Analytical Solution of Mathieu Equation
Yerchuck, Dmitri; Dovlatova, Alla; Yerchak, Yauhen; Borovik, Felix
2014-01-01
The general solution of the homogeneous damped Mathieu equation in the analytical form, allowing its practical using in many applications, including superconductivity studies, without numerical calculations has been found.
Strongly nonlinear oscillators analytical solutions
Cveticanin, Livija
2014-01-01
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for profess...
Analytical solutions for heat conduction
International Nuclear Information System (INIS)
Fraley, S.K.
1976-01-01
Green's functions are found for steady state heat conduction in a composite rectangular parallelepiped (RPP) and in a composite right circular cylinder (RCC) assuming no contact resistance. These Green's functions may then be used to provide analytical solutions for arbitrary internal source distributions and surface temperature distributions within the RPP or RCC
ANALYTIC SOLUTIONS OF MATRIX RICCATI EQUATIONS WITH ANALYTIC COEFFICIENTS
Curtain, Ruth; Rodman, Leiba
2010-01-01
For matrix Riccati equations of platoon-type systems and of systems arising from PDEs, assuming the coefficients are analytic or rational functions in a suitable domain, analyticity of the stabilizing solution is proved under various hypotheses. General results on analytic behavior of stabilizing
Analytical solution of population balance equation involving ...
Indian Academy of Sciences (India)
the analytical solution from spatially distributed systems. Indeed in McCoy and Madras. [19], the solution is given in terms of moments, and for this reason it is not possible to see explicitly the effect of the particle volume v appearing in the analytical solution. Also, as for these moments, there is no exact way to get back to the ...
Analytical solution of one dimensional temporally dependent ...
African Journals Online (AJOL)
user
It helps understand the contaminant or pollutants concentration distribution behavior through an open medium like air, rivers, lakes or porous ... van Genuchten and Alves (1982) complied the analytical solutions with first order decay and zero order production term. Yates. (1990, 1992) obtain the analytical solution for one ...
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
Analytical solution of population balance equation involving ...
Indian Academy of Sciences (India)
This paper presents an effective analytical simulation to solve population balance equation (PBE), involving particulate aggregation and breakage, by making use of appropriate solution(s) of associated complementary equation via auxiliary equation method (AEM). Travelling wave solutions of the complementary equation ...
Insight solutions are correct more often than analytic solutions
Salvi, Carola; Bricolo, Emanuela; Kounios, John; Bowden, Edward; Beeman, Mark
2016-01-01
How accurate are insights compared to analytical solutions? In four experiments, we investigated how participants’ solving strategies influenced their solution accuracies across different types of problems, including one that was linguistic, one that was visual and two that were mixed visual-linguistic. In each experiment, participants’ self-judged insight solutions were, on average, more accurate than their analytic ones. We hypothesised that insight solutions have superior accuracy because they emerge into consciousness in an all-or-nothing fashion when the unconscious solving process is complete, whereas analytic solutions can be guesses based on conscious, prematurely terminated, processing. This hypothesis is supported by the finding that participants’ analytic solutions included relatively more incorrect responses (i.e., errors of commission) than timeouts (i.e., errors of omission) compared to their insight responses. PMID:27667960
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 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.
Surface solitons in waveguide arrays: Analytical solutions.
Kominis, Yannis; Papadopoulos, Aristeidis; Hizanidis, Kyriakos
2007-08-06
A novel phase-space method is employed for the construction of analytical stationary solitary waves located at the interface between a periodic nonlinear lattice of the Kronig-Penney type and a linear or nonlinear homogeneous medium as well as at the interface between two dissimilar nonlinear lattices. The method provides physical insight and understanding of the shape of the solitary wave profile and results to generic classes of localized solutions having either zero or nonzero semi-infinite backgrounds. For all cases, the method provides conditions involving the values of the propagation constant of the stationary solutions, the linear refractive index and the dimensions of each part in order to assure existence of solutions with specific profile characteristics. The evolution of the analytical solutions under propagation is investigated for cases of realistic configurations and interesting features are presented such as their remarkable robustness which could facilitate their experimental observation.
ANALYTICAL BENDING SOLUTION OF ALL CLAMPED ISOTROPIC ...
African Journals Online (AJOL)
The analytical bending solution of all clamped rectangular plate on Winkler foundation using characteristic orthogonal polynomials (COPs) was studied. This was achieved by partially integrating the governing differential equation of rectangular plate on elastic foundation four times with respect to its independents x and y ...
Analytic vortex solutions on compact hyperbolic surfaces
International Nuclear Information System (INIS)
Maldonado, Rafael; Manton, Nicholas S
2015-01-01
We construct, for the first time, abelian Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given implicitly in terms of Schwarz triangle functions and analytic solutions are available for certain highly symmetric configurations. (paper)
Recovery of uranium from analytical waste solution
International Nuclear Information System (INIS)
Kumar, Pradeep; Anitha, M.; Singh, D.K.
2016-01-01
Dispersion fuels are considered as advance fuel for the nuclear reactor. Liquid waste containing significant quantity of uranium gets generated during chemical characterization of dispersion fuel. The present paper highlights the effort in devising a counter current solvent extraction process based on the synergistic mixture of D2EHPA and Cyanex 923 to recover uranium from such waste solutions. A typical analytical waste solution was found to have the following composition: U 3 O 8 (∼3 g/L), Al: 0.3 g/L, V: 15 ppm, Phosphoric acid: 3M, sulphuric acid : 1M and nitric acid : 1M. The aqueous solution is composed of mixture of either 3M phosphoric acid and 1M sulphuric acid or 1M sulphuric acid and 1M nitric acid, keeping metallic concentrations in the above mentioned range. Different organic solvents were tested. Based on the higher extraction of uranium with synergistic mixture of 0.5M D2EHPA + 0.125M Cyanex 923, it was selected for further investigation in the present work
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 ...
An Iteration Method Generating Analytical Solutions for Blasius Problem
Yun, Beong In
2011-01-01
We derive a new iteration method for finding solution of the generalized Blasius problem. This method results in the analytical series solutions which are consistent with the existing series solutions for some special cases.
Analytical Solution for Stellar Density in Globular Clusters
Indian Academy of Sciences (India)
Abstract. In this paper, four parameters analytical solution will be established for the stellar density function in globular clusters. The solution could be used for any arbitrary order of outward decrease of the cluster's density.
Analytical solution of population balance equation involving ...
Indian Academy of Sciences (India)
This paper presents an effective analytical simulation to solve population balance equation (PBE), involving particulate aggregation and breakage, by making use ... The domain part of the email address of all email addresses used by the office of Indian Academy of Sciences, including those of the staff, the journals, various ...
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.
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 ...
Analytical solution of groundwater waves in unconfined aquifers with ...
Indian Academy of Sciences (India)
The present first-order solution compares well with the previous analytical solutions and a 2D FEFLOW solution for a steep beach slope. This is due to the fact that the higher-order Boussinesq equationcaptures the streamlines better than ordinary Boussinesq equation based on Dupuit's assumption. The slope of the beach ...
Analytic solutions of nonlinear neutral and advanced differential equatios
Directory of Open Access Journals (Sweden)
Joseph Wiener
1986-01-01
Full Text Available A study is made of local existence and uniqueness theorems for analytic solutions of nonlinear differential equations of neutral and advanced types. These results are of special interest for advanced eauations whose solutions, in general, lose their margin of smoothness. Furthermore, existence of entire solutions is established for linear advanced differential systems with polynomial coefficients.
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 ...
Analytical solution of strongly nonlinear Duffing oscillators
Directory of Open Access Journals (Sweden)
A.M. El-Naggar
2016-06-01
Full Text Available In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε is defined such that the value of α is always small regardless of the magnitude of the original parameter ε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to α. Approximate solution obtained by the present method is compared with the solution of energy balance method, homotopy perturbation method, global error minimization method and lastly numerical solution. We observe from the results that this method is very simple, easy to apply, and gives a very good accuracy not only for small parameter εbut also for large values of ε.
Analytical solution of strongly nonlinear Duffing oscillators
El-Naggar, A.M.; Ismail, G.M.
2016-01-01
In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε)α=α(ε) is defined such that the value of α is always small regardless of the magnitude of the original parameter εε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to αα. Approximate solution obtained by the present method is compared with the solution of energy balance m...
An analytical solution of fractional burgers equation
Directory of Open Access Journals (Sweden)
Pang Jing
2017-01-01
Full Text Available Using the fractional complex transform, the fractional partial differential equations can be reduced to ordinary differential equations which can be solved by the auxiliary equation method. Non-linear superposition formulation of Riccati equation is applied, and a complex infinite sequence solution is obtained.
Analytic solution of the lifeguard problem
De Luca, Roberto; Di Mauro, Marco; Naddeo, Adele
2018-03-01
A simple version due to Feynman of Fermat’s principle is analyzed. It deals with the path a lifeguard on a beach must follow to reach a drowning swimmer. The solution for the exact point, P(x, 0) , at the beach-sea boundary, corresponding to the fastest path to the swimmer, is worked out in detail and the analogy with light traveling at the air-water boundary is described. The results agree with the known conclusion that the shortest path does not coincide with the fastest one. The relevance of the subject for a basic physics course, at an advanced high school level, is pointed out.
Analytical solutions to SSC coil end design
International Nuclear Information System (INIS)
Bossert, R.C.; Brandt, J.S.; Carson, J.A.; Fulton, H.J.; Lee, G.C.; Cook, J.M.
1989-03-01
As part of the SCC magnet effort, Fermilab will build and test a series of one meter model SSC magnets. The coils in these magnets will be constructed with several different end configurations. These end designs must satisfy both mechanical and magnetic criteria. Only the mechanical problem will be addressed. Solutions will attempt to minimize stresses and provide internal support for the cable. Different end designs will be compared in an attempt to determine which is most appropriate for the SSC dipole. The mathematics required to create each end configuration will be described. The computer aided design, programming and machine technology needed to make the parts will be reviewed. 2 refs., 10 figs
Speciation—targets, analytical solutions and markets
Łobiński, Ryszard
1998-02-01
An analysis of speciation-relevant issues leads to the conclusion that, despite the rapidly increasing number of reports, the field has reached a level of virtual stagnation in terms of research originality and market perspectives. A breakthrough is in sight but requires an advanced interdisciplinary collaboration of chemists-analysts with clinicians, ecotoxicologists and nutricionists aimed at the definition of metal (metalloid)-dependent problems relevant to human health. The feedback from analytical chemists will be stimulated by a wider availability of efficient HPLC (CZE)-inductively coupled plasma mass spectrometry (ICP MS) interfaces, chromatographic software for ICP AES and MS and sensitive on-line methods for compound identification (electrospray MS/MS). The maturity of purge and trap thermal desorption techniques and capillary GC chromatography is likely to be reflected by an increasing number of commercial dedicated systems for small molecules containing Hg, Pb, Sn and metalloids. The pre-requisite of success for such systems is the integration of a sample preparation step (based on focused low-power microwave technology) into the marketed set-up.
Analytical solution of groundwater waves in unconfined aquifers with ...
Indian Academy of Sciences (India)
A new analytical solution is derived for tide-driven groundwater waves in coastal aquifers using higher-order Boussinesq equation. The homotopy perturbation solution is derived using a virtual perturbation approach without any pre-defined physical parameters. The secular term removal is performed using a combinationof ...
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.
Analytical solutions of advection-dispersion equation for varying ...
African Journals Online (AJOL)
Analytical solutions are obtained for a one-dimensional advection–dispersion equation with variable coefficients in a longitudinal domain. Two cases are considered. In the first one the solute dispersion is time dependent along a uniform flow in a semi-infinite domain while in the second case the dispersion and the velocity ...
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.
Analytic solution of a five-direction radiation transport model
International Nuclear Information System (INIS)
Cramer, S.N.
1988-01-01
In order to test certain spatial and angular dependent Monte Carlo biasing techniques, a one-dimensional, one energy, two-media, five-direction radiation transport model has been devised for which an analytic solution exists. Although this solution is too long to be conveniently expressed in an explicit form, it can be easily evaluated on the smallest of computers. This solution is discussed in this paper. 1 ref
Analytical solutions of the simplified Mathieu’s equation
Directory of Open Access Journals (Sweden)
Nicolae MARCOV
2016-03-01
Full Text Available Consider a second order differential linear periodic equation. The periodic coefficient is an approximation of the Mathieu’s coefficient. This equation is recast as a first-order homogeneous system. For this system we obtain analytical solutions in an explicit form. The first solution is a periodic function. The second solution is a sum of two functions, the first is a continuous periodic function, but the second is an oscillating function with monotone linear increasing amplitude. We give a formula to directly compute the slope of this increase, without knowing the second numeric solution. The periodic term of the second solution may be computed directly. The coefficients of fundamental matrix of the system are analytical functions.
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...
Analytic Solution to Shell Boundary – Value Problems
Directory of Open Access Journals (Sweden)
Yu. I. Vinogradov
2015-01-01
Full Text Available Object of research is to find analytical solution to the shell boundary – value problems, i.e. to consider the solution for a class of problems concerning the mechanics of hoop closed shells strain.The objective of work is to create an analytical method to define a stress – strain state of shells under non-axisymmetric loading. Thus, a main goal is to derive the formulas – solutions of the linear ordinary differential equations with variable continuous coefficients.The partial derivative differential equations of mechanics of shells strain by Fourier's method of variables division are reduced to the system of the differential equations with ordinary derivatives. The paper presents the obtained formulas to define solutions of the uniform differential equations and received on their basis formulas to define a particular solution depending on a type of the right parts of the differential equations.The analytical algorithm of the solution of a boundary task uses an approach to transfer the boundary conditions to the randomly chosen point of an interval of changing independent variable through the solution of the canonical matrix ordinary differential equation with the subsequent solution of system of algebraic equations for compatibility of boundary conditions at this point. Efficiency of algorithm is based on the fact that the solution of the ordinary differential equations is defined as the values of Cauchy – Krylova functions, which meet initial arbitrary conditions.The results of researches presented in work are useful to experts in the field of calculus mathematics, dealing with solution of systems of linear ordinary differential equations and creation of effective analytical computing methods to solve shell boundary – value problems.
On the General Analytical Solution of the Kinematic Cosserat Equations
Michels, Dominik L.
2016-09-01
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
Analytical 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.
The analytical solution to the problem of statistical induction
Rodolfo de Cristofaro
2007-01-01
This article is a somewhat personal review of the history and substance of the problem of statistical induction. The main approaches proposed for solving this problem have been examined according to their merits, whit special reference to the analytical solution supported by Carnap. This solution has been re-examined in view of certain results, and is proposed again to the attention of the statisticians.
The analytical solution to the problem of statistical induction
Directory of Open Access Journals (Sweden)
Rodolfo de Cristofaro
2007-10-01
Full Text Available This article is a somewhat personal review of the history and substance of the problem of statistical induction. The main approaches proposed for solving this problem have been examined according to their merits, whit special reference to the analytical solution supported by Carnap. This solution has been re-examined in view of certain results, and is proposed again to the attention of the statisticians.
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 \
New analytical solutions for bosonic field trapping in thick branes
Energy Technology Data Exchange (ETDEWEB)
Landim, R.R. [Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará (Brazil); Alencar, G., E-mail: geovamaciel@gmail.com [Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará (Brazil); Tahim, M.O. [Universidade Estadual do Ceará, Faculdade de Educação, Ciências e Letras do Sertão Central, R. Epitácio Pessoa, 2554, 63.900-000 Quixadá, Ceará (Brazil); Costa Filho, R.N. [Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará (Brazil)
2014-04-04
New analytical solutions for gravity, scalar and vector field localization in Randall–Sundrum (RS) models are found. A smooth version of the warp factor with an associated function f(z)=exp(3A(z)/2) inside the walls (|z|
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 ...
Analytical construction of peaked solutions for the nonlinear ...
African Journals Online (AJOL)
These results demonstrate the existence of peaked pulses propagating through a pair plasma. The algebraic decay rate of the pulses are determined analytically, as well. The method discussed here can be applied to approximate solutions to similar nonlinear partial differential equations of nonlinear Schrödinger type.
An Analytical Method For The Solution Of Reactor Dynamic Equations
African Journals Online (AJOL)
Nigeria Journal of Pure and Applied Physics ... One of the challenges of modelling nuclear reactor dynamics on microcomputers is that of finding robust techniques which guarantee the required level of accuracy and at ... In this paper, an analytical method for the solution of nuclear reactor dynamic equations is presented.
General analytical shakedown solution for structures with kinematic hardening materials
Guo, Baofeng; Zou, Zongyuan; Jin, Miao
2016-09-01
The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems: a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.
Analytical Solution for Stellar Density in Globular Clusters MA Sharaf ...
Indian Academy of Sciences (India)
A. M. Sendi. Department of Astronomy, Faculty of Science, King Abdul Aziz University, Jeddah,. Saudi Arabia. ∗ e-mail: sharaf_adel@hotmail.com. Received 2008 April 9; revised 2009 April 9; accepted 2009 April 9. Abstract. In this paper, four parameters analytical solution will be established for the stellar density function ...
Analytical solution of groundwater waves in unconfined aquifers with ...
Indian Academy of Sciences (India)
Selva Balaji Munusamy
2017-07-29
Jul 29, 2017 ... groundwater table becomes essential. Analytical solution of tide–aquifer interaction is important from field appli- cation [1] point of view. In the present work, the water table wave propagations in coastal aquifers are solved using a homotopy perturbation method with simple har- monic sinusoidal functions ...
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
The big bang and inflation united by an analytic solution
International Nuclear Information System (INIS)
Bars, Itzhak; Chen, Shih-Hung
2011-01-01
Exact analytic solutions for a class of scalar-tensor gravity theories with a hyperbolic scalar potential are presented. Using an exact solution we have successfully constructed a model of inflation that produces the spectral index, the running of the spectral index, and the amplitude of scalar perturbations within the constraints given by the WMAP 7 years data. The model simultaneously describes the big bang and inflation connected by a specific time delay between them so that these two events are regarded as dependent on each other. In solving the Friedmann equations, we have utilized an essential Weyl symmetry of our theory in 3+1 dimensions which is a predicted remaining symmetry of 2T-physics field theory in 4+2 dimensions. This led to a new method of obtaining analytic solutions in the 1T field theory which could in principle be used to solve more complicated theories with more scalar fields. Some additional distinguishing properties of the solution includes the fact that there are early periods of time when the slow-roll approximation is not valid. Furthermore, the inflaton does not decrease monotonically with time; rather, it oscillates around the potential minimum while settling down, unlike the slow-roll approximation. While the model we used for illustration purposes is realistic in most respects, it lacks a mechanism for stopping inflation. The technique of obtaining analytic solutions opens a new window for studying inflation, and other applications, more precisely than using approximations.
Quantifying risks with exact analytical solutions of derivative pricing distribution
Zhang, Kun; Liu, Jing; Wang, Erkang; Wang, Jin
2017-04-01
Derivative (i.e. option) pricing is essential for modern financial instrumentations. Despite of the previous efforts, the exact analytical forms of the derivative pricing distributions are still challenging to obtain. In this study, we established a quantitative framework using path integrals to obtain the exact analytical solutions of the statistical distribution for bond and bond option pricing for the Vasicek model. We discuss the importance of statistical fluctuations away from the expected option pricing characterized by the distribution tail and their associations to value at risk (VaR). The framework established here is general and can be applied to other financial derivatives for quantifying the underlying statistical distributions.
Analytical exact solution of the non-linear Schroedinger equation
International Nuclear Information System (INIS)
Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da
2011-01-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
On the Partial Analytical Solution of the Kirchhoff Equation
Michels, Dominik L.
2015-09-01
We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have the disadvantage that the quality of solutions decreases enormously with increasing temporal step sizes, which results from the numerical stiffness of the underlying partial differential equations. To prevent that, we apply a differential Thomas decomposition and a Lie symmetry analysis to derive explicit analytical solutions to specific parts of the Kirchhoff system. These solutions are general and depend on arbitrary functions, which we set up according to the numerical solution of the remaining parts. In contrast to a purely numerical handling, this reduces the numerical solution space and prevents the system from becoming unstable. The differential Kirchhoff equation describes the dynamic equilibrium of one-dimensional continua, i.e. slender structures like fibers. We evaluate the advantage of our method by simulating a cilia carpet.
ADVAN-style analytical solutions for common pharmacokinetic models.
Abuhelwa, Ahmad Y; Foster, David J R; Upton, Richard N
2015-01-01
The analytical solutions to compartmental pharmacokinetic models are well known, but have not been presented in a form that easily allows for complex dosing regimen and changes in covariate/parameter values that may occur at discrete times within and/or between dosing intervals. Laplace transforms were used to derive ADVAN-style analytical solutions for 1, 2, and 3 compartment pharmacokinetic linear models of intravenous and first-order absorption drug administration. The equations calculate the change in drug amounts in each compartment of the model over a time interval (t; t = t2 - t1) accounting for any dose or covariate events acting in the time interval. The equations were coded in the R language and used to simulate the time-course of drug amounts in each compartment of the systems. The equations were validated against commercial software [NONMEM (Beal, Sheiner, Boeckmann, & Bauer, 2009)] output to assess their capability to handle both complex dosage regimens and the effect of changes in covariate/parameter values that may occur at discrete times within or between dosing intervals. For all tested pharmacokinetic models, the time-course of drug amounts using the ADVAN-style analytical solutions were identical to NONMEM outputs to at least four significant figures, confirming the validity of the presented equations. To our knowledge, this paper presents the ADVAN-style equations for common pharmacokinetic models in the literature for the first time. The presented ADVAN-style equations overcome obstacles to implementing the classical analytical solutions in software, and have speed advantages over solutions using differential equation solvers. The equations presented in this paper fill a gap in the pharmacokinetic literature, and it is expected that these equations will facilitate the investigation of useful open-source software for modelling pharmacokinetic data. Copyright © 2015 Elsevier Inc. All rights reserved.
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...
Explicit analytical solution of the nonlinear Vlasov Poisson system
International Nuclear Information System (INIS)
Skarka, V.; Mahajan, S.M.; Fijalkow, E.
1993-10-01
In order to describe the time evolution of an inhomogeneous collisionless plasma the nonlinear Vlasov equation is solved perturbatively, using the subdynamics approach and the diagrammatic techniques. The solution is given in terms of a double perturbation series, one with respect to the nonlinearities and the other with respect to the interaction between particles. The infinite sum of interaction terms can be performed exactly due to the property of dynamical factorization. Following the methodology, the exact solution in each order with respect to nonlinearities is computed. For a choice of initial perturbation the first order exact solution is numerically integrated in order to find the local density excess. The approximate analytical solution is found to be in excellent agreement with exact numerical integration as well as with ab initio numerical simulations. Analytical computation gives a better insight into the problem and it has the advantage to be simpler, and also accessible in some range of parameters where it is difficult to find numerical solutions. (author). 27 refs, 12 figs
Semi-analytical solution to arbitrarily shaped beam scattering
Wang, Wenjie; Zhang, Huayong; Sun, Yufa
2017-07-01
Based on the field expansions in terms of appropriate spherical vector wave functions and the method of moments scheme, an exact semi-analytical solution to the scattering of an arbitrarily shaped beam is given. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are presented to a spheroid and a circular cylinder of finite length, and the scattering properties are analyzed concisely.
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.)
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.
Small-scale engagement model with arrivals: analytical solutions
International Nuclear Information System (INIS)
Engi, D.
