Boundary Layer
Momen, Mostafa; Bou-Zeid, Elie
2017-09-01
Geophysical boundary-layer flows feature complex dynamics that often evolve with time; however, most current knowledge centres on the steady-state problem. In these atmospheric and oceanic boundary layers, the pressure gradient, buoyancy, Coriolis, and frictional forces interact to determine the statistical moments of the flow. The resulting equations for the non-stationary mean variables, even when succinctly closed, remain challenging to handle mathematically. Here, we derive a simpler physical model that reduces these governing unsteady Reynolds-averaged Navier-Stokes partial differential equations into a single first-order ordinary differential equation with non-constant coefficients. The reduced model is straightforward to solve under arbitrary forcing, even when the statistical moments are non-stationary and the viscosity varies in time and space. The model is successfully validated against large-eddy simulation for, (1) time-variable pressure gradients, and (2) linearly time-variable buoyancy. The new model is shown to have a superior performance compared to the classic Blackadar solutions (and later improvements on these solutions), and it covers a much wider range of conditions.
The Analytical Solution of Parabolic Volterra Integro-Differential Equations in the Infinite Domain
Directory of Open Access Journals (Sweden)
Yun Zhao
2016-09-01
Full Text Available This article focuses on obtaining analytical solutions for d-dimensional, parabolic Volterra integro-differential equations with different types of frictional memory kernel. Based on Laplace transform and Fourier transform theories, the properties of the Fox-H function and convolution theorem, analytical solutions for the equations in the infinite domain are derived under three frictional memory kernel functions. The analytical solutions are expressed by infinite series, the generalized multi-parameter Mittag-Leffler function, the Fox-H function and the convolution form of the Fourier transform. In addition, graphical representations of the analytical solution under different parameters are given for one-dimensional parabolic Volterra integro-differential equations with a power-law memory kernel. It can be seen that the solution curves are subject to Gaussian decay at any given moment.
Directory of Open Access Journals (Sweden)
Lev Abolnikov
2000-01-01
Full Text Available A bulk M/G/1 system is considered that responds to large increases (decreases of the queue during the service act by alternating between two service modes. The switching rule is based on two up and down thresholds for total arrivals over the service act. A necessary and sufficient condition for the ergodicity of a Markov chain embedded into the main queueing process is found. Both complex-analytic and matrix-analytic solutions are obtained for the steady-state distribution. Under the assumption of the same service time distribution in both modes, a combined complex-matrix-analytic method is introduced. The technique of matrix unfolding is used, which reduces the problem to a matrix iteration process with the block size much smaller than in the direct application of the matrix-analytic method.
A family of analytical solutions of a nonlinear diffusion-convection equation
Hayek, Mohamed
2018-01-01
Despite its popularity in many engineering fields, the nonlinear diffusion-convection equation has no general analytical solutions. This work presents a family of closed-form analytical traveling wave solutions for the nonlinear diffusion-convection equation with power law nonlinearities. This kind of equations typically appears in nonlinear problems of flow and transport in porous media. The solutions that are addressed are simple and fully analytical. Three classes of analytical solutions are presented depending on the type of the nonlinear diffusion coefficient (increasing, decreasing or constant). It has shown that the structure of the traveling wave solution is strongly related to the diffusion term. The main advantage of the proposed solutions is that they are presented in a unified form contrary to existing solutions in the literature where the derivation of each solution depends on the specific values of the diffusion and convection parameters. The proposed closed-form solutions are simple to use, do not require any numerical implementation, and may be implemented in a simple spreadsheet. The analytical expressions are also useful to mathematically analyze the structure and properties of the solutions.
Directory of Open Access Journals (Sweden)
Huaying Zhao
Full Text Available Fluorescence optical detection in sedimentation velocity analytical ultracentrifugation allows the study of macromolecules at nanomolar concentrations and below. This has significant promise, for example, for the study of systems of high-affinity protein interactions. Here we describe adaptations of the direct boundary modeling analysis approach implemented in the software SEDFIT that were developed to accommodate unique characteristics of the confocal fluorescence detection system. These include spatial gradients of signal intensity due to scanner movements out of the plane of rotation, temporal intensity drifts due to instability of the laser and fluorophores, and masking of the finite excitation and detection cone by the sample holder. In an extensive series of experiments with enhanced green fluorescent protein ranging from low nanomolar to low micromolar concentrations, we show that the experimental data provide sufficient information to determine the parameters required for first-order approximation of the impact of these effects on the recorded data. Systematic deviations of fluorescence optical sedimentation velocity data analyzed using conventional sedimentation models developed for absorbance and interference optics are largely removed after these adaptations, resulting in excellent fits that highlight the high precision of fluorescence sedimentation velocity data, thus allowing a more detailed quantitative interpretation of the signal boundaries that is otherwise not possible for this system.
Zhao, Huaying; Casillas, Ernesto; Shroff, Hari; Patterson, George H.; Schuck, Peter
2013-01-01
Fluorescence optical detection in sedimentation velocity analytical ultracentrifugation allows the study of macromolecules at nanomolar concentrations and below. This has significant promise, for example, for the study of systems of high-affinity protein interactions. Here we describe adaptations of the direct boundary modeling analysis approach implemented in the software SEDFIT that were developed to accommodate unique characteristics of the confocal fluorescence detection system. These include spatial gradients of signal intensity due to scanner movements out of the plane of rotation, temporal intensity drifts due to instability of the laser and fluorophores, and masking of the finite excitation and detection cone by the sample holder. In an extensive series of experiments with enhanced green fluorescent protein ranging from low nanomolar to low micromolar concentrations, we show that the experimental data provide sufficient information to determine the parameters required for first-order approximation of the impact of these effects on the recorded data. Systematic deviations of fluorescence optical sedimentation velocity data analyzed using conventional sedimentation models developed for absorbance and interference optics are largely removed after these adaptations, resulting in excellent fits that highlight the high precision of fluorescence sedimentation velocity data, thus allowing a more detailed quantitative interpretation of the signal boundaries that is otherwise not possible for this system. PMID:24204779
Solution of fourth order three-point boundary value problem using ADM and RKM
Directory of Open Access Journals (Sweden)
Ghazala Akram
2016-06-01
Full Text Available In this paper, a computational method is proposed, for solving linear and nonlinear fourth order three-point boundary value problem (BVP and the system of nonlinear BVP. This method is based on the Adomian decomposition method (ADM and the reproducing kernel method (RKM. The solution of linear fourth order three-point boundary value problem (BVP is determined by the reproducing kernel method, and the solution of nonlinear fourth order three-point BVP is determined using the combination of Adomian decomposition method and reproducing kernel method. The approximate solutions are given in the form of series. Numerical results are shown to illustrate the accuracy of the present method.
Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin
2016-01-01
This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.
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
Analytic Solutions to Coherent Control of the Dirac Equation
Campos, Andre G.; Cabrera, Renan; Rabitz, Herschel A.; Bondar, Denys I.
2017-10-01
A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell's equations, which yield a desired evolution. In particular, we show how to achieve dispersionless rotation and translation of wave packets. Additionally, this formalism can handle control interactions beyond electromagnetic. This work reveals unexpected flexibility of the Dirac equation for control applications, which may open new prospects for quantum technologies.
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.
Solution of potential flow past an elastic body using the boundary element technique
Taylor, Norma F.
1988-12-01
This thesis describes the development of a Fortran computer code which models the interaction between an incompressible, potential flow and a homogeneous, elastic structure. The boundary element technique was chosen because of its ability to numerically approximate both the fluid and structural behavior with a common definition of the fluid/structure boundary. The ability to accurately model solid and fluid boundaries can be quite important in the fields of aeroelasticity and structural analysis. The nature of these boundaries is what determines the final solution to a problem of fluid flow past an elastic body. Often the complexity of defining and tracking the boundary and its associated boundary conditions has led the user to assumptions of rigid bodies, and therefore rigid boundaries. Certainly the tasks of defining the domain grids for finite difference and finite element techniques have not simplified this process. In the computer code developed for this thesis the fluid and structural governing equations are simultaneously solved to determine the pressure about the structure and the corresponding elastic deformations. The deformations are applied to the original boundary, resulting in a new geometry. This new geometry is used to recalculate the pressure field about the structure, and the process is iterated until a final steady-state solution is obtained.
Analytical Solutions for Predicting Underwater Explosion Gas Bubble Behaviour
2010-11-01
décrit différents modèles analytiques élaborés antérieurement pour prévoir la croissance et l’implosion radiales en champ libre des bulles gazeuses...9.80665 Air pressure (kPa), Pair 101.325 101.325 4.4 Code Development The visualization software IDL was used to develop a code for calculating the...models and assumptions provide better predictions. Using the visualization software IDL the various analytical models and similitude equations, a code
Analytical solution of a stochastic content-based network model
Energy Technology Data Exchange (ETDEWEB)
Mungan, Muhittin [Department of Physics, Faculty of Arts and Sciences, Bogazici University, 34342 Bebek Istanbul (Turkey); Guersey Institute, PO Box 6, Cengelkoey, 34680 Istanbul (Turkey); Kabakoglu, Alkan [Department of Physics, Faculty of Arts and Sciences, Koc University, 34450 Sariyer Istanbul (Turkey); Dipartimento di Fisica, Universita di Padova, I-35131 Padova (Italy); Balcan, Duygu [Department of Physics, Faculty of Sciences and Letters, Istanbul Technical University, Maslak 34469, Istanbul (Turkey); Erzan, Ayse [Guersey Institute, PO Box 6, Cengelkoey, 34680 Istanbul (Turkey); Department of Physics, Faculty of Sciences and Letters, Istanbul Technical University, Maslak 34469, Istanbul (Turkey)
2005-11-04
We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behaviour to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show any scaling behaviour.
Jin, Guoyong; Su, Zhu
2015-01-01
This book develops a uniform accurate method which is capable of dealing with vibrations of laminated beams, plates and shells with arbitrary boundary conditions including classical boundaries, elastic supports and their combinations. It also provides numerous solutions for various configurations including various boundary conditions, laminated schemes, geometry and material parameters, which fill certain gaps in this area of reach and may serve as benchmark solutions for the readers. For each case, corresponding fundamental equations in the framework of classical and shear deformation theory are developed. Following the fundamental equations, numerous free vibration results are presented for various configurations including different boundary conditions, laminated sequences and geometry and material properties. The proposed method and corresponding formulations can be readily extended to static analysis.
Analytical 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. .
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.
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.
A Hybrid Analytical-Numerical Solution to the Laminar Flow inside Biconical Ducts
National Research Council Canada - National Science Library
Thiago Antonini Alves; Ricardo Alan Verdú Ramos; Cassio Roberto Macedo Maia
2015-01-01
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...
Semi-Analytic Solution of HIV and TB Co-Infection Model BOLARIN ...
African Journals Online (AJOL)
ADOWIE PERE
. +. −. + +. +. +. +. − + +. +. −. +. +. −. +. (66). RESULTS AND DISCUSSION. In this section, we use maple software to plot the graph of semi-analytic solution of our model equations. Since, most of the parameters were not readily available ...
A Comparative Evaluation of Numerical and Analytical Solutions to the Biadhesive Single-Lap Joint
Halil Özer; Özkan Öz
2014-01-01
This paper attempts to address the detailed verification of Zhao’s analytical solution including the moment effect with the two- and three-dimensional finite element results. Zhao compared the analytical results with only the 2D FEA results and used the constant bond-length ratio for the biadhesive bondline. In this study, overlap surfaces of the adherends and the adhesives were modelled using surface-to-surface contact elements. Both analytical and numerical analyses were performed using fou...
First integrals and analytical solutions of the nonlinear fin problem ...
Indian Academy of Sciences (India)
2016-07-06
Jul 6, 2016 ... first integrals of the nonlinear straight fin problem are constructed by three methods, namely, Noether's classical method, partial Noether ... Fin equation; Lie symmetry; first integrals; exact solutions. PACS Nos 02.20.Tw; 02.30.Hq. 1. ... to some new integrable systems via reciprocal trans- formations [1].
Analytical solutions of time–space fractional, advection–dispersion ...
Indian Academy of Sciences (India)
and time–space fractional Whitham–Broer–Kaup (FWBK) equation that have significant roles in hydrology. We introduce ... The symmetry reductions and exact independent solutions based on optimal system are investigated .... used travelling wave transformation to reduce (2) to a nonlinear system of third-order fractional ...
Explicit Analytical Solution of a Pendulum with Periodically Varying Length
Yang, Tianzhi; Fang, Bo; Li, Song; Huang, Wenhu
2010-01-01
A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In this paper,…
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.)
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
2016-10-18
Oct 18, 2016 ... gested technique would be expected to perform better, with more exact solutions compared to the traditional exp(−ϕ(η))-expansion method. References. [1] N T Shawagfeh, Appl. Math. Comput. 31(2–3), 517 (2002). [2] A A Kilbas, H M Srivastava and J J Trujillo, Comput. Math. Appl. 204, 1079 (2006) ...
Analytical solution of mass transfer effects on unsteady flow past an ...
African Journals Online (AJOL)
This paper discussed the analytical solution of unsteady free convection and mass transfer flow past an accelerated infinite vertical porous flat plate with suction, heat generation and chemical species when the plate accelerates in its own plane. The governing equations are solved analytically using perturbation technique.
Comment on ``Modeling of metal electrodeposits: Analytical solutions''
Chazalviel, J.-N.; Fleury, V.
1996-10-01
When the equations of ionic motion for electrodeposition in a one-dimensional cell filled with a dilute binary electrolyte are solved under fixed-boundary conditions, a diffusion-limited current, independent of applied potential, is obtained. This result is well expected in the framework of the quasineutrality approximation. In this framework, the assumption by Huang and Hibbert [Phys. Rev. E. 52, 5065 (1995)] of an electrical-migration term in the evolution equation for the concentration is incorrect. However, a term of the same form, though smaller, may appear either from the concentration dependence of the mobilities or from an electro-osmotic effect if the electrolyte is embedded in a gel or a porous medium.
Analytical solutions of stellar winds in B-A type supergiants stars
Araya, Ignacio; Cure, Michel
2013-06-01
An analytical solution for the δ-slow hydrodynamic solution (Cure et al. 2011) in B-A type supergiants stars is developed. The methodology is based on the analytical solutions of a) Villata (1992), which is described in terms of the stellar and wind parameters and b) Muller & Vink (2008), which is described in terms of fitting parameters from a numerical solution (hydrodynamic). These methodologies only apply for fast solutions, for that reason the line acceleration term (gL) of Muller & Vink method is modified in order to obtain an analytical solution for the δ-slow solution. To find a relationship between the parameters from the fit and the stellar and wind parameters, a computational grid, based on the grid of stellar models from Ekstrom et al. (2012), is created for B-A type supergiants stars with δ-slow hydrodynamic solution. Finally, an analytical solution for B-A type supergiants stars is obtained based on the Lambert W function (Corless et al. 1996). Comparing with the numerical solutions, the terminal velocity has a median relative error below 4% and the mass loss rate has a median relative error below 5%. In addition, we calculated the wind-momentum luminosity relationship (WLR) with the models from the computational grid and compared with the observations, showing a very good agreement.
Power Control at Grid Connected Converters and Analytical Solution of Steady States
Viktor Valouch; Jiří Škramlík; Zdeněk Muller; Jan Švec; Josef Tlustý
2015-01-01
The paper presents a power control technique at grid connected converters under unbalanced voltage conditions. The current positive and negative sequences during grid voltage sags are controlled to ensure a proper exchange of active and reactive powers without power ripples. An analytical solution in a closed form of the B6 and B4 converters working with an optimized half a period switching symmetry is presented. The analytical solution may be applied for the converters connected to highly un...
Mustafa, M.T.; Arif, A.F.M.; Masood, Khalid
2014-01-01
A new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented. It is based on an effective combination of Lie symmetry method, homotopy perturbation method, finite element method, and simulation based error reduction techniques. Implementation of the proposed approach is demonstrated by applying it to determine approximate analytic solutions of real life problems consisting of transient nonlinear heat conduction in semi-infinite bars...
Solution matching for a three-point boundary-value problem on atime scale
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Martin Eggensperger
2004-07-01
Full Text Available Let $mathbb{T}$ be a time scale such that $t_1, t_2, t_3 in mathbb{T}$. We show the existence of a unique solution for the three-point boundary value problem $$displaylines{ y^{DeltaDeltaDelta}(t = f(t, y(t, y^Delta(t, y^{DeltaDelta}(t, quad t in [t_1, t_3] cap mathbb{T},cr y(t_1 = y_1, quad y(t_2 = y_2, quad y(t_3 = y_3,. }$$ We do this by matching a solution to the first equation satisfying a two-point boundary conditions on $[t_1, t_2] cap mathbb{T}$ with a solution satisfying a two-point boundary conditions on $[t_2, t_3] cap mathbb{T}$.