1977-04-01
This report presents an analytical model of small-scale battles. The specific impetus for this effort was provided by a need to characterize hypothetical battles between guards at a nuclear facility and their potential adversaries. The solution procedure can be used to find measures of a number of critical parameters; for example, the win probabilities and the expected duration of the battle. Numerical solutions are obtainable if the total number of individual combatants on the opposing sides is less than 10. For smaller force size battles, with one or two combatants on each side, symbolic solutions can be found. The symbolic solutions express the output parameters abstractly in terms of symbolic representations of the input parameters while the numerical solutions are expressed as numerical values. The input parameters are derived from the probability distributions of the attrition and arrival processes. The solution procedure reduces to solving sets of linear equations that have been constructed from the input parameters. The approach presented in this report does not address the problems associated with measuring the inputs. Rather, this report attempts to establish a relatively simple structure within which small-scale battles can be studied
JOVIAN STRATOSPHERE AS A CHEMICAL TRANSPORT SYSTEM: BENCHMARK ANALYTICAL SOLUTIONS
Energy Technology Data Exchange (ETDEWEB)
Zhang Xi; Shia Runlie; Yung, Yuk L., E-mail: xiz@gps.caltech.edu [Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125 (United States)
2013-04-20
We systematically investigated the solvable analytical benchmark cases in both one- and two-dimensional (1D and 2D) chemical-advective-diffusive systems. We use the stratosphere of Jupiter as an example but the results can be applied to other planetary atmospheres and exoplanetary atmospheres. In the 1D system, we show that CH{sub 4} and C{sub 2}H{sub 6} are mainly in diffusive equilibrium, and the C{sub 2}H{sub 2} profile can be approximated by modified Bessel functions. In the 2D system in the meridional plane, analytical solutions for two typical circulation patterns are derived. Simple tracer transport modeling demonstrates that the distribution of a short-lived species (such as C{sub 2}H{sub 2}) is dominated by the local chemical sources and sinks, while that of a long-lived species (such as C{sub 2}H{sub 6}) is significantly influenced by the circulation pattern. We find that an equator-to-pole circulation could qualitatively explain the Cassini observations, but a pure diffusive transport process could not. For slowly rotating planets like the close-in extrasolar planets, the interaction between the advection by the zonal wind and chemistry might cause a phase lag between the final tracer distribution and the original source distribution. The numerical simulation results from the 2D Caltech/JPL chemistry-transport model agree well with the analytical solutions for various cases.
Analytical solution of Mori's equation with secant hyperbolic memory
International Nuclear Information System (INIS)
Tankeshwar, K.; Pathak, K.N.
1993-07-01
The equation of motion of the auto-correlation function has been solved analytically using a secant-hyperbolic form of the memory function. The analytical results obtained for the long time expansion together with the short time expansion provide a good description over the whole time domain as judged by their comparison with the numerical solution of Mori's equation of motion. We also find that the time evolution of the auto-correlation function is determined by a single parameter τ which is related to the frequency sum rules up to the fourth order. The auto-correlation function has been found to show simple decaying or oscillatory behaviour depending on whether the parameter τ is greater than or less than some critical values. Similarities as well as differences in time evolution of the auto-correlation have been discussed for exponential, secant-hyperbolic and Gaussian approaches of the memory function. (author). 16 refs, 5 figs
Biological and analytical studies of peritoneal dialysis solutions
Directory of Open Access Journals (Sweden)
N. Hudz
2018-04-01
Full Text Available The purpose of our work was to conduct biological and analytical studies of the peritoneal dialysis (PD solutions containing glucose and sodium lactate and establish correlations between cell viability of the Vero cell line and values of analytical indexes of the tested solutions. The results of this study confirm the cytotoxicity of the PD solutions even compared with the isotonic solution of sodium chloride, which may be due to the low pH of the solutions, presence of glucose degradation products (GDPs and high osmolarity of the solutions, and unphysiological concentrations of glucose and sodium lactate. However, it is not yet known what factors or their combination and to what extent cause the cytotoxicity of PD solutions. In the neutral red (NR test the weak, almost middle (r = -0.496 and 0.498, respectively and unexpected correlations were found between reduced viability of monkey kidney cells and increased pH of the PD solutions and between increased cell viability and increased absorbance at 228 nm of the tested PD solutions. These two correlations can be explained by a strong correlation (r = -0.948 between a decrease in pH and an increase in the solution absorbance at 228 nm. The opposite effect was observed in the MTT test. The weak, but expected correlations (r = 0.32 and -0.202, respectively were found between increased cell viability and increased pH in the PD solutions and between decreased cell viability and increased absorbance at 228 nm of the tested PD solutions. The middle and weak correlations (r = 0.56 and 0.29, respectively were detected between increased cell viability and increased lactate concentration in the NR test and MTT test. The data of these correlations can be partially explained by the fact that a correlation with a coefficient r = -0.34 was found between decreased pH in the solutions and increased lactate concentration. The very weak correlations (0.138 and 0.196, respectively were found between increased cell
Mathematical Model of Suspension Filtration and Its Analytical Solution
Directory of Open Access Journals (Sweden)
Normahmad Ravshanov
2013-01-01
Full Text Available The work develops advanced mathematical model and computing algorithm to analyze, predict and identify the basic parameters of filter units and their variation ranges. Numerical analytic solution of liquid ionized mixtures filtration was got on their basis. Computing experiments results are presented in graphics form. Calculation results analysis enables to determine the optimum performance of filter units, used for liquid ionized mixtures filtration, food preparation, drug production and water purification. Selection of the most suitable parameters contributes to the improvement of economic and technological efficiency of production and filter units working efficiency.
Analytical solution of the toroidal constant tension solenoid
International Nuclear Information System (INIS)
Gralnick, S.L.; Tenney, F.H.
1975-01-01
The coil shape is determined by requiring that the curvature of the flexible conductor be proportional to the distance from the toroidal axis. The resulting second order differential equation for the coil coordinates can be integrated once but for the second and final integration no closed form has been found and the integration has been done numerically. This solution of this differential equation is analytical in terms of an absolutely and uniformly convergent infinite series. The series converges quite rapidly and in practice ignoring all but the first five terms of the series introduces an error of less than 2 percent
Analytical solutions for tsunami runup on a plane beach
DEFF Research Database (Denmark)
Madsen, Per A.; Schäffer, Hemming Andreas
2010-01-01
In the literature it has so far been common practice to consider solitary waves N-waves (composed of solitary waves) as the appropriate model of tsunamis approaching the shoreline. Unfortunately, this approach is based on a tie between the nonlinearity and the horizontal length scale (or duration......) of the wave, which is not realistic for geophysical tsunamis. To resolve this problem, we first derive analytical solutions to the nonlinear shallow-water (NSW) equations for the runup/rundown of single waves, where the duration and the wave height can be specified separately. The formulation is then extended...
Analytic solution to a class of integro-differential equations
Directory of Open Access Journals (Sweden)
Xuming Xie
2003-03-01
Full Text Available In this paper, we consider the integro-differential equation $$ epsilon^2 y''(x+L(xmathcal{H}(y=N(epsilon,x,y,mathcal{H}(y, $$ where $mathcal{H}(y[x]=frac{1}{pi}(Pint_{-infty}^{infty} frac{y(t}{t-x}dt$ is the Hilbert transform. The existence and uniqueness of analytic solution in appropriately chosen space is proved. Our method consists of extending the equation to an appropriately chosen region in the complex plane, then use the Contraction Mapping Theorem.
An Exact Analytical Solution to Exponentially Tapered Piezoelectric Energy Harvester
Directory of Open Access Journals (Sweden)
H. Salmani
2015-01-01
Full Text Available It has been proven that tapering the piezoelectric beam through its length optimizes the power extracted from vibration based energy harvesting. This phenomenon has been investigated by some researchers using semianalytical, finite element and experimental methods. In this paper, an exact analytical solution is presented to calculate the power generated from vibration of exponentially tapered unimorph and bimorph with series and parallel connections. The mass normalized mode shapes of the exponentially tapered piezoelectric beam with tip mass are implemented to transfer the proposed electromechanical coupled equations into modal coordinates. The steady states harmonic solution results are verified both numerically and experimentally. Results show that there exist values for tapering parameter and electric resistance in a way that the output power per mass of the energy harvester will be maximized. Moreover it is concluded that the electric resistance must be higher than a specified value for gaining more power by tapering the beam.
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.
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.
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.
Concerning an analytical solution of some families of Kepler’s transcendental equation
Directory of Open Access Journals (Sweden)
Slavica M. Perovich
2016-03-01
Full Text Available The problem of finding an analytical solution of some families of Kepler transcendental equation is studied in some detail, by the Special Trans Functions Theory – STFT. Thus, the STFT mathematical approach in the form of STFT iterative methods with a novel analytical solutions are presented. Structure of the STFT solutions, numerical results and graphical simulations confirm the validity of the basic principle of the STFT. In addition, the obtained analytical results are compared with the calculated values of other analytical methods for alternative proving its significance. Undoubtedly, the proposed novel analytical approach implies qualitative improvement in comparison with conventional numerical and analytical methods.
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.
Analytical solution of differential equation with cubic nonlinearity
Инхиреева, Т. А.; Козловских, Александр Владимирович
2016-01-01
This paper considers method of Cauchy problem solution for nonlinear differential equation. Source of solution error and way of eliminating it is studied. Solution obtained with suggestedmethod is compared with solution obtained with built-in MATLAB functions.
Solution of the isotopic depletion equation using decomposition method and analytical solution
Energy Technology Data Exchange (ETDEWEB)
Prata, Fabiano S.; Silva, Fernando C.; Martinez, Aquilino S., E-mail: fprata@con.ufrj.br, E-mail: fernando@con.ufrj.br, E-mail: aquilino@lmp.ufrj.br [Coordenacao dos Programas de Pos-Graduacao de Engenharia (PEN/COPPE/UFRJ), RJ (Brazil). Programa de Engenharia Nuclear
2011-07-01
In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes found in a typical PWR reactor. Part of this chain allows feedback reactions of (n,2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code, that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time. (author)
Solution of the isotopic depletion equation using decomposition method and analytical solution
International Nuclear Information System (INIS)
Prata, Fabiano S.; Silva, Fernando C.; Martinez, Aquilino S.
2011-01-01
In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes found in a typical PWR reactor. Part of this chain allows feedback reactions of (n,2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code, that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time. (author)
Analytical solutions for efficient interpretation of single-well push-pull tracer tests
Single-well push-pull tracer tests have been used to characterize the extent, fate, and transport of subsurface contamination. Analytical solutions provide one alternative for interpreting test results. In this work, an exact analytical solution to two-dimensional equations descr...
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
2016-10-18
expansion method is implemented to find exact solutions of ... and can be used as an alternative for finding exact solutions of nonlinear equations in mathematical physics. A ... engineering, such as, solid mechanics, plasma physics,.
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
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
Ji Juan-Juan
2017-01-01
Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.
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.
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
2016-10-18
Oct 18, 2016 ... Abstract. In this article, a variety of solitary wave solutions are found for some nonlinear equations. In math- ematical 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 ...
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
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 a fractional complex transform to convert the particular partial differential equation of ...
On analytical solution of the Navier-Stokes equations
International Nuclear Information System (INIS)
Scheffel, J.
2001-04-01
An analytical method for solving the dissipative, nonlinear and non-stationary Navier-Stokes equations is presented. Velocity and pressure is expanded in power series of cartesian coordinates and time. The method is applied to 2-D incompressible gravitational flow in a bounded, rectangular domain
Analytical solutions for one-dimensional advection– dispersion ...
Indian Academy of Sciences (India)
Laplace transformation technique is defined by equation (6), and is used to get the analytical solu- tions. The Laplace transformation may be defined as: If f (x, t) is any function defined in a ≤ x ≤ b and t > 0, then its Laplace transform with ...... streams; J. Sanitary Engineering Division, Proc. ASCE. 90 53–78. Doetsch G 1970 ...
Analytical solutions for J 2-perturbed unbounded equatorial orbits
Martinusi, Vladimir; Gurfil, Pini
2013-01-01
While solutions for bounded orbits about oblate spheroidal planets have been presented before, similar solutions for unbounded motion are scarce. This paper develops solutions for unbounded motion in the equatorial plane of an oblate spheroidal planet, while taking into account only the J 2 harmonic in the gravitational potential. Two cases are distinguished: A pseudo-parabolic motion, obtained for zero total specific energy, and a pseudo-hyperbolic motion, characterized by positive total specific energy. The solutions to the equations of motion are expressed using elliptic integrals. The pseudo-parabolic motion unveils a new orbit, termed herein the fish orbit, which has not been observed thus far in the perturbed two-body problem. The pseudo-hyperbolic solutions show that significant differences exist between the Keplerian flyby and the flyby performed under the the J 2 zonal harmonic. Numerical simulations are used to quantify these differences.
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.
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
, is used to solve this equation. This method is able to obtain rapidly convergent successive approximations of exact solution without any restrictive approximations or the transformations that may change the physical behaviour of the problem.
Analytical Solution of Pantograph Equation with Incommensurate Delay
Patade, Jayvant; Bhalekar, Sachin
2017-08-01
Pantograph equation is a delay differential equation (DDE) arising in electrodynamics. This paper studies the pantograph equation with two delays. The existence, uniqueness, stability and convergence results for DDEs are presented. The series solution of the proposed equation is obtained by using Daftardar-Gejji and Jafari method and given in terms of a special function. This new special function has several properties and relations with other functions. Further, we generalize the proposed equation to fractional-order case and obtain its solution.
Non-linear analytical solutions for laterally loaded sandwich plates
DEFF Research Database (Denmark)
Riber, Hans Jørgen
1997-01-01
. The results of the analytical calculations are discussed and compared with numerical non-linear finite difference calculations and large-deflection experiments of equivalent plates. The presented methods lead to good results for plate response and provide the engineer with an alternative method for the design...... of sandwich plates subjected to high lateral loading. (C) 1997 Published by Elsevier Science Ltd. All rights reserved....
Selecting analytical tools for characterization of polymersomes in aqueous solution
DEFF Research Database (Denmark)
Habel, Joachim Erich Otto; Ogbonna, Anayo; Larsen, Nanna
2015-01-01
Selecting the appropriate analytical methods for characterizing the assembly and morphology of polymer-based vesicles, or polymersomes are required to reach their full potential in biotechnology. This work presents and compares 17 different techniques for their ability to adequately report size, ...... for characterizing polymersomes per se but the comparative overview is also intended to serve as a starting point for selecting methods for characterizing polymersomes with encapsulated compounds or polymersomes with incorporated biomolecules (e.g. membrane proteins)....
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.
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.
Analytical solution using computer algebra of a biosensor for detecting toxic substances in water
Rúa Taborda, María. Isabel
2014-05-01
In a relatively recent paper an electrochemical biosensor for water toxicity detection based on a bio-chip as a whole cell was proposed and numerically solved and analyzed. In such paper the kinetic processes in a miniaturized electrochemical biosensor system was described using the equations for specific enzymatic reaction and the diffusion equation. The numerical solution shown excellent agreement with the measured data but such numerical solution is not enough to design efficiently the corresponding bio-chip. For this reason an analytical solution is demanded. The object of the present work is to provide such analytical solution and then to give algebraic guides to design the bio-sensor. The analytical solution is obtained using computer algebra software, specifically Maple. The method of solution is the Laplace transform, with Bromwich integral and residue theorem. The final solution is given as a series of Bessel functions and the effective time for the bio-sensor is computed. It is claimed that the analytical solutions that were obtained will be very useful to predict further current variations in similar systems with different geometries, materials and biological components. Beside of this the analytical solution that we provide is very useful to investigate the relationship between different chamber parameters such as cell radius and height; and electrode radius.
Two-dimensional analytical solution for nodal calculation of nuclear reactors
International Nuclear Information System (INIS)
Silva, Adilson C.; Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S.
2017-01-01
Highlights: • A proposal for a coarse mesh nodal method is presented. • The proposal uses the analytical solution of the two-dimensional neutrons diffusion equation. • The solution is performed homogeneous nodes with dimensions of the fuel assembly. • The solution uses four average fluxes on the node surfaces as boundary conditions. • The results show good accuracy and efficiency. - Abstract: In this paper, the two-dimensional (2D) neutron diffusion equation is analytically solved for two energy groups (2G). The spatial domain of reactor core is divided into a set of nodes with uniform nuclear parameters. To determine iteratively the multiplication factor and the neutron flux in the reactor we combine the analytical solution of the neutron diffusion equation with an iterative method known as power method. The analytical solution for different types of regions that compose the reactor is obtained, such as fuel and reflector regions. Four average fluxes in the node surfaces are used as boundary conditions for analytical solution. Discontinuity factors on the node surfaces derived from the homogenization process are applied to maintain averages reaction rates and the net current in the fuel assembly (FA). To validate the results obtained by the analytical solution a relative power density distribution in the FAs is determined from the neutron flux distribution and compared with the reference values. The results show good accuracy and efficiency.
Selecting analytical tools for characterization of polymersomes in aqueous solution
DEFF Research Database (Denmark)
Habel, Joachim Erich Otto; Ogbonna, Anayo; Larsen, Nanna
2015-01-01
/purification. Of the analytical methods tested, Cryo-transmission electron microscopy and atomic force microscopy (AFM) turned out to be advantageous for polymersomes with smaller diameter than 200 nm, whereas confocal microscopy is ideal for diameters >400 nm. Polymersomes in the intermediate diameter range can be characterized...... using freeze fracture Cryo-scanning electron microscopy (FF-Cryo-SEM) and nanoparticle tracking analysis (NTA). Small angle X-ray scattering (SAXS) provides reliable data on bilayer thickness and internal structure, Cryo-TEM on multilamellarity. Taken together, these tools are valuable...
Lee, Ping I
2011-10-10
The purpose of this review is to provide an overview of approximate analytical solutions to the general moving boundary diffusion problems encountered during the release of a dispersed drug from matrix systems. Starting from the theoretical basis of the Higuchi equation and its subsequent improvement and refinement, available approximate analytical solutions for the more complicated cases involving heterogeneous matrix, boundary layer effect, finite release medium, surface erosion, and finite dissolution rate are also discussed. Among various modeling approaches, the pseudo-steady state assumption employed in deriving the Higuchi equation and related approximate analytical solutions appears to yield reasonably accurate results in describing the early stage release of a dispersed drug from matrices of different geometries whenever the initial drug loading (A) is much larger than the drug solubility (C(s)) in the matrix (or A≫C(s)). However, when the drug loading is not in great excess of the drug solubility (i.e. low A/C(s) values) or when the drug loading approaches the drug solubility (A→C(s)) which occurs often with drugs of high aqueous solubility, approximate analytical solutions based on the pseudo-steady state assumption tend to fail, with the Higuchi equation for planar geometry exhibiting a 11.38% error as compared with the exact solution. In contrast, approximate analytical solutions to this problem without making the pseudo-steady state assumption, based on either the double-integration refinement of the heat balance integral method or the direct simplification of available exact analytical solutions, show close agreement with the exact solutions in different geometries, particularly in the case of low A/C(s) values or drug loading approaching the drug solubility (A→C(s)). However, the double-integration heat balance integral approach is generally more useful in obtaining approximate analytical solutions especially when exact solutions are not
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.
Analytical solutions for ozone generation by point to plane corona discharge
International Nuclear Information System (INIS)
Bestman, A.R.
1990-12-01
A recent mathematical model developed for ozone production is tackled analytically by asymptotic approximation. The results obtained are compared with existing numerical solutions. The comparison shows good agreement. (author). 3 refs, 1 fig
Large deflection of clamped circular plate and accuracy of its approximate analytical solutions
Zhang, Yin
2016-02-01
A different set of governing equations on the large deflection of plates are derived by the principle of virtual work (PVW), which also leads to a different set of boundary conditions. Boundary conditions play an important role in determining the computation accuracy of the large deflection of plates. Our boundary conditions are shown to be more appropriate by analyzing their difference with the previous ones. The accuracy of approximate analytical solutions is important to the bulge/blister tests and the application of various sensors with the plate structure. Different approximate analytical solutions are presented and their accuracies are evaluated by comparing them with the numerical results. The error sources are also analyzed. A new approximate analytical solution is proposed and shown to have a better approximation. The approximate analytical solution offers a much simpler and more direct framework to study the plate-membrane transition behavior of deflection as compared with the previous approaches of complex numerical integration.
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.
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. .
Analytical solution of groundwater waves in unconfined aquifers with ...
Indian Academy of Sciences (India)
Selva Balaji Munusamy
2017-07-29
Jul 29, 2017 ... 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 the slope of the beach face.
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.)
Analytical solution of advection–diffusion equation in heterogeneous ...
Indian Academy of Sciences (India)
(33 and 34) become the respective solutions for instantaneous source and continuous source given by Basha and El-Habel (1993). The para- meter k = 0 in above form leads to constant diffusion coefficient discussed in case (i). The integral (38) may not be evaluated directly, hence numerical integration is carried out.
Analytical solutions of one-dimensional advection– diffusion ...
Indian Academy of Sciences (India)
Advection–diffusion equation describes the solute transport due to combined effect of diffusion and convection in a medium. It is a partial differen- tial equation of parabolic type, derived on the principle of conservation of mass using Fick's law. Due to the growing surface and subsurface hydro- environment degradation and ...
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
A comparative study with the other methods gives validity to the technique and shows that the method providesadditional solutions. Graphical representations along with the numerical data reinforce the efficacy of the procedure used. The specified idea is very effective, pragmatic for partial differential equations of fractional ...
An analytical solution based on mobility and multicriteria ...
Indian Academy of Sciences (India)
C AMALI
2017-10-14
Oct 14, 2017 ... selection algorithm is needed to select the target network for maximizing the end user satisfaction. The existing works do not .... then a handover is performed to the target network for high- velocity users. If the network with ...... pricing scheme is considered to provide solutions for the challenges behind the ...
Analytical Solutions to Non-linear Mechanical Oscillation Problems
DEFF Research Database (Denmark)
Kaliji, H. D.; Ghadimi, M.; Barari, Amin
2011-01-01
using He Chengtian’s interpolation. The comparison of the obtained results from Max-Min method with time marching solution and the results achieved from literature verifies its convenience and effectiveness. It is predictable that He’s Max-Min Method will find wide application in various engineering...
Analytical solutions of weakly coupled map lattices using recurrence relations
Energy Technology Data Exchange (ETDEWEB)
Sotelo Herrera, Dolores, E-mail: dsh@dfmf.uned.e [Applied Maths, EUITI, UPM, Ronda de Valencia, 3-28012 Madrid (Spain); San Martin, Jesus [Applied Maths, EUITI, UPM, Ronda de Valencia, 3-28012 Madrid (Spain); Dep. Fisica Matematica y de Fluidos, UNED, Senda del Rey 9-28040 Madrid (Spain)
2009-07-20
By using asymptotic methods recurrence relations are found that rule weakly CML evolution, with both global and diffusive coupling. The solutions obtained from these relations are very general because they do not hold restrictions about boundary conditions, initial conditions and number of oscilators in the CML. Furthermore, oscillators are ruled by an arbitraty C{sup 2} function.
An Analytical Solution for Acoustic Emission Source Location for Known P Wave Velocity System
Directory of Open Access Journals (Sweden)
Longjun Dong
2014-01-01
Full Text Available This paper presents a three-dimensional analytical solution for acoustic emission source location using time difference of arrival (TDOA measurements from N receivers, N⩾5. The nonlinear location equations for TDOA are simplified to linear equations, and the direct analytical solution is obtained by solving the linear equations. There are not calculations of square roots in solution equations. The method solved the problems of the existence and multiplicity of solutions induced by the calculations of square roots in existed close-form methods. Simulations are included to study the algorithms' performance and compare with the existing technique.
Analytical solution 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.
A note on analytical solutions of nonlinear fractional 2D heat ...
Indian Academy of Sciences (India)
2016-09-09
Sep 9, 2016 ... use a relatively new analytical technique called q-homotopy analysis method to obtain analytical solutions to both cases in the form of convergent series with easily computable components. Our numerical analysis enables us to show the effects of non-local terms and the fractional-order derivative on the ...
Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations
Directory of Open Access Journals (Sweden)
U. Filobello-Nino
2015-01-01
Full Text Available This paper proposes power series method (PSM in order to find solutions for singular partial differential-algebraic equations (SPDAEs. We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.
New analytical solution for pyle-popovich's peritoneal dialysis model
Energy Technology Data Exchange (ETDEWEB)
Hamada, Hiroyuki; Sakiyama, Ryoichi; Okamoto, Masahiro; Tojo, Kakuji [Kyushi Institute of Technology, Fukuoka (Japan); Yamashita, Akihiro [Shonan Institute of Technology, Kanagwa (Japan)
1999-08-01
Continuous Ambulatory Peritoneal Dialysis (CAPD) is one of the standard treatments for kidney disease patients. A washing solution, called dialysate, is put into the peritoneal cavity to remove waste products and excess amounts of water in CAPD. The dialysate is exchanged four to five times a day by the patient. However, it is not easy to prescribe CAPD therapy, which may have precluded popularization of CAPD therapy. Popovich et al. constructed a mathematical model (P-P model) that applies to the prescription of the treatment schedule. It requires, however, a number of iterative calculations to obtain a exact numerical solution because the model is a set of nonlinear simultaneous ordinary differential equations. In this paper, the authors derived a new approximated analytical solution by employing a time-discrete technique, assuming all the parameters to be constant within each piecewise period of time for the P-P model. We have also described an algorithm of a numerical calculation with the new solution for clinical use with another analytical solution (Vonesh's solution). The new analytical solution consists of a forward solution (FW solution). The new analytical solution consists of a forward solution (FW solution), that is the solution for the plasma and dialysate concentrations from t{sub i} to t{sub i+1}(t{sub i}
Analytical solutions for space charge fields in TPC drift volumes
Rossegger, S; Schnizer, B
2011-01-01
At high particle rates and high multiplicities, Time Projection Chambers can suffer from field distortions due to slow moving ions that accumulate within the drift volume. These variations modify the electron trajectory along the drift path, affecting the tracking performance of the detector. In order to calculate the track distortions due to an arbitrary space charge distribution in a TPC, novel representations of the Green's function for a TPC-like geometry were worked out. This analytical approach permits accurate predictions of track distortions due to an arbitrary space charge distribution (by solving the Langevin equation) as well as the possibility to benchmark common numerical methods to calculate such space charge fields. (C) 2011 Elsevier B.V. All rights reserved.
Analytical solution for dynamic pressurization of viscoelastic fluids
International Nuclear Information System (INIS)
Hashemabadi, S.H.; Etemad, S.Gh.; Thibault, J.; Golkar Naranji, M.R.
2003-01-01
The flow of simplified Phan-Thien-Tanner model fluid between parallel plates is studied analytically for the case where the upper plate moves at constant velocity. Two forms of the stress coefficient, linear and exponential, are used in the constitutive equation. For the linear stress coefficient, the dimensionless pressure gradient, the velocity profile and the product of friction factor and Reynolds number are obtained for a wide range of flow rate, Deborah number and elongational parameter. The results indicate the strong effects of the viscoelastic parameter on the velocity profile, the extremum of the velocity, and the friction factor. A correlation for the maximum pressure rise in single screw extruders is proposed. For the exponential stress coefficient, only velocity profiles were obtained and compared with velocity profiles obtained with the linear stress coefficient
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 ...
Analytic electrostatic solution of an axisymmetric accelerator gap
International Nuclear Information System (INIS)
Boyd, J.K.
1995-01-01
Numerous computer codes calculate beam dynamics of particles traversing an accelerating gap. In order to carry out these calculations the electric field of a gap must be determined. The electric field is obtained from derivatives of the scalar potential which solves Laplace's equation and satisfies the appropriate boundary conditions. An integral approach for the solution of Laplace's equation is used in this work since the objective is to determine the potential and fields without solving on a traditional spatial grid. The motivation is to quickly obtain forces for particle transport, and eliminate the need to keep track of a large number of grid point fields. The problem then becomes one of how to evaluate the appropriate integral. In this work the integral solution has been converted to a finite sum of easily computed functions. Representing the integral solution in this manner provides a readily calculable formulation and avoids a number of difficulties inherent in dealing with an integral that can be weakly convergent in some regimes, and is, in general, highly oscillatory
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.
Analytical solutions for Dirac and Klein-Gordon equations using Backlund transformations
Energy Technology Data Exchange (ETDEWEB)
Zabadal, Jorge R.; Borges, Volnei, E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio, E-mail: marciophd@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Centro de Estudos Interdisciplinares
2015-07-01
This work presents a new analytical method for solving Klein-Gordon type equations via Backlund transformations. The method consists in mapping the Klein-Gordon model into a first order system of partial differential equations, which contains a generalized velocity field instead of the Dirac matrices. This system is a tensor model for quantum field theory whose space solution is wider than the Dirac model in the original form. Thus, after finding analytical expressions for the wave functions, the Maxwell field can be readily obtained from the Dirac equations, furnishing a self-consistent field solution for the Maxwell-Dirac system. Analytical and numerical results are reported. (author)
Analytical Solution of Generalized Space-Time Fractional Cable Equation
Directory of Open Access Journals (Sweden)
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.
Order-by-order Analytic Solution to the BFKL Equation
Ross, D.A.
2014-01-01
We propose a regularization of the BFKL equation which allows for its solution in each order of perturbation theory by means of a sum over multiple poles. This sum can be presented in a rather simple formula for the Fourier transform in the azimuthal angle of the gluon Green function. In order to test our method, we have compared a few orders in the expansion to previous results by Del Duca, Dixon, Duhr and Pennington, finding agreement. Our formalism is general and can be applied to other, more complicated, kernels.
A Semi Analytical Solution for the Optimum Insulation Thickness Problem
International Nuclear Information System (INIS)
Abdullah, A.M.; Mina, A.R.
1995-01-01
The problem of optimizing the thickness of insulation installed on large hot vessels has been solved using a semi-analytical method. Unlike the previous studies, the derived mathematical expressions for the optimum thickness and total cost of burned fuel and insulating material has been formulated in a general form which facilitates their application to any fuel and insulation characteristics and life time of the system. Moreover, the system analysis took into consideration the normally expected annual increase in fuel price. Also an expression for the net saving in fuel cost-due to the installation of insulation has been derived. The results showed that the required optimum insulation thickness increases as the lifetime of a vessel and fuel price based on the results it is recommended to: (i) Estimate the virtual lifetime of a vessel to calculate the corresponding correct optimum thickness of insulation, (ii) Install an insulation which is thicker somewhat (say 10%) than the optimum one to compensate for both the expected annual increase in fuel price and the natural deterioration in the thermal and mechanical characteristics of the insulation material. 4 figs
An Analytical Solution for Cylindrical Concrete Tank on Deformable Soil
Directory of Open Access Journals (Sweden)
Shirish Vichare
2010-07-01
Full Text Available Cylindrical concrete tanks are commonly used in wastewater treatment plants. These are usually clarifier tanks. Design codes of practice provide methods to calculate design forces in the wall and raft of such tanks. These methods neglect self-weight of tank material and assume extreme, namely ‘fixed’ and ‘hinged’ conditions for the wall bottom. However, when founded on deformable soil, the actual condition at the wall bottom is neither fixed nor hinged. Further, the self-weight of the tank wall does affect the design forces. Thus, it is required to offer better insight of the combined effect of deformable soil and bottom raft stiffness on the design forces induced in such cylindrical concrete tanks. A systematic analytical method based on fundamental equations of shells is presented in this paper. Important observations on variation of design forces across the wall and the raft with different soil conditions are given. Set of commonly used tanks, are analysed using equations developed in the paper and are appended at the end.
Finite analytic numerical solution axisymmetric Navier-Stokes and energy equations
International Nuclear Information System (INIS)
Chen, C.; Yoon, Y.H.
1983-01-01
Convective heat transfer for steady-state laminar flow in axisymmetric coordinates is considered. Numerical solutions for flow pattern and temperature distribution are obtained by the finite analytic numerical method applied to the Navier-Stokes equations expressed in terms of vorticity and stream function, and the energy equation. The finite analytic numerical method differs from other numerical methods in that it utilizes a local analytic solution in an element of the problem to construct the total numerical solution. Finite analytic solutions of vorticity, stream function, temperature, and heat transfer coefficients for flow with Reynolds numbers of 5, 100, 1000, and 2000, and Prandtl numbers of 0.1, 1.0, and 10.0 with uniform grid sizes, are reported for an axisymmetric pipe with a sudden expansion and contraction. The wall temperature is considered to be isothermal and differs from the inlet temperature. It is shown that the finite analytic is stable converges rapidly, and simulates the convection of fluid flow accurately, since the local analytic solution is capable of simulating automatically the influence of skewed convection through the element boundary on the interior nodal values, thereby minimizing the false numerical diffusion
Analytical Lie-algebraic solution of a 3D sound propagation problem in the ocean
Energy Technology Data Exchange (ETDEWEB)
Petrov, P.S., E-mail: petrov@poi.dvo.ru [Il' ichev Pacific Oceanological Institute, 43 Baltiyskaya str., Vladivostok, 690041 (Russian Federation); Prants, S.V., E-mail: prants@poi.dvo.ru [Il' ichev Pacific Oceanological Institute, 43 Baltiyskaya str., Vladivostok, 690041 (Russian Federation); Petrova, T.N., E-mail: petrova.tn@dvfu.ru [Far Eastern Federal University, 8 Sukhanova str., 690950, Vladivostok (Russian Federation)
2017-06-21
The problem of sound propagation in a shallow sea with variable bottom slope is considered. The sound pressure field produced by a time-harmonic point source in such inhomogeneous 3D waveguide is expressed in the form of a modal expansion. The expansion coefficients are computed using the adiabatic mode parabolic equation theory. The mode parabolic equations are solved explicitly, and the analytical expressions for the modal coefficients are obtained using a Lie-algebraic technique. - Highlights: • A group-theoretical approach is applied to a problem of sound propagation in a shallow sea with variable bottom slope. • An analytical solution of this problem is obtained in the form of modal expansion with analytical expressions of the coefficients. • Our result is the only analytical solution of the 3D sound propagation problem with no translational invariance. • This solution can be used for the validation of the numerical propagation models.
New integrable models and analytical solutions in f (R ) cosmology with an ideal gas
Papagiannopoulos, G.; Basilakos, Spyros; Barrow, John D.; Paliathanasis, Andronikos
2018-01-01
In the context of f (R ) gravity with a spatially flat FLRW metric containing an ideal fluid, we use the method of invariant transformations to specify families of models which are integrable. We find three families of f (R ) theories for which new analytical solutions are given and closed-form solutions are provided.
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Lund, Erik; Thomsen, Ole Thybo
2010-01-01
In this work, an analytical method, which is referred to as Parameter-expansion Method is used to obtain the exact solution for the problem of nonlinear vibrations of an inextensible beam. It is shown that one term in the series expansion is sufficient to obtain a highly accurate solution, which...
Analytical solution for viscous incompressible Stokes flow in a spherical shell
Thieulot, Cedric
2017-01-01
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,
Manufactured analytical solutions for isothermal full-Stokes ice sheet models
Directory of Open Access Journals (Sweden)
A. Sargent
2010-08-01
Full Text Available We present the detailed construction of a manufactured analytical solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed.
The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions.
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.
Analytical Structuring of Periodic and Regular Cascading Solutions in Self-Pulsing Lasers
Directory of Open Access Journals (Sweden)
Belkacem Meziane
2008-01-01
Full Text Available A newly proposed strong harmonic-expansion method is applied to the laser-Lorenz equations to analytically construct a few typical solutions, including the first few expansions of the well-known period-doubling cascade that characterizes the system in its self-pulsing regime of operation. These solutions are shown to evolve in accordance with the driving frequency of the permanent solution that we recently reported to illustrate the system. The procedure amounts to analytically construct the signal Fourier transform by applying an iterative algorithm that reconstitutes the first few terms of its development.
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
Directory of Open Access Journals (Sweden)
Ilmārs Grants
2016-06-01
Full Text Available Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.
Analytical SN solutions in heterogeneous slabs using symbolic algebra computer programs
International Nuclear Information System (INIS)
Warsa, J.S.
2002-01-01
A modern symbolic algebra computer program, MAPLE, is used to compute solutions to the well-known analytical discrete ordinates, or S N , solutions in one-dimensional, slab geometry. Symbolic algebra programs compute the solutions with arbitrary precision and are free of spatial discretization error so they can be used to investigate new discretizations for one-dimensional slab, geometry S N methods. Pointwise scalar flux solutions are computed for several sample calculations of interest. Sample MAPLE command scripts are provided to illustrate how easily the theory can be translated into a working solution and serve as a complete tool capable of computing analytical S N solutions for mono-energetic, one-dimensional transport problems
Grants, Ilmārs; Bojarevičs, Andris; Gerbeth, Gunter
2016-06-01
Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.
Directory of Open Access Journals (Sweden)
Soheil Salahshour
2015-02-01
Full Text Available In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville or a solution with increasing length of their support (Hukuhara difference. Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.
Analytical solution for the simultaneous heat and mass transfer problem in air washers
Energy Technology Data Exchange (ETDEWEB)
Santos, J.C. [Department of Mechanical Production Engineering, Regional University of Cariri, Av. Leao Sampaio, S/N - Juazeiro do Norte, Ceara 63040-000 (Brazil); Medeiros, J.M. [Federal Institute of Education, Science and Technology of Pernambuco, Rodovia PE-60 km 14, Ipojuca, Pernambuco 55590-000 (Brazil); dos Santos, J.C.; Gurgel, J.M. [Department of Mechanical Engineering, Federal University of Paraiba, LES/UFPB - Cidade Universitaria, Joao Pessoa, Paraiba 58090-900 (Brazil); Marcondes, F. [Department of Metallurgical Engineering and Material Science, Federal University of Ceara, Campus do Pici, Bloco 714 Fortaleza, Ceara 60455-760 (Brazil)
2011-01-15
An analytical solution approach for the simultaneous heat and mass transfer problem in air washers operating as evaporative coolers is presented. A one-dimensional model using the coupled mass and energy balance equations in the air washer is presented. Then, starting from a linear approach for the experimental curve of the air saturation, an analytical solution for the model was derived. The solution showed an excellent agreement with the available results found in the literature. The influence of several important parameters for the cooling process such as temperature and ambient air humidity, air flow rate and feeding water temperature, in the air cooling rate was investigated. The efficacy of the process can be greatly increased by reducing the cooling water temperature and the applied air flow rate. The analytical solution can be easily included into the models used for simulating desiccant air-conditioning systems operating in conjunction with air washers. (author)
Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies
Mirels, Harold
1959-01-01
Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.
Analytical multi-soliton solutions of a (2+1)-dimensional breaking soliton equation.
Wang, Shao-Fu
2016-01-01
The analytical solutions for a (2+1)-dimensional breaking solution equation is proposed in this paper by using mapping and projective method darboux transformation, and Some exact propagating solutions are constructed for this Breaking equation, and the M × N multi-soliton could be obtained by using Weierstrassp function and setting the perfect parameters. The potential application of breaking Soliton equation will be of great interest in future research.
Analytical approximate solutions for a general class of nonlinear delay differential equations.
Căruntu, Bogdan; Bota, Constantin
2014-01-01
We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.
Analytic, High-beta Solutions of the Helical Grad-Shafranov Equation
International Nuclear Information System (INIS)
Smith, D.R.; Reiman, A.H.
2004-01-01
We present analytic, high-beta (β ∼ 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
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.
International Nuclear Information System (INIS)
Sathiyasheela, T.
2009-01-01
Point kinetics equations (P. K. E) are system of differential equations, which is solved simultaneously to get the neutron density as a function of time for a given reactivity input. P. K. E are stiff differential equations, computational solution through the conventional explicit method will give a stable consistent result only for smaller time steps. Analytical solutions are available either with step or ramp reactivity insertion without considering the source power contribution. When a reactor operates at low power, the neutron source gives a considerable contribution to the net reactor power. Similarly, when the reactor is brought to delayed critical with the presence of external source, the sub critical reactor kinetics studies with source power are important to understand the power behavior as a function of reactivity insertion rate with respect to the initial reactivity. In the present work, P.K.E with one group delayed neutron are solved analytically to determine the reactor power as a function of reactivity insertion rate in the presence of neutron source. The analytical solution is a combination of converging two infinite series. Truncated infinite series is the analytical solution of P.K E. A general formulation is made by Combining both the ramp reactivity and step reactivity solution. So that the analytical solution could be useful in analyzing either step and ramp reactivity insertion exclusively or the combination of both. This general formulation could be useful in analyzing many reactor operations, like the air bubble passing through the core, stuck rod conditions, uncontrolled withdrawal of controlled rod, discontinuous lifting of control rod, lowering of rod and etc. Results of analytical solutions are compared against the results of numerical solution which is developed based on Cohen's method. The comparisons are found to be good for all kind of positive and negative ramp reactivity insertions, with or without the combination of step reactivity
Kurylyk, Barret L.; Irvine, Dylan J.
2016-02-01
This study details the derivation and application of a new analytical solution to the one-dimensional, transient conduction-advection equation that is applied to trace vertical subsurface fluid fluxes. The solution employs a flexible initial condition that allows for nonlinear temperature-depth profiles, providing a key improvement over most previous solutions. The boundary condition is composed of any number of superimposed step changes in surface temperature, and thus it accommodates intermittent warming and cooling periods due to long-term changes in climate or land cover. The solution is verified using an established numerical model of coupled groundwater flow and heat transport. A new computer program FAST (Flexible Analytical Solution using Temperature) is also presented to facilitate the inversion of this analytical solution to estimate vertical groundwater flow. The program requires surface temperature history (which can be estimated from historic climate data), subsurface thermal properties, a present-day temperature-depth profile, and reasonable initial conditions. FAST is written in the Python computing language and can be run using a free graphical user interface. Herein, we demonstrate the utility of the analytical solution and FAST using measured subsurface temperature and climate data from the Sendia Plain, Japan. Results from these illustrative examples highlight the influence of the chosen initial and boundary conditions on estimated vertical flow rates.
Joekar-Niasar, V.
2013-01-25
Upscaling electroosmosis in porous media is a challenge due to the complexity and scale-dependent nonlinearities of this coupled phenomenon. "Pore-network modeling" for upscaling electroosmosis from pore scale to Darcy scale can be considered as a promising approach. However, this method requires analytical solutions for flow and transport at pore scale. This study concentrates on the development of analytical solutions of flow and transport in a single rectangular channel under combined effects of electrohydrodynamic forces. These relations will be used in future works for pore-network modeling. The analytical solutions are valid for all regimes of overlapping electrical double layers and have the potential to be extended to nonlinear Boltzmann distribution. The innovative aspects of this study are (a) contribution of overlapping of electrical double layers to the Stokes flow as well as Nernst-Planck transport has been carefully included in the analytical solutions. (b) All important transport mechanisms including advection, diffusion, and electromigration have been included in the analytical solutions. (c) Fully algebraic relations developed in this study can be easily employed to upscale electroosmosis to Darcy scale using pore-network modeling. © 2013 Springer Science+Business Media Dordrecht.
Directory of Open Access Journals (Sweden)
Jie Peng
Full Text Available The vacuum preloading is an effective method which is widely used in ground treatment. In consolidation analysis, the soil around prefabricated vertical drain (PVD is traditionally divided into smear zone and undisturbed zone, both with constant permeability. In reality, the permeability of soil changes continuously within the smear zone. In this study, the horizontal permeability coefficient of soil within the smear zone is described by an exponential function of radial distance. A solution for vacuum preloading consolidation considers the nonlinear distribution of horizontal permeability within the smear zone is presented and compared with previous analytical results as well as a numerical solution, the results show that the presented solution correlates well with the numerical solution, and is more precise than previous analytical solution.
ANALYTICAL SOLUTION OF BASIC SHIP HYDROSTATICS INTEGRALS USING POLYNOMIAL RADIAL BASIS FUNCTIONS
Dario Ban; Josip Bašić
2015-01-01
One of the main tasks of ship's computational geometry is calculation of basic integrals of ship's hydrostatics. In order to enable direct computation of those integrals it is necessary to describe geometry using analytical methods, like description using radial basis functions (RBF) with L1 norm. Moreover, using the composition of cubic and linear Polynomial radial basis functions, it is possible to give analytical solution of general global 2D description of ship geometry with discontinuiti...
Ali, Rustam; Saha, Asit; Chatterjee, Prasanta
2017-12-01
Analytical electron acoustic solitary wave (EASW) solution is investigated in the presence of periodic force for an unmagnetized plasma consisting of cold electron fluid, superthermal hot electrons, and stationary ions. Employing the reductive perturbation technique, the forced Korteg-de Vries (KdV) equation is derived for electron acoustic waves. For the first time, an analytical solution for EASWs is derived in the presence of periodic force. The effects of the ratio between hot electron and cold electron number densities at equilibrium (α), spectral index (κ), speed of the traveling wave (M), strength (f0), and frequency (ω) of the periodic force are studied on the analytical solution of EASWs. It is observed that the parameters α, κ, M, f0, and ω affect significantly the structures of the electron acoustic solitary waves. The results may have relevance in laboratory plasmas as well as in space plasma environments.
International Nuclear Information System (INIS)
Liu Hongzhun; Pan Zuliang; Li Peng
2006-01-01
In this article, we will derive an equality, where the Taylor series expansion around ε = 0 for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Baecklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Baecklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.
Analytic solution of magnetic induction distribution of ideal hollow spherical field sources
Xu, Xiaonong; Lu, Dingwei; Xu, Xibin; Yu, Yang; Gu, Min
2017-12-01
The Halbach type hollow spherical permanent magnet arrays (HSPMA) are volume compacted, energy efficient field sources, and capable of producing multi-Tesla field in the cavity of the array, which have attracted intense interests in many practical applications. Here, we present analytical solutions of magnetic induction to the ideal HSPMA in entire space, outside of array, within the cavity of array, and in the interior of the magnet. We obtain solutions using concept of magnetic charge to solve the Poisson's and Laplace's equations for the HSPMA. Using these analytical field expressions inside the material, a scalar demagnetization function is defined to approximately indicate the regions of magnetization reversal, partial demagnetization, and inverse magnetic saturation. The analytical field solution provides deeper insight into the nature of HSPMA and offer guidance in designing optimized one.
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....
Power Control at Grid Connected Converters and Analytical Solution of Steady States
Directory of Open Access Journals (Sweden)
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.
An analytical solution describing the shape of a yield stress material subjected to an overpressure
DEFF Research Database (Denmark)
Hovad, Emil; Spangenberg, Jon; Larsen, P.
2016-01-01
Many fluids and granular materials are able to withstand a limited shear stress without flowing. These materials are known as yields stress materials. Previously, an analytical solution was presented to quantify the yield stress for such materials. The yields stress is obtained based on the density...... as well as the spread length and height of the material when deformed in a box due to gravity. In the present work, the analytical solution is extended with the addition of an overpressure that acts over the entire body of the material. This extension enables finding the shape of a yield stress material...