Nearly perfect nonmagnetic invisibility cloaking: Analytic solutions and parametric studies
Castaldi, Giuseppe; Gallina, Ilaria; Galdi, Vincenzo
2009-09-01
Coordinate-transformation approaches to invisibility cloaking rely on the design of an anisotropic, spatially inhomogeneous “transformation medium” capable of suitably rerouting the energy flux around the region to conceal without causing any scattering in the exterior region. It is well known that the inherently magnetic properties of such medium limit the high-frequency scaling of practical “metamaterial” implementations based on subwavelength inclusions (e.g., split-ring resonators). Thus, for the optical range, nonmagnetic implementations, based on approximate reductions of the constitutive parameters, have been proposed. In this paper, we present an alternative approach to nonmagnetic coordinate-transformation cloaking, based on the mapping from a nearly transparent, anisotropic and spatially inhomogeneous virtual domain. We show that, unlike its counterparts in the literature, our approach is amenable to exact analytic treatment, and that its overall performance is comparable to that of a nonideal (lossy, dispersive, parameter truncated) implementation of standard (magnetic) cloaking.
Analytical Solution of Generalized Space-Time Fractional Cable Equation
Ram K. Saxena; Zivorad Tomovski; Trifce Sandev
2015-01-01
In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are compared with those presented in this paper. By using the Bernstein characterization theorem we find ...
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Adib Samin
2015-08-01
Full Text Available Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.
Commentary on local and boundary regularity of weak solutions to Navier-Stokes equations
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Zdenek Skalak
2004-01-01
Full Text Available We present results on local and boundary regularity for weak solutions to the Navier-Stokes equations. Beginning with the regularity criterion proved recently in [14] for the Cauchy problem, we show that this criterion holds also locally. This is also the case for some other results: We present two examples concerning the regularity of weak solutions stemming from the regularity of two components of the vorticity ([2] or from the regularity of the pressure ([3]. We conclude by presenting regularity criteria near the boundary based on the results in [10] and [16].
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Ying Wang
2015-03-01
Full Text Available In this article, we study the existence of multiple positive solutions for singular semipositone boundary-value problem (BVP with integral boundary conditions on infinite intervals. By using the properties of the Green's function and the Guo-Krasnosel'skii fixed point theorem, we obtain the existence of multiple positive solutions under conditions concerning the nonlinear functions. The method in this article can be used for a large number of problems. We illustrate the validity of our results with an example in the last section.
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
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FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
An Approximate Solution for Boundary Value Problems in Structural Engineering and Fluid Mechanics
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A. Barari
2008-01-01
Full Text Available Variational iteration method (VIM is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iteration method (VIM. The results reveal that this method is very effective and simple, and that it yields the exact solutions. It was shown that this method can be used effectively for solving linear and nonlinear boundary value problems.
Analytic P{sub 1} solutions for time-dependent, thermal radiative transfer in several geometries
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McClarren, Ryan G. [Computational Physics and Methods Group (CCS-2), Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545 (United States)], E-mail: ryanmc@lanl.gov; Paul Holloway, James [Department of Nuclear Engineering and Radiological Sciences, College of Engineering, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109 2104 (United States); Brunner, Thomas A. [Sandia National Laboratories, P.O. Box 5800, MS 1186, Albuquerque, NM 87185 1186 (United States)
2008-02-15
We present several solutions for the time-dependent P{sub 1} approximation (telegrapher's equation) coupled to thermal radiative transfer with C{sub v}{proportional_to}T{sup 3}. Our solutions are based on the energy density Green's function in slab geometry, which we derive exactly. The analytic P{sub 1} solution is compared with analytic transport and diffusion solutions on one of the Su-Olson benchmark problems. Also, we transform the slab geometry Green's function into the solution from a point source (the 1D spherical Green's function) and an infinite line source (the 1D cylindrical Green's function). We evaluate the P{sub 1} solution to the line source and compare the result with a solution generated by a P{sub n} numerical method.
Analytical solutions for Dirac and Klein-Gordon equations using Backlund transformations
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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)
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M. I. Popov
2016-01-01
Full Text Available The approximate analytical solution of a problem about nonstationary free convection in the conductive and laminar mode of the Newtonian liquid in square area at the instantaneous change of temperature of a sidewall and lack of heat fluxes is submitted on top and bottom the bases. The equations of free convection in an approximation of Oberbeka-Bussinesk are linearized due to neglect by convective items. For reduction of number of hydrothermal parameters the system is given to the dimensionless look by introduction of scales for effect and explanatory variables. Transition from classical variables to the variables "whirlwind-a flow function" allowed to reduce system to a nonstationary heat conduction equation and a nonstationary nonuniform biharmonic equation, and the first is not dependent on the second. The decision in the form of a flow function is received by application integral a sine - Fourier transforms with terminating limits to a biharmonic equation at first on a variable x, and then on a variable y. The flow function has an appearance of a double series of Fourier on sine with coefficients in an integral form. Coefficients of a row represent integrals from unknown functions. On the basis of a hypothesis of an express type of integrals coefficients are calculated from the linear equation system received from boundary conditions on partial derivatives of function. Dependence of structure of a current on Prandtl's number is investigated. The cards of streamlines and isolines of components of speed describing development of a current from the moment of emergence before transition to a stationary state are received. The schedules of a field of vectors of speeds in various time illustrating dynamics of a current are provided. Reliability of a hypothesis of an express type of integral coefficients is confirmed by adequacy to physical sense and coherence of the received results with the numerical solution of a problem.
Holst, Michael; Meier, Caleb; Tsogtgerel, G.
2017-11-01
In this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the Einstein constraint equations on compact manifolds with boundary. By building in a natural way on our recent work in Holst and Tsogtgerel (Class Quantum Gravity 30:205011, 2013), and Holst et al. (Phys Rev Lett 100(16):161101, 2008, Commun Math Phys 288(2):547-613, 2009), and also on the work of Maxwell (J Hyperbolic Differ Eqs 2(2):521-546, 2005a, Commun Math Phys 253(3):561-583, 2005b, Math Res Lett 16(4):627-645, 2009) and Dain (Class Quantum Gravity 21(2):555-573, 2004), under reasonable assumptions on the data we prove existence of both near- and far-from-constant mean curvature (CMC) solutions for a class of Robin boundary conditions commonly used in the literature for modeling black holes, with a third existence result for CMC appearing as a special case. Dain and Maxwell addressed initial data engineering for space-times that evolve to contain black holes, determining solutions to the conformal formulation on an asymptotically Euclidean manifold in the CMC setting, with interior boundary conditions representing excised interior black hole regions. Holst and Tsogtgerel compiled the interior boundary results covered by Dain and Maxwell, and then developed general interior conditions to model the apparent horizon boundary conditions of Dainand Maxwell for compact manifolds with boundary, and subsequently proved existence of solutions to the Lichnerowicz equation on compact manifolds with such boundary conditions. This paper picks up where Holst and Tsogtgerel left off, addressing the general non-CMC case for compact manifolds with boundary. As in our previous articles, our focus here is again on low regularity data and on the interaction between different types of boundary conditions. While our work here serves primarily to extend the solution theory for the compact with boundary case, we also develop several technical tools that have
Analytical Solution of Generalized Space-Time Fractional Cable Equation
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Ram K. Saxena
2015-04-01
Full Text Available In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are compared with those presented in this paper. By using the Bernstein characterization theorem we find the conditions under which the even moments are non-negative.
Solutions of the Helmholtz equation with boundary conditions for force-free magnetic fields
Rasband, S. N.; Turner, L.
1981-01-01
It is shown that the solution, with one ignorable coordinate, for the Taylor minimum energy state (resulting in a force-free magnetic field) in either a straight cylindrical or a toroidal geometry with arbitrary cross section can be reduced to the solution of either an inhomogeneous Helmholtz equation or a Grad-Shafranov equation with simple boundary conditions. Standard Green's function theory is, therefore, applicable. Detailed solutions are presented for the Taylor state in toroidal and cylindrical domains having a rectangular cross section. The focus is on solutions corresponding to the continuous eigenvalue spectra. Singular behavior at 90 deg corners is explored in detail.
Analytic crack solutions for tilt fields around hydraulic fractures
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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.
Fixed time versus fixed range reverberation calculation: analytical solution.
Harrison, Chris H; Ainslie, Michael A
2010-07-01
Reverberation is commonly calculated by estimating the propagation loss to and from an elementary area, defined by transmitted pulse length and beam width, and treating the resulting backscatter from the area as a function of its range. In reality reverberation is strictly a function of time and contributions for a given time come from many ranges. Closed-form solutions are given for reverberation calculated both at fixed range and at fixed time isovelocity water and some variants of Lambert's law and linear reflection loss with an abrupt critical angle. These are derived by considering the shape of the two-way scattered multipath pulse envelope from a point scatterer. The ratio of these two solutions is shown to depend on the dominant propagation angle spread for the particular range or time. The ratio is largest at intermediate ranges (though typically less than 1 dB) and depends explicitly on the critical angle. At longer ranges mode-stripping reduces the propagation angle spread and the ratio reduces ultimately to unity. At short range the ratio is also close to unity although interpreting it requires care.
An Analytical Solution for Cylindrical Concrete Tank on Deformable Soil
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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.
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.
Dynamics of Atmospheric Boundary Layers: Large-Eddy Simulations and Reduced Analytical Models
Momen, Mostafa
Real-world atmospheric and oceanic boundary layers (ABL) involve many inherent complexities, the understanding and modeling of which manifestly exceeds our current capabilities. Previous studies largely focused on the "textbook ABL", which is (quasi) steady and barotropic. However, it is evident that the "real-world ABL", even over flat terrain, rarely meets such simplifying assumptions. The present thesis aims to illustrate and model four complicating features of ABLs that have been overlooked thus far despite their ubiquity: 1) unsteady pressure gradients in neutral ABLs (Chapters 2 and 3), 2) interacting effects of unsteady pressure gradients and static stability in diabatic ABLs (Chapter 4), 3) time-variable buoyancy fluxes (Chapter 5) , and 4) impacts of baroclinicity in neutral and diabatic ABLs (Chapter 6). State-of-the-art large-eddy simulations will be used as a tool to explain the underlying physics and to validate analytical models we develop for these features. Chapter 2 focuses on the turbulence equilibrium: when the forcing time scale is comparable to the turbulence time scale, the turbulence is shown to be out of equilibrium, and the velocity profiles depart from the log-law; However, for longer, and surprisingly for shorter forcing times, quasi-equilibrium is maintained. In Chapter 3, a reduced analytical model, based on the Navier-Stokes equations, will be introduced and shown to be analogous to a damped oscillator where inertial, Coriolis, and friction forces mirror the mass, spring, and damper, respectively. When a steady buoyancy (stable or unstable) is superposed on the unsteady pressure gradient, the same model structure can be maintained, but the damping term, corresponding to friction forces and vertical coupling, needs to account for stability. However, for the reverse case with variable buoyancy flux and stability, the model needs to be extended to allow time-variable damper coefficient. These extensions of the analytical model are
Analytical Lie-algebraic solution of a 3D sound propagation problem in the ocean
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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.
Valent, Tullio
1988-01-01
In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be sides being quite spontaneous, allows us to consider a great many inter esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b]...
Analytical solutions for spin response functions in model storage rings with Siberian Snakes
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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.
Hemker, K.; Bakker, M.
2006-01-01
Analytical solutions are derived for steady state groundwater flow in a heterogeneous, anisotropic, semiconfined aquifer. The aquifer consists of a number of horizontal layers, while each layer consists of a number of homogeneous cells with different hydraulic conductivity tensors. An exact solution
Salama, Amgad
2013-09-01
In this work the problem of flow in three-dimensional, axisymmetric, heterogeneous porous medium domain is investigated numerically. For this system, it is natural to use cylindrical coordinate system, which is useful in describing phenomena that have some rotational symmetry about the longitudinal axis. This can happen in porous media, for example, in the vicinity of production/injection wells. The basic feature of this system is the fact that the flux component (volume flow rate per unit area) in the radial direction is changing because of the continuous change of the area. In this case, variables change rapidly closer to the axis of symmetry and this requires the mesh to be denser. In this work, we generalize a methodology that allows coarser mesh to be used and yet yields accurate results. This method is based on constructing local analytical solution in each cell in the radial direction and moves the derivatives in the other directions to the source term. A new expression for the harmonic mean of the hydraulic conductivity in the radial direction is developed. Apparently, this approach conforms to the analytical solution for uni-directional flows in radial direction in homogeneous porous media. For the case when the porous medium is heterogeneous or the boundary conditions is more complex, comparing with the mesh-independent solution, this approach requires only coarser mesh to arrive at this solution while the traditional methods require more denser mesh. Comparisons for different hydraulic conductivity scenarios and boundary conditions have also been introduced. © 2013 Elsevier B.V.
Approximate series solution of nonlinear singular boundary value problems arising in physiology.
Singh, Randhir; Kumar, Jitendra; Nelakanti, Gnaneshwar
2014-01-01
We introduce an efficient recursive scheme based on Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components. In fact, we develop the recursive scheme without any undetermined coefficients while computing the solution components. Unlike the classical ADM, the proposed method avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. The uniqueness of the solution is discussed. The convergence and error analysis of the proposed method are also established. The accuracy and reliability of the proposed method are examined by four numerical examples.
Stability of solutions in boundary layer flow and heat transfer over a stretching cylinder
Najib, Najwa; Bachok, Norfifah; Arifin, Norihan Md.
2017-08-01
The boundary layer flow and heat transfer in viscous fluid passing through a stretching cylinder with present of mass suction are investigated. The governing equations of boundary layer in the form of partial differential equation are transformed into ordinary differential equations using appropriate similarity variables. The systems of ordinary differential equations are then reduced to first order system before being solved numerically. The results for skin friction coeffiecient, local Nusselt number, velocity and temperature profiles are presented. The effects of mass suction with different values of curvature parameter on the flow and heat transfer characteristics indicate that the dual solutions are found to exist. The stability analysis is performed to verify which solution (first or second solution) is linearly stable and thus the physical meaning is realizable. In the presence of mass suction, the dual solutions exist along stretching cylinder.
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.
The secular analytical solution of the orbital plane using Lindstedt-Poincaré method
Yu, Shengxian; Zhao, Changyin; Zhang, Wei
2017-11-01
Nowadays, the increasing amount of space objects makes the space so crowded that the satellites in orbit endure severe environment. Hence how to efficiently search and catalog these space objects becomes an urgent problem to be solved. In the paper, in order to contribute to this problem, the secular analytical solution of the orbital plane for medium and high orbit objects is studied. For medium and high orbit objects, the Earth's oblateness and the lunisolar gravitational perturbations are considered. The double averaging method is used to first average the system. For small to medium orbit inclinations and small eccentricities, and then the differential equations can be rewritten in an expansion form. Combining the Lindstedt-Poincaré procedure and the solution for differential equations with special coefficients, the third-order analytical solutions can be derived step by step. Finally, two kinds of comparisons are carried out. One is the comparison between the analytical solution and the results derived by integrating the simplified model. It aims to verify the validity of these methods. The other one is the comparison with the integration results of the normal model to show the accuracy of the analytical solution. Both of the two comparisons results work well. The accuracy of the analytical solution can be maintained at the order of O (10-3) for the duration of 200 yrs.
An Analytical Solution for Predicting the Vibration-Fatigue-Life in Bimodal Random Processes
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Chaoshuai Han
2017-01-01
Full Text Available Predicting the vibration-fatigue-life of engineering structures subjected to random loading is a critical issue for. Frequency methods are generally adopted to deal with this problem. This paper focuses on bimodal spectra methods, including Jiao-Moan method, Fu-Cebon method, and Modified Fu-Cebon method. It has been proven that these three methods can give acceptable fatigue damage results. However, these three bimodal methods do not have analytical solutions. Jiao-Moan method uses an approximate solution, Fu-Cebon method, and Modified Fu-Cebon method needed to be calculated by numerical integration which is obviously not convenient in engineering application. Thus, an analytical solution for predicting the vibration-fatigue-life in bimodal spectra is developed. The accuracy of the analytical solution is compared with numerical integration. The results show that a very good agreement between an analytical solution and numerical integration can be obtained. Finally, case study in offshore structures is conducted and a bandwidth correction factor is computed through using the proposed analytical solution.