Analytical solution of space charge limited current for spherical and cylindrical objects
International Nuclear Information System (INIS)
Oksuz, L.
2006-01-01
Analytical solutions for space charge limited currents in collisionless, electron-free sheaths are given for Cartesian, spherical, and cylindrical geometries. Constant current and current density are assumed. Until now, the problem of space charge limited current has not been solved either directly, in terms of series expansions, or numerically, for spherical and cylindrical objects. Analytical results show that the geometry of the system is important for determining the space charge limited current, sheath thickness, and sheath potential profile. This solution method can be used to solve similar nonlinear differential equations
Domains of analyticity for response solutions in strongly dissipative forced systems
International Nuclear Information System (INIS)
Corsi, Livia; Feola, Roberto; Gentile, Guido
2013-01-01
We study the ordinary differential equation εx ¨ +x . +εg(x)=εf(ωt), where g and f are real-analytic functions, with f quasi-periodic in t with frequency vector ω. If c 0 ∈R is such that g(c 0 ) equals the average of f and g′(c 0 ) ≠ 0, under very mild assumptions on ω there exists a quasi-periodic solution close to c 0 with frequency vector ω. We show that such a solution depends analytically on ε in a domain of the complex plane tangent more than quadratically to the imaginary axis at the origin
Analytical Solutions to Nonlinear Conservative Oscillator with Fifth-Order Nonlinearity
DEFF Research Database (Denmark)
Sfahania, M. G.; Ganji, S. S.; Barari, Amin
2010-01-01
are presented to obtain an approximate solution. The major concern is to assess the accuracy of these approximate methods in predicting the system response within a certain range of system parameters by examining their ability to establish an actual (numerical) solution. Therefore, the analytical results......This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach...
International Nuclear Information System (INIS)
Jing, Wu; Chun-Yan, Xiao
2010-01-01
The solutions to the electromagnetic field excited by a long axial current outside a conductive and magnetic cylindrical shell of finite length are studied in this paper. The more accurate analytical solutions are obtained by solving the proper boundary value problems by the separation variable method. Then the solutions are simplified according to asymptotic formulas of Bessel functions. Compared with the accurate solutions, the simplified solutions do not contain the Bessel functions and the inverse operation of the singular matrix, and can be calculated out fast by computers. The simplified solutions are more suitable for the cylindrical shell of high permeability and conductivity excited by a high frequency source. Both of the numerical results and the physical experimental results validate the simplified solutions obtained. (classical areas of phenomenology)
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.
International Nuclear Information System (INIS)
Baxter, Mathew; Van Gorder, Robert A
2013-01-01
We obtain solutions to a transformation of the axially symmetric Ernst equation, which governs a class of exact solutions of Einstein's field equations. Physically, the equation serves as a model of axially symmetric stationary vacuum gravitational fields. By an application of the method of homotopy analysis, we are able to construct approximate analytic solutions to the relevant boundary value problem in the case where exact solutions are not possible. The results presented constitute a solution for a complicated nonlinear and singular initial value problem. Through appropriate selection of the auxiliary linear operator and convergence control parameter, we are able to obtain low order approximations which minimize residual error over the problem domain. The benefit to such approach is that we obtain very accurate approximations after computing very few terms, hence the computational efficiency is high. Finally, an exact solution is provided in a special case, and this corresponds to the analytical solutions obtained in the more general case. The approximate solutions agree qualitatively with the exact solutions. (paper)
An Analytical Time Domain Solution for the Forced Vibration Analysis of Thick-Walled Cylinders
Directory of Open Access Journals (Sweden)
Bashir Movahedian
Full Text Available Abstract In this paper, we propose a time domain analytical solution for the forced vibration analysis of thick-walled hollow cylinders in presence of polar orthotropy. In this regard, solution of the governing equation is decomposed into two parts. The role of the first one is to satisfy boundary conditions utilizing the method of separation of variables besides of Fourier series expansion of the non-homogenous boundary conditions. The second part has been also expressed as the series of orthogonal characteristic functions with the aim of satisfaction of initial conditions. The proposed analytical solution has been implemented to evaluate the dynamic response of the cylinder in solution of some sample problems which are chosen from previous studies.
International Nuclear Information System (INIS)
Esmail, S.F.H.
2011-01-01
The mathematical formulation of numerous physical problems a results in differential equations actually partial or ordinary differential equations.In our study we are interested in solutions of partial differential equations.The aim of this work is to calculate the concentrations of the pollution, by solving the atmospheric diffusion equation(ADE) using different mathematical methods of solution. It is difficult to solve the general form of ADE analytically, so we use some assumptions to get its solution.The solutions of it depend on the eddy diffusivity profiles(k) and the wind speed u. We use some physical assumptions to simplify its formula and solve it. In the present work, we solve the ADE analytically in three dimensions using Green's function method, Laplace transform method, normal mode method and these separation of variables method. Also, we use ADM as a numerical method. Finally, comparisons are made with the results predicted by the previous methods and the observed data.
Analytical solution for a linearly graded-index-profile planar waveguide.
Touam, T; Yergeau, F
1993-01-20
An analytical solution is presented for the TE modes of a planar waveguide structure comprising a high-index guiding layer and a buried layer with a profile such that the square of the index varies linearly and matches the substrate and high-index guiding layer. The electric-field profiles and the dispersion relation are obtained and discussed, and a solution by the WKB method is compared.
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.
Liu, Albert Tianxiang; Zaveri, Rahul A.; Seinfeld, John H.
2014-01-01
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.
The Analytical Solution of the Transient Radial Diffusion Equation with a Nonuniform Loss Term.
Loridan, V.; Ripoll, J. F.; De Vuyst, F.
2017-12-01
Many works have been done during the past 40 years to perform the analytical solution of the radial diffusion equation that models the transport and loss of electrons in the magnetosphere, considering a diffusion coefficient proportional to a power law in shell and a constant loss term. Here, we propose an original analytical method to address this challenge with a nonuniform loss term. The strategy is to match any L-dependent electron losses with a piecewise constant function on M subintervals, i.e., dealing with a constant lifetime on each subinterval. Applying an eigenfunction expansion method, the eigenvalue problem becomes presently a Sturm-Liouville problem with M interfaces. Assuming the continuity of both the distribution function and its first spatial derivatives, we are able to deal with a well-posed problem and to find the full analytical solution. We further show an excellent agreement between both the analytical solutions and the solutions obtained directly from numerical simulations for different loss terms of various shapes and with a diffusion coefficient DLL L6. We also give two expressions for the required number of eigenmodes N to get an accurate snapshot of the analytical solution, highlighting that N is proportional to 1/√t0, where t0 is a time of interest, and that N increases with the diffusion power. Finally, the equilibrium time, defined as the time to nearly reach the steady solution, is estimated by a closed-form expression and discussed. Applications to Earth and also Jupiter and Saturn are discussed.
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
DEFF Research Database (Denmark)
Dinca, Andreea; Miclea, P. T.; Lupei, V.
1998-01-01
The paper describes the application of the complete-admittance matching in the design of two dichroic mirrors. The matching stacks were analytically synthesized and all solutions with 1, 2 and 3 periods were investigated in order to obtain a large transmission band and preserve the high reflectance...
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…
Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.
2018-04-01
We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.
Analytical Solution for 2D Inter-Well Porous Flow in a Rectangular Reservoir
Directory of Open Access Journals (Sweden)
Junfeng Ding
2018-04-01
Full Text Available Inter-well fluid flows through porous media are commonly encountered in the production of groundwater, oil, and geothermal energy. In this paper, inter-well porous flow inside a rectangular reservoir is solved based on the complex variable function theory combined with the method of mirror images. In order to derive the solution analytically, the inter-well flow is modeled as a 2D flow in a homogenous and isotropic porous medium. The resulted exact analytical solution takes the form of an infinite series, but it can be truncated to give high accuracy approximation. In terms of nine cases of inter-well porous flow associated with enhanced geothermal systems, the applications of the obtained analytical solution are demonstrated, and the convergence properties of the truncated series are investigated. It is shown that the convergent rate of the truncated series increases with the symmetric level of well distribution inside the reservoir, and the adoption of Euler transform significantly accelerates the convergence of alternating series cases associated with asymmetric well distribution. In principle, the analytical solution proposed in this paper can be applied to other scientific and engineering fields, as long as the involved problem is governed by 2D Laplace equation in a rectangular domain and subject to similar source/sink and boundary conditions, i.e., isolated point sources/sinks and uniform Dirichlet or homogeneous Neumann boundary conditions.
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...
Analytical and numerical solutions of the Schrödinger–KdV equation
Indian Academy of Sciences (India)
journal of. January 2012 physics pp. 59–90. Analytical and numerical solutions of the Schrödinger–KdV equation. MANEL LABIDI1, GHODRAT EBADI2, ESSAID ZERRAD3 and. ANJAN BISWAS4,∗. 1Laboratory of Engineering Mathematics, Tunisia Polytechnic School, University of Carthage,. BP 743, La Marsa 2070, ...
Analytical closed-form solution of three-phase four-switch PWM rectifier
Czech Academy of Sciences Publication Activity Database
Škramlík, Jiří; Valouch, Viktor; Klíma, J.; Pecha, I.
2010-01-01
Roč. 55, č. 3 (2010), s. 223-235 ISSN 0001-7043 R&D Projects: GA MPO FT-TA5/123 Institutional research plan: CEZ:AV0Z20570509 Keywords : four-switch PWM rectifier * space vector modulation * closed-form analytical solution Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering
Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method
Directory of Open Access Journals (Sweden)
De-Gang Wang
2012-01-01
Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.
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.
Revisiting the approximate analytical solution of fractional-order gas dynamics equation
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
Xiaonong Xu
2017-09-01
Full Text Available 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.
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.
Application of an analytical method for solution of thermal hydraulic conservation equations
Energy Technology Data Exchange (ETDEWEB)
Fakory, M.R. [Simulation, Systems & Services Technologies Company (S3 Technologies), Columbia, MD (United States)
1995-09-01
An analytical method has been developed and applied for solution of two-phase flow conservation equations. The test results for application of the model for simulation of BWR transients are presented and compared with the results obtained from application of the explicit method for integration of conservation equations. The test results show that with application of the analytical method for integration of conservation equations, the Courant limitation associated with explicit Euler method of integration was eliminated. The results obtained from application of the analytical method (with large time steps) agreed well with the results obtained from application of explicit method of integration (with time steps smaller than the size imposed by Courant limitation). The results demonstrate that application of the analytical approach significantly improves the numerical stability and computational efficiency.
Directory of Open Access Journals (Sweden)
S. Das
2013-12-01
Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.
Directory of Open Access Journals (Sweden)
Mohammad Mehdi Rashidi
2008-01-01
Full Text Available The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.
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.
Solution standards for quality control of nuclear-material analytical measurements
International Nuclear Information System (INIS)
Clark, J.P.
1981-01-01
Analytical chemistry measurement control depends upon reliable solution standards. At the Savannah River Plant Control Laboratory over a thousand analytical measurements are made daily for process control, product specification, accountability, and nuclear safety. Large quantities of solution standards are required for a measurement quality control program covering the many different analytical chemistry methods. Savannah River Plant produced uranium, plutonium, neptunium, and americium metals or oxides are dissolved to prepare stock solutions for working or Quality Control Standards (QCS). Because extensive analytical effort is required to characterize or confirm these solutions, they are prepared in large quantities. These stock solutions are diluted and blended with different chemicals and/or each other to synthesize QCS that match the matrices of different process streams. The target uncertainty of a standard's reference value is 10% of the limit of error of the methods used for routine measurements. Standard Reference Materials from NBS are used according to special procedures to calibrate the methods used in measuring the uranium and plutonium standards so traceability can be established. Special precautions are required to minimize the effects of temperature, radiolysis, and evaporation. Standard reference values are periodically corrected to eliminate systematic errors caused by evaporation or decay products. Measurement control is achieved by requiring analysts to analyze a blind QCS each shift a measurement system is used on plant samples. Computer evaluation determines whether or not a measurement is within the +- 3 sigma control limits. Monthly evaluations of the QCS measurements are made to determine current bias correction factors for accountability measurements and detect significant changes in the bias and precision statistics. The evaluations are also used to plan activities for improving the reliability of the analytical chemistry measurements
Tran, A. B.; Vu, M. N.; Nguyen, S. T.; Dong, T. Q.; Le-Nguyen, K.
2018-02-01
This paper presents analytical solutions to heat transfer problems around a crack and derive an adaptive model for effective thermal conductivity of cracked materials based on singular integral equation approach. Potential solution of heat diffusion through two-dimensional cracked media, where crack filled by air behaves as insulator to heat flow, is obtained in a singular integral equation form. It is demonstrated that the temperature field can be described as a function of temperature and rate of heat flow on the boundary and the temperature jump across the cracks. Numerical resolution of this boundary integral equation allows determining heat conduction and effective thermal conductivity of cracked media. Moreover, writing this boundary integral equation for an infinite medium embedding a single crack under a far-field condition allows deriving the closed-form solution of temperature discontinuity on the crack and particularly the closed-form solution of temperature field around the crack. These formulas are then used to establish analytical effective medium estimates. Finally, the comparison between the developed numerical and analytical solutions allows developing an adaptive model for effective thermal conductivity of cracked media. This model takes into account both the interaction between cracks and the percolation threshold.
An accurate analytical solution of a zero-dimensional greenhouse model for global warming
International Nuclear Information System (INIS)
Foong, S K
2006-01-01
In introducing the complex subject of global warming, books and papers usually use the zero-dimensional greenhouse model. When the ratio of the infrared radiation energy of the Earth's surface that is lost to outer space to the non-reflected average solar radiation energy is small, the model admits an accurate approximate analytical solution-the resulting energy balance equation of the model is a quartic equation that can be solved analytically-and thus provides an alternative solution and instructional strategy. A search through the literature fails to find an analytical solution, suggesting that the solution may be new. In this paper, we review the model, derive the approximation and obtain its solution. The dependence of the temperature of the surface of the Earth and the temperature of the atmosphere on seven parameters is made explicit. A simple and convenient formula for global warming (or cooling) in terms of the percentage change of the parameters is derived. The dependence of the surface temperature on the parameters is illustrated by several representative graphs
Jin, Congrui; Davoodabadi, Ali; Li, Jianlin; Wang, Yanli; Singler, Timothy
2017-03-01
Due to the development of novel micro-fabrication techniques to produce ultra-thin materials and increasing interest in thin biological membranes, in recent years, the mechanical characterization of thin films has received a significant amount of attention. To provide a more accurate solution for the relationship among contact radius, load and deflection, the fundamental and widely applicable problem of spherical indentation of a freestanding circular membrane have been revisited. The work presented here significantly extends the previous contributions by providing an exact analytical solution to the governing equations of Föppl-Hecky membrane indented by a frictionless spherical indenter. In this study, experiments of spherical indentation has been performed, and the exact analytical solution presented in this paper is compared against experimental data from existing literature as well as our own experimental results.
Baseline configuration for GNSS attitude determination with an analytical least-squares solution
International Nuclear Information System (INIS)
Chang, Guobin; Wang, Qianxin; Xu, Tianhe
2016-01-01
The GNSS attitude determination using carrier phase measurements with 4 antennas is studied on condition that the integer ambiguities have been resolved. The solution to the nonlinear least-squares is often obtained iteratively, however an analytical solution can exist for specific baseline configurations. The main aim of this work is to design this class of configurations. Both single and double difference measurements are treated which refer to the dedicated and non-dedicated receivers respectively. More realistic error models are employed in which the correlations between different measurements are given full consideration. The desired configurations are worked out. The configurations are rotation and scale equivariant and can be applied to both the dedicated and non-dedicated receivers. For these configurations, the analytical and optimal solution for the attitude is also given together with its error variance–covariance matrix. (paper)
Rasmuson, Anders
1984-10-01
An analytical solution is derived for the problem of radionuclide migration in fissured rock, where the rock blocks are modelled as spheres. The solution differs from a previous one mainly in the inlet boundary condition. In the present paper the case of constant source strength is treated instead of a decaying step release. The solution developed here is considerably more complex. Processes that are accounted for are advection and longitudinal dispersion in the fissures, external and internal diffusion into spherical rock blocks, sorption onto the fissure surfaces, and sorption within the matrix and radioactive decay. The solution is obtained in the form of an infinite single integral depending in general on six dimensionless parameters. The steady state solution includes five dimensionless quantities. A comparison with previously published results for a system of parallel fractures is made. It is shown that if the area-to-volume ratio of the slabs and the spherical rock blocks is the same, identical breakthrough curves are produced for short and long contact times. In the intermediate range the solution with spherical rock blocks will give earlier breakthrough and higher steady state concentrations. It is shown that the analytical solution for parallel fractures, previously given as an infinite double integral, may be derived as an infinite single integral. The numerical evaluation is thereby considerably simplified. Examples demonstrate the impact of hydrodynamic dispersion and water transport time on radionuclide transport in situations considered to be realistic repository conditions.
Analytical steady-state solutions for water-limited cropping systems using saline irrigation water
Skaggs, T. H.; Anderson, R. G.; Corwin, D. L.; Suarez, D. L.
2014-12-01
Due to the diminishing availability of good quality water for irrigation, it is increasingly important that irrigation and salinity management tools be able to target submaximal crop yields and support the use of marginal quality waters. In this work, we present a steady-state irrigated systems modeling framework that accounts for reduced plant water uptake due to root zone salinity. Two explicit, closed-form analytical solutions for the root zone solute concentration profile are obtained, corresponding to two alternative functional forms of the uptake reduction function. The solutions express a general relationship between irrigation water salinity, irrigation rate, crop salt tolerance, crop transpiration, and (using standard approximations) crop yield. Example applications are illustrated, including the calculation of irrigation requirements for obtaining targeted submaximal yields, and the generation of crop-water production functions for varying irrigation waters, irrigation rates, and crops. Model predictions are shown to be mostly consistent with existing models and available experimental data. Yet the new solutions possess advantages over available alternatives, including: (i) the solutions were derived from a complete physical-mathematical description of the system, rather than based on an ad hoc formulation; (ii) the analytical solutions are explicit and can be evaluated without iterative techniques; (iii) the solutions permit consideration of two common functional forms of salinity induced reductions in crop water uptake, rather than being tied to one particular representation; and (iv) the utilized modeling framework is compatible with leading transient-state numerical models.
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.
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 b...
On analytic solutions of (1+3)D relativistic ideal hydrodynamic equations
International Nuclear Information System (INIS)
Lin Shu; Liao Jinfeng
2010-01-01
In this paper, we find various analytic (1+3)D solutions to relativistic ideal hydrodynamic equations based on embedding of known low-dimensional scaling solutions. We first study a class of flows with 2D Hubble embedding, for which a single ordinary differential equation for the remaining velocity field can be derived. Using this equation, all solutions with transverse 2D Hubble embedding and power law ansatz for the remaining longitudinal velocity field will be found. Going beyond the power law ansatz, we further find a few solutions with transverse 2D Hubble embedding and nontrivial longitudinal velocity field. Finally we investigate general scaling flows with each component of the velocity fields scaling independently, for which we also find all possible solutions.
An Analytical Solution for Lateral Buckling Critical Load Calculation of Leaning-Type Arch Bridge
Directory of Open Access Journals (Sweden)
Ai-rong Liu
2014-01-01
Full Text Available An analytical solution for lateral buckling critical load of leaning-type arch bridge was presented in this paper. New tangential and radial buckling models of the transverse brace between the main and stable arch ribs are established. Based on the Ritz method, the analytical solution for lateral buckling critical load of the leaning-type arch bridge with different central angles of main arch ribs and leaning arch ribs under different boundary conditions is derived for the first time. Comparison between the analytical results and the FEM calculated results shows that the analytical solution presented in this paper is sufficiently accurate. The parametric analysis results show that the lateral buckling critical load of the arch bridge with fixed boundary conditions is about 1.14 to 1.16 times as large as that of the arch bridge with hinged boundary condition. The lateral buckling critical load increases by approximately 31.5% to 41.2% when stable arch ribs are added, and the critical load increases as the inclined angle of stable arch rib increases. The differences in the center angles of the main arch rib and the stable arch rib have little effect on the lateral buckling critical load.
ANALYTICAL SOLUTION OF BASIC SHIP HYDROSTATICS INTEGRALS USING POLYNOMIAL RADIAL BASIS FUNCTIONS
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Dario Ban
2015-09-01
Full Text Available One of the main tasks of ship's computational geometry is calculation of basic integrals of ship's hydrostatics. In order to enable direct computation of those integrals it is necessary to describe geometry using analytical methods, like description using radial basis functions (RBF with L1 norm. Moreover, using the composition of cubic and linear Polynomial radial basis functions, it is possible to give analytical solution of general global 2D description of ship geometry with discontinuities in the form of polynomials, thus enabling direct calculation of basic integrals of ship hydrostatics.
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 results obtained in this study are compared with the numerical results released in the literature. A close agreement of the two sets of results indicates the accuracy of the HAM. The method can obtain an expression that is acceptable for all values of effective parameters and is also able to control...
Fast semi-analytical solution of Maxwell's equations in Born approximation for periodic structures.
Pisarenco, Maxim; Quintanilha, Richard; van Kraaij, Mark G M M; Coene, Wim M J
2016-04-01
We propose a fast semi-analytical approach for solving Maxwell's equations in Born approximation based on the Fourier modal method (FMM). We show that, as a result of Born approximation, most matrices in the FMM algorithm become diagonal, thus allowing a reduction of computational complexity from cubic to linear. Moreover, due to the analytical representation of the solution in the vertical direction, the number of degrees of freedom in this direction is independent of the wavelength. The method is derived for planar illumination with two basic polarizations (TE/TM) and an arbitrary 2D geometry infinitely periodic in one horizontal direction.
Leij, Feike J; Bradford, Scott A
2009-11-20
The transport of solutes and colloids in porous media is influenced by a variety of physical and chemical nonequilibrium processes. A combined physical-chemical nonequilibrium (PCNE) model was therefore used to describe general mass transport. The model partitions the pore space into "mobile" and "immobile" flow regions with first-order mass transfer between these two regions (i.e, "physical" nonequilibrium or PNE). Partitioning between the aqueous and solid phases can either proceed as an equilibrium or a first-order process (i.e, "chemical" nonequilibrium or CNE) for both the mobile and immobile regions. An analytical solution for the PCNE model is obtained using iterated Laplace transforms. This solution complements earlier semi-analytical and numerical approaches to model solute transport with the PCNE model. The impact of selected model parameters on solute breakthrough curves is illustrated. As is well known, nonequilibrium results in earlier solute breakthrough with increased tailing. The PCNE model allows greater flexibility to describe this trend; for example, a closer resemblance between solute input and effluent pulse. Expressions for moments and transfer functions are presented to facilitate the analytical use of the PCNE model. Contours of mean breakthrough time, variance, and spread of the colloid breakthrough curves as a function of PNE and CNE parameters demonstrate the utility of a model that accounts for both physical and chemical nonequilibrium processes. The model is applied to describe representative colloid breakthrough curves in Ottawa sands reported by Bradford et al. (2002). An equilibrium model provided a good description of breakthrough curves for the bromide tracer but could not adequately describe the colloid data. A considerably better description was provide by the simple CNE model but the best description, especially for the larger 3.2-microm colloids, was provided by the PCNE model.
Semi-analytical solutions of groundwater flow in multi-zone (patchy) wedge-shaped aquifers
Samani, Nozar; Sedghi, Mohammad M.
2015-03-01
Alluvial fans are potential sites of potable groundwater in many parts of the world. Characteristics of alluvial fans sediments are changed radially from high energy coarse-grained deposition near the apex to low energy fine-grained deposition downstream so that patchy wedge-shaped aquifers with radial heterogeneity are formed. The hydraulic parameters of the aquifers (e.g. hydraulic conductivity and specific storage) change in the same fashion. Analytical or semi-analytical solutions of the flow in wedge-shaped aquifers are available for homogeneous cases. In this paper we derive semi-analytical solutions of groundwater flow to a well in multi-zone wedge-shaped aquifers. Solutions are provided for three wedge boundary configurations namely: constant head-constant head wedge, constant head-barrier wedge and barrier-barrier wedge. Derivation involves the use of integral transforms methods. The effect of heterogeneity ratios of zones on the response of the aquifer is examined. The results are presented in form of drawdown and drawdown derivative type curves. Heterogeneity has a significant effect on over all response of the pumped aquifer. Solutions help understanding the behavior of heterogeneous multi-zone aquifers for sustainable development of the groundwater resources in alluvial fans.
An Analytical Solution of Partially Penetrating Hydraulic Fractures in a Box-Shaped Reservoir
Directory of Open Access Journals (Sweden)
He Zhang
2015-01-01
Full Text Available This paper presents a new method to give an analytical solution in Laplace domain directly that is used to describe pressure transient behavior of partially penetrating hydraulic fractures in a box-shaped reservoir with closed boundaries. The basic building block of the method is to solve diffusivity equation with the integration of Dirac function over the distance that is presented for the first time. Different from the traditional method of using the source solution and Green’s function presented by Gringarten and Ramey, this paper uses Laplace transform and Fourier transform to solve the diffusivity equation and the analytical solution obtained is accurate and simple. The effects of parameters including fracture height, fracture length, the position of the fracture, and reservoir width on the pressure and pressure derivative are fully investigated. The advantage of the analytical solution is easy to incorporate storage coefficient and skin factor. It can also reduce the amount of computation and compute efficiently and quickly.
Effects of Unsaturated Zones on Baseflow Recession: Analytical Solution and Application
Zhan, H.; Liang, X.; Zhang, Y. K.
2017-12-01
Unsaturated flow is an important process in baseflow recessions and its effect is rarely investigated. A mathematical model for a coupled unsaturated-saturated flow in a horizontally unconfined aquifer with time-dependent infiltrations is presented. Semi-analytical solutions for hydraulic heads and discharges are derived using Laplace transform and Cosine transform. The solutions are compared with solutions of the linearized Boussinesq equation (LB solution) and the linearized Laplace equation (LL solution), respectively. The result indicates that a larger dimensionless constitutive exponent κD of the unsaturated zone leads to a smaller discharge during the infiltration period and a larger discharge after the infiltration. The lateral discharge of the unsaturated zone is significant when κD≤1, and becomes negligible when κD≥100. For late times, the power index b of the recession curve-dQ/dt aQb, is 1 and independent of κD, where Q is the baseflow and a is a constant lumped aquifer parameter. For early times, b is approximately equal to 3 but it approaches infinity when t→1. The present solution is applied to synthetic and field cases. The present solution matched the synthetic data better than both the LL and LB solutions, with a minimum relative error of 16% for estimate of hydraulic conductivity. The present solution was applied to the observed streamflow discharge in Iowa, and the estimated values of the aquifer parameters were reasonable.
Ferrás, L. L.; Afonso, A. M.; Alves, M. A.; Nóbrega, J. M.; Pinho, F. T.
2016-09-01
In this work, we present a series of solutions for combined electro-osmotic and pressure-driven flows of viscoelastic fluids in microchannels. The solutions are semi-analytical, a feature made possible by the use of the Debye-Hückel approximation for the electrokinetic fields, thus restricted to cases with small electric double-layers, in which the distance between the microfluidic device walls is at least one order of magnitude larger than the electric double-layer thickness. To describe the complex fluid rheology, several viscoelastic differential constitutive models were used, namely, the simplified Phan-Thien-Tanner model with linear, quadratic or exponential kernel for the stress coefficient function, the Johnson-Segalman model, and the Giesekus model. The results obtained illustrate the effects of the Weissenberg number, the Johnson-Segalman slip parameter, the Giesekus mobility parameter, and the relative strengths of the electro-osmotic and pressure gradient-driven forcings on the dynamics of these viscoelastic flows.
A Generic analytical solution for modelling pumping tests in wells intersecting fractures
Dewandel, Benoît; Lanini, Sandra; Lachassagne, Patrick; Maréchal, Jean-Christophe
2018-04-01
The behaviour of transient flow due to pumping in fractured rocks has been studied for at least the past 80 years. Analytical solutions were proposed for solving the issue of a well intersecting and pumping from one vertical, horizontal or inclined fracture in homogeneous aquifers, but their domain of application-even if covering various fracture geometries-was restricted to isotropic or anisotropic aquifers, whose potential boundaries had to be parallel or orthogonal to the fracture direction. The issue thus remains unsolved for many field cases. For example, a well intersecting and pumping a fracture in a multilayer or a dual-porosity aquifer, where intersected fractures are not necessarily parallel or orthogonal to aquifer boundaries, where several fractures with various orientations intersect the well, or the effect of pumping not only in fractures, but also in the aquifer through the screened interval of the well. Using a mathematical demonstration, we show that integrating the well-known Theis analytical solution (Theis, 1935) along the fracture axis is identical to the equally well-known analytical solution of Gringarten et al. (1974) for a uniform-flux fracture fully penetrating a homogeneous aquifer. This result implies that any existing line- or point-source solution can be used for implementing one or more discrete fractures that are intersected by the well. Several theoretical examples are presented and discussed: a single vertical fracture in a dual-porosity aquifer or in a multi-layer system (with a partially intersecting fracture); one and two inclined fractures in a leaky-aquifer system with pumping either only from the fracture(s), or also from the aquifer between fracture(s) in the screened interval of the well. For the cases with several pumping sources, analytical solutions of flowrate contribution from each individual source (fractures and well) are presented, and the drawdown behaviour according to the length of the pumped screened interval of
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...
International Nuclear Information System (INIS)
Totović, A R; Crnjanski, J V; Krstić, M M; Gvozdić, D M
2014-01-01
In this paper, we analyze two semiconductor optical amplifier (SOA) structures, traveling-wave and reflective, with the active region made of the bulk material. The model is based on the stationary traveling-wave equations for forward and backward propagating photon densities of the signal and the amplified spontaneous emission, along with the stationary carrier rate equation. We start by introducing linear approximation of the carrier density spatial distribution, which enables us to find solutions for the photon densities in a closed analytical form. An analytical approach ensures a low computational resource occupation and an easy analysis of the parameters influencing the SOA’s response. The comparison of the analytical and numerical results shows high agreement for a wide range of the input optical powers and bias currents. (paper)
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.
New Analytic Solution to the Lane-Emden Equation of Index 2
Directory of Open Access Journals (Sweden)
S. S. Motsa
2012-01-01
Full Text Available We present two new analytic methods that are used for solving initial value problems that model polytropic and stellar structures in astrophysics and mathematical physics. The applicability, effectiveness, and reliability of the methods are assessed on the Lane-Emden equation which is described by a second-order nonlinear differential equation. The results obtained in this work are also compared with numerical results of Horedt (1986 which are widely used as a benchmark for testing new methods of solution. Good agreement is observed between the present results and the numerical results. Comparison is also made between the proposed new methods and existing analytical methods and it is found that the new methods are more efficient and have several advantages over some of the existing analytical methods.
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...
Directory of Open Access Journals (Sweden)
Xiao-Chuan Li
2011-01-01
Full Text Available The transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain is derived to Hamiltonian system. In symplectic geometry space with the origin variables—displacements, electric potential, and magnetic potential, as well as their duality variables—lengthways stress, electric displacement, and magnetic induction, on the basis of the obtained eigensolutions of zero-eigenvalue, the eigensolutions of nonzero-eigenvalues are also obtained. The former are the basic solutions of Saint-Venant problem, and the latter are the solutions which have the local effect, decay drastically with respect to distance, and are covered in the Saint-Venant principle. So the complete solution of the problem is given out by the symplectic eigensolutions expansion. Finally, a few examples are selected and their analytical solutions are presented.
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.)
Pauritsch, Marcus; Birk, Steffen; Hergarten, Stefan; Kellerer-Pirklbauer, Andreas; Winkler, Gerfried
2014-05-01
Rock glaciers as aquifer systems in alpine catchments may strongly influence the hydrological characteristics of these catchments. Thus, they have a high impact on the ecosystem and potential natural hazards such as for example debris flow. Therefore, knowledge of the hydrodynamic processes, internal structure and properties of these aquifers is important for resource management and risk assessment. The investigation of such aquifers often turns out to be expensive and technically complicated because of their strongly limited accessibility. Analytical solutions of discharge recession provide a quick and easy way to estimate aquifer parameters. However, due to simplifying assumptions the validity of the interpretation is often questionable. In this study we compared results of an analytical solution of discharge recessions with results based on a numerical model. This was done in order to analyse the range of uncertainties and the applicability of the analytical method in alpine catchment areas. The research area is a 0.76 km² large catchment in the Seckauer Tauern Range, Austria. The dominant aquifer in this catchment is a rock glacier, namely the Schöneben Rock Glacier. This relict rock glacier (i.e. containing no permafrost at present) covers an area of 0.11 km² and is drained by one spring at the rock glacier front. The rock glacier consists predominantly of gneissic sediments (mainly coarse-grained, blocky at the surface) and extends from 1720 to 1905 m a.s.l.. Discharge of the rock glacier spring is automatically measured since 2002. Electric conductivity and water temperature is monitored since 2008. An automatic weather station was installed in 2011 in the central part of the catchment. Additionally data of geophysical surveys (refraction seismic and ground penetrating radar) have been used to analyse the base slope and inner structure of the rock glacier. The measured data are incorporated into a numerical model implemented in MODFLOW. The numerical
Analytical approximate solutions of the time-domain diffusion equation in layered slabs.
Martelli, Fabrizio; Sassaroli, Angelo; Yamada, Yukio; Zaccanti, Giovanni
2002-01-01
Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.
An analytical solution for the nonlinear energy spectrum equation by the decomposition method
Energy Technology Data Exchange (ETDEWEB)
Goulart, A [Universidade Federal do Pampa, Av. Tiaraju810, 97546-550 Alegrete, RS (Brazil); Vilhena, M T M B de; Bodmann, B E J [Universidade Federal do Rio Grande do Sul, Av. Osvaldo Aranha 99/4, 90460-900 Porto Alegre, RS (Brazil); Moreira, D [Universidade Federal do Pampa, Rua Carlos Barbosa S/N, 96412-420 Bage, RS (Brazil)], E-mail: bardo.bodmann@ufrgs.br
2008-10-24
We discuss the isotropic turbulence decay and solve the energy density spectrum (EDS) equation considering the inertial transfer energy and viscosity terms, using the Heisenberg parameterization. In the present approach, buoyant and shear terms are neglected and turbulence is assumed to be homogeneous and isotropic. The nonlinear integro-differential equation is solved by Adomian's generic decomposition method, which yields an analytical recursive expression and upon truncation gives an approximate solution. We show the resulting EDS and the time-dependent decay of the intensity of the turbulent kinetic energy. Our results prove consistent the Heisenberg parameterization for the transfer term of the inertial energy. The analytical character of the solution permits a validation of the nonlinear details of the physical model.
International Nuclear Information System (INIS)
Petersen, Claudio Z.; Vilhena, Marco Tullio; Bodmann, Bardo; Dulla, Sandra; Ravetto, Piero
2011-01-01
The three-dimensions multigroup neutron kinetics diffusion equations is considered to predict the behavior of neutrons in a nuclear reactor. In this work we develop a method that allows to construct an analytical solution to the equations of kinetic space. The spatial kinetic model has a crucial problem for a quasi real-time prediction of reactor power, especially at start-up, shut-down or change in power, by virtue of the stiff character of the equations. In order to circumvent problems that typically occur in numerical approaches, we solve the neutron kinetics diffusion equation in a homogeneous parallelepiped analytically, considering two energy groups and six group of delayed neutrons. Applying the GITT (generalized integral transform technique) in the vertical direction, we cast the original problem into a two-dimensional one with known solution. We report on numerical results, and comparisons against the ones of the literature. (author)
International Nuclear Information System (INIS)
Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.
2009-01-01
In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)
Analytical solution for viscous incompressible Stokes flow in a spherical shell
Directory of Open Access Journals (Sweden)
C. Thieulot
2017-11-01
Full Text Available 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.
A three-dimensional analytical solution for radioactive contaminant dispersion in the atmosphere
Energy Technology Data Exchange (ETDEWEB)
Costa, Camila P.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica (PROMEC)]. E-mails: vilhena@pq.cnpq.br; camila@mecanica.ufrgs.br; Moreira, Davidson M. [Universidade Federal de Pelotas (UFPEL), Bage, RS (Brazil). Centro de Ciencias Exatas e Tecnologicas]. E-mail: davidson@pq.cnpq.br; Tirabassi, Tiziano [Institute of Sciences Atmospherics and Climate (ISAC/CNR), Bologna (Italy)]. E-mail: t.tirabassi@isac.cnr.it
2007-07-01
In this work, we report an analytical solution for steady-state three-dimensional advection-diffusion equation for simulation of radioactive pollutant in atmosphere considering a vertically inhomogeneous Planetary Boundary Layer. The main idea relies in solution of the steady-state three-dimensional advection-diffusion equation by the combined ADMM and GILTT techniques. We also report numerical simulation assuming power wind profile and we compare with the ones achieved by the GILTT method with Gaussian in y-direction as well experimental data. (author)
Analytical solution for the mode conversion equations with steep exponential density profiles
International Nuclear Information System (INIS)
Alava, M.J.; Heikkinen, J.A.
1992-01-01
A general analytical solution for the converted power from the fast magnetosonic wave to an ion Bernstein wave in a magnetized plasma with an exponential steeply increasing density profile is given in the closed form. The solution covers both the conversion at the lower-hybrid resonance and the conversion through the density gradient for small parallel wave numbers. As an application, the conversion coefficients at the scrape-off layer plasma are estimated in the context of ion cyclotron heating of a tokamak plasma
International Nuclear Information System (INIS)
Lancaster, H.
1982-01-01
Although the SUPERFISH program is used for calculating the design parameters of an RFQ structure with complex vanes, an analytical solution for electrical properties of an RFQ with simple vanes provides insight into the parametric behavior of these more complicated resonators. The fields in an inclined plane wave guide with proper boundary conditions match those in one quadrant of an RFQ. The principle of duality is used to exploit the solutions to a radial transmission line in solving the field equations. Calculated are the frequency equation, frequency sensitivity factors, electric field, magnetic field, stored energy (U), power dissipation, and quality factor
Xie, Dexuan; Volkmer, Hans W.; Ying, Jinyong
2016-04-01
The nonlocal dielectric approach has led to new models and solvers for predicting electrostatics of proteins (or other biomolecules), but how to validate and compare them remains a challenge. To promote such a study, in this paper, two typical nonlocal dielectric models are revisited. Their analytical solutions are then found in the expressions of simple series for a dielectric sphere containing any number of point charges. As a special case, the analytical solution of the corresponding Poisson dielectric model is also derived in simple series, which significantly improves the well known Kirkwood's double series expansion. Furthermore, a convolution of one nonlocal dielectric solution with a commonly used nonlocal kernel function is obtained, along with the reaction parts of these local and nonlocal solutions. To turn these new series solutions into a valuable research tool, they are programed as a free fortran software package, which can input point charge data directly from a protein data bank file. Consequently, different validation tests can be quickly done on different proteins. Finally, a test example for a protein with 488 atomic charges is reported to demonstrate the differences between the local and nonlocal models as well as the importance of using the reaction parts to develop local and nonlocal dielectric solvers.
Gupta, Sumeet; Poulikakos, Dimos; Kurtcuoglu, Vartan
2008-09-01
We present here the analytical solution of transient, laminar, viscous flow of an incompressible, Newtonian fluid driven by a harmonically oscillating pressure gradient in a straight elliptic annulus. The analytical formulation is based on the exact solution of the governing fluid flow equations known as Navier-Stokes equations. We validate the analytical solution using a finite-volume computational fluid dynamics approach. As the analytical solution includes Mathieu and modified Mathieu functions, we also present a stepwise procedure for their evaluation for large complex arguments typically associated with viscous flows. We further outline the procedure for evaluating the associated Fourier coefficients and their eigenvalues. We finally apply the analytical solution to investigate the cerebrospinal fluid flow in the human spinal cavity, which features a shape similar to an elliptic annulus.
Hantush, Mohamed M.; Govindaraju, Rao S.
2003-08-01
Predicting the behavior of volatile organic compounds in soils or sediments is necessary for managing their use and designing appropriate remedial systems to eliminate potential threats to the environment, particularly the air and groundwater resources. In this effort, based on continuity of mass flux, we derive a mass flux boundary condition of the third type in terms of physically based mass transfer rate coefficients, describing the resistance to mass inflow of the soil-air interface, and obtain one-dimensional analytical solutions for transport and degradation of volatile organic compounds in semi-infinite structured soils under steady, unsaturated flow conditions. The advective-dispersive mass balance formulation allows for mobile-immobile liquid phase and vapor diffusive mass transfer, with linear equilibrium adsorption and liquid-vapor phase partitioning in the dynamic and stagnant soil regions. The mass transfer rate coefficients of volatile organic chemicals across the soil-air interface are expressed in terms of solute properties and hydrodynamic characteristics of resistive soil and air-boundary layers. The solutions estimate solute vapor flux from soil surface and describe mobile-phase solute concentration as a function of depth in the soil and time. In particular, solutions were derived for: (1) zero-initial concentration in the soil profile subject to a continuous and pulsed source at the soil surface; and (2) depletion from the soil following an initially contaminated soil profile. Sensitivity analysis with respect to different dimensionless parameters is conducted and the effect on solute concentration and vapor flux of such parameters as volatilization mass transfer velocity relative to infiltration, soil Peclet number, biochemical decay, and diffusive mass transfer into the immobile phase, is plotted and the results are discussed. The mass transfer rate coefficients and the analytical solutions are applied to simulate transport of an example
Analytical Solutions of Fractional Differential Equations Using the Convenient Adomian Series
Directory of Open Access Journals (Sweden)
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 predicting the transient seepage from a subsurface drainage system
Xin, Pei; Dan, Han-Cheng; Zhou, Tingzhang; Lu, Chunhui; Kong, Jun; Li, Ling
2016-05-01
Subsurface drainage systems have been widely used to deal with soil salinization and waterlogging problems around the world. In this paper, a mathematical model was introduced to quantify the transient behavior of the groundwater table and the seepage from a subsurface drainage system. Based on the assumption of a hydrostatic pressure distribution, the model considered the pore-water flow in both the phreatic and vadose soil zones. An approximate analytical solution for the model was derived to quantify the drainage of soils which were initially water-saturated. The analytical solution was validated against laboratory experiments and a 2-D Richards equation-based model, and found to predict well the transient water seepage from the subsurface drainage system. A saturated flow-based model was also tested and found to over-predict the time required for drainage and the total water seepage by nearly one order of magnitude, in comparison with the experimental results and the present analytical solution. During drainage, a vadose zone with a significant water storage capacity developed above the phreatic surface. A considerable amount of water still remained in the vadose zone at the steady state with the water table situated at the drain bottom. Sensitivity analyses demonstrated that effects of the vadose zone were intensified with an increased thickness of capillary fringe, capillary rise and/or burying depth of drains, in terms of the required drainage time and total water seepage. The analytical solution provides guidance for assessing the capillary effects on the effectiveness and efficiency of subsurface drainage systems for combating soil salinization and waterlogging problems.
Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.
2016-01-01
We consider the stationary sine-Gordon equation on metric graphs with simple topologies. The vertex boundary conditions are provided by flux conservation and matching of derivatives at the star graph vertex. Exact analytical solutions are obtained. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.
Kovář, Jiří; Slaný, Petr; Stuchlík, Zdeněk; Karas, Vladimír; Trova, Audrey
2017-12-01
We introduce a general transformation leading to an integral form of pressure equations characterizing equilibrium configurations of charged perfect fluid circling in strong gravitational and combined electromagnetic fields. The transformation generalizes our recent analytical treatment applicable to electric or magnetic fields treated separately along with the gravitational one. As an example, we present a particular solution for a fluid circling close to a charged rotating black hole immersed in an asymptotically uniform magnetic field.
Big data analytics as a service infrastructure: challenges, desired properties and solutions
International Nuclear Information System (INIS)
Martín-Márquez, Manuel
2015-01-01
CERN's accelerator complex generates a very large amount of data. A large volumen of heterogeneous data is constantly generated from control equipment and monitoring agents. These data must be stored and analysed. Over the decades, CERN's researching and engineering teams have applied different approaches, techniques and technologies for this purpose. This situation has minimised the necessary collaboration and, more relevantly, the cross data analytics over different domains. These two factors are essential to unlock hidden insights and correlations between the underlying processes, which enable better and more efficient daily-based accelerator operations and more informed decisions. The proposed Big Data Analytics as a Service Infrastructure aims to: (1) integrate the existing developments; (2) centralise and standardise the complex data analytics needs for CERN's research and engineering community; (3) deliver real-time, batch data analytics and information discovery capabilities; and (4) provide transparent access and Extract, Transform and Load (ETL), mechanisms to the various and mission-critical existing data repositories. This paper presents the desired objectives and properties resulting from the analysis of CERN's data analytics requirements; the main challenges: technological, collaborative and educational and; potential solutions. (paper)
Starn, J. J.
2013-12-01
Particle tracking often is used to generate particle-age distributions that are used as impulse-response functions in convolution. A typical application is to produce groundwater solute breakthrough curves (BTC) at endpoint receptors such as pumping wells or streams. The commonly used semi-analytical particle-tracking algorithm based on the assumption of linear velocity gradients between opposing cell faces is computationally very fast when used in combination with finite-difference models. However, large gradients near pumping wells in regional-scale groundwater-flow models often are not well represented because of cell-size limitations. This leads to inaccurate velocity fields, especially at weak sinks. Accurate analytical solutions for velocity near a pumping well are available, and various boundary conditions can be imposed using image-well theory. Python can be used to embed these solutions into existing semi-analytical particle-tracking codes, thereby maintaining the integrity and quality-assurance of the existing code. Python (and associated scientific computational packages NumPy, SciPy, and Matplotlib) is an effective tool because of its wide ranging capability. Python text processing allows complex and database-like manipulation of model input and output files, including binary and HDF5 files. High-level functions in the language include ODE solvers to solve first-order particle-location ODEs, Gaussian kernel density estimation to compute smooth particle-age distributions, and convolution. The highly vectorized nature of NumPy arrays and functions minimizes the need for computationally expensive loops. A modular Python code base has been developed to compute BTCs using embedded analytical solutions at pumping wells based on an existing well-documented finite-difference groundwater-flow simulation code (MODFLOW) and a semi-analytical particle-tracking code (MODPATH). The Python code base is tested by comparing BTCs with highly discretized synthetic steady
Analytical Solutions of the Gravitational Field Equations in de Sitter and Anti-de Sitter Spacetimes
Da Rocha, R.; Capelas Oliveira, E.