Analytical Structuring of Periodic and Regular Cascading Solutions in Self-Pulsing Lasers
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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.
Successive Iteration of Positive Solutions for Fourth-Order Two-Point Boundary Value Problems
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Yongping Sun
2013-01-01
Full Text Available We are concerned with a fourth-order two-point boundary value problem. We prove the existence of positive solutions and establish iterative schemes for approximating the solutions. The interesting point of our method is that the nonlinear term is involved with all lower-order derivatives of unknown function, and the iterative scheme starts off with a known cubic function or the zero function. Finally we give two examples to verify the effectiveness of the main results.
Positive solutions for a nonlinear periodic boundary-value problem with a parameter
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Jingliang Qiu
2012-08-01
Full Text Available Using topological degree theory with a partially ordered structure of space, sufficient conditions for the existence and multiplicity of positive solutions for a second-order nonlinear periodic boundary-value problem are established. Inspired by ideas in Guo and Lakshmikantham [6], we study the dependence of positive periodic solutions as a parameter approaches infinity, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$
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Jinhua Wang
2010-01-01
Full Text Available We consider the existence and uniqueness of positive solution to nonzero boundary values problem for a coupled system of fractional differential equations. The differential operator is taken in the standard Riemann-Liouville sense. By using Banach fixed point theorem and nonlinear differentiation of Leray-Schauder type, the existence and uniqueness of positive solution are obtained. Two examples are given to demonstrate the feasibility of the obtained results.
Positive Solutions for Integral Boundary Value Problem with ϕ-Laplacian Operator
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Ding Yonghong
2011-01-01
Full Text Available We consider the existence, multiplicity of positive solutions for the integral boundary value problem with -Laplacian , , , , where is an odd, increasing homeomorphism from onto . We show that it has at least one, two, or three positive solutions under some assumptions by applying fixed point theorems. The interesting point is that the nonlinear term is involved with the first-order derivative explicitly.
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
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Vladislav V. Kravchenko
2017-01-01
Full Text Available A complete family of solutions for the one-dimensional reaction-diffusion equation, uxx(x,t-q(xu(x,t=ut(x,t, with a coefficient q depending on x is constructed. The solutions represent the images of the heat polynomials under the action of a transmutation operator. Their use allows one to obtain an explicit solution of the noncharacteristic Cauchy problem with sufficiently regular Cauchy data as well as to solve numerically initial boundary value problems. In the paper, the Dirichlet boundary conditions are considered; however, the proposed method can be easily extended onto other standard boundary conditions. The proposed numerical method is shown to reveal good accuracy.
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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.
Analytical solution of linear ordinary differential equations by differential transfer matrix method
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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.
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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.
Thompson, J. F.; Warsi, Z. U. A.; Mastin, C. W.
1982-01-01
A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.
Numerical solution of system of boundary value problems using B-spline with free parameter
Gupta, Yogesh
2017-01-01
This paper deals with method of B-spline solution for a system of boundary value problems. The differential equations are useful in various fields of science and engineering. Some interesting real life problems involve more than one unknown function. These result in system of simultaneous differential equations. Such systems have been applied to many problems in mathematics, physics, engineering etc. In present paper, B-spline and B-spline with free parameter methods for the solution of a linear system of second-order boundary value problems are presented. The methods utilize the values of cubic B-spline and its derivatives at nodal points together with the equations of the given system and boundary conditions, ensuing into the linear matrix equation.
On the Existence of Positive Solutions for a Fourth-Order Boundary Value Problem
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Yumei Zou
2017-01-01
Full Text Available By using the method of order reduction and the fixed point index, the existence of positive solutions for a fourth-order boundary value problem is studied. We provide conditions under which the existence results hold. Such conditions are related to the first eigenvalue corresponding to the relevant linear differential equation with dependence on the derivatives of unknown function.
On the Existence of Positive Solutions for a Fourth-Order Boundary Value Problem
Yumei Zou
2017-01-01
By using the method of order reduction and the fixed point index, the existence of positive solutions for a fourth-order boundary value problem is studied. We provide conditions under which the existence results hold. Such conditions are related to the first eigenvalue corresponding to the relevant linear differential equation with dependence on the derivatives of unknown function.
Baconneau, O.; van den Berg, G.J.B.; Brauner, C.-M.; Hulshof, J.
2004-01-01
We study travelling wave solutions of a one-dimensional two-phase Free Boundary Problem, which models premixed flames propagating in a gaseous mixture with dust. The model combines diffusion of mass and temperature with reaction at the flame front, the reaction rate being temperature dependent. The
Bifurcation from infinity and multiple solutions for first-order periodic boundary-value problems
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Zhenyan Wang
2011-10-01
Full Text Available In this article, we study the existence and multiplicity of solutions for the first-order periodic boundary-value problem $$displaylines{ u'(t-a(tu(t=lambda u(t+g(u(t-h(t, quad tin (0, T,cr u(0=u(T. }$$
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Tengfei Shen
2015-12-01
Full Text Available This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result.
Existence of Positive, Negative, and Sign-Changing Solutions to Discrete Boundary Value Problems
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Shi Haiping
2011-01-01
Full Text Available By using critical point theory, Lyapunov-Schmidt reduction method, and characterization of the Brouwer degree of critical points, sufficient conditions to guarantee the existence of five or six solutions together with their sign properties to discrete second-order two-point boundary value problem are obtained. An example is also given to demonstrate our main result.
Existence of solutions for a boundary problem involving p(x-biharmonic operator
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Abdel Rachid El Amrouss
2013-01-01
Full Text Available In this paper, we establish the existence of at least three solutions to a boundary problem involving the p(x-biharmonic operator. Our technical approach is based on theorem obtained by B. Ricceri's variational principale and local mountain pass theorem without (Palais.Smale condition.
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Mohamed Jleli
2014-01-01
Full Text Available A class of nonlinear multipoint boundary value problems for singular fractional differential equations is considered. By means of a coupled fixed point theorem on ordered sets, some results on the existence and uniqueness of positive solutions are obtained.
A New Iterative Scheme for the Solution of Tenth Order Boundary ...
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Tonistar
doi.org/10.4314/njbas.v24i1.12. ISSN 0794-5698. A New Iterative Scheme for the Solution of Tenth Order Boundary Value. Problems Using First-Kind Chebychev Polynomials. 1E.J. Mamadu and 2*I.N. Njoseh. 1Department of Mathematics ...
Existence of infinitely many nodal solutions for a superlinear Neumann boundary value problem
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Aixia Qian
2005-11-01
Full Text Available We study the existence of a class of nonlinear elliptic equation with Neumann boundary condition, and obtain infinitely many nodal solutions. The study of such a problem is based on the variational methods and critical point theory. We prove the conclusion by using the symmetric mountain-pass theorem under the Cerami condition.
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An Yukun
2011-01-01
Full Text Available Abstract This paper deals with the periodic boundary value problems where is a constant and in which case the associated Green's function may changes sign. The existence result of positive solutions is established by using the fixed point index theory of cone mapping.
Existence of One-Signed Solutions of Discrete Second-Order Periodic Boundary Value Problems
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Ruyun Ma
2012-01-01
Full Text Available We prove the existence of one-signed periodic solutions of second-order nonlinear difference equation on a finite discrete segment with periodic boundary conditions by combining some properties of Green's function with the fixed-point theorem in cones.
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Yuji Liu
2004-01-01
Full Text Available A new fixed point theorem on cones is applied to obtain the existence of at least two positive solutions of a higher-order three-point boundary value problem for the differential equation subject to a class ofboundary value conditions. The associated Green's function is given. Some results obtained recently are generalized.
L^p-continuity of solutions to parabolic free boundary problems
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Abdeslem Lyaghfouri
2015-07-01
Full Text Available In this article, we consider a class of parabolic free boundary problems. We establish some properties of the solutions, including L^infinity-regularity in time and a monotonicity property, from which we deduce strong L^p-continuity in time.
Positive non-symmetric solutions of a non-linear boundary value problem
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Samuel Peres
2013-11-01
Full Text Available This paper deals with a non-linear second order ordinary differential equation with symmetric non-linear boundary conditions, where both of the non-linearities are of power type. It provides results concerning the existence and multiplicity of positive non-symmetric solutions for values of parameters not considered before. The main tool is the shooting method.
Positive solutions of multi-point boundary value problem of fractional differential equation
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De-xiang Ma
2015-07-01
Full Text Available By means of two fixed-point theorems on a cone in Banach spaces, some existence and multiplicity results of positive solutions of a nonlinear fractional differential equation boundary value problem are obtained. The proofs are based upon some properties of Green’s function, which are also the key of the paper.
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Jian Liu
2013-09-01
Full Text Available In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.
Triple solutions for multi-point boundary-value problem with p-Laplace operator
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Yansheng Liu
2009-11-01
Full Text Available Using a fixed point theorem due to Avery and Peterson, this article shows the existence of solutions for multi-point boundary-value problem with p-Laplace operator and parameters. Also, we present an example to illustrate the results obtained.
High regularity of the solution of a nonlinear parabolic boundary-value problem
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Luminita Barbu
2002-05-01
Full Text Available The aim of this paper is to report some results concerning high regularity of the solution of a nonlinear parabolic problem with a linear parabolic differential equation in one spatial dimension and nonlinear boundary conditions. We show that any regularity can be reached provided that appropriate smoothness of the data and compatibility assumptions are required.
L1-Solutions of Boundary Value Problems for Implicit Fractional Order Differential Equations
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Mouffak Benchohra
2015-12-01
Full Text Available The aim of this paper is to present new results on the existence of solutions for a class of boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem.
Huiqin Lu
2012-01-01
By constructing a special cone in ${C}^{1}[0,2\\pi ]$ and the fixed point theorem, this paper investigates second-order singular semipositone periodic boundary value problems with dependence on the first-order derivative and obtains the existence of multiple positive solutions. Further, an example is given to demonstrate the applications of our main results.
A Coupling Technique for Analytical Solution of Time Fractional Biological Population Model
Mohan, R; Prajapati
2013-01-01
In this study, homotopy perturbation transform method (HPTM) is used to obtain the approximate analytical solutions of time fractional biological population model. The solution procedure obtained by proposed method indicate that the approach is easy to implement and accurate. Some numerical examples are given in the support of the validity of the method. These results reveal that the proposed method is very effective and easy to use. The comparisons between exact solution and approximate solu...
Santosh Soni
2011-01-01
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...
Analytic solution of Riccati equations occurring in open-loop Nash multiplayer differential games
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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.
SASRST: Semi-Analytic Solutions for 1-D Radiative Shock Tubes
Ramsey, Jon P.
2017-07-01
SASRST, a small collection of Python scripts, attempts to reproduce the semi-analytical one-dimensional equilibrium and non-equilibrium radiative shock tube solutions of Lowrie & Rauenzahn (2007) and Lowrie & Edwards (2008), respectively. The included code calculates the solution for a given set of input parameters and also plots the results using Matplotlib. This software was written to provide validation for numerical radiative shock tube solutions produced by a radiation hydrodynamics code.
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Cecilie Friis
2017-06-01
Full Text Available Land-based production provides societies with indispensable goods such as food, feed, fibre, and energy. Yet, with economic globalisation and global population growth, the environmental and social trade-offs of their production are ever more complex. This is particularly so since land use changes are increasingly embedded in networks of long-distance flows of, e.g., material, energy, and information. The resulting scientific and governance challenge is captured in the emerging telecoupling framework addressing socioeconomic and environmental interactions and feedbacks between distal human-environment systems. Understanding telecouplings, however, entails a number of fundamental analytical problems. When dealing with global connectivity, a central question is how and where to draw system boundaries between coupled systems. In this article, we explore the analytical implications of setting system boundaries in the study of a recent telecoupled land use change: the expansion of Chinese banana plantation investments in Luang Namtha Province, Laos. Based on empirical material from fieldwork in Laos in 2014 and 2015, and drawing on key concepts from the ‘systems thinking’ literature, we illustrate how treating the system and its boundaries as epistemological constructs enable us to capture the differentiated involvement of actors, as well as the socio-economic and environmental effects of this land use change. In discussing our results, the need for more explicit attention to the trade-offs and implications of scale and boundary choices when defining systems is emphasised.
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.
On Perturbation Solutions for Axisymmetric Bending Boundary Values of a Deep Thin Spherical Shell
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Rong Xiao
2014-01-01
Full Text Available On the basis of the general theory of elastic thin shells and the Kirchhoff-Love hypothesis, a fundamental equation for a thin shell under the moment theory is established. In this study, the author derives Reissner’s equation with a transverse shear force Q1 and the displacement component w. These basic unknown quantities are derived considering the axisymmetry of the deep, thin spherical shell and manage to constitute a boundary value question of axisymmetric bending of the deep thin spherical shell under boundary conditions. The asymptotic solution is obtained by the composite expansion method. At the end of this paper, to prove the correctness and accuracy of the derivation, an example is given to compare the numerical solution by ANSYS and the perturbation solution. Meanwhile, the effects of material and geometric parameters on the nonlinear response of axisymmetric deep thin spherical shell under uniform external pressure are also analyzed in this paper.
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Yanmei Sun
2012-01-01
Full Text Available By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.
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.
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Handlovičová Angela
2016-01-01
Full Text Available In this paper, the numerical solution to the Helmholtz equation with impedance boundary condition, based on the Finite volume method, is discussed. We used the Robin boundary condition using exterior points. Properties of the weak solution to the Helmholtz equation and numerical solution are presented. Further the numerical experiments, comparing the numerical solution with the exact one, and the computation of the experimental order of convergence are presented.
Use of Green's functions in the numerical solution of two-point boundary value problems
Gallaher, L. J.; Perlin, I. E.
1974-01-01
This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.
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...... in the literature and are solved analytically by means of the Homotopy Analysis Method (HAM). The comparison of results from this paper and those published in the literature confirms the precise accuracy of the HAM. The resulting analytical equation from HAM is valid for entire physical domain and effective...
Analytical solution for fractional derivative gas-flow equation in porous media
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Mohamed F. El Amin
Full Text Available 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. Keywords: Fractional derivative, Porous media, Natural gas, Reservoir modeling, Infinite series solutions
An analytical solution to the equation of motion for the damped nonlinear pendulum
DEFF Research Database (Denmark)
Johannessen, Kim
2014-01-01
An analytical approximation of the solution to the differential equation describing the oscillations of the damped nonlinear pendulum at large angles is presented. The solution is expressed in terms of the Jacobi elliptic functions by including a parameter-dependent elliptic modulus. The analytical...... of the damped nonlinear pendulum is presented, and it is shown that the period of oscillation is dependent on time. It is established that, in general, the period is longer than that of a linearized model, asymptotically approaching the period of oscillation of a damped linear pendulum....
An Approximate Analytical Solution of Sloshing Frequencies for a Liquid in Various Shape Aqueducts
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Yuchun Li
2014-01-01
Full Text Available An approximate analytical solution of sloshing frequencies for a liquid in the various shape aqueducts is formulated by using the Ritz method. The present approximate method is, respectively, applied to find the sloshing frequencies of the liquid in rectangular, trapezoid, oval, circular, U-shaped tanks (aqueducts, and various shape tuned liquid dampers (TLD. The first three antisymmetric and symmetric frequencies by the present approach are within 5% accuracy compared to the other analytical, numerical, and experimental values. The approximate solutions of this paper for the various shape aqueducts are acceptable to the engineering applications.
An analytical solution describing the shape of a yield stress material subjected to an overpressure
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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...
Power Control at Grid Connected Converters and Analytical Solution of Steady States
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Viktor Valouch
2015-01-01
Full Text Available The paper presents a power control technique at grid connected converters under unbalanced voltage conditions. The current positive and negative sequences during grid voltage sags are controlled to ensure a proper exchange of active and reactive powers without power ripples. An analytical solution in a closed form of the B6 and B4 converters working with an optimized half a period switching symmetry is presented. The analytical solution may be applied for the converters connected to highly unbalanced grids and for different grid filter topologies.