2009-01-01
The generalized Laplace partial differential equation, describing gravitational fields, is investigated in de Sitter spacetime from several metric approaches—such as the Riemann, Beltrami, Börner-Dürr, and Prasad metrics—and analytical solutions of the derived Riccati radial differential equations are explicitly obtained. All angular differential equations trivially have solutions given by the spherical harmonics and all radial differential equations can be written as Riccati ordinary differential equations, which analytical solutions involve hypergeometric and Bessel functions. In particular, the radial differential equations predict the behavior of the gravitational field in de Sitter and anti-de Sitter spacetimes, and can shed new light on the investigations of quasinormal modes of perturbations of electromagnetic and gravitational fields in black hole neighborhood. The discussion concerning the geometry of de Sitter and anti-de Sitter spacetimes is not complete without mentioning how the wave equation behaves on such a background. It will prove convenient to begin with a discussion of the Laplace equation on hyperbolic space, partly since this is of interest in itself and also because the wave equation can be investigated by means of an analytic continuation from the hyperbolic space. We also solve the Laplace equation associated to the Prasad metric. After introducing the so called internal and external spaces—corresponding to the symmetry groups SO(3,2) and SO(4,1) respectively—we show that both radial differential equations can be led to Riccati ordinary differential equations, which solutions are given in terms of associated Legendre functions. For the Prasad metric with the radius of the universe independent of the parametrization, the internal and external metrics are shown to be of AdS-Schwarzschild-like type, and also the radial field equations arising are shown to be equivalent to Riccati equations whose solutions can be written in terms of
Capacity of the circular plate condenser: analytical solutions for large gaps between the plates
International Nuclear Information System (INIS)
Rao, T V
2005-01-01
A solution of Love's integral equation (Love E R 1949 Q. J. Mech. Appl. Math. 2 428), which forms the basis for the analysis of the electrostatic field due to two equal circular co-axial parallel conducting plates, is considered for the case when the ratio, τ, of distance of separation to radius of the plates is greater than 2. The kernel of the integral equation is expanded into an infinite series in odd powers of 1/τ and an approximate kernel accurate to O(τ -(2N+1) ) is deduced therefrom by terminating the series after an arbitrary but finite number of terms, N. The approximate kernel is rearranged into a degenerate form and the integral equation with this kernel is reduced to a system of N linear equations. An explicit analytical solution is obtained for N = 4 and the resulting analytical expression for the capacity of the circular plate condenser is shown to be accurate to O(τ -9 ). Analytical expressions of lower orders of accuracy with respect to 1/τ are deduced from the four-term (i.e., N 4) solution and predictions (of capacity) from the expressions of different orders of accuracy (with respect to 1/τ) are compared with very accurate numerical solutions obtained by solving the linear system for large enough N. It is shown that the O(τ -9 ) approximation predicts the capacity extremely well for any τ ≥ 2 and an O(τ -3 ) approximation gives, for all practical purposes, results of adequate accuracy for τ ≥ 4. It is further shown that an approximate solution, applicable for the case of large distances of separation between the plates, due to Sneddon (Sneddon I N 1966 Mixed Boundary Value Problems in Potential Theory (Amsterdam: North-Holland) pp 230-46) is accurate to O(τ -6 ) for τ ≥ 2
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...
International Nuclear Information System (INIS)
Teixeira, Paulo Cleber Mendonca
2002-12-01
In this study, an analytical solution of the neutron transport equation in an annular reactor is presented with a short and rotating neutron source of the type S(x) δ (x- Vt), where V is the speed of annular pulsed reactor. The study is an extension of a previous study by Williams [12] carried out with a pulsed source of the type S(x) δ (t). In the new concept of annular pulsed reactor designed to produce continuous high flux, the core consists of a subcritical annular geometry pulsed by a rotating modulator, producing local super prompt critical condition, thereby giving origin to a rotating neutron pulse. An analytical solution is obtained by opening up of the annular geometry and applying one energy group transport theory in one dimension using applied mathematical techniques of Laplace transform and Complex Variables. The general solution for the flux consists of a fundamental mode, a finite number of harmonics and a transient integral. A condition which limits the number of harmonics depending upon the circumference of the annular geometry has been obtained. Inverse Laplace transform technique is used to analyse instability condition in annular reactor core. A regenerator parameter in conjunction with perimeter of the ring and nuclear properties is used to obtain stable and unstable harmonics and to verify if these exist. It is found that the solution does not present instability in the conditions stated in the new concept of annular pulsed reactor. (author)
A closed-form analytical solution for thermal single-well injection-withdrawal tests
Jung, Yoojin; Pruess, Karsten
2012-03-01
Thermal single-well injection-withdrawal (SWIW) tests entail pumping cold water into a hot and usually fractured reservoir, and monitoring the temperature recovery during subsequent backflow. Such tests have been proposed as a potential means to characterize properties of enhanced geothermal systems (EGS), such as fracture spacing, connectivity, and porosity. In this paper we develop an analytical solution for thermal SWIW tests, using an idealized model of a single vertical fracture with linear flow geometry embedded in impermeable conductive wall rocks. The analytical solution shows that the time dependence of temperature recovery is dominated by the heat exchange between fracture and matrix rock, but strong thermal diffusivities of rocks as compared to typical solute diffusivities are not necessarily advantageous for characterizing fracture-matrix interactions. The effect of fracture aperture on temperature recovery during backflow is weak, particularly when the fracture aperture is smaller than 0.1 cm. The solution also shows that temperature recovery during backflow is independent of the applied injection and backflow rates. This surprising result implies that temperature recovery is independent of the height of the fracture, or the specific fracture-matrix interface areas per unit fracture length, suggesting that thermal SWIW tests will not be able to characterize fracture growth that may be achieved by stimulation treatments.
Performance of the analytical solutions for Taylor dispersion process in open channel flow
Zeng, L.; Wu, Zi; Fu, Xudong; Wang, Guangqian
2015-09-01
The present paper provides a systematical analysis for concentration distribution of Taylor dispersion in laminar open channel flow, seeking fundamental understandings for the physical process of solute transport that generally applies to natural rivers. As a continuation and a direct numerical verification of the previous theoretical work (Wu, Z., Chen, G.Q., 2014. Journal of Hydrology, 519: 1974-1984.), in this paper we attempt to understand that to what extent the obtained analytical solutions are valid for the multi-dimensional concentration distribution, which is vital for the key conclusion of the so-called slow-decaying transient effect. It is shown that as a first estimation, even asymptotically, the longitudinal skewness of the concentration distribution should be incorporated to predict the vertical concentration correctly. Thus the traditional truncation of the concentration expansion is considered to be insufficient for the first estimation. The analytical solution by the two-scale perturbation analysis with modifications up to the second order is shown to be a most economical solution to give a reasonably good prediction.
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.
A new semi-analytical solution for inertial waves in a rectangular parallelepiped
Nurijanyan, S.; Bokhove, O.; Maas, L. R. M.
2013-12-01
A study of inertial gyroscopic waves in a rotating homogeneous fluid is undertaken both theoretically and numerically. A novel approach is presented to construct a semi-analytical solution of a linear three-dimensional fluid flow in a rotating rectangular parallelepiped bounded by solid walls. The three-dimensional solution is expanded in vertical modes to reduce the dynamics to the horizontal plane. On this horizontal plane, the two dimensional solution is constructed via superposition of "inertial" analogs of surface Poincaré and Kelvin waves reflecting from the walls. The infinite sum of inertial Poincaré waves has to cancel the normal flow of two inertial Kelvin waves near the boundaries. The wave system corresponding to every vertical mode results in an eigenvalue problem. Corresponding computations for rotationally modified surface gravity waves are in agreement with numerical values obtained by Taylor ["Tidal oscillations in gulfs and basins," Proc. London Math. Soc., Ser. 2 XX, 148-181 (1921)], Rao ["Free gravitational oscillations in rotating rectangular basins," J. Fluid Mech. 25, 523-555 (1966)] and also, for inertial waves, by Maas ["On the amphidromic structure of inertial waves in a rectangular parallelepiped," Fluid Dyn. Res. 33, 373-401 (2003)] upon truncation of an infinite matrix. The present approach enhances the currently available, structurally concise modal solution introduced by Maas. In contrast to Maas' approach, our solution does not have any convergence issues in the interior and does not suffer from Gibbs phenomenon at the boundaries. Additionally, an alternative finite element method is used to contrast these two semi-analytical solutions with a purely numerical one. The main differences are discussed for a particular example and one eigenfrequency.
Nischang, Ivo
2014-08-08
Porous monolithic poly(styrene-co-divinylbenzene) stationary phases in 4.6mm ID analytical format have been investigated with respect to their transport properties probed by solutes of biological origin varying vastly in size. Elucidation of several properties of these benchmark and robust materials gave complementary insight. These are: (i) the porous polymers' apparent dry-state microscopic appearance, (ii) the columns porosity probed by the biomolecules and modulated by mobile phase solvent composition, (iii) the impact of probe solute size on apparent retention at varying mobile phase solvent compositions, and (iv) the elution performance under both nonretained and retained elution conditions. By varying the volume percentage of acetonitrile in the mobile phase, it is demonstrated that the monolithic scaffold shows a variable porosity experienced in particular by the larger sized solutes, while the smaller solutes are gradually less affected. The nanoscale swelling and solvation of porous monolithic adsorbents resulting in gel porosity varied with mobile phase solvent composition was, therefore, indicated. The plate height curves for the solutes under nonretained conditions show a moderate increase at increased flow velocity while approaching plateau values. These plateau values were in conjunction with a trend of a decreased performance at an increased molecular weight of the solute. The systematic shape of the plate height curves at increased flow velocity indicates pre-asymptotic dispersion. This is because the column bed aspect ratio of length-to-diameter is equal or smaller than 10. Imposing retention on the solutes at a constant flow velocity deteriorates isocratic elution performance, more pronouncedly for the larger sized solutes at even weak retention. This is explained with slow pore fluid-gel interface diffusion. Additionally, the apparent retention factor for elution of the probe solutes becomes a function of flow rate, consequently a function of
Approximate analytical solution to the Boussinesq equation with a sloping water-land boundary
Tang, Yuehao; Jiang, Qinghui; Zhou, Chuangbing
2016-04-01
An approximate solution is presented to the 1-D Boussinesq equation (BEQ) characterizing transient groundwater flow in an unconfined aquifer subject to a constant water variation at the sloping water-land boundary. The flow equation is decomposed to a linearized BEQ and a head correction equation. The linearized BEQ is solved using a Laplace transform. By means of the frozen-coefficient technique and Gauss function method, the approximate solution for the head correction equation can be obtained, which is further simplified to a closed-form expression under the condition of local energy equilibrium. The solutions of the linearized and head correction equations are discussed from physical concepts. Especially for the head correction equation, the well posedness of the approximate solution obtained by the frozen-coefficient method is verified to demonstrate its boundedness, which can be further embodied as the upper and lower error bounds to the exact solution of the head correction by statistical analysis. The advantage of this approximate solution is in its simplicity while preserving the inherent nonlinearity of the physical phenomenon. Comparisons between the analytical and numerical solutions of the BEQ validate that the approximation method can achieve desirable precisions, even in the cases with strong nonlinearity. The proposed approximate solution is applied to various hydrological problems, in which the algebraic expressions that quantify the water flow processes are derived from its basic solutions. The results are useful for the quantification of stream-aquifer exchange flow rates, aquifer response due to the sudden reservoir release, bank storage and depletion, and front position and propagation speed.
Benchmarking the invariant embedding method against analytical solutions in model transport problems
International Nuclear Information System (INIS)
Malin, Wahlberg; Imre, Pazsit
2005-01-01
The purpose of this paper is to demonstrate the use of the invariant embedding method in a series of model transport problems, for which it is also possible to obtain an analytical solution. Due to the non-linear character of the embedding equations, their solution can only be obtained numerically. However, this can be done via a robust and effective iteration scheme. In return, the domain of applicability is far wider than the model problems investigated in this paper. The use of the invariant embedding method is demonstrated in three different areas. The first is the calculation of the energy spectrum of reflected (sputtered) particles from a multiplying medium, where the multiplication arises from recoil production. Both constant and energy dependent cross sections with a power law dependence were used in the calculations. The second application concerns the calculation of the path length distribution of reflected particles from a medium without multiplication. This is a relatively novel and unexpected application, since the embedding equations do not resolve the depth variable. The third application concerns the demonstration that solutions in an infinite medium and a half-space are interrelated through embedding-like integral equations, by the solution of which the reflected flux 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. (authors)
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.
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)
Analytical solutions of the two-dimensional Dirac equation for a topological channel intersection
Anglin, J. R.; Schulz, A.
2017-01-01
Numerical simulations in a tight-binding model have shown that an intersection of topologically protected one-dimensional chiral channels can function as a beam splitter for noninteracting fermions on a two-dimensional lattice [Qiao, Jung, and MacDonald, Nano Lett. 11, 3453 (2011), 10.1021/nl201941f; Qiao et al., Phys. Rev. Lett. 112, 206601 (2014), 10.1103/PhysRevLett.112.206601]. Here we confirm this result analytically in the corresponding continuum k .p model, by solving the associated two-dimensional Dirac equation, in the presence of a "checkerboard" potential that provides a right-angled intersection between two zero-line modes. The method by which we obtain our analytical solutions is systematic and potentially generalizable to similar problems involving intersections of one-dimensional systems.
An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem
International Nuclear Information System (INIS)
Milazzo, A; Orlando, C; Alaimo, A
2009-01-01
Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the definition of the bending moment. Moreover, the influences of the electro-mechanic, magneto-mechanic and electromagnetic coupling on the stiffness of the bimorph stem from the computation of the beam equivalent stiffness constants. Free and forced vibration analyses of both multiphase and laminated magneto-electro-elastic composite beams are carried out to check the effectiveness and reliability of the proposed analytic solution
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.
Exact Analytical Solutions in Three-Body Problems and Model of Neutrino Generator
Directory of Open Access Journals (Sweden)
Takibayev N.Zh.
2010-04-01
Full Text Available Exact analytic solutions are obtained in three-body problem for the scattering of light particle on the subsystem of two ﬁxed centers in the case when pair potentials have a separable form. Solutions show an appearance of new resonance states and dependence of resonance energy and width on distance between two ﬁxed centers. The approach of exact analytical solutions is expanded to the cases when two-body scattering amplitudes have the Breit-Wigner’s form and employed for description of neutron resonance scattering on subsystem of two heavy nuclei ﬁxed in nodes of crystalline lattice. It is shown that some resonance states have widths close to zero at the certain values of distance between two heavy scatterer centers, this gives the possibility of transitions between states. One of these transitions between three-body resonance states could be connected with process of electron capture by proton with formation of neutron and emission of neutrino. This exoenergic process leading to the cooling of star without nuclear reactions is discussed.
Tao, Wanghai; Wang, Quanjiu; Lin, Henry
2018-03-01
Soil and water loss from farmland causes land degradation and water pollution, thus continued efforts are needed to establish mathematical model for quantitative analysis of relevant processes and mechanisms. In this study, an approximate analytical solution has been developed for overland flow model and sediment transport model, offering a simple and effective means to predict overland flow and erosion under natural rainfall conditions. In the overland flow model, the flow regime was considered to be transitional with the value of parameter β (in the kinematic wave model) approximately two. The change rate of unit discharge with distance was assumed to be constant and equal to the runoff rate at the outlet of the plane. The excess rainfall was considered to be constant under uniform rainfall conditions. The overland flow model developed can be further applied to natural rainfall conditions by treating excess rainfall intensity as constant over a small time interval. For the sediment model, the recommended values of the runoff erosion calibration constant (cr) and the splash erosion calibration constant (cf) have been given in this study so that it is easier to use the model. These recommended values are 0.15 and 0.12, respectively. Comparisons with observed results were carried out to validate the proposed analytical solution. The results showed that the approximate analytical solution developed in this paper closely matches the observed data, thus providing an alternative method of predicting runoff generation and sediment yield, and offering a more convenient method of analyzing the quantitative relationships between variables. Furthermore, the model developed in this study can be used as a theoretical basis for developing runoff and erosion control methods.
Benchmarking the invariant embedding method against analytical solutions in model transport problems
Directory of Open Access Journals (Sweden)
Wahlberg Malin
2006-01-01
Full Text Available The purpose of this paper is to demonstrate the use of the invariant embedding method in a few model transport problems for which it is also possible to obtain an analytical solution. The use of the method is demonstrated in three different areas. The first is the calculation of the energy spectrum of sputtered particles from a scattering medium without absorption, where the multiplication (particle cascade is generated by recoil production. Both constant and energy dependent cross-sections with a power law dependence were treated. The second application concerns the calculation of the path length distribution of reflected particles from a medium without multiplication. This is a relatively novel application, since the embedding equations do not resolve the depth variable. The third application concerns the demonstration that solutions in an infinite medium and in a half-space are interrelated through embedding-like integral equations, by the solution of which the flux reflected from a half-space can be reconstructed from solutions in an infinite medium or vice versa. In all cases, the invariant embedding method proved to be robust, fast, and monotonically converging to the exact solutions.
Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential
Energy Technology Data Exchange (ETDEWEB)
Onate, C.A., E-mail: oaclems14@physicist.net [Physics Department, University of Benin (Nigeria); Onyeaju, M.C.; Ikot, A.N. [Theoretical Physics Group, Physics Department, University of Port Harcourt (Nigeria)
2016-12-15
The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.
International Nuclear Information System (INIS)
Saez, D.G.; Borroto, M.
1996-01-01
The paper presents the parameters for a semiempirical equation of an exponential-polynomial type for the description of the transmission data of the different qualities of the Co-60 radiation in finite means of concrete (2350 kg m -3 ) and lead. This equation and the expression obtained for the relationship of scatter-to-incident exposure, help in the development of a computerized analytical solution of the Simpkin's method for shielding calculations in Co-60 teletherapy rooms. The results were compared with the values offered in the NCRP-49 for the same conditions, obtaining an acceptable correlation. (authors). 8 refs., 2 tabs
Original analytic solution of a half-bridge modelled as a statically indeterminate system
Oanta, Emil M.; Panait, Cornel; Raicu, Alexandra; Barhalescu, Mihaela
2016-12-01
The paper presents an original computer based analytical model of a half-bridge belonging to a circular settling tank. The primary unknown is computed using the force method, the coefficients of the canonical equation being calculated using either the discretization of the bending moment diagram in trapezoids, or using the relations specific to the polygons. A second algorithm based on the method of initial parameters is also presented. Analyzing the new solution we came to the conclusion that most of the computer code developed for other model may be reused. The results are useful to evaluate the behavior of the structure and to compare with the results of the finite element models.
Analytical solutions for the fractional diffusion-advection equation describing super-diffusion
Directory of Open Access Journals (Sweden)
Gómez Francisco
2016-01-01
Full Text Available This paper presents the alternative construction of the diffusion-advection equation in the range (1; 2. The fractional derivative of the Liouville-Caputo type is applied. Analytical solutions are obtained in terms of Mittag-Leffler functions. In the range (1; 2 the concentration exhibits the superdiffusion phenomena and when the order of the derivative is equal to 2 ballistic diffusion can be observed, these behaviors occur in many physical systems such as semiconductors, quantum optics, or turbulent diffusion. This mathematical representation can be applied in the description of anomalous complex processes.
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.
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.
Analytical solutions for the magnetoelectric effect of multilayered magneto-electro-elastic media
International Nuclear Information System (INIS)
Wang Jianguo; Li Xuefeng
2008-01-01
The state vector equations of space axisymmetric problems for transversely isotropic magneto-electro-elastic media are established in terms of the governing equations of the problem. The method is based on the mixed formulation of the stresses, displacements, electric displacements and magnetic induction on the surface. Using the Hankel integral transform and the theory of ordinary differential equations, the state vector solutions for a single-layer magneto-electro-elastic media are presented in the Hankel transform space. Boussinesq's solution for the magneto-electro-elastic half-space problem is obtained in the Hankel integral form. A general analytical formulation for the transversely isotropic, multilayered magneto-electro-elastic axisymmetric problems is presented by using the transfer matrix method. Numerical results are given. We have observed that the stacking sequences have a clear influence on most physical quantities. These features should be of special interest in the design of magneto-electro-elastic composite structures
Data collapse, scaling functions, and analytical solutions of generalized growth models.
Cabella, Brenno Caetano Troca; Martinez, Alexandre Souto; Ribeiro, Fabiano
2011-06-01
We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.
Analytical solution of laminar-laminar stratified two-phase flows with curved interfaces
Energy Technology Data Exchange (ETDEWEB)
Brauner, N.; Rovinsky, J.; Maron, D.M. [Tel-Aviv Univ. (Israel)
1995-09-01
The present study represents a complete analytical solution for laminar two-phase flows with curved interfaces. The solution of the Navier-Stokes equations for the two-phases in bipolar coordinates provides the `flow monograms` describe the relation between the interface curvature and the insitu flow geometry when given the phases flow rates and viscosity ratios. Energy considerations are employed to construct the `interface monograms`, whereby the characteristic interfacial curvature is determined in terms of the phases insitu holdup, pipe diameter, surface tension, fluids/wall adhesion and gravitation. The two monograms are then combined to construct the system `operational monogram`. The `operational monogram` enables the determination of the interface configuration, the local flow characteristics, such as velocity profiles, wall and interfacial shear stresses distribution as well as the integral characteristics of the two-phase flow: phases insitu holdup and pressure drop.
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 solution of laminar-laminar stratified two-phase flows with curved interfaces
International Nuclear Information System (INIS)
Brauner, N.; Rovinsky, J.; Maron, D.M.
1995-01-01
The present study represents a complete analytical solution for laminar two-phase flows with curved interfaces. The solution of the Navier-Stokes equations for the two-phases in bipolar coordinates provides the 'flow monograms' describe the relation between the interface curvature and the insitu flow geometry when given the phases flow rates and viscosity ratios. Energy considerations are employed to construct the 'interface monograms', whereby the characteristic interfacial curvature is determined in terms of the phases insitu holdup, pipe diameter, surface tension, fluids/wall adhesion and gravitation. The two monograms are then combined to construct the system 'operational monogram'. The 'operational monogram' enables the determination of the interface configuration, the local flow characteristics, such as velocity profiles, wall and interfacial shear stresses distribution as well as the integral characteristics of the two-phase flow: phases insitu holdup and pressure drop
Analytical general solutions for static wormholes in f ( R , T ) gravity
Energy Technology Data Exchange (ETDEWEB)
Moraes, P.H.R.S.; Correa, R.A.C.; Lobato, R.V., E-mail: moraes.phrs@gmail.com, E-mail: fis04132@gmail.com, E-mail: ronaldo.lobato@icranet.org [ITA-Instituto Tecnológico de Aeronáutica, 12228-900, São José dos Campos, SP (Brazil)
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.
International Nuclear Information System (INIS)
Ceolin, Celina; Vilhena, Marco T.; Bodmann, Bardo E.J.; Alvim, Antonio Carlos Marques
2011-01-01
The authors solved analytically the neutron kinetic equations in a homogeneous slab, assuming the multi group energy model and six delayed neutron precursor groups by the Generalized Integral Laplace Transform Technique (GILTT) for a multi-layered slab. To this end, averaged values for the nuclear parameters in the multi-layered slab are used and the solution is constructed following the idea of Adomian's decomposition method upon reducing the heterogeneous problem to a set of recursive problems with constant parameters in the multi-layered slab. More specifically, the corrections that render the initially homogeneous problem into a heterogeneous one are plugged into the equation as successive source terms. To the best of our knowledge this sort of solution is novel and not found in literature. We further present some numerical simulations. (author)
Penkov, V. B.; Levina, L. V.; Novikova, O. S.; Shulmin, A. S.
2018-03-01
Herein we propose a methodology for structuring a full parametric analytical solution to problems featuring elastostatic media based on state-of-the-art computing facilities that support computerized algebra. The methodology includes: direct and reverse application of P-Theorem; methods of accounting for physical properties of media; accounting for variable geometrical parameters of bodies, parameters of boundary states, independent parameters of volume forces, and remote stress factors. An efficient tool to address the task is the sustainable method of boundary states originally designed for the purposes of computerized algebra and based on the isomorphism of Hilbertian spaces of internal states and boundary states of bodies. We performed full parametric solutions of basic problems featuring a ball with a nonconcentric spherical cavity, a ball with a near-surface flaw, and an unlimited medium with two spherical cavities.
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.
International Nuclear Information System (INIS)
Abourabia, A.M.; Hassan, K.M.; Selima, E.S.
2010-01-01
We consider the solutions of the compound Korteweg-de Vries (KdV)-Burgers equation with variable coefficients (vccKdV-B) that describe the propagation of undulant bores in shallow water with certain dissipative effects. The Weiss-Tabor-Carnevale (WTC)-Kruskal algorithm is applied to study the integrability of the vccKdV-B equation. We found that the vccKdV-B equation is not Painleve integrable unless the variable coefficients satisfy certain constraints. We used the outcome of the truncated Painleve expansion to construct the Backlund transformation, and three families of new analytical solutions for the vccKdV-B equation are obtained. The dispersion relation and its characteristics are illustrated. The stability for the vccKdV-B equation is analyzed by using the phase portrait method. (author)
Energy Technology Data Exchange (ETDEWEB)
Abourabia, A.M.; Hassan, K.M.; Selima, E.S., E-mail: am_abourabia@yahoo.com [Menoufiya Univ., Faculty of Science, Dept. of Mathematics, Shebin El-koom (Egypt)
2010-03-15
We consider the solutions of the compound Korteweg-de Vries (KdV)-Burgers equation with variable coefficients (vccKdV-B) that describe the propagation of undulant bores in shallow water with certain dissipative effects. The Weiss-Tabor-Carnevale (WTC)-Kruskal algorithm is applied to study the integrability of the vccKdV-B equation. We found that the vccKdV-B equation is not Painleve integrable unless the variable coefficients satisfy certain constraints. We used the outcome of the truncated Painleve expansion to construct the Backlund transformation, and three families of new analytical solutions for the vccKdV-B equation are obtained. The dispersion relation and its characteristics are illustrated. The stability for the vccKdV-B equation is analyzed by using the phase portrait method. (author)
Three-dimensional transport theory: An analytical solution of an internal beam searchlight problem-I
International Nuclear Information System (INIS)
Williams, M.M.R.
2009-01-01
We describe a number of methods for obtaining analytical solutions and numerical results for three-dimensional one-speed neutron transport problems in a half-space containing a variety of source shapes which emit neutrons mono-directionally. For example, we consider an off-centre point source, a ring source and a disk source, or any combination of these, and calculate the surface scalar flux as a function of the radial and angular co-ordinates. Fourier transforms in the transverse directions are used and a Laplace transform in the axial direction. This enables the Wiener-Hopf method to be employed, followed by an inverse Fourier-Hankel transform. Some additional transformations are introduced which enable the inverse Hankel transforms involving Bessel functions to be evaluated numerically more efficiently. A hybrid diffusion theory method is also described which is shown to be a useful guide to the general behaviour of the solutions of the transport equation.
Directory of Open Access Journals (Sweden)
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.
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.
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.
Gazzillo, Domenico; Munaò, Gianmarco; Prestipino, Santi
2016-06-21
We study a pure fluid of heteronuclear sticky Janus dumbbells, considered to be the result of complete chemical association between unlike species in an initially equimolar mixture of hard spheres (species A) and sticky hard spheres (species B) with different diameters. The B spheres are particles whose attractive surface layer is infinitely thin. Wertheim's two-density integral equations are employed to describe the mixture of AB dumbbells together with unbound A and B monomers. After Baxter factorization, these equations are solved analytically within the associative Percus-Yevick approximation. The limit of complete association is taken at the end. The present paper extends to the more general, heteronuclear case of A and B species with size asymmetry a previous study by Wu and Chiew [J. Chem. Phys. 115, 6641 (2001)], which was restricted to dumbbells with equal monomer diameters. Furthermore, the solution for the Baxter factor correlation functions qij (αβ)(r) is determined here in a fully analytic way, since we have been able to find explicit analytic expressions for all the intervening parameters.
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.
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 solutions to non-Fickian subsurface dispersion in uniform groundwater flow
Zou, S.; Xia, J.; Koussis, Antonis D.
1996-01-01
Analytical solutions are obtained by the Fourier transform technique for the one-, two-, and three-dimensional transport of a conservative solute injected instantaneously in a uniform groundwater flow. These solutions account for dispersive non-linearity caused by the heterogeneity of the hydraulic properties of aquifer systems and can be used as building blocks to construct solutions by convolution (principle of superposition) for source conditions other than slug injection. The dispersivity is assumed to vary parabolically with time and is thus constant for the entire system at any given time. Two approaches for estimating time-dependent dispersion parameters are developed for two-dimensional plumes. They both require minimal field tracer test data and, therefore, represent useful tools for assessing real-world aquifer contamination sites. The first approach requires mapped plume-area measurements at two specific times after the tracer injection. The second approach requires concentration-versus-time data from two sampling wells through which the plume passes. Detailed examples and comparisons with other procedures show that the methods presented herein are sufficiently accurate and easier to use than other available methods.
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.
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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.
An analytical solution to assess the SH seismoelectric response of the vadose zone
Monachesi, L. B.; Zyserman, F. I.; Jouniaux, L.
2018-03-01
We derive an analytical solution of the seismoelectric conversions generated in the vadose zone, when this region is crossed by a pure shear horizontal (SH) wave. Seismoelectric conversions are induced by electrokinetic effects linked to relative motions between fluid and porous media. The considered model assumes a one-dimensional soil constituted by a single layer on top of a half space in contact at the water table, and a shearing force located at the earth's surface as the wave source. The water table is an interface expected to induce a seismoelectric interfacial response (IR). The top layer represents a porous rock which porous space is partially saturated by water and air, while the half-space is completely saturated with water, representing the saturated zone. The analytical expressions for the coseismic fields and the interface responses, both electric and magnetic, are derived by solving Pride's equations with proper boundary conditions. An approximate analytical expression of the solution is also obtained, which is very simple and applicable in a fairly broad set of situations. Hypothetical scenarios are proposed to study and analyse the dependence of the electromagnetic fields on various parameters of the medium. An analysis of the approximate solution is also made together with a comparison to the exact solution. The main result of the present analysis is that the amplitude of the interface response generated at the water table is found to be proportional to the jump in the electric current density, which in turn depends on the saturation contrast, poro-mechanical and electrical properties of the medium and on the amplitude of the solid displacement produced by the source. This result is in agreement with the one numerically obtained by the authors, which has been published in a recent work. We also predict the existence of an interface response located at the surface, and that the electric interface response is several orders of magnitude bigger than
In-core LOCA-s: analytical solution for the delayed mixing model for moderator poison concentration
International Nuclear Information System (INIS)
Firla, A.P.
1995-01-01
Solutions to dynamic moderator poison concentration model with delayed mixing under single pressure tube / calandria tube rupture scenario are discussed. Such a model is described by a delay differential equation, and for such equations the standard ways of solution are not directly applicable. In the paper an exact, direct time-domain analytical solution to the delayed mixing model is presented and discussed. The obtained solution has a 'marching' form and is easy to calculate numerically. Results of the numerical calculations based on the analytical solution indicate that for the expected range of mixing times the existing uniform mixing model is a good representation of the moderator poison mixing process for single PT/CT breaks. However, for postulated multi-pipe breaks ( which is very unlikely to occur ) the uniform mixing model is not adequate any more; at the same time an 'approximate' solution based on Laplace transform significantly overpredicts the rate of poison concentration decrease, resulting in excessive increase in the moderator dilution factor. In this situation the true, analytical solution must be used. The analytical solution presented in the paper may also serve as a bench-mark test for the accuracy of the existing poison mixing models. Moreover, because of the existing oscillatory tendency of the solution, special care must be taken in using delay differential models in other applications. (author). 3 refs., 3 tabs., 8 figs
Energy Technology Data Exchange (ETDEWEB)
Peralta, J.; López-Valverde, M. A. [Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Imamura, T. [Institute of Space and Astronautical Science-Japan Aerospace Exploration Agency 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan); Read, P. L. [Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford (United Kingdom); Luz, D. [Centro de Astronomia e Astrofísica da Universidade de Lisboa (CAAUL), Observatório Astronómico de Lisboa, Tapada da Ajuda, 1349-018 Lisboa (Portugal); Piccialli, A., E-mail: peralta@iaa.es [LATMOS, UVSQ, 11 bd dAlembert, 78280 Guyancourt (France)
2014-07-01
This paper is the second in a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases where the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere.
General analytical solutions for DC/AC circuit-network analysis
Rubido, Nicolás; Grebogi, Celso; Baptista, Murilo S.
2017-06-01
In this work, we present novel general analytical solutions for the currents that are developed in the edges of network-like circuits when some nodes of the network act as sources/sinks of DC or AC current. We assume that Ohm's law is valid at every edge and that charge at every node is conserved (with the exception of the source/sink nodes). The resistive, capacitive, and/or inductive properties of the lines in the circuit define a complex network structure with given impedances for each edge. Our solution for the currents at each edge is derived in terms of the eigenvalues and eigenvectors of the Laplacian matrix of the network defined from the impedances. This derivation also allows us to compute the equivalent impedance between any two nodes of the circuit and relate it to currents in a closed circuit which has a single voltage generator instead of many input/output source/sink nodes. This simplifies the treatment that could be done via Thévenin's theorem. Contrary to solving Kirchhoff's equations, our derivation allows to easily calculate the redistribution of currents that occurs when the location of sources and sinks changes within the network. Finally, we show that our solutions are identical to the ones found from Circuit Theory nodal analysis.
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Xiao-Li Ding
2018-01-01
Full Text Available In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results.
International Nuclear Information System (INIS)
Oliveira, Fernando Luiz de
2008-01-01
This work describes an analytical solution obtained by the expansion method for the spatial kinetics using the diffusion model with delayed emission for source transients in homogeneous media. In particular, starting from simple models, and increasing the complexity, numerical results were obtained for different types of source transients. An analytical solution of the one group without precursors was solved, followed by considering one precursors family. The general case of G-groups with R families of precursor although having a closed form solution, cannot be solved analytically, since there are no explicit formulae for the eigenvalues, and numerical methods must be used to solve such problem. To illustrate the general solution, the multi-group (three groups) time-dependent problem without precursors was solved and the numerical results of a finite difference code were compared with the exact results for different transients. (author)
Energy Technology Data Exchange (ETDEWEB)
Palma, Daniel A.P. [CEFET QUIMICA de Nilopolis/RJ, 21941-914 Rio de Janeiro (Brazil)], E-mail: agoncalves@con.ufrj.br; Martinez, Aquilino S.; Goncalves, Alessandro C. [COPPE/UFRJ - Programa de Engenharia Nuclear, Rio de Janeiro (Brazil)
2009-09-15
The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Martinez, Aquilino S.; Goncalves, Alessandro C.
2009-01-01
The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.
DEFF Research Database (Denmark)
Pedersen, Thomas Quistgaard
In this paper we derive an approximate analytical solution to the optimal con- sumption and portfolio choice problem of an infinitely-lived investor with power utility defined over the difference between consumption and an external habit. The investor is assumed to have access to two tradable......, and introduces an additional component that works as a hedge against changes in the investor's habit level. In an empirical application, we calibrate the model to U.S. data and show that habit formation has significant effects on both the optimal consumption and portfolio choice compared to a standard CRRA...... assets: a risk free asset with constant return and a risky asset with a time-varying premium. We extend the ap- proach proposed by Campbell and Viceira (1999), which builds on log-linearizations of the Euler equation, intertemporal budget constraint, and portfolio return, to also contain the log...
Analytic solutions to a family of boundary-value problems for Ginsburg-Landau type equations
Vassilev, V. M.; Dantchev, D. M.; Djondjorov, P. A.
2017-10-01
We consider a two-parameter family of nonlinear ordinary differential equations describing the behavior of a critical thermodynamic system, e.g., a binary liquid mixture, of film geometry within the framework of the Ginzburg-Landau theory by means of the order-parameter. We focus on the case in which the confining surfaces are strongly adsorbing but prefer different components of the mixture, i.e., the order-parameter tends to infinity at one of the boundaries and to minus infinity at the other one. We assume that the boundaries of the system are positioned at a finite distance from each other and give analytic solutions to the corresponding boundary-value problems in terms of Weierstrass and Jacobi elliptic functions.
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.
THE ELUDATION OF A CRITIC ON THE CORE-PERIPHERY MODEL - THE ANALYTIC SOLUTION –
Directory of Open Access Journals (Sweden)
Viorica PUSCACIU
2005-01-01
Full Text Available One of the major critiques of Paul Krugman’s standard core-periphery model (1991, which modelforms the bottom of so called ‘The New Economic Geography’, is the impossibility of his analyticsolution, reason for which difficult digital simulations are enforced. Getting a function and ananalytic solution enables a better description of the process of agglomeration and at the same time,the presentation of the authors, with title of novelty, of graphics on the logarithmic scale, whichaligns as a complementary form to the traditional ones. The adaptation and the presentation of themodel with a software help, as Maple computer program, permits also the complete understanding ofthe solvable analytic model.
An analytic solution to the critical problem of neutron transport in plane geometry
International Nuclear Information System (INIS)
Coppa, G.; Ravetto, P.; Sumini, M.
1987-01-01
The linear transport equation in slab geometry is given an analytic solution by means of a series expansion of the unknown, using Helmholtz eigenfunctions, and suitably introducing a space independent term which can account for vacuum boundary conditions. A second-order form of the transport equation is taken into consideration. Only materially homogeneous systems showing isotropic scattering properties are investigated and the absence of external sources is supposed. An exact infinite system of equations for the coefficients of the expansion is derived. The truncation of the series leads to approximations, some numerical results of which are presented. The total neutron current and its relationship to the total flux, together with the presence of a zero-gradient current, will also be discussed. (orig.) [de
Decoupling the NLO coupled DGLAP evolution equations: an analytic solution to pQCD
International Nuclear Information System (INIS)
Block, Martin M.; Durand, Loyal; Ha, Phuoc; McKay, Douglas W.
2010-01-01
Using repeated Laplace transforms, we turn coupled, integral-differential singlet DGLAP equations into NLO (next-to-leading) coupled algebraic equations, which we then decouple. After two Laplace inversions we find new tools for pQCD: decoupled NLO analytic solutions F s (x,Q 2 )=F s (F s0 (x),G 0 (x)), G(x,Q 2 )=G(F s0 (x), G 0 (x)). F s , G are known NLO functions and F s0 (x)≡F s (x,Q 0 2 ), G 0 (x)≡G(x,Q 0 2 ) are starting functions for evolution beginning at Q 2 =Q 0 2 . We successfully compare our u and d non-singlet valence quark distributions with MSTW results (Martin et al., Eur. Phys. J. C 63:189, 2009). (orig.)
Analytical Solution of Relativistic Few-Body Bound Systems with a Generalized Yukawa Potential
Aslanzadeh, M.; Rajabi, A. A.
2016-03-01
We have investigated in this paper the few-body bound systems in a simple semi-relativistic scheme. For this aim, we introduced a spin independent relativistic description for a few-identical body system by presenting the analytical solution of few-particle Klein-Gordon equation. Performing calculations in D-dimensional configuration on the basis of the hypercentral approach, we reduced the few-body Klein-Gordon equation to a Schrödinger-like form. This equation is solved by using the Nikiforov-Uvarov method, through which the energy equations and eigenfunctions for a few-body bound system are obtained. We used the spin- and isospin-independent generalized Yukawa potential in our calculations, and the dependence of the few-body binding energies on the potential parameters has been investigated.
Simplified analytical solutions for free drops during NCT for radioactive material packagings
International Nuclear Information System (INIS)
Gupta, N.K.
1997-01-01
To ensure structural integrity during normal conditions of transport (NCT), Federal regulations in 10CFR71.71 require that the nuclear material package designs be evaluated for the effects of free drops. The vessel stress acceptance criteria for these drops are given in Regulatory Guide 7.6 and ASME Section III Code. During initial phases of the package design, the effects of the NCT free drops can be evaluated by simplified analytical solutions which will ensure that the safety margins specified in R. G. 7.6 are met. These safety margins can be verified during the final stages of the package design with dynamic analyses using finite element methods. This paper calculates the maximum impact open-quotes gclose quotes loading on the vessels using single degree of freedom models for different drop orientations. Only end, bottom, and corner drops are analyzed for cylindrical packages or packages with cylindrical ends
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.
Analytic Bayesian solution of the two-stage poisson-type problem in probabilistic risk analysis
International Nuclear Information System (INIS)
Frohner, F.H.
1985-01-01
The basic purpose of probabilistic risk analysis is to make inferences about the probabilities of various postulated events, with an account of all relevant information such as prior knowledge and operating experience with the specific system under study, as well as experience with other similar systems. Estimation of the failure rate of a Poisson-type system leads to an especially simple Bayesian solution in closed form if the prior probabilty implied by the invariance properties of the problem is properly taken into account. This basic simplicity persists if a more realistic prior, representing order of magnitude knowledge of the rate parameter, is employed instead. Moreover, the more realistic prior allows direct incorporation of experience gained from other similar systems, without need to postulate a statistical model for an underlying ensemble. The analytic formalism is applied to actual nuclear reactor data
Analytic solutions of QCD evolution equations for parton cascades inside nuclear matter at small x
International Nuclear Information System (INIS)
Geiger, K.
1994-01-01
An analytical method is presented to solve generalized QCD evolution equations for the time development of parton cascades in a nuclear environment. In addition to the usual parton branching processes in vacuum, these evolution equations provide a consistent description of interactions with the nuclear medium by accounting for stimulated branching processes, fusion, and scattering processes that are specific to QCD in a medium. Closed solutions for the spectra of produced partons with respect to the variables time, longitudinal momentum, and virtuality are obtained under some idealizing assumptions about the composition of the nuclear medium. Several characteristic features of the resulting parton distributions are discussed. One of the main conclusions is that the evolution of a parton shower in a medium is dilated as compared to free space and is accompanied by an enhancement of particle production. These effects become stronger with increasing nuclear density
Directory of Open Access Journals (Sweden)
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.
Hydrodynamics of Highly Viscous Flow past a Compound Particle: Analytical Solution
Directory of Open Access Journals (Sweden)
Longhua Zhao
2016-11-01
Full Text Available To investigate the translation of a compound particle in a highly viscous, incompressible fluid, we carry out an analytic study on flow past a fixed spherical compound particle. The spherical object is considered to have a rigid kernel covered with a fluid coating. The fluid within the coating has a different viscosity from that of the surrounding fluid and is immiscible with the surrounding fluid. The inertia effect is negligible for flows both inside the coating and outside the object. Thus, flows are in the Stokes regime. Taking advantage of the symmetry properties, we reduce the problem in two dimensions and derive the explicit formulae of the stream function in the polar coordinates. The no-slip boundary condition for the rigid kernel and the no interfacial mass transfer and force equilibrium conditions at fluid interfaces are considered. Two extreme cases: the uniform flow past a sphere and the uniform flow past a fluid drop, are reviewed. Then, for the fluid coating the spherical object, we derive the stream functions and investigate the flow field by the contour plots of stream functions. Contours of stream functions show circulation within the fluid coating. Additionally, we compare the drag and the terminal velocity of the object with a rigid sphere or a fluid droplet. Moreover, the extended results regarding the analytical solution for a compound particle with a rigid kernel and multiple layers of fluid coating are reported.
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: , 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'.
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.
Directory of Open Access Journals (Sweden)
Chun-Fu Chen
2014-03-01
Full Text Available Linear analytical study on the mechanical sensitivity in large deflection of unsymmetrically layered and laterally loaded piezoelectric plate under pretension is conducted. von Karman plate theory for large deflection is utilized but extended to the case of an unsymmetrically layered plate embedded with a piezoelectric layer. The governing equations thus obtained are simplified by omitting the arising nonlinear terms, yielding a Bessel or modified Bessel equation for the lateral slope. Depending on the relative magnitude of the piezoelectric effect, for both cases, analytical solutions of various geometrical responses are developed and formulated via Bessel and modified Bessel functions. The associated ultimate radial stresses are further derived following lamina constitutive law to evaluate the mechanical sensitivity of the considered plate. For a nearly monolithic plate under a very low applied voltage, the results are in good agreement with those for a single-layered case due to pure mechanical load available in literature, and thus the present approach is checked. For a two-layered unsymmetric plate made of typical silicon-based materials, a sound piezoelectric effect is illustrated particularly in a low pretension condition.
Wu, Yang; Kelly, Damien P
2014-12-12
The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of [Formula: see text] and [Formula: see text] type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Formula: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Formula: see text], where [Formula: see text] is the replica order. These circular replicas are shown to be fundamentally
Sági, Gyuri; Csay, Tamás; Szabó, László; Pátzay, György; Csonka, Emil; Takács, Erzsébet; Wojnárovits, László
2015-03-15
By combining a large variety of analytical techniques this study aimed at elaborating methods to follow up the degradation of sulfonamides in an advanced oxidation process (AOP): irradiation with ionizing radiation in dilute aqueous solution. In this process, besides other radicals, hydroxyl radicals are produced. As pulse radiolysis experiments show the basic initial reaction is hydroxyl radical addition to the benzene ring, forming cyclohexadienyl radical intermediates. In aerated solutions these radicals transform to peroxy radicals. Among the first formed products aromatic molecules hydroxylated in the benzene rings or in some cases in the heterocyclic rings were observed by LC-MS/MS. Chemical oxygen demand (COD) measurements indicate that at the early reaction period of degradation one hydroxyl radical induces incorporation of 1.5 O atoms into the products. Comparison of the COD and TOC (total organic carbon content) results shows gradual oxidation. Simultaneously with hydroxylation ring opening also takes place. The kinetics of inorganic SO4(2-) and NH4(+) formation, analyzed by ion chromatography, is similar to the kinetics of ring degradation (UV spectroscopy), however, there is a delayed formation of NO3(-). The latter ions may be produced in oxidative degradation of smaller N containing fragments. The S atoms of the sulfonamides remain in the solution (ICP-MS measurements) after degradation, whereas some part of the N atoms leaves the solution probably in the form of N2 (total nitrogen content (TN) measurements). Degradation is accompanied by a high pH drop due to formation of SO4(2-), NO3(-) and smaller organic acids. The degradation goes through many simultaneous and consecutive reactions, and with the applied methods the different stages of degradation can be characterized. Copyright © 2014 Elsevier B.V. All rights reserved.