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D. A. Eliseev
2015-01-01
Full Text Available The solution stability of an initial boundary problem for a linear hybrid system of differential equations, which models the rotation of a rigid body with two elastic rods located in the same plane is studied in the paper. To an axis passing through the mass center of the rigid body perpendicularly to the rods location plane is applied the stabilizing moment proportional to the angle of the system rotation, derivative of the angle, integral of the angle. The external moment provides a feedback. A method of studying the behavior of solutions of the initial boundary problem is proposed. This method allows to exclude from the hybrid system of differential equations partial differential equations, which describe the dynamics of distributed elements of a mechanical system. It allows us to build one equation for an angle of the system rotation. Its characteristic equation defines the stability of solutions of all the system. In the space of feedback-coefficients the areas that provide the asymptotic stability of solutions of the initial boundary problem are built up.
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Zhiyong Wang
2008-09-01
Full Text Available In this paper, we study the existence of positive solutions for the nonlinear nth-order with m-point singular boundary-value problem. By using the fixed point index theory and a new fixed point theorem in cones, the existence of countably many positive solutions for a nonlinear singular boundary value problem are obtained.
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V. Rukavishnikov
2014-01-01
Full Text Available The existence and uniqueness of the Rv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.
Developing Semi-Analytical solutions for Saint-Venant Equations in the Uniform Flow Region
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M.M. Heidari
2016-09-01
-Venant equations. The got transcendental function can then be simplified using various methods to get a model expressed as a rational function of s (the Laplace variable, possibly including a time delay. It is therefore important to develop simple analytical models able to accurately reproduce the dynamic behavior of the system in realistic conditions. Materials and Methods: Changes in water demand can create transient flow in irrigation networks. The Saint Venant equations are the equations governing open channel flow when unsteady flow propagates. In this research, the finite volume method using the time splitting scheme was employed to develop a computer code for solving the one dimensional unsteady flow equations. Considering stationary regime and small variations around it, the Saint-Venant equations around initial condition was linearized. The Laplace transform is applied to the linearized saint venant equations, leading to an ordinary differential equation in the space variable x and parameterized by the Laplace variable s. The integration of this equation lead to a transfer matrix, and gives the discharge Q*(x, s at any location with respect for the upstream discharge. This matrix is coupled with the downstream boundary condition and developed an equation that solved using Simpson integration algorithm. It should be noted numerical solution of developed equation is easier than solving fully dynamic saint venant and is less sensitive to the spatial step and the researcher simply writing code. Results and Discussion: Froud Number (F, variation of inflow discharge (ΔQ/Q, and dimensionless parameter of KF2 in which K is the kinematic flow number, are effective factors on accuracy of developed equation. In order to determine the effect of the factors on accuracy of presenting formula, several simulations were performed using numerical model. The presented formula and numerical model were compared for 10, 20 and 30 percent discharge variation and error calculated, the maximum
A Boundary Element Solution to the Problem of Interacting AC Fields in Parallel Conductors
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Einar M. Rønquist
1984-04-01
Full Text Available The ac fields in electrically insulated conductors will interact through the surrounding electromagnetic fields. The pertinent field equations reduce to the Helmholtz equation inside each conductor (interior problem, and to the Laplace equation outside the conductors (exterior problem. These equations are transformed to integral equations, with the magnetic vector potential and its normal derivative on the boundaries as unknowns. The integral equations are then approximated by sets of algebraic equations. The interior problem involves only unknowns on the boundary of each conductor, while the exterior problem couples unknowns from several conductors. The interior and the exterior problem are coupled through the field continuity conditions. The full set of equations is solved by standard Gaussian elimination. We also show how the total current and the dissipated power within each conductor can be expressed as boundary integrals. Finally, computational results for a sample problem are compared with a finite difference solution.
Sousa, A. N. Laurindo; Ojeda-González, A.; Prestes, A.; Klausner, V.; Caritá, L. A.
2017-12-01
This work aims to demonstrate the analytical solution of the Grad-Shafranov (GS) equation or generalized Ampere's law, which is important in the studies of self-consistent 2.5-D solution for current sheet structures. A detailed mathematical development is presented to obtain the generating function as shown by Walker (RSPSA 91, 410, 1915). Therefore, we study the general solution of the GS equation in terms of the Walker's generating function in details without omitting any step. The Walker's generating function g(ζ) is written in a new way as the tangent of an unspecified function K(ζ). In this trend, the general solution of the GS equation is expressed as exp(- 2Ψ) = 4|K '(ζ)|2/cos2[K(ζ) - K(ζ ∗)]. In order to investigate whether our proposal would simplify the mathematical effort to find new generating functions, we use Harris's solution as a test, in this case K(ζ) = arctan(exp(i ζ)). In summary, one of the article purposes is to present a review of the Harris's solution. In an attempt to find a simplified solution, we propose a new way to write the GS solution using g(ζ) = tan(K(ζ)). We also present a new analytical solution to the equilibrium Ampere's law using g(ζ) = cosh(b ζ), which includes a generalization of the Harris model and presents isolated magnetic islands.
Sousa, A. N. Laurindo; Ojeda-González, A.; Prestes, A.; Klausner, V.; Caritá, L. A.
2018-02-01
This work aims to demonstrate the analytical solution of the Grad-Shafranov (GS) equation or generalized Ampere's law, which is important in the studies of self-consistent 2.5-D solution for current sheet structures. A detailed mathematical development is presented to obtain the generating function as shown by Walker (RSPSA 91, 410, 1915). Therefore, we study the general solution of the GS equation in terms of the Walker's generating function in details without omitting any step. The Walker's generating function g( ζ) is written in a new way as the tangent of an unspecified function K( ζ). In this trend, the general solution of the GS equation is expressed as exp(- 2Ψ) = 4| K '( ζ)|2/cos2[ K( ζ) - K( ζ ∗)]. In order to investigate whether our proposal would simplify the mathematical effort to find new generating functions, we use Harris's solution as a test, in this case K( ζ) = arctan(exp( i ζ)). In summary, one of the article purposes is to present a review of the Harris's solution. In an attempt to find a simplified solution, we propose a new way to write the GS solution using g( ζ) = tan( K( ζ)). We also present a new analytical solution to the equilibrium Ampere's law using g( ζ) = cosh( b ζ), which includes a generalization of the Harris model and presents isolated magnetic islands.
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Zhenlai Han
2012-11-01
Full Text Available In this article, we consider the following boundary-value problem of nonlinear fractional differential equation with $p$-Laplacian operator $$displaylines{ D_{0+}^eta(phi_p(D_{0+}^alpha u(t+a(tf(u=0, quad 0
Liu, Albert Tianxiang; Zaveri, Rahul A.; Seinfeld, John H.
2014-06-01
We present the exact analytical solution of the transient equation of gas-phase diffusion of a condensing vapor to, and diffusion and reaction in, an aqueous droplet. Droplet-phase reaction is represented by first-order chemistry. The solution facilitates study of the dynamic nature of the vapor uptake process as a function of droplet size, Henry's law coefficient, and first-order reaction rate constant for conversion in the droplet phase.
Shallal, Muhannad A.; Jabbar, Hawraz N.; Ali, Khalid K.
2018-03-01
In this paper, we constructed a travelling wave solution for space-time fractional nonlinear partial differential equations by using the modified extended Tanh method with Riccati equation. The method is used to obtain analytic solutions for the space-time fractional Klein-Gordon and coupled conformable space-time fractional Boussinesq equations. The fractional complex transforms and the properties of modified Riemann-Liouville derivative have been used to convert these equations into nonlinear ordinary differential equations.
Finite analytic numerical solution of two-dimensional channel flow over a backward-facing step
Ho, K.-S.; Chen, C.-J.
1986-01-01
Laminar channel flow over a backward-facing step is investigated. The finite analytic (FA) method is used to obtain the numerical solution. The FA solutions predict the recirculation zone lengths and the recirculated mass flow rates for Reynolds numbers, Re, of 25, 50, 73, 125, 191 and 229 which correlate well with experimental measurements. The general flow patterns of the recirculation region flows for the Reynolds numbers considered in this study are similar to each other.
Symmetry Analysis and Exact Solutions of the 2D Unsteady Incompressible Boundary-Layer Equations
Han, Zhong; Chen, Yong
2017-01-01
To find intrinsically different symmetry reductions and inequivalent group invariant solutions of the 2D unsteady incompressible boundary-layer equations, a two-dimensional optimal system is constructed which attributed to the classification of the corresponding Lie subalgebras. The comprehensiveness and inequivalence of the optimal system are shown clearly under different values of invariants. Then by virtue of the optimal system obtained, the boundary-layer equations are directly reduced to a system of ordinary differential equations (ODEs) by only one step. It has been shown that not only do we recover many of the known results but also find some new reductions and explicit solutions, which may be previously unknown. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of China under Grant Nos. 11275072, 11435005, 11675054, and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213
Exact solutions to plaquette Ising models with free and periodic boundaries
Mueller, Marco; Johnston, Desmond A.; Janke, Wolfhard
2017-01-01
An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (1972) [1], who later dubbed it the fuki-nuke, or "no-ceiling", model. Defining new spin variables as the product of nearest-neighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fuki-nuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (2010) [2]. We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.
Exact solutions to plaquette Ising models with free and periodic boundaries
Energy Technology Data Exchange (ETDEWEB)
Mueller, Marco, E-mail: Marco.Mueller@itp.uni-leipzig.de [Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig (Germany); Johnston, Desmond A., E-mail: D.A.Johnston@hw.ac.uk [Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, Scotland (United Kingdom); Janke, Wolfhard, E-mail: Wolfhard.Janke@itp.uni-leipzig.de [Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig (Germany)
2017-01-15
An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (1972) , who later dubbed it the fuki-nuke, or “no-ceiling”, model. Defining new spin variables as the product of nearest-neighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fuki-nuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (2010) . We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.
Czech Academy of Sciences Publication Activity Database
Haslinger, Jaroslav; Kučera, R.; Šátek, V.
2017-01-01
Roč. 22, October 2017 (2017), s. 1-14 ISSN 1081-2865 R&D Projects: GA MŠk LQ1602; GA ČR(CZ) GA17-01747S Institutional support: RVO:68145535 Keywords : Stokes system * threshold slip boundary conditions * solution dependent slip function Subject RIV: BA - General Mathematics Impact factor: 2.953, year: 2016 http://journals.sagepub.com/doi/abs/10.1177/1081286517716222
Infinitely many solutions for a fourth-order boundary-value problem
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Seyyed Mohsen Khalkhali
2012-09-01
Full Text Available In this article we consider the existence of infinitely many solutions to the fourth-order boundary-value problem $$displaylines{ u^{iv}+alpha u''+eta(x u=lambda f(x,u+h(u,quad xin]0,1[cr u(0=u(1=0,cr u''(0=u''(1=0,. }$$ Our approach is based on variational methods and critical point theory.
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Feng Hanying
2011-01-01
Full Text Available The expression and properties of Green's function for a class of nonlinear fractional differential equations with integral boundary conditions are studied and employed to obtain some results on the existence of positive solutions by using fixed point theorem in cones. The proofs are based on the reduction of the problem considered to the equivalent Fredholm integral equation of the second kind. The results significantly extend and improve many known results even for integer-order cases.
Monotone and convex positive solutions for fourth-order multi-point boundary value problems
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Chunfang Shen
2011-01-01
Full Text Available Abstract The existence results of multiple monotone and convex positive solutions for some fourth-order multi-point boundary value problems are established. The nonlinearities in the problems studied depend on all order derivatives. The analysis relies on a fixed point theorem in a cone. The explicit expressions and properties of associated Green's functions are also given. MSC: 34B10; 34B15.
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Abdelkader Boucherif
2006-06-01
Full Text Available In this paper we investigate the existence of positive solutions of two-point boundary value problems for nonlinear second order differential equations of the form $(py^{\\prime}^{\\prime}(t+q(ty(t=f(t,y(t,y^{\\prime}(t$, where $f$ is a Carathéodory function, which may change sign, with respect to its second argument, infinitely many times.
An optimal existence theorem for positive solutions of a four-point boundary value problem
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Man Kam Kwong
2009-12-01
Full Text Available We are interested in the existence of positive solutions to a four-point boundary value problem of the differential equation $ y''(t + a(tf(y(t=0 $ on $ [0,1] $. The value of $y$ at $0$ and $1$ are each a multiple of $y(t$ at an interior point. Many known existence criteria are based on the limiting values of $ f(u/u $ as $u$ approaches $0$ and infinity.
Student Solutions Manual to Boundary Value Problems and Partial Differential Equations
Powers, David L
2005-01-01
This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.Provides students with exercises that skillfully illustrate the techniques used in the text to solve science and engineering problemsNearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercisesMany exercises based on current engineering applications
Yan, Yan
2015-01-01
We study a new optimization scheme that generates smooth and robust solutions for Dirichlet velocity boundary control (DVBC) of conjugate heat transfer (CHT) processes. The solutions to the DVBC of the incompressible Navier-Stokes equations are typically nonsmooth, due to the regularity degradation of the boundary stress in the adjoint Navier-Stokes equations. This nonsmoothness is inherited by the solutions to the DVBC of CHT processes, since the CHT process couples the Navier-Stokes equations of fluid motion with the convection-diffusion equations of fluid-solid thermal interaction. Our objective in the CHT boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the fluid system and a prescribed temperature profile and the cost of the control.Our strategy to resolve the nonsmoothness of the boundary control solution is based on two features, namely, the objective function with a regularization term on the gradient of the control profile on both the continuous and the discrete levels, and the optimization scheme with either explicit or implicit smoothing effects, such as the smoothed Steepest Descent and the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) methods. Our strategy to achieve the robustness of the solution process is based on combining the smoothed optimization scheme with the numerical continuation technique on the regularization parameters in the objective function. In the section of numerical studies, we present two suites of experiments. In the first one, we demonstrate the feasibility and effectiveness of our numerical schemes in recovering the boundary control profile of the standard case of a Poiseuille flow. In the second one, we illustrate the robustness of our optimization schemes via solving more challenging DVBC problems for both the channel flow and the flow past a square cylinder, which use initial
Analytical solutions and numerical modeling for a dam-break problem in inclined channels
Pelinovsky, Efim; Didenkulova, Ira; Didenkulov, Oleg; Rodin, Artem
2016-04-01
Here we obtain different analytical solutions of the shallow-water equations for inviscid nonlinear waves in inclined channels. (i) The first solution describes Riemann wave moving up or down alone the channel slope. It requires the initial fluid flow, which often accompanies waves generated by landslides. This solution is valid for a finite time before the wave breaks. (ii) The second solution generalizes the classical dam-break problem for the case of a dam located in the inclined channel. In this case the cross-section of the channel influences the speed of wave propagation inside the channel, and therefore changes wave dynamics inside the channel compare to the plane beach. (iii) The third solution describes the intermediate stage of the wave front dynamics for a dam of a large height. This solution is derived with the use of generalized Carrier-Greenspan approach developed early by Didenkulova & Pelinovsky (2011) and Rybkin et al (2014). Some of the analytical solutions are tested with the means of numerical modeling. The numerical modeling is carried out using the CLAWPACK software based on nonlinear shallow water equations. Application of the described solutions to possible laboratory experiments is discussed.
Transient analytical solution of a solar still integrated with a tubular solar energy collector
Energy Technology Data Exchange (ETDEWEB)
Yadav, Y.P. [L.N. Mithila Univ., Physics Dept., Bihar (India); Yadav, B.P. [R.J. Coll., Physics Dept., Chapra, Bihar (India)
1998-12-01
A transient analytical solution has been obtained of a solar still integrated with a tubular solar energy collector. Explicit expressions were derived for the temperatures of various components of the system as a function of time and space coordinates and in terms of geometrical, operational and meteorological parameters. This facilitates evolving the optimum design of the system. (Author)
Analytic solutions for colloid transport with time- or depth-dependent retention in porous media
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...
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...
Sanskrityayn, Abhishek; Kumar, Naveen
2016-12-01
Some analytical solutions of one-dimensional advection-diffusion equation (ADE) with variable dispersion coefficient and velocity are obtained using Green's function method (GFM). The variability attributes to the heterogeneity of hydro-geological media like river bed or aquifer in more general ways than that in the previous works. Dispersion coefficient is considered temporally dependent, while velocity is considered spatially and temporally dependent. The spatial dependence is considered to be linear and temporal dependence is considered to be of linear, exponential and asymptotic. The spatio-temporal dependence of velocity is considered in three ways. Results of previous works are also derived validating the results of the present work. To use GFM, a moving coordinate transformation is developed through which this ADE is reduced into a form, whose analytical solution is already known. Analytical solutions are obtained for the pollutant's mass dispersion from an instantaneous point source as well as from a continuous point source in a heterogeneous medium. The effect of such dependence on the mass transport is explained through the illustrations of the analytical solutions.
Analytical Solution of Unsteady Gravity Flows of A Power-Law Fluid ...
African Journals Online (AJOL)
We present an analytical study of unsteady non-linear rheological effects of a power-law fluid under gravity. The fluid flows through a porous medium. The governing equations are derived and similarity solutions are determined. The results show the existence of traveling waves. It is assumed that the viscosity is temperature ...
Several numerical and analytical solutions of the radiative transfer equation (RTE) for plane albedo were compared for solar light reflection by sea water. The study incorporated the simplest case, that being a semi-infinite one-dimensional plane-parallel absorbing and scattering...
Big Data Analytics Solutions: The Implementation Challenges in the Financial Services Industry
Ojo, Michael O.
2016-01-01
The challenges of Big Data (BD) and Big Data Analytics (BDA) have attracted disproportionately less attention than the overwhelmingly espoused benefits and game-changing promises. While many studies have examined BD challenges across multiple industry verticals, very few have focused on the challenges of implementing BDA solutions. Fewer of these…
Exact analytic solutions for a Dirac electron moving in graphene under magnetic fields
Energy Technology Data Exchange (ETDEWEB)
Kuru, S [Department of Physics, Faculty of Science, Ankara University, 06100 Ankara (Turkey); Negro, J; Nieto, L M, E-mail: sengul.kuru@science.ankara.edu.t, E-mail: jnegro@fta.uva.e, E-mail: luismi@metodos.fam.cie.uva.e [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, E-47071 Valladolid (Spain)
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.
On the analytical solution of Fornberg–Whitham equation with the ...
Indian Academy of Sciences (India)
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 ...
On the analytical solution of Fornberg–Whitham equation with the ...
Indian Academy of Sciences (India)
Fornberg–Whitham equation with respect to the new fractional derivative introduced in. [15]. The aim is to ... fractional derivative to obtain analytical solution of the equations considered. Finally, we compare the ..... Acknowledgements. The authors are grateful to the financial support extended by the King Fahd University of.
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.
Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method
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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.
Revisiting the approximate analytical solution of fractional-order gas dynamics equation
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Mohammad Tamsir
2016-06-01
Full Text Available In this paper, an approximate analytical solution of the time fractional gas dynamics equation arising in the shock fronts, is obtained using a recent semi-analytical method referred as fractional reduced differential transform method. The fractional derivatives are considered in the Caputo sense. To validate the efficiency and reliability of the method, four numerical examples of the linear and nonlinear gas dynamics equations are considered. Computed results are compared with results available in the literature. It is found that obtained results agree excellently with DTM, and FHATM. The solutions behavior and its effects for different values of the fractional order are shown graphically. The main advantage of the method is easiness to implement and requires small size of computation. Hence, it is a very effective and efficient semi-analytical method for solving the fractional order gas dynamics equation.
Boundary integral equation methods and numerical solutions thin plates on an elastic foundation
Constanda, Christian; Hamill, William
2016-01-01
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...
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.
A Comparative Evaluation of Numerical and Analytical Solutions to the Biadhesive Single-Lap Joint
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Halil Özer
2014-01-01
Full Text Available This paper attempts to address the detailed verification of Zhao’s analytical solution including the moment effect with the two- and three-dimensional finite element results. Zhao compared the analytical results with only the 2D FEA results and used the constant bond-length ratio for the biadhesive bondline. In this study, overlap surfaces of the adherends and the adhesives were modelled using surface-to-surface contact elements. Both analytical and numerical analyses were performed using four different biadhesive bondline configurations. The 3D FEA results reveal the existence of complex stress state at the overlap ends. However, the general results show that analytical and numerical results were in a good agreement.
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.
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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.
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.
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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.
Analytical Solutions of Classical and Fractional KP-Burger Equation and Coupled KdV equation
Ghosh, Uttam; Sarkar, Susmita; Das, Shantanu
2016-01-01
Evaluation of analytical solutions of non-linear partial differential equations (both classical and fractional) is a rising subject in Applied Mathematics because its applications in Physical biological and social sciences. In this paper we have used generalized Tanh method to find the exact solution of KP-Burger equation and coupled KdV equation. The fractional Sub-equation method has been used to find the solution of fractional KP-Burger equation and fractional coupled KdV equations. The ex...
Tapsanit, Piyawath; Yamashita, Masatsugu; Otani, Chiko
2014-01-13
The analytical solutions of the electromagnetic waves in the inhomogeneous cylindrical hyperlens (CH) comprising concentric cylindrical layers (CCLs) with multiple point sources located either outside the structure in the focusing process or inside the core in the magnifying process are obtained by means of Green's function analysis. The solutions are consistent with FDTD simulation in both processes. The sub-wavelength focal spot λ/16.26 from two point sources with wavelength 465 nm is demonstrated in the CH made by alternating silver and silica CCLs. Our solutions are expected to be the efficient tools for designing the sub-wavelength focusing and imaging cylindrical hyperlens.
An Analytical Solution by HAM for Nonlinear Simulation of Deepwater SCR Installation
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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.
Garnier, Alain; Gaillet, Bruno
2015-12-01
Not so many fermentation mathematical models allow analytical solutions of batch process dynamics. The most widely used is the combination of the logistic microbial growth kinetics with Luedeking-Piret bioproduct synthesis relation. However, the logistic equation is principally based on formalistic similarities and only fits a limited range of fermentation types. In this article, we have developed an analytical solution for the combination of Monod growth kinetics with Luedeking-Piret relation, which can be identified by linear regression and used to simulate batch fermentation evolution. Two classical examples are used to show the quality of fit and the simplicity of the method proposed. A solution for the combination of Haldane substrate-limited growth model combined with Luedeking-Piret relation is also provided. These models could prove useful for the analysis of fermentation data in industry as well as academia. © 2015 Wiley Periodicals, Inc.
Analytic solution for a static black hole in the RSII model
Dai, De-Chang; Stojkovic, Dejan
2011-10-01
We present here a static solution for a large black hole (whose horizon radius is larger than the AdS radius) located on the brane in RSII model. According to some arguments based on the AdS/CFT conjecture, a solution for the black hole located on the brane in RSII model must encode quantum gravitational effects and therefore cannot be static. We demonstrated that a static solution can be found if the bulk is not empty. The stress energy tensor of the matter distribution in the bulk for the solution we found is physical (i.e. it is non-singular with the energy density and pressure not violating any energy conditions). The scale of the solution is given by a parameter “a”. For large values of the parameter “a” we have a limit of an almost empty AdS bulk. It is interesting that the solution cannot be transformed into the Schwarzschild-like form and does not reduce to the Schwarzschild solution on the brane. We also present two other related static solutions. At the end, we discuss why the numerical methods failed so far in finding static solutions in this context, including the solutions we found analytically here.
Analytic solution for a static black hole in the RSII model
Energy Technology Data Exchange (ETDEWEB)
Dai Dechang [Department of Physics, SUNY at Buffalo, Buffalo, NY 14260-1500 (United States); Stojkovic, Dejan, E-mail: ds77@buffalo.edu [Department of Physics, SUNY at Buffalo, Buffalo, NY 14260-1500 (United States)
2011-10-19
We present here a static solution for a large black hole (whose horizon radius is larger than the AdS radius) located on the brane in RSII model. According to some arguments based on the AdS/CFT conjecture, a solution for the black hole located on the brane in RSII model must encode quantum gravitational effects and therefore cannot be static. We demonstrated that a static solution can be found if the bulk is not empty. The stress energy tensor of the matter distribution in the bulk for the solution we found is physical (i.e. it is non-singular with the energy density and pressure not violating any energy conditions). The scale of the solution is given by a parameter 'a'. For large values of the parameter 'a' we have a limit of an almost empty AdS bulk. It is interesting that the solution cannot be transformed into the Schwarzschild-like form and does not reduce to the Schwarzschild solution on the brane. We also present two other related static solutions. At the end, we discuss why the numerical methods failed so far in finding static solutions in this context, including the solutions we found analytically here.
Approximate semi-analytical solutions for the steady-state expansion of a contactor plasma
Camporeale, E.; Hogan, E. A.; MacDonald, E. A.
2015-04-01
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 American Institute of Aeronautics, Astronautics Conf. vol 1), Korsun and Tverdokhlebova (1997 33rd Joint Prop. Conf. (Seattle, WA) AIAA-97-3065), and Ashkenazy and Fruchtman (2001 27th Int. Electric Propulsion Conf. (Pasadena, CA)). 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.
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.
On the numerical solution of the diffusion equation with a nonlocal boundary condition
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Dehghan Mehdi
2003-01-01
Full Text Available Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines (MOL semidiscretization approach is used to transform the model partial differential equation into a system of first-order linear ordinary differential equations (ODEs. The partial derivative with respect to the space variable is approximated by a second-order finite-difference approximation. The solution of the resulting system of first-order ODEs satisfies a recurrence relation which involves a matrix exponential function. Numerical techniques are developed by approximating the exponential matrix function in this recurrence relation. We use a partial fraction expansion to compute the matrix exponential function via Pade approximations, which is particularly useful in parallel processing. The algorithm is tested on a model problem from the literature.
Energy Technology Data Exchange (ETDEWEB)
Sun Tao; Morgan, Hywel; Green, Nicolas G [Nanoscale Systems Integration Group, School of Electronics and Computer Science, University of Southampton, SO17 1BJ (United Kingdom)], E-mail: ts04r@ecs.soton.ac.uk, E-mail: ng2@ecs.soton.ac.uk
2008-12-01
In AC electrokinetics, the application of an AC electric field to a suspension of particles results in the manipulation and separation of the particles also the movement of the fluid. One application is dielectrophoresis (DEP). The second effect is travelling wave dielectrophoresis (twDEP). This paper presents the analytical solutions of the dielectrophoretic and travelling wave forces for the interdigitated electrode arrays energised with either a two- or four-phase signal, respectively. The torque that rotates the particle in the four-phase travelling wave arrays is also analytically solved.
Efficient robust control of first order scalar conservation laws using semi-analytical solutions
Li, Yanning
2014-01-01
This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using initial density control and boundary flow control, as a Linear Program. We then show that this framework can be extended to arbitrary control problems involving the control of subsets of the initial and boundary conditions. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP/MILP. Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality.
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Abdelhalim Ebaid
2014-01-01
Full Text Available The exact solution for any physical model is of great importance in the applied science. Such exact solution leads to the correct physical interpretation and it is also useful in validating the approximate analytical or numerical methods. The exact solution for the peristaltic transport of a Jeffrey fluid with variable viscosity through a porous medium in an asymmetric channel has been achieved. The main advantage of such exact solution is the avoidance of any kind of restrictions on the viscosity parameter α, unlike the previous study in which the restriction α ≪ 1 has been put to achieve the requirements of the regular perturbation method. Hence, various plots have been introduced for the exact effects of the viscosity parameter, Daray’s number, porosity, amplitude ratio, Jeffrey fluid parameter, and the amplitudes of the waves on the pressure rise and the axial velocity. These exact effects have been discussed and further compared with those approximately obtained in the literature by using the regular perturbation method. The comparisons reveal that remarkable differences have been detected between the current exact results and those approximately obtained in the literature for the axial velocity profile and the pressure rise.
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Ramzi Alsaedi
2014-01-01
Full Text Available We give global estimates on some potential of functions in a bounded domain of the Euclidean space ${\\mathbb{R}}^n\\; (n\\geq 2$. These functions may be singular near the boundary and are globally comparable to a product of a power of the distance to the boundary by some particularly well behaved slowly varying function near zero. Next, we prove the existence and uniqueness of a positive solution for the integral equation $u=V(a u^{\\sigma}$ with $0\\leq \\sigma <1$, where V belongs to a class of kernels that contains in particular the potential kernel of the classical Laplacian $V=(-\\Delta^{-1}$ or the fractional laplacian $V=(-\\Delta^{\\alpha/2}$, $0<\\alpha<2$.
R. Haggerty
2013-01-01
In this technical note, a steady-state analytical solution of concentrations of a parent solute reacting to a daughter solute, both of which are undergoing transport and multirate mass transfer, is presented. Although the governing equations are complicated, the resulting solution can be expressed in simple terms. A function of the ratio of concentrations, In (daughter...
Microchannel electrokinetics of charged analytes in buffered solutions near floating electrodes
DEFF Research Database (Denmark)
Andersen, Mathias Bækbo; Wolfcale, Trevor; Gregersen, Misha Marie
to accurately predict such behavior in these flow regimes. Experimentally, using conventional fluorescence microscopy, we investigated the concentration gradient (as well as the associated electroosmosis, induced-charge electro-osmosis, and electrophoresis) of the charged analyte near the floating electrode......We present both experimental and numerical studies of nonlinear electrokinetic flow of buffered solutions seeded with dilute analytes in a straight microchannel (0.6 μm high, 250 μm wide, and 9000 μm long) with a 0.15 μm high 60 μm wide electrode situated at the bottom center of the channel...... as a function of analyte (1 to 10 μM fluorescein and bodipy) and buffer (1 to 10 mM borate and posphate) concentrations and an externally applied voltage drop (50 to 100 V) along the channel. We have implemented a nonlinear continuum kinetics model of the system involving the electric potential, the buffer flow...
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.
AN ANALYTICAL SOLUTION OF KINEMATIC WAVE EQUATIONS FOR OVERLAND FLOW UNDER GREEN-AMPT INFILTRATION
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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.
Chernov, A. A.; Pil'nik, A. A.
2018-02-01
Analytical solution of the segregation problem is found for the arbitrary crystal growth law using the quasi-steady-state approximation. The segregation in this case is caused by the displacement of dissolved gas by moving plane crystallization front. The effect of solidification shrinkage on the crystallization process was taken into account. The comparison made between obtained solution and existing exact solutions shows good agreement. It is shown that in the case of "equilibrium crystallization" (when the growth rate is inversely proportional to time) the solution of the problem becomes self-similar. In this case gas concentration at the crystallization front instantly increases to a certain value and than stays the same during the whole process. At the same time the diffusion layer thickness increases proportionally to time. The conditions for the inevitability of gaseous release leading to the formation of pores in solidified material is formulated for the general case.
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.)
Ebaid, Abdelhalim
2013-01-01
The formation of liver zones is modeled by a system of two integropartial differential equations. In this research, we introduce the mathematical formulation of these integro-partial differential equations obtained by Bass et al. in 1987. For better understanding of this mathematical formulation, we present a medical introduction for the liver in order to make the formulation as clear as possible. In applied mathematics, the Adomian decomposition method is an effective procedure to obtain analytic and approximate solutions for different types of operator equations. This Adomian decomposition method is used in this work to solve the proposed model analytically. The stationary solutions (as time tends to infinity) are also obtained through it, which are in full agreement with those obtained by Bass et al. in 1987.
Analytical Solutions of a Model for Brownian Motion in the Double Well Potential
Liu, Ai-Jie; Zheng, Lian-Cun; Ma, Lian-Xi; Zhang, Xin-Xin
2015-01-01
In this paper, the analytical solutions of Schrödinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker—Planck equation known as the Klein—Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schrödinger equation. The analytical results obtained from the two different methods agree with each other well. The double well potential is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function.
Comparative analysis of analytical solutions for F2P(x ,t ) in the DGLAP approach
Choudhury, D. K.; Borah, Neelakshi N. K.
2017-01-01
Coupled Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations involving singlet quark and gluon distributions are explored by a Taylor expansion at small x as two first-order partial differential equations in two variables: Bjorken x and t (t =l n Q/2Λ2). The system of equations are then solved by Lagrange's method and the method of characteristics. We obtain the proton structure function F2P(x ,t ) by combining the corresponding nonsinglet and singlet structure functions with both methods. Analytical solutions for F2P(x ,t ) thus obtained are compared with the recent data published by the H1 and ZEUS Collaborations as well as with NNPDF3.0 parametrization, and their compatibility is checked. Comparative analysis favors the analytical solution by Lagrange's method; the plausible reasons behind that are also discussed.
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.
Analytical and experimental analysis of solute transport in heterogeneous porous media.
Wu, Lei; Gao, Bin; Tian, Yuan; Muñoz-Carpena, Rafael
2014-01-01
Knowledge of solute transport in heterogeneous porous media is crucial to monitor contaminant fate and transport in soil and groundwater systems. In this study, we present new findings from experimental and mathematical analysis to improve current understanding of solute transport in structured heterogeneous porous media. Three saturated columns packed with different sand combinations were used to examine the breakthrough behavior of bromide, a conservative tracer. Experimental results showed that bromide had different breakthrough responses in the three types of sand combinations, indicating that heterogeneity in hydraulic conductivity has a significant effect on the solute transport in structured heterogeneous porous media. Simulations from analytical solutions of a two-domain solute transport model matched experimental breakthrough data well for all the experimental conditions tested. Experimental and model results show that under saturated flow conditions, advection dominates solute transport in both fast-flow and slow-flow domains. The sand with larger hydraulic conductivity provided a preferential flow path for solute transport (fast-flow domain) that dominates the mass transfer in the heterogeneous porous media. Importantly, the transport in the slow-flow domain and mass exchange between the domains also contribute to the flow and solute transport processes and thus must be considered when investigating contaminant transport in heterogeneous porous media.
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.
An analytical solution for the two-group kinetic neutron diffusion equation in cylindrical geometry
Energy Technology Data Exchange (ETDEWEB)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio, E-mail: julio.lombaldo@ufrgs.br, E-mail: vilhena@pq.cnpq.br [Programa de Pos Graduacao em Matematica Aplicada (DMPA/UFRGS), Universidade Federal do Rio Grande do Sul Porto Alegre, RS (Brazil); Bodmann, Bardo Ernst, E-mail: bardo.bodmann@ufrgs.br [Programa de Pos-Graduacao em Engenharia Mecanica (PROMEC/UFRGS), Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil)
2011-07-01
Recently the two-group Kinetic Neutron Diffusion Equation with six groups of delay neutron precursor in a rectangle was solved by the Laplace Transform Technique. In this work, we report on an analytical solution for this sort of problem but in cylindrical geometry, assuming a homogeneous and infinite height cylinder. The solution is obtained applying the Hankel Transform to the Kinetic Diffusion equation and solving the transformed problem by the same procedure used in the rectangle. We also present numerical simulations and comparisons against results available in literature. (author)
Analytical solutions of the space-time fractional Telegraph and advection-diffusion equations
Tawfik, Ashraf M.; Fichtner, Horst; Schlickeiser, Reinhard; Elhanbaly, A.
2018-02-01
The aim of this paper is to develop a fractional derivative model of energetic particle transport for both uniform and non-uniform large-scale magnetic field by studying the fractional Telegraph equation and the fractional advection-diffusion equation. Analytical solutions of the space-time fractional Telegraph equation and space-time fractional advection-diffusion equation are obtained by use of the Caputo fractional derivative and the Laplace-Fourier technique. The solutions are given in terms of Fox's H function. As an illustration they are applied to the case of solar energetic particles.
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Mabrouk Briki
2016-05-01
Full Text Available In this paper, a fourth-order boundary value problem on the half-line is considered and existence of solutions is proved using a minimization principle and the mountain pass theorem.
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.
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Guotao Wang
2012-02-01
D^\\alpha_{0^+} u(t +a(tf(u(\\theta(t=0,&03\\,\\, (n\\in\\mathbb{N},~D^\\alpha_{0^+}$ is the standard Riemann-Liouville fractional derivative of order $\\alpha,$ $f: [0,\\infty\\to [0,\\infty,$ $a: [0,1]\\to (0,\\infty$ and $\\theta: (0,1\\to (0,1]$ are continuous functions. By applying fixed point index theory and Leggett-Williams fixed point theorem, sufficient conditions for the existence of multiple positive solutions to the above boundary value problem are established.
Existence of Triple Positive Solutions for Second-Order Discrete Boundary Value Problems
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Yanping Guo
2007-01-01
Full Text Available By using a new fixed-point theorem introduced by Avery and Peterson (2001, we obtain sufficient conditions for the existence of at least three positive solutions for the equation Δ2x(k−1+q(kf(k,x(k,Δx(k=0, for k∈{1,2,…,n−1}, subject to the following two boundary conditions: x(0=x(n=0 or x(0=Δx(n−1=0, where n≥3.
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Chengjun Yuan
2012-02-01
where $\\lambda$ is a parameter, $a, b, \\xi,\\eta$ satisfy $\\xi,\\eta\\in(0,1$, $0
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R. C. Mittal
2014-01-01
Full Text Available We present a technique based on collocation of cubic B-spline basis functions to solve second order one-dimensional hyperbolic telegraph equation with Neumann boundary conditions. The use of cubic B-spline basis functions for spatial variable and its derivatives reduces the problem into system of first order ordinary differential equations. The resulting system subsequently has been solved by SSP-RK54 scheme. The accuracy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and in good agreement with the exact solution.
Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition
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Stanislav I. POHOZAEV
2004-01-01
Full Text Available We consider the equation Delta u = 0 posed in Q := (0;+inftyimes Omega, Omega:= { x=(x',x_N/ x'in R^{N-1}, x_N >0}, with the dynamical boundary conditionB(t,x',0u_{tt} + A(t,x',0u_t - u_{x_N} geq D(t, x',0|u|^q on Sigma := (0,+infty imes R^{N-1} imes {0} and give conditions on the coeﬃcient functions A(t,x',0; B(t,x',0 and D(t;x',0 for the nonexistence of global solutions.
Positive solutions for systems of nth order three-point nonlocal boundary value problems
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Johnny Henderson
2007-09-01
Full Text Available Intervals of the parameter $\\lambda$ are determined for which there exist positive solutions for the system of nonlinear differential equations, $u^{(n} + \\lambda a(t f(v = 0, \\ v^{(n} +\\lambda b(t g(u = 0, $ for $0 < t <1$, and satisfying three-point nonlocal boundary conditions, $u(0 = 0, u'(0 = 0, \\ldots, u^{(n-2}(0 = 0, \\ u(1=\\alpha u(\\eta, v(0 = 0, v'(0 = 0, \\ldots, v^{(n-2}(0 = 0, \\ v(1=\\alpha v(\\eta$. A Guo-Krasnosel'skii fixed point theorem is applied.
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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 Solutions of Fractional Differential Equations Using the Convenient Adomian Series
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Xiang-Chao Shi
2014-01-01
Full Text Available Due to the memory trait of the fractional calculus, numerical or analytical solution of higher order becomes very difficult even impossible to obtain in real engineering problems. Recently, a new and convenient way was suggested to calculate the Adomian series and the higher order approximation was realized. In this paper, the Adomian decomposition method is applied to nonlinear fractional differential equation and the error analysis is given which shows the convenience.
An analytical solution for stability-performance dilemma of hydronic radiators
DEFF Research Database (Denmark)
Tahersima, Fatemeh; Stoustrup, Jakob; Rasmussen, Henrik
2013-01-01
a gain scheduling controller based on a proposed linear parameter varying model of radiator dynamics. The model is parameterized based on the operating flow rate, room temperature and radiator specifications. Parameters of the model are derived based on the proposed analytic solution that describes...... dissipated heat by a radiator to ambient air. It is shown via simulations that the designed controller based on the proposed linear parameter varying (LPV) model performs excellent and remains stable in the whole operating conditions....
Huang, Ching-Sheng; Yeh, Hund-Der; Chang, Chia-Hao
2012-05-01
This paper develops a general mathematical model for describing head fluctuations in an aquifer of long but narrow islands subject to a dual tide effect. The upper boundary condition of the aquifer is represented by an equation combining the simplified free surface equation with a leakage term. Such an equation is considered as a general expression representing the upper boundary condition of a confined, unconfined, or leaky confined aquifer. The closed-form solution of the model represented by two series terms is developed by the direct Fourier method and finite Fourier sine transform. One of the series can reduce to a closed-form expression by means of contour integral and residue theorem. If the width of the island is very large, this solution gives the predicted head almost the same as that of the solution for an aquifer subject to a single tide effect. It is found that the presence of an upper aquitard produces significant vertical flow in the lower leaky confined aquifer even if the aquitard permeability is low. Neglecting such vertical flow may result in an overestimate of hydraulic head in the leaky confined aquifer. The attenuation factor and phase lag predicted from the present solution subject to the dual tide effect agree well with those estimated from 57 day head fluctuation data observed at Garden Island, Australia.
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.
Conjugate Gradient Method with Ritz Method for the Solution of Boundary Value Problems
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Victor Onomza WAZIRI
2007-01-01
Full Text Available In this paper, we wish to determine the optimal control of a one-variable boundary value problem using the Ritz algorithm. The posed optimal control problem was inadequate to achieve our goal using the Conjugate Gradient Method version developed by (Harsdoff, 1976. It is anticipated that other operators from some given different problems may sustain the application of the algorithm if the approximate solutions terms are properly chosen quadratic functionals. The graphical solution given at the end of section five of the paper, however, shows that our problem can not have an optimal minimum value since the minimum output is not unique. The optimal value obtained using Mathcad program codes may constitute a conjugate gradient approximate numerical value. As observed from the graphical output, Ritz algorithm could give credence for wider horizon in the engineering computational methods for vibrations of mechanical components and simulates.
An efficient numerical technique for the solution of nonlinear singular boundary value problems
Singh, Randhir; Kumar, Jitendra
2014-04-01
In this work, a new technique based on Green's function and the Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems (SBVPs) is proposed. The technique relies on constructing Green's function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on the ADM, the proposed technique avoids solving a sequence of transcendental equations for the undetermined coefficients. It approximates the solution in the form of a series with easily computable components. Additionally, the convergence analysis and the error estimate of the proposed method are supplemented. The reliability and efficiency of the proposed method are demonstrated by several numerical examples. The numerical results reveal that the proposed method is very efficient and accurate.
Multiple Solutions for a Nonlinear Fractional Boundary Value Problem via Critical Point Theory
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Yang Wang
2017-01-01
Full Text Available This paper is concerned with the existence of multiple solutions for the following nonlinear fractional boundary value problem: DT-αaxD0+αux=fx,ux, x∈0,T, u0=uT=0, where α∈1/2,1, ax∈L∞0,T with a0=ess infx∈0,Tax>0, DT-α and D0+α stand for the left and right Riemann-Liouville fractional derivatives of order α, respectively, and f:0,T×R→R is continuous. The existence of infinitely many nontrivial high or small energy solutions is obtained by using variant fountain theorems.
Multiple solutions to a boundary value problem for an n-th order nonlinear difference equation
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Susan D. Lauer
1998-11-01
Full Text Available We seek multiple solutions to the n-th order nonlinear difference equation $$Delta^n x(t= (-1^{n-k} f(t,x(t,quad t in [0,T]$$ satisfying the boundary conditions $$x(0 = x(1 = cdots = x(k - 1 = x(T + k + 1 = cdots = x(T+ n = 0,.$$ Guo's fixed point theorem is applied multiple times to an operator defined on annular regions in a cone. In addition, the hypotheses invoked to obtain multiple solutions to this problem involves the condition (A $f:[0,T] imes {mathbb R}^+ o {mathbb R}^+$ is continuous in $x$, as well as one of the following: (B $f$ is sublinear at $0$ and superlinear at $infty$, or (C $f$ is superlinear at $0$ and sublinear at $infty$.
Existence of solutions to fractional boundary-value problems with a parameter
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Ya-Ning Li
2013-06-01
Full Text Available This article concerns the existence of solutions to the fractional boundary-value problem $$displaylines{ -frac{d}{dt} ig(frac{1}{2} {}_0D_t^{-eta}+ frac{1}{2}{}_tD_{T}^{-eta}igu'(t=lambda u(t+abla F(t,u(t,quad hbox{a.e. } tin[0,T], cr u(0=0,quad u(T=0. }$$ First for the eigenvalue problem associated with it, we prove that there is a sequence of positive and increasing real eigenvalues; a characterization of the first eigenvalue is also given. Then under different assumptions on the nonlinearity F(t,u, we show the existence of weak solutions of the problem when $lambda$ lies in various intervals. Our main tools are variational methods and critical point theorems.
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.
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.
Analytical and exact solutions of the spherical and cylindrical diodes of Langmuir-Blodgett law
Torres-Cordoba, Rafael; Martinez-Garcia, Edgar
2017-10-01
This paper discloses the exact solutions of a mathematical model that describes the cylindrical and spherical electron current emissions within the context of a physics approximation method. The solution involves analyzing the 1D nonlinear Poisson equation, for the radial component. Although an asymptotic solution has been previously obtained, we present a theoretical solution that satisfies arbitrary boundary conditions. The solution is found in its parametric form (i.e., φ(r )=φ(r (τ)) ) and is valid when the electric field at the cathode surface is non-zero. Furthermore, the non-stationary spatial solution of the electric potential between the anode and the cathode is also presented. In this work, the particle-beam interface is considered to be at the end of the plasma sheath as described by Sutherland et al. [Phys. Plasmas 12, 033103 2005]. Three regimes of space charge effects—no space charge saturation, space charge limited, and space charge saturation—are also considered.
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Hua-Cheng Zhou
2016-02-01
Full Text Available This article is devoted to investigating the existence of solutions to fractional multi-point boundary-value problems at resonance in a Hilbert space. More precisely, the dimension of the kernel of the fractional differential operator with the boundary conditions be any positive integer. We point out that the problem is new even when the system under consideration is reduced to a second-order ordinary differential system with resonant boundary conditions. We show that the considered system admits at least a solution by applying coincidence degree theory first introduced by Mawhin. An example is presented to illustrate our results.
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...... of the numerical Method of Auxiliary Sources for a range of scattering configurations....... 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...
Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase
Bleher, P M
2005-01-01
The six-vertex model, or the square ice model, with domain wall boundary conditions (DWBC) has been introduced and solved for finite $N$ by Korepin and Izergin. The solution is based on the Yang-Baxter equations and it represents the free energy in terms of an $N\\times N$ Hankel determinant. Paul Zinn-Justin observed that the Izergin-Korepin formula can be re-expressed in terms of the partition function of a random matrix model with a nonpolynomial interaction. We use this observation to obtain the large $N$ asymptotics of the six-vertex model with DWBC in the disordered phase. The solution is based on the Riemann-Hilbert approach and the Deift-Zhou nonlinear steepest descent method. As was noticed by Kuperberg, the problem of enumeration of alternating sign matrices (the ASM problem) is a special case of the the six-vertex model. We compare the obtained exact solution of the six-vertex model with known exact results for the 1, 2, and 3 enumerations of ASMs, and also with the exact solution on the so-called f...
Tasbozan, Orkun; Çenesiz, Yücel; Kurt, Ali; Baleanu, Dumitru
2017-11-01
Modelling of physical systems mathematically, produces nonlinear evolution equations. Most of the physical systems in nature are intrinsically nonlinear, therefore modelling such systems mathematically leads us to nonlinear evolution equations. The analysis of the wave solutions corresponding to the nonlinear partial differential equations (NPDEs), has a vital role for studying the nonlinear physical events. This article is written with the intention of finding the wave solutions of Nizhnik-Novikov-Veselov and Klein-Gordon equations. For this purpose, the exp-function method, which is based on a series of exponential functions, is employed as a tool. This method is an useful and suitable tool to obtain the analytical solutions of a considerable number of nonlinear FDEs within a conformable derivative.
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Sobhan Mosayebidorcheh
2013-01-01
Full Text Available The boundary layer equation of the pseudoplastic fluid over a flat plate is considered. This equation is a boundary value problem (BVP with the high nonlinearity and a boundary condition at infinity. To solve such problems, powerful numerical techniques are usually used. Here, through using differential transform method (DTM, the BVP is replaced by two initial value problems (IVP and then multi-step differential transform method (MDTM is applied to solve them. The differential equation and its boundary conditions are transformed to a set of algebraic equations, and the Taylor series of solution is calculated in every sub domain. In this solution, there is no need for restrictive assumptions or linearization. Finally, DTM results are compared with the numerical solution of the problem, and a good accuracy of the proposed method is observed.
Yang, X. I. A.; Meneveau, C.
2017-03-01
In recent years, there has been growing interest in large-eddy simulation (LES) modelling of atmospheric boundary layers interacting with arrays of wind turbines on complex terrain. However, such terrain typically contains geometric features and roughness elements reaching down to small scales that typically cannot be resolved numerically. Thus subgrid-scale models for the unresolved features of the bottom roughness are needed for LES. Such knowledge is also required to model the effects of the ground surface `underneath' a wind farm. Here we adapt a dynamic approach to determine subgrid-scale roughness parametrizations and apply it for the case of rough surfaces composed of cuboidal elements with broad size distributions, containing many scales. We first investigate the flow response to ground roughness of a few scales. LES with the dynamic roughness model which accounts for the drag of unresolved roughness is shown to provide resolution-independent results for the mean velocity distribution. Moreover, we develop an analytical roughness model that accounts for the sheltering effects of large-scale on small-scale roughness elements. Taking into account the shading effect, constraints from fundamental conservation laws, and assumptions of geometric self-similarity, the analytical roughness model is shown to provide analytical predictions that agree well with roughness parameters determined from LES. This article is part of the themed issue 'Wind energy in complex terrains'.
Yang, X I A; Meneveau, C
2017-04-13
In recent years, there has been growing interest in large-eddy simulation (LES) modelling of atmospheric boundary layers interacting with arrays of wind turbines on complex terrain. However, such terrain typically contains geometric features and roughness elements reaching down to small scales that typically cannot be resolved numerically. Thus subgrid-scale models for the unresolved features of the bottom roughness are needed for LES. Such knowledge is also required to model the effects of the ground surface 'underneath' a wind farm. Here we adapt a dynamic approach to determine subgrid-scale roughness parametrizations and apply it for the case of rough surfaces composed of cuboidal elements with broad size distributions, containing many scales. We first investigate the flow response to ground roughness of a few scales. LES with the dynamic roughness model which accounts for the drag of unresolved roughness is shown to provide resolution-independent results for the mean velocity distribution. Moreover, we develop an analytical roughness model that accounts for the sheltering effects of large-scale on small-scale roughness elements. Taking into account the shading effect, constraints from fundamental conservation laws, and assumptions of geometric self-similarity, the analytical roughness model is shown to provide analytical predictions that agree well with roughness parameters determined from LES.This article is part of the themed issue 'Wind energy in complex terrains'. © 2017 The Author(s).
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. Copyright © 2016 Elsevier B.V. All rights reserved.
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.
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M.C. Raju
2014-12-01
Full Text Available An analytical solution of MHD free convective, dissipative boundary layer flow past a vertical porous surface in the presence of thermal radiation, chemical reaction and constant suction, under the influence of uniform magnetic field which is applied normal to the surface is studied. The governing equations are solved analytically using a regular perturbation technique. The expressions for velocity, temperature and concentration fields are obtained. With the aid of these, the expressions for the coefficient of skin friction, the rate of heat transfer in the form of Nusselt number and the rate of mass transfer in the form of Sherwood number are derived. Finally the effects of various physical parameters of the flow quantities are studied with the help of graphs and tables. It is observed that the velocity and concentration increase during a generative reaction and decrease in a destructive reaction. The same observed to be true for the behavior of the fluid temperature. The presence of magnetic field and radiation diminishes the velocity and also the temperature.
Analytical solution to the transient beam loading effects of a superconducting cavity
Huang, Ran; He, Yuan; Wang, Zhi-Jun; Yue, Wei-Ming; Wu, An-Dong; Tao, Yue; Yang, Qiong; Zhang, Cong; Zhao, Hong-Wei; Li, Zhi-Hui
2017-10-01
Transient beam loading is one of the key issues in any high beam current intensity superconducting accelerators, and needs to be carefully investigated. The core problem in the analysis is to obtain the time evolution of effective cavity voltage under transient beam loading. To simplify the problem, the second order ordinary differential equation describing the behavior of the effective cavity voltage is intuitively simplified to a first order one, with the aid of two critical approximations which lack proof of their validity. In this paper, the validity is examined mathematically in some specific cases, resulting in a criterion for the simplification. It is popular to solve the approximate equation for the effective cavity voltage numerically, while this paper shows that it can also be solved analytically under the step function approximation for the driven term. With the analytical solution to the effective cavity voltage, the transient reflected power from the cavity and the energy gain of the central particle in the bunch can also be calculated analytically. The validity of the step function approximation for the driven term is examined by direct evaluations. After that, the analytical results are compared with the numerical ones. Supported by National Natural Science Foundation of China (11525523, 91426303)
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Iftikhar Ahmed
2014-04-01
Full Text Available This paper deals with the evolution r-Laplacian equation with absorption and nonlinear boundary condition. By using differential inequality techniques, global existence and blow-up criteria of nonnegative solutions are determined. Moreover, upper bound of the blow-up time for the blow-up solution is obtained.
Even number of positive solutions for 3nth order three-point boundary value problem on time scales
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K. Prasad
2011-12-01
Full Text Available We establish the existence of at least two positive solutions for the 3nth order three-point boundary value problem on time scales by using Avery-Henderson fixed point theorem. We also establish the existence of at least 2m positive solutions for an arbitrary positive integer m.
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Mitsuhiro Nakao
2014-01-01
Full Text Available We prove the existence and uniqueness of a global decaying solution to the initial boundary value problem for the quasilinear wave equation with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a 'loan' method and use a difference inequality on the energy.
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Bila Adolphe Kyelem
2017-04-01
Full Text Available In this article, we prove the existence of solutions for some discrete nonlinear difference equations subjected to a potential boundary type condition. We use a variational technique that relies on Szulkin's critical point theory, which ensures the existence of solutions by ground state and mountain pass methods.
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Giai Giang Vo
2015-01-01
Full Text Available This paper is devoted to the study of a wave equation with a boundary condition of many-point type. The existence of weak solutions is proved by using the Galerkin method. Also, the uniqueness and the stability of solutions are established.
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.
Exact Analytical Solutions in Three-Body Problems and Model of Neutrino Generator
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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 time periodic electroosmotic flows: analogies to Stokes' second problem.
Duttat, P; Beskok, A
2001-11-01
Analytical solutions of time periodic electroosmotic flows in two-dimensional straight channels are obtained as a function of a nondimensional parameter kappa, which is based on the electric double-layer (EDL) thickness, kinematic viscosity, and frequency of the externally applied electric field. A parametric study as a function of kappa reveals interesting physics, ranging from oscillatory "pluglike" flows to cases analogous to the oscillating flat plate in a semi-infinite flow domain (Stokes' second problem). The latter case differs from the Stokes' second solution within the EDL, since the flow is driven with an oscillatory electric field rather than an oscillating plate. The analogous case of plate oscillating with the Helmholtz-Smoluchowski velocity matches our analytical solution in the bulk flow region. This indicates that the instantaneous Helmholtz-Smoluchowski velocity is the appropriate electroosmotic slip condition even for high-frequency excitations. The velocity profiles for large kappa values show inflection points very near the walls with localized vorticity extrema that are stronger than the Stokes layers. This have the potential to result in low Reynolds number flow instabilities. It is also shown that, unlike the steady pure electroosmotic flows, the bulk flow region of time periodic electroosmotic flows are rotational when the diffusion length scales are comparable to and less than the half channel height.
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.
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.
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Xingwei Wang
2014-01-01
Full Text Available Due to the uneven distribution of pollutions and blur edge of pollutant area, there will exist uncertainty of source term shape in advective-diffusion equation model of contaminant transport. How to generalize those irregular source terms and deal with those uncertainties is very critical but rarely studied in previous research. In this study, the fate and transport of contaminant from rectangular and elliptic source geometry were simulated based on a three-dimensional analytical solute transport model, and the source geometry generalization guideline was developed by comparing the migration of contaminant. The result indicated that the variation of source area size had no effect on pollution plume migration when the plume migrated as far as five times of source side length. The migration of pollution plume became slower with the increase of aquifer thickness. The contaminant concentration was decreasing with scale factor rising, and the differences among various scale factors became smaller with the distance to field increasing.
Analytical solution of nucleate pool boiling heat transfer model based on macrolayer
Danish, Mohd; Al Mesfer, Mohammed K.
2018-02-01
In the present work, a transient heat conduction model has been developed for heat transfer through macrolayer in nucleate regime of pool boiling. The developed heat transfer model was solved analytically (Laplace Transform) using appropriate initial and boundary conditions. The influence of macrolayer thickness, wall superheat, and time on conduction heat flux has been predicted. The average conduction heat flux as a function of wall superheat and macrolayer thickness has also been predicted. The findings of the study have been compared with experimental results, and they are in reasonable agreement. For higher values of wall superheat, which correspond to nucleate pool boiling, predicted results agree with experimental data. Findings also substantiate the assertion that heat conduction across the macrolayer constitutes the major mode of heat transfer from the heated wall to the boiling liquid in the macrolayer regime of pool boiling.
Analytical solution of nucleate pool boiling heat transfer model based on macrolayer
Danish, Mohd; Al Mesfer, Mohammed K.
2017-08-01
In the present work, a transient heat conduction model has been developed for heat transfer through macrolayer in nucleate regime of pool boiling. The developed heat transfer model was solved analytically (Laplace Transform) using appropriate initial and boundary conditions. The influence of macrolayer thickness, wall superheat, and time on conduction heat flux has been predicted. The average conduction heat flux as a function of wall superheat and macrolayer thickness has also been predicted. The findings of the study have been compared with experimental results, and they are in reasonable agreement. For higher values of wall superheat, which correspond to nucleate pool boiling, predicted results agree with experimental data. Findings also substantiate the assertion that heat conduction across the macrolayer constitutes the major mode of heat transfer from the heated wall to the boiling liquid in the macrolayer regime of pool boiling.
Benchmarking the invariant embedding method against analytical solutions in model transport problems
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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.
Analytical solutions for the fractional diffusion-advection equation describing super-diffusion
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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.
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Iakovlev Roman
2017-01-01
Full Text Available The paper presents the results of a study devoted to the problem of improving the energy efficiency of mechanical motion of anthropomorphic robotic systems. Achieving higher energy efficiency is largely due to the implementation of improvements directly in the algorithms that ensure the movement of a robotic system. For this purpose, several existing analytical methods for solving the inverse kinematics problem for robotic walking platforms were analyzed. According to the survey, key areas where modification can improve the energy efficiency of mechanical motion in various RS are identified. The paper discusses the algorithm developed to optimize the solutions of the inverse kinematics problem in terms of energy consumption.
Analytical solutions for the fractional diffusion-advection equation describing super-diffusion
Gómez, Francisco; Escalante, Enrique; Calderón, Celia; Morales, Luis; González, Mario; Laguna, Rodrigo
2016-01-01
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.
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. Copyright © 2013 Elsevier Ltd. All rights reserved.
DeChant, Lawrence Justin
1998-01-01
In spite of rapid advances in both scalar and parallel computational tools, the large number of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical, With this restriction, it is concluded that an important family of methods for mathematical/computational development are reduced or approximate fluid flow models. In this study a combined perturbation/numerical modeling methodology is developed which provides a rigorously derived family of solutions. The mathematical model is computationally more efficient than classical boundary layer but provides important two-dimensional information not available using quasi-1-d approaches. An additional strength of the current methodology is its ability to locally predict static pressure fields in a manner analogous to more sophisticated parabolized Navier Stokes (PNS) formulations. To resolve singular behavior, the model utilizes classical analytical solution techniques. Hence, analytical methods have been combined with efficient numerical methods to yield an efficient hybrid fluid flow model. In particular, the main objective of this research has been to develop a system of analytical and numerical ejector/mixer nozzle models, which require minimal empirical input. A computer code, DREA Differential Reduced Ejector/mixer Analysis has been developed with the ability to run sufficiently fast so that it may be used either as a subroutine or called by an design optimization routine. Models are of direct use to the High Speed Civil Transport Program (a joint government/industry project seeking to develop an economically.viable U.S. commercial supersonic transport vehicle) and are currently being adopted by both NASA and industry. Experimental validation of these models is provided by comparison to results obtained from open literature and Limited Exclusive Right Distribution (LERD) sources, as well as dedicated experiments performed at Texas A&M. These experiments have
Moura, Deberton; Barcelos, Vithor; Samanamud, Gisella Rossana Lamas; França, Alexandre Boscaro; Lofrano, Renata; Loures, Carla Cristina Almeida; Naves, Luzia Lima Rezende; Amaral, Mateus Souza; Naves, Fabiano Luiz
2018-02-14
Amoxicillin is a useful antibiotic to combat bacterial infections. However, this drug can cause serious problems when discarded in waterways due to its great bioaccumulation potential. This compound can be treated via advanced oxidation processes (AOPs), which are capable of converting amoxicillin into carbon dioxide and water. In this context, the use of ozone as an oxidizer has excelled in amoxicillin degradation. This paper aims at treating a synthetic solution of amoxicillin (0.1 g L -1 ) in a reactor with ozone bubbling. A Design of Experiment (DoE) with a response surface known as Central Composite Design (CCD) was used to optimize the treatment process. In addition, a Normal Boundary Intersection (NBI) method was used in the construction of a Pareto boundary chart. Results after 1-h treatment showed a reduction of 53% of the initial organic matter from a designed model using factors, such as pH, ozone generator power, and O 3 flow. A model was built from the CCD with score of 0.9929. Thus, the model was able to represent the real scenario with confidence.
Liu, Jiangen; Zhang, Yufeng
2018-01-01
This paper gives an analytical study of dynamic behavior of the exact solutions of nonlinear Korteweg-de Vries equation with space-time local fractional derivatives. By using the improved (G‧ G )-expansion method, the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solutions and soliton-like solutions, are obtained for the first time. They can better help us further understand the physical phenomena and provide a strong basis. Meanwhile, some solutions are presented through 3D-graphs.
Existence and boundary behavior of positive solutions for a Sturm-Liouville problem
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Syrine Masmoudi
2016-01-01
Full Text Available In this paper, we discuss existence, uniqueness and boundary behavior of a positive solution to the following nonlinear Sturm-Liouville problem \\[\\begin{aligned}&\\frac{1}{A}(Au^{\\prime }^{\\prime }+a(tu^{\\sigma}=0\\;\\;\\text{in}\\;(0,1,\\\\ &\\lim\\limits_{t\\to 0}Au^{\\prime}(t=0,\\quad u(1=0,\\end{aligned}\\] where \\(\\sigma \\lt 1\\, \\(A\\ is a positive differentiable function on \\((0,1\\ and \\(a\\ is a positive measurable function in \\((0,1\\ satisfying some appropriate assumptions related to the Karamata class. Our main result is obtained by means of fixed point methods combined with Karamata regular variation theory.
A symmetric solution of a multipoint boundary value problem at resonance
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We apply a coincidence degree theorem of Mawhin to show the existence of at least one symmetric solution of the nonlinear second-order multipoint boundary value problem u ″ ( t = f ( t , u ( t , | u ′ ( t | , t ∈ ( 0 , 1 , u ( 0 = ∑ i = 1 n μ i u ( ξ i , u ( 1 − t = u ( t , t ∈ ( 0 , 1 ] , where 0 < ξ 1 < ξ 2 < … ≤ ξ n 1 / 2 , ∑ i = 1 n μ i = 1 , f : [ 0 , 1 ] × ℝ 2 → ℝ with f ( t , x , y = f ( 1 − t , x , y , ( t , x , y ∈ [ 0 , 1 ] × ℝ 2 , satisfying the Carathéodory conditions.
Li, Can; Deng, Wei-Hua
2014-07-01
Following the fractional cable equation established in the letter [B.I. Henry, T.A.M. Langlands, and S.L. Wearne, Phys. Rev. Lett. 100 (2008) 128103], we present the time-space fractional cable equation which describes the anomalous transport of electrodiffusion in nerve cells. The derivation is based on the generalized fractional Ohm's law; and the temporal memory effects and spatial-nonlocality are involved in the time-space fractional model. With the help of integral transform method we derive the analytical solutions expressed by the Green's function; the corresponding fractional moments are calculated; and their asymptotic behaviors are discussed. In addition, the explicit solutions of the considered model with two different external current injections are also presented.
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.
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Ben Minnaert
2017-09-01
Full Text Available Wireless power transfer from one transmitter to multiple receivers through inductive coupling is slowly entering the market. However, for certain applications, capacitive wireless power transfer (CWPT using electric coupling might be preferable. In this work, we determine closed-form expressions for a CWPT system with one transmitter and two receivers. We determine the optimal solution for two design requirements: (i maximum power transfer, and (ii maximum system efficiency. We derive the optimal loads and provide the analytical expressions for the efficiency and power. We show that the optimal load conductances for the maximum power configuration are always larger than for the maximum efficiency configuration. Furthermore, it is demonstrated that if the receivers are coupled, this can be compensated for by introducing susceptances that have the same value for both configurations. Finally, we numerically verify our results. We illustrate the similarities to the inductive wireless power transfer (IWPT solution and find that the same, but dual, expressions apply.
Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method
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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.
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.
Exact and Analytic-Numerical Solutions of Lagging Models of Heat Transfer in a Semi-Infinite Medium
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M. A. Castro
2013-01-01
conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.
Hasheminejad, Seyyed M.; Ghaheri, Ali; Rezaei, Shahed
2012-01-01
A two-dimensional analytical model is developed to describe the free extensional vibrations of thin elastic plates of elliptical planform with or without a confocal cutout under general elastically restrained edge conditions, based on the Navier displacement equation of motion for a state of plane stress. The model has been simplified by invoking the Helmholtz decomposition theorem, and the method of separation of variables in elliptic coordinates is used to solve the resulting uncoupled governing equations in terms of products of (even and odd) angular and radial Mathieu functions. Extensive numerical results are presented in an orderly fashion for the first three anti-symmetric/symmetric natural frequencies of elliptical plates of selected geometries under different combinations of classical (clamped and free) and flexible boundary conditions. Also, the occurrences of "frequency veering" between various modes of the same symmetry group and interchange of the associated mode shapes in the veering region are noted and discussed. Moreover, selected 2D deformed mode shapes are presented in vivid graphical form. The accuracy of solutions is checked through appropriate convergence studies, and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature. The set of data reported herein is believed to be the first rigorous attempt to obtain the in-plane vibration frequencies of solid and annular thin elastic elliptical plates for a wide range of plate eccentricities.
Maksimova, N.V.; Akhmetov, R. G.
2013-01-01
The work deals with a boundary value problem for a quasilinear partial elliptical equation. The equation describes a stationary process of convective diffusion near a cylinder and takes into account the value of a chemical reaction for large Peclet numbers and for large constant of chemical reaction. The quantity the rate constant of the chemical reaction and Peclet number is assumed to have a constant value. The leading term of the asymptotics of the solution is constructed in the boundary l...
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Zhang Peiguo
2011-01-01
Full Text Available Abstract By obtaining intervals of the parameter λ, this article investigates the existence of a positive solution for a class of nonlinear boundary value problems of second-order differential equations with integral boundary conditions in abstract spaces. The arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator. MSC: 34B15; 34B16.
Charyyar Ashyralyyev; Gulzipa Akyuz; Mutlu Dedeturk
2017-01-01
In this work, we consider an inverse elliptic problem with Bitsadze-Samarskii type multipoint nonlocal and Neumann boundary conditions. We construct the first and second order of accuracy difference schemes (ADSs) for problem considered. We stablish stability and coercive stability estimates for solutions of these difference schemes. Also, we give numerical results for overdetermined elliptic problem with multipoint Bitsadze-Samarskii type nonlocal and Neumann boundary...
An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere
Swidinsky, Andrei; Liu, Lifei
2017-11-01
We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.
Analytical solution to the circularity problem in the discounted cash flow valuation framework
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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.
Analytical Close-form Solutions for Three-dimensional Datum Transformation with Big Rotation Angles
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LI Bofeng
2016-03-01
Full Text Available The small rotation angles are typically involved in the traditional geodetic datum transformation, for which one can iteratively solve for its linearized model with ignoring its second-smaller terms. However, the big rotation angles are introduced to transform the outcomes from the advanced space surveying techniques. For this transformation model with big rotation angles, all elements of rotation matrix are usually parameterized as unknown parameters and then solved with the constrained adjustment theory by using the orthogonal condition of rotation matrix. With three-dimensional datum transformation with big rotation angles as example, this paper derives the analytical close-form solutions by formularizing the coordinates of multi-points as a matrix and using the orthogonal condition of rotation matrix. Expanding the transformation model with introducing the errors to common points of both datum, we derive out its analytical solutions as well. The results of simulation computations show that the presented three-dimensional datum transformation can realize the comparable transformation result while the new method can outcome the complicated and time-consuming iterations, therefore improving the computation efficiency.
Ciotti, Luca; Pellegrini, Silvia
2017-10-01
One of the most active fields of research of modern-day astrophysics is that of massive black hole formation and coevolution with the host galaxy. In these investigations, ranging from cosmological simulations, to semi-analytical modeling, to observational studies, the Bondi solution for accretion on a central point-mass is widely adopted. In this work we generalize the classical Bondi accretion theory to take into account the effects of the gravitational potential of the host galaxy, and of radiation pressure in the optically thin limit. Then, we present the fully analytical solution, in terms of the Lambert-Euler W-function, for isothermal accretion in Jaffe and Hernquist galaxies with a central black hole. The flow structure is found to be sensitive to the shape of the mass profile of the host galaxy. These results and the formulae that are provided, most importantly, the one for the critical accretion parameter, allow for a direct evaluation of all flow properties, and are then useful for the abovementioned studies. As an application, we examine the departure from the true mass accretion rate of estimates obtained using the gas properties at various distances from the black hole, under the hypothesis of classical Bondi accretion. An overestimate is obtained from regions close to the black hole, and an underestimate outside a few Bondi radii; the exact position of the transition between the two kinds of departure depends on the galaxy model.
The environmental effect on the fluorescence intensity in solution. An analytical model.
Galbán, Javier; Mateos, Elena; Cebolla, Vicente; Domínguez, Andrés; Delgado-Camón, Arancha; de Marcos, Susana; Sanz-Vicente, Isabel; Sanz, Vanesa
2009-11-01
In this paper a mathematical model describing the non-specific interactions of the medium surrounding a fluorophore on its fluorescence intensity is proposed. The model, which has been developed for quantitative analytical applications, is based on the following general ideas: (1) the medium affects the fluorescence quantum yield across the non-radiative decay constant (k(nr)); (2) the k(nr) can be simplified to the singlet-to-triplet intersystem crossing (k(ISC)) constants; (3) k(ISC) follows the energy gap law and then depends on the singlet and triplet energy difference, and (4) the medium, due to solvation, changes the energy of both excited levels (singlet and triplet), then the constants and finally the fluorescence intensity. In our model, the strength of the fluorophore solvation by the solvent (represented by its refraction index, n, dielectric constant, epsilon, and electric charge) changes the singlet (excited)-to-fundamental and the singlet-to-triplet energy gaps, thus the k(ISC) and k(IC) (internal conversion constant) values and in consequence the fluorescence quantum yield. The final model relates the fluorescence intensity (F) with the solvent dielectric constant and refraction index. Finally, the model is particularized for the case of a medium composed of a solvent and a solute, obtaining an F-to-solute concentration relationship and enabling this fact to be used for analytical applications. The very first experimental data are shown demonstrating the fulfilment of this model.
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Lingju Kong
2013-04-01
Full Text Available We study the existence of multiple solutions to the boundary value problem $$displaylines{ frac{d}{dt}Big(frac12{}_0D_t^{-eta}(u'(t+frac12{}_tD_T^{-eta}(u'(t Big+lambda abla F(t,u(t=0,quad tin [0,T],cr u(0=u(T=0, }$$ where $T>0$, $lambda>0$ is a parameter, $0leqeta<1$, ${}_0D_t^{-eta}$ and ${}_tD_T^{-eta}$ are, respectively, the left and right Riemann-Liouville fractional integrals of order $eta$, $F: [0,T]imesmathbb{R}^Nomathbb{R}$ is a given function. Our interest in the above system arises from studying the steady fractional advection dispersion equation. By applying variational methods, we obtain sufficient conditions under which the above equation has at least three solutions. Our results are new even for the special case when $eta=0$. Examples are provided to illustrate the applicability of our results.
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Olaniyi Samuel Iyiola
2014-09-01
Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous 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 non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.
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Cercignani, C. [Politecnico di Milano, Milan (Italy)
1996-08-01
Recently R. Illner and the author proved that, under a physically realistic truncation on the collision kernel, the Boltzmann equation in the one-dimensional slab [0,1] with general diffusive boundary conditions at 0 and 1 has a global weak solution in the traditional sense. Here it is proved that when the Maxwellians associated with the boundary conditions at x=0 and x = 1 are the same Maxwellian M{sub w}, then the solution is uniformly bounded and tends to M{sub w} for t {r_arrow}{infinity}.
Multiferroic phase boundaries and properties of BiFeO3-based solid solutions
Ye, Zuo-Guang
The presence of morphotropic phase boundary in ferroelectric solid solutions (FE-MPB) is known to be crucial for high piezoelectricity. Similarly, magnetic MPB (M-MPB) is found in a few ferromagnets and is proved to be greatly beneficial to the magnetostricitive response. One naturally asks if in multiferroics that exhibit both ferroelectricity and (ferro-/antiferro-)magnetism, the FE-MPB and M-MPB could exist simultaneously, and if so, what the relation between these two kinds of MPB would be, and how they would affect the properties. In this paper, we report the studies of ferroelectric and magnetic double morphotropic phase boundaries in BiFeO3-based multiferroics. The effects of dysprosium ion on the structure and local polar domains of the BiFeO3-based systems were investigated firstly in the Dy-substituted solid solutions of 0.66Bi1-x DyxFeO3-0.34PbTiO3. It is found that the substitution of Dy affects the structural symmetry and phase component of the multiferroic solid solution, and thereby enhances its ferroelectric order. A (weak) ferromagnetic state is induced at room temperature for the rhombohedral compositions with x >= 0.10. The introduction of Dy into 0.66BiFeO3-0.34PbTiO3 leads to the breaking of its antiferromagnetic order below Néel temperature and thereby the formation of (weak) ferromagnetic ordering at room temperature when the substitution rate exceeds a critical value (x >= 0.10), making the 0.66Bi1-x DyxFeO3-0.34PbTiO3 system one of rare room-temperature ferromagnetic and ferroelectric materials, i.e. a true multifrroic. A comprehensive ferroelectric-magnetic phase diagram is established in terms of temperature and composition, which depicts the coexistence of a FE-MPB and a FM-MPB. These two kinds of MPBs overlap with each other. Such unusual coincidence of both magnetic MPB and ferroelectric MPB, the so-called double MPB, points to new kinds of couplings among the multiple physical quantities so that such effects as magnetoelectricity
Peralta, J.; Imamura, T.; Read, P. L.; Luz, D.; Piccialli, A.; López-Valverde, M. A.
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.
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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.
Field-Analytical approach of land-sea records for elucidating the Younger Dryas Boundary syndrome
Ge, T.; Courty, M. M.; Guichard, F.
2009-12-01
Linking lonsdaleite crystals, carbon spherules and diamond polymorphs from the North American dark layers at 12.9 cal yr B.P. to a cosmic event has questioned the nature and timing of the related impact processes. A global signal should trace the invoked airshocks and/or surface impacts from a swarm of comets or carbonaceous chondrites. Here we report on the contextual analytical study of debris fall events from three reference sequences of the Younger Dyras period (11-13 ka cal BP) : (1) sand dune fields along the French Atlantic coast at the Audenge site; (2) A 10 m record of detrital/bioorganic accumulation in the southern basin of the Caspian Sea with regular sedimentation rate (0.1 to 3 mm per year) from 14 to 2-ka BP cal; (3) the Paijan sequence (Peruvian coastal desert) offering fossiliferous fluvial layers with the last large mammals and aquatic fauna at 13 ka BP sealed by abiotic sand dunes. The three sequences display one remarkable layer of exogenous air-transported microdebris that is part of a complex time series of recurrent fine dust/wildfire events. The sharp debris-rich microfacies and its association to ashes derived from calcination of the local vegetation suggest instantaneous deposition synchronous to a high intensity wildfire. The debris assemblage comprises microtektite-like glassy spherules, partly devitrified glass shards, unmelted to partly melted sedimentary and igneous clasts, terrestrial native metals, and carbonaceous components. The later occur as grape-clustered polymers, vitrified graphitic carbon, amorphous carbon spherules with a honeycomb pattern, and green carbon fibres with recrystallized quartz and metal blebs. Evidence for high temperature formation from a heterogeneous melt with solid debris and volatile components derived from carbonaceous precursors supports an impact origin from an ejecta plume. The association of debris deposition to total firing would trace a high energy airburst with surface effects of the fireball. In
Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid
2014-11-01
In this paper, we present a reliable algorithm to calculate positive solutions of homogeneous nonlinear boundary value problems (BVPs). The algorithm converts the nonlinear BVP to an equivalent nonlinear Fredholm- Volterra integral equation.We employ the multistage Adomian decomposition method for BVPs on two or more subintervals of the domain of validity, and then solve the matching equation for the flux at the interior point, or interior points, to determine the solution. Several numerical examples are used to highlight the effectiveness of the proposed scheme to interpolate the interior values of the solution between boundary points. Furthermore we demonstrate two novel techniques to accelerate the rate of convergence of our decomposition series solutions by increasing the number of subintervals and adjusting the lengths of subintervals in the multistage Adomian decomposition method for BVPs.
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Javed Ali
2012-01-01
Full Text Available We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHAM. The proposed method is capable to handle a wide variety of linear and nonlinear problems effectively. The numerical results given by OHAM are compared with the exact solutions and the solutions obtained by Adomian decomposition (ADM, variational iteration (VIM, homotopy perturbation (HPM, and variational iteration decomposition method (VIDM. The results show that the proposed method is more effective and reliable.
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Puskar Raj SHARMA
2012-01-01
Full Text Available Aim of the paper is to investigate solution of twodimensional linear parabolic partial differential equation with non-local boundary conditions using Homotopy Perturbation Method (HPM. This method is not only reliable in obtaining solution of such problems in series form with high accuracy but it also guarantees considerable saving of the calculation volume and time as compared to other methods. The application of the method has been illustrated through an example
Analytical Solution for Elliptical Cloaks Based on The Frequency Selective Surface
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E. Ghasemi Mizuji
2015-01-01
Full Text Available In this paper the elliptical dielectric cylinder which is covered with FSS cloak is considered. Frequency selective surface cloak which Alu named it mantle cloak is one of the recent techniques for cloaking. In this method an appropriate FSS can act as cloaking device for suppressing the scattering of object in the desired frequency. With using this method the dimension of the cloaks is extremely reduced. By this proposed structure, the RCS of elliptical cylinder is reduced about 10-20 dB and designed cloak has an appropriate performance. The analytical solution for the wave in each layer is presented and with using simulation, the electric field and the scattering pattern has been drawn.
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Shibib Khalid S.
2017-01-01
Full Text Available The exact analytical solution of axis-symmetry transient temperature and Tresca failure stress in pulsed mode solid-state laser rod is derived using integral transform method. The result obtained from this work is compared with previously published data and good agreement is found. The effect of increasing period is studied, and it is found that at constant pulse width as the period is increased, the allowable pumping power is increased too. Furthermore, the effect of changing pulse width with a constant period is studied, and it is found that as the pulse width is increased, the allowable pumping power is decreased. The effect of duty cycle is studied also and it is found that as duty cycle is increased the allowable pumping power is decreased. This work permits proper selection of pulse width, period and duty cycle to avoid laser rod fracture while obtaining maximum output laser power in the designing of laser system.
A finite volume method for cylindrical heat conduction problems based on local analytical solution
Li, Wang
2012-10-01
A new finite volume method for cylindrical heat conduction problems based on local analytical solution is proposed in this paper with detailed derivation. The calculation results of this new method are compared with the traditional second-order finite volume method. The newly proposed method is more accurate than conventional ones, even though the discretized expression of this proposed method is slightly more complex than the second-order central finite volume method, making it cost more calculation time on the same grids. Numerical result shows that the total CPU time of the new method is significantly less than conventional methods for achieving the same level of accuracy. © 2012 Elsevier Ltd. All rights reserved.
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Birol İbiş
2014-12-01
Full Text Available The purpose of this paper was to obtain the analytical approximate solution of time-fractional Fornberg–Whitham, equation involving Jumarie’s modified Riemann–Liouville derivative by the fractional variational iteration method (FVIM. FVIM provides the solution in the form of a convergent series with easily calculable terms. The obtained approximate solutions are compared with the exact or existing numerical results in the literature to verify the applicability, efficiency and accuracy of the method.
An Analytical Solution for Block Toppling Failure of Rock Slopes during an Earthquake
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Songfeng Guo
2017-09-01
Full Text Available Toppling failure is one of the most common failure types in the field. It always occurs in rock masses containing a group of dominant discontinuities dipping into the slope. Post-earthquake investigation has shown that many toppling rock slope failures have occurred during earthquakes. In this study, an analytical solution is presented on the basis of limit equilibrium analysis. The acceleration of seismic load as well as joint persistence within the block base, were considered in the analysis. The method was then applied into a shake table test of an anti-dip layered slope model. As predicted from the analytical method, blocks topple or slide from slope crest to toe progressively and the factor of safety decreases as the inputting acceleration increases. The results perfectly duplicate the deformation features and stability condition of the physical model under the shake table test. It is shown that the presented method is more universal than the original one and can be adopted to evaluate the stability of the slope with potential toppling failure under seismic loads.