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Sangwoo Park
2016-04-01
Full Text Available Groundwater flow is one of the most important factors for the design of a ground heat exchanger (GHEX since the thermal environment of the ground around the buried GHEX is significantly affected by heat convection due to the groundwater flow. Several preceding studies have been conducted to develop analytical solutions to the heat transfer model of GHEX with consideration of groundwater flow. One of these solutions is the combined heat transfer model of conduction and convection. However, the developed combined analytical models are inapplicable to all of the configurations of ordinary GHEXs because these solutions assume that the inner part of the borehole is thermally inert or consists of the same material as that of the surrounding ground. In this paper, the applicability of the combined solid cylindrical heat source model, which is the most suitable to energy piles until now, was evaluated by performing a series of numerical analyses. In the numerical analysis, the inner part of the borehole was modeled as two different materials (i.e., permeable ground formation and impermeable fill such as concrete to evaluate applicability of the analytical solution along with different diameter-length (D/L ratios of borehole. In a small value of the D/L ratio, the analytical solution to the combined heat transfer model is in good agreement with the result of numerical analysis. On the other hand, when increasing the D/L ratio, the analytical solution significantly overestimates the effect of groundwater flow on the heat transfer of GHEXs because the analytical solution disregards the existence of the impermeable region in the borehole. Consequently, such tendency is more critical in the GHEX with a large D/L ratio such as large-diameter energy piles.
Analytical Solutions for Rumor Spreading Dynamical Model in a Social Network
Fallahpour, R.; Chakouvari, S.; Askari, H.
2015-03-01
In this paper, Laplace Adomian decomposition method is utilized for evaluating of spreading model of rumor. Firstly, a succinct review is constructed on the subject of using analytical methods such as Adomian decomposion method, Variational iteration method and Homotopy Analysis method for epidemic models and biomathematics. In continue a spreading model of rumor with consideration of forgetting mechanism is assumed and subsequently LADM is exerted for solving of it. By means of the aforementioned method, a general solution is achieved for this problem which can be readily employed for assessing of rumor model without exerting any computer program. In addition, obtained consequences for this problem are discussed for different cases and parameters. Furthermore, it is shown the method is so straightforward and fruitful for analyzing equations which have complicated terms same as rumor model. By employing numerical methods, it is revealed LADM is so powerful and accurate for eliciting solutions of this model. Eventually, it is concluded that this method is so appropriate for this problem and it can provide researchers a very powerful vehicle for scrutinizing rumor models in diverse kinds of social networks such as Facebook, YouTube, Flickr, LinkedIn and Tuitor.
Paradis, Charles J.; McKay, Larry D.; Perfect, Edmund; Istok, Jonathan D.; Hazen, Terry C.
2018-03-01
The analytical solution describing the one-dimensional displacement of the center of mass of a tracer during an injection, drift, and extraction test (push-pull test) was expanded to account for displacement during the injection phase. The solution was expanded to improve the in situ estimation of effective porosity. The truncated equation assumed displacement during the injection phase was negligible, which may theoretically lead to an underestimation of the true value of effective porosity. To experimentally compare the expanded and truncated equations, single-well push-pull tests were conducted across six test wells located in a shallow, unconfined aquifer comprised of unconsolidated and heterogeneous silty and clayey fill materials. The push-pull tests were conducted by injection of bromide tracer, followed by a non-pumping period, and subsequent extraction of groundwater. The values of effective porosity from the expanded equation (0.6-5.0%) were substantially greater than from the truncated equation (0.1-1.3%). The expanded and truncated equations were compared to data from previous push-pull studies in the literature and demonstrated that displacement during the injection phase may or may not be negligible, depending on the aquifer properties and the push-pull test parameters. The results presented here also demonstrated the spatial variability of effective porosity within a relatively small study site can be substantial, and the error-propagated uncertainty of effective porosity can be mitigated to a reasonable level (effective porosity of fine-grained fill material.
Benoit, Denise N; Zhu, Huiguang; Lilierose, Michael H; Verm, Raymond A; Ali, Naushaba; Morrison, Adam N; Fortner, John D; Avendano, Carolina; Colvin, Vicki L
2012-11-06
Many of the solution phase properties of nanoparticles, such as their colloidal stability and hydrodynamic diameter, are governed by the number of stabilizing groups bound to the particle surface (i.e., grafting density). Here, we show how two techniques, analytical ultracentrifugation (AUC) and total organic carbon analysis (TOC), can be applied separately to the measurement of this parameter. AUC directly measures the density of nanoparticle-polymer conjugates while TOC provides the total carbon content of its aqueous dispersions. When these techniques are applied to model gold nanoparticles capped with thiolated poly(ethylene glycol), the measured grafting densities across a range of polymer chain lengths, polymer concentrations, and nanoparticle diameters agree to within 20%. Moreover, the measured grafting densities correlate well with the polymer content determined by thermogravimetric analysis of solid conjugate samples. Using these tools, we examine the particle core diameter, polymer chain length, and polymer solution concentration dependence of nanoparticle grafting densities in a gold nanoparticle-poly(ethylene glycol) conjugate system.
A Note on an Analytic Solution for an Incompressible Fluid-Conveying Pipeline System
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Vincent O. S. Olunloyo
2017-01-01
Full Text Available This paper presents an integral transform analytic solution to the equations governing a fluid-conveying pipeline segment where a gyroscopic or Coriolis force effect is taken into consideration. The mathematical model idealizes a segment of the pipeline as an elastic beam conveying an incompressible fluid. It is clearly shown that when such a system is supported at both ends and in a free motion, the Coriolis force dissipates no energy (or simply does not work as it generates conjugate complex vibratory components for all flow velocities. It is demonstrated that the modal natural frequencies can be computed from the algebraic products of the complex frequency pairs. Clearly, the patterns of the characteristics of the system’s natural frequencies are seen partly when the real and imaginary components are plotted, as widely seen in the literature. Nonetheless, results from this study revealed that a continuity profile exists to connect the subcritical, critical, and postcritical vibratory behaviours when the absolute values are plotted for any velocity. In the meantime, the efficacy and versatility of this method against the usual assumed spatial or temporal modal solutions are demonstrated by confirming the predictions and validity of results of earlier workers such as Paidoussis, Ziegler, and others where pre- and postdivergence behaviours are exhibited.
Analytical quality-by-design approach for sample treatment of BSA-containing solutions.
Taevernier, Lien; Wynendaele, Evelien; D Hondt, Matthias; De Spiegeleer, Bart
2015-02-01
The sample preparation of samples containing bovine serum albumin (BSA), e.g., as used in transdermal Franz diffusion cell (FDC) solutions, was evaluated using an analytical quality-by-design (QbD) approach. Traditional precipitation of BSA by adding an equal volume of organic solvent, often successfully used with conventional HPLC-PDA, was found insufficiently robust when novel fused-core HPLC and/or UPLC-MS methods were used. In this study, three factors (acetonitrile (%), formic acid (%) and boiling time (min)) were included in the experimental design to determine an optimal and more suitable sample treatment of BSA-containing FDC solutions. Using a QbD and Derringer desirability ( D ) approach, combining BSA loss, dilution factor and variability, we constructed an optimal working space with the edge of failure defined as D <0.9. The design space is modelled and is confirmed to have an ACN range of 83±3% and FA content of 1±0.25%.
Exact analytic solution of position-dependent mass Schrödinger equation
Rajbongshi, Hangshadhar
2018-03-01
Exact analytic solution of position-dependent mass Schrödinger equation is generated by using extended transformation, a method of mapping a known system into a new system equipped with energy eigenvalues and corresponding wave functions. First order transformation is performed on D-dimensional radial Schrödinger equation with constant mass by taking trigonometric Pöschl-Teller potential as known system. The exactly solvable potentials with position-dependent mass generated for different choices of mass functions through first order transformation are also taken as known systems in the second order transformation performed on D-dimensional radial position-dependent mass Schrödinger equation. The solutions are fitted for "Zhu and Kroemer" ordering of ambiguity. All the wave functions corresponding to nonzero energy eigenvalues are normalizable. The new findings are that the normalizability condition of the wave functions remains independent of mass functions, and some of the generated potentials show a family relationship among themselves where power law potentials also get related to non-power law potentials and vice versa through the transformation.
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Md. Nur Alam
2017-11-01
Full Text Available In this article, a variety of solitary wave solutions are observed for microtubules (MTs. We approach the problem by treating the solutions as nonlinear RLC transmission lines and then find exact solutions of Nonlinear Evolution Equations (NLEEs involving parameters of special interest in nanobiosciences and biophysics. We determine hyperbolic, trigonometric, rational and exponential function solutions and obtain soliton-like pulse solutions for these equations. A comparative study against other methods demonstrates the validity of the technique that we developed and demonstrates that our method provides additional solutions. Finally, using suitable parameter values, we plot 2D and 3D graphics of the exact solutions that we observed using our method. Keywords: Analytical method, Exact solutions, Nonlinear evolution equations (NLEEs of microtubules, Nonlinear RLC transmission lines
Jhang, R.; Liou, T.
2013-12-01
Carbon capture and sequestration (CCS) is believed to be an economically feasible technology to mitigate global warming by capturing carbon dioxide (CO2), the major component of greenhouse gases, from the atmosphere and injecting it into deep geological formations.Several mechanisms can help trap CO2 in the pore space of a geological reservoir, stratigraphic and structural trapping, hydrodynamic trapping, and geochemical trapping.Besides these trapping mechanisms, another important issue that deserves careful attention is the risk of CO2 leakage. The common ';constant injection rate' scenario may induce high pressure buildup that will endanger the mechanical integrity as well as the sealing capability of the cap rock. Instead of injecting CO2 at a constant mass rate, CO2 can be injected into the reservoir by fixing the pressure (usually the bottom-hole pressure) in the injection borehole. By doing so, the inevitable pressure buildup associated with the constant injection scheme can be completely eliminated in the constant pressure injection scheme. In this paper, a semi-analytical solution for CO2 injection with constant pressure was developed. For simplicity, structural and geochemical trapping mechanisms were not considered. Therefore, a horizontal reservoir with infinite radial extent was considered. Prior to injection, the reservoir is fully saturated with the formation brine. It is assumed that CO2 does not mix with brine such that a sharp interface is formed once CO2 invades the brine-saturated pores. Because of the density difference between CO2 and brine, CO2 resides above the interface. Additional assumptions were also made when building up the brine and CO2 mass balance equations: (1) both of the fluids and the geological formations are incompressible, (2) capillary pressure is neglected, (3)there is no fluid flow in the vertical direction, and the horizontal flow satisfies the Darcy's law.In order to solve for the height of brine-CO2 interface, the two
Kong, Dali; Zhang, Keke; Schubert, Gerald
2017-02-01
It is expected that the Juno spacecraft will provide an accurate spectrum of the Jovian zonal gravitational coefficients that would be affected by both the deep zonal flow, if it exists, and the basic rotational distortion. We derive the first analytical solution, under the spheroidal-shape approximation, for the density anomaly induced by an internal zonal flow in rapidly rotating Jupiter-like planets. We compare the density anomaly of the analytical solution to that obtained from a fully numerical solution based on a three-dimensional finite element method; the two show excellent agreement. We apply the analytical solution to a rapidly rotating Jupiter-like planet and show that there exists a close relationship between the spatial structure of the zonal flow and the spectrum of zonal gravitational coefficients. We check the accuracy of the spheroidal-shape approximation by computing both the spheroidal and non-spheroidal solutions with exactly the same physical parameters. We also discuss implications of the new analytical solution for interpreting the future high-precision gravitational measurements of the Juno spacecraft.
Energy Technology Data Exchange (ETDEWEB)
Peralta, J.; López-Valverde, M. A. [Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Imamura, T. [Institute of Space and Astronautical Science-Japan Aerospace Exploration Agency 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan); Read, P. L. [Department of Physics, University of Oxford, Clarendon Laboratory, 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 first of 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 when 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 first part, only waves that are direct solutions of the generic dispersion relation are studied—acoustic and inertia-gravity waves. Concerning inertia-gravity waves, we found that in the cases of short horizontal wavelengths, null background wind, or propagation in the equatorial region, only pure gravity waves are possible, while for the limit of large horizontal wavelengths and/or null static stability, the waves are inertial. The correspondence between classical atmospheric approximations and wave filtering has been examined too, and we carried out a classification of the mesoscale waves found in the clouds of Venus at different vertical levels of its atmosphere. Finally, the classification of waves in exoplanets is discussed and we provide a list of possible candidates with cyclostrophic regimes.
Energy Technology Data Exchange (ETDEWEB)
Mathias, S.A.; Gluyas, J.G.; Oldenburg, C.M.; Tsang, C.-F.
2010-05-21
Mathematical tools are needed to screen out sites where Joule-Thomson cooling is a prohibitive factor for CO{sub 2} geo-sequestration and to design approaches to mitigate the effect. In this paper, a simple analytical solution is developed by invoking steady-state flow and constant thermophysical properties. The analytical solution allows fast evaluation of spatiotemporal temperature fields, resulting from constant-rate CO{sub 2} injection. The applicability of the analytical solution is demonstrated by comparison with non-isothermal simulation results from the reservoir simulator TOUGH2. Analysis confirms that for an injection rate of 3 kg s{sup -1} (0.1 MT yr{sup -1}) into moderately warm (>40 C) and permeable formations (>10{sup -14} m{sup 2} (10 mD)), JTC is unlikely to be a problem for initial reservoir pressures as low as 2 MPa (290 psi).
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Yang Shen
Full Text Available China is a country with vast territory, but economic development and population growth have reduced the usable land resources in recent years. Therefore, reclamation by pumping and filling is carried out in eastern coastal regions of China in order to meet the needs of urbanization. However, large areas of reclaimed land need rapid drainage consolidation treatment. Based on past researches on how to improve the treatment efficiency of soft clay using vacuum preloading combined with electro-osmosis, a two-dimensional drainage plane model was proposed according to the Terzaghi and Esrig consolidation theory. However, the analytical solution using two-dimensional plane model was never involved. Current analytical solutions can't have a thorough theoretical analysis of practical engineering and give relevant guidance. Considering the smearing effect and the rectangle arrangement pattern, an analytical solution is derived to describe the behavior of pore-water and the consolidation process by using EKG (electro-kinetic geo synthetics materials. The functions of EKG materials include drainage, electric conduction and corrosion resistance. Comparison with test results is carried out to verify the analytical solution. It is found that the measured value is larger than the applied vacuum degree because of the stacking effect of the vacuum preloading and electro-osmosis. The trends of the mean measured value and the mean analytical value processes are comparable. Therefore, the consolidation model can accurately assess the change in pore-water pressure and the consolidation process during vacuum preloading combined with electro-osmosis.
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I. L. Katsev
2010-10-01
Full Text Available We present here the aerosol retrieval technique FAR that uses radiative transfer computations in the process of retrieval rather than look-up tables (LUT. This approach provides operational satellite data processing due to the use of the accurate and extremely fast radiative transfer code RAY previously developed by authors along with approximate analytical solutions of the radiative transfer theory. The model of the stratified atmosphere is taken as two coupled layers. Both layers include aerosol scattering and absorption, molecular scattering and gas absorption. The atmosphere parameters are assumed to change from pixel to pixel in the lower atmosphere layer, but the upper stratified layer of the atmosphere over 2–3 km is supposed to be horizontally homogenous for the frame under retrieval. The model of the land spectral albedo is taken as a weighted sum of two a priory chosen basic spectra.
The aerosol optical thickness (AOT, Angström exponent and the weight in the land spectral albedo are optimized in the iteration process using the least-squares technique with fast computations of the derivatives of radiative characteristics with respect to retrieved values. The aerosol model and, hence, the aerosol phase function and single scattering albedo, is predefined and does not change in the iteration process. The presented version of FAR is adjusted to process the MERIS data. But it is important that the developed technique can be adapted for processing data of various satellite instruments (including any spectral multi-angle polarization-sensitive sensors.
The use of approximate analytical radiative transfer solutions considerably speeds up data processing but may lead to about 15–20% increase of AOT retrieval errors. This approach is advantageous when just the satellite data processing time rather than high accuracy of the AOT retrieval is crucial. A good example is monitoring the trans-boundary transfer of aerosol
Petrov, Pavel S; Sturm, Frédéric
2016-03-01
A problem of sound propagation in a shallow-water waveguide with a weakly sloping penetrable bottom is considered. The adiabatic mode parabolic equations are used to approximate the solution of the three-dimensional (3D) Helmholtz equation by modal decomposition of the acoustic pressure field. The mode amplitudes satisfy parabolic equations that admit analytical solutions in the special case of the 3D wedge. Using the analytical formula for modal amplitudes, an explicit and remarkably simple expression for the acoustic pressure in the wedge is obtained. The proposed solution is validated by the comparison with a solution of the 3D penetrable wedge problem obtained using a fully 3D parabolic equation that includes a leading-order cross term correction.
The analytic solution for the power series expansion of Heun function
International Nuclear Information System (INIS)
Choun, Yoon Seok
2013-01-01
The Heun function generalizes all well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric 2 F 1 , 1 F 1 and 0 F 1 functions. Heun functions are applicable to diverse areas such as theory of black holes, lattice systems in statistical mechanics, solution of the Schrödinger equation of quantum mechanics, and addition of three quantum spins. In this paper I will apply three term recurrence formula (Y.S. Choun, (arXiv:1303.0806), 2013) to the power series expansion in closed forms of Heun function (infinite series and polynomial) including all higher terms of A n ’s. Section 3 contains my analysis on applying the power series expansions of Heun function to a recent paper (R.S. Maier, Math. Comp. 33 (2007) 811–843). Due to space restriction final equations for the 192 Heun functions are not included in the paper, but feel free to contact me for the final solutions. Section 4 contains two additional examples using the power series expansions of Heun function. This paper is 3rd out of 10 in series “Special functions and three term recurrence formula (3TRF)”. See Section 5 for all the papers in the series. The previous paper in series deals with three term recurrence formula (3TRF). The next paper in the series describes the integral forms of Heun function and its asymptotic behaviors analytically. -- Highlights: •Power series expansion for infinite series of Heun function using 3 term rec. form. •Power series for polynomial which makes B n term terminated of Heun function. •Applicable to areas such as the Teukolsky equation in Kerr–Newman–de Sitter geometries
ANALYTIC SOLUTION FOR SELF-REGULATED COLLECTIVE ESCAPE OF COSMIC RAYS FROM THEIR ACCELERATION SITES
International Nuclear Information System (INIS)
Malkov, M. A.; Diamond, P. H.; Sagdeev, R. Z.; Aharonian, F. A.; Moskalenko, I. V.
2013-01-01
Supernova remnants (SNRs), as the major contributors to the galactic cosmic rays (CRs), are believed to maintain an average CR spectrum by diffusive shock acceleration regardless of the way they release CRs into the interstellar medium (ISM). However, the interaction of the CRs with nearby gas clouds crucially depends on the release mechanism. We call into question two aspects of a popular paradigm of the CR injection into the ISM, according to which they passively and isotropically diffuse in the prescribed magnetic fluctuations as test particles. First, we treat the escaping CR and the Alfvén waves excited by them on an equal footing. Second, we adopt field-aligned CR escape outside the source, where the waves become weak. An exact analytic self-similar solution for a CR ''cloud'' released by a dimmed accelerator strongly deviates from the test-particle result. The normalized CR partial pressure may be approximated as P(p,z,t)=2[|z| 5/3 +z dif 5/3 (p,t)] -3/5 exp[-z 2 /4D ISM (p)t], where p is the momentum of CR particle, and z is directed along the field. The core of the cloud expands as z dif ∝√(D NL (p)t) and decays in time as p∝2z -1 dif (t). The diffusion coefficient D NL is strongly suppressed compared to its background ISM value D ISM : D NL ∼ D ISM exp (– Π) ISM for sufficiently high field-line-integrated CR partial pressure, Π. When Π >> 1, the CRs drive Alfvén waves efficiently enough to build a transport barrier (p≈2/∣z∣— p edestal ) that strongly reduces the leakage. The solution has a spectral break at p = p br , where p br satisfies the equation D NL (p br ) ≅ z 2 /t.
Paradis, Charles J.; McKay, Larry D.; Perfect, Edmund; Istok, Jonathan D.; Hazen, Terry C.
2017-10-01
The analytical solution describing the one-dimensional displacement of the center of mass of a tracer during an injection, drift, and extraction test (push-pull test) was expanded to account for displacement during the injection phase. The solution was expanded to improve the in situ estimation of effective porosity. The truncated equation assumed displacement during the injection phase was negligible, which may theoretically lead to an underestimation of the true value of effective porosity. To experimentally compare the expanded and truncated equations, single-well push-pull tests were conducted across six test wells located in a shallow, unconfined aquifer comprised of unconsolidated and heterogeneous silty and clayey fill materials. The push-pull tests were conducted by injection of bromide tracer, followed by a non-pumping period, and subsequent extraction of groundwater. The values of effective porosity from the expanded equation (0.6-5.0%) were substantially greater than from the truncated equation (0.1-1.3%). The expanded and truncated equations were compared to data from previous push-pull studies in the literature and demonstrated that displacement during the injection phase may or may not be negligible, depending on the aquifer properties and the push-pull test parameters. The results presented here also demonstrated the spatial variability of effective porosity within a relatively small study site can be substantial, and the error-propagated uncertainty of effective porosity can be mitigated to a reasonable level (< ± 0.5%). The tests presented here are also the first that the authors are aware of that estimate, in situ, the effective porosity of fine-grained fill material.
Analytical Solutions to Coupled HM Problems to Highlight the Nonlocal Nature of Aquifer Storage
De Simone, Silvia; Carrera, Jesús
2017-11-01
Specific storage reflects the volumetric deformation capacity of permeable media. Classical groundwater hydrology equates elastic storage to medium compressibility (plus fluid compressibility times porosity). However, it is unclear if storage behavior can be represented by a single parameter. Hydraulic gradients act as body forces that push the medium in the direction of flow causing it to deform instantaneously everywhere, i.e., even in regions where pressure would not have changed according to conventional fluid flow. Therefore, actual deformation depends not only on the mechanical properties of the medium but also on aquifer geometry and on surrounding strata, which act like constraints to displacements. Here we discuss the question and highlight the nonlocal nature of storage (i.e., the volume of water released at a point depends on the poroelastic response over the whole aquifer). Proper evaluation of transient pressure and water release from storage requires acknowledging the hydromechanical coupling, which generally involves the use of numerical methods. We propose analytical solutions to the HM problem of fluid injection (extraction) into finite aquifers with one-dimensional or cylindrical geometries. We find that pressure response is much faster (virtually instantaneous) and larger than expected from traditional purely hydraulic solutions when aquifer deformation is restrained, whereas the pressure response is reversed (i.e., pressure drop in response to injection) when the permeable medium is free to deform. These findings suggest that accounting for hydromechanical coupling may be required when hydraulic testing is performed in low permeability media, which is becoming increasingly demanded for energy-related applications.
Analytic Solution for Self-regulated Collective Escape of Cosmic Rays from Their Acceleration Sites
Malkov, M. A.; Diamond, P. H.; Sagdeev, R. Z.; Aharonian, F. A.; Moskalenko, I. V.
2013-05-01
Supernova remnants (SNRs), as the major contributors to the galactic cosmic rays (CRs), are believed to maintain an average CR spectrum by diffusive shock acceleration regardless of the way they release CRs into the interstellar medium (ISM). However, the interaction of the CRs with nearby gas clouds crucially depends on the release mechanism. We call into question two aspects of a popular paradigm of the CR injection into the ISM, according to which they passively and isotropically diffuse in the prescribed magnetic fluctuations as test particles. First, we treat the escaping CR and the Alfvén waves excited by them on an equal footing. Second, we adopt field-aligned CR escape outside the source, where the waves become weak. An exact analytic self-similar solution for a CR "cloud" released by a dimmed accelerator strongly deviates from the test-particle result. The normalized CR partial pressure may be approximated as {P}(p,z,t)=2[|z|^{5/3}+z_{dif}^{5/3}(p,t)]^{-3/5}\\exp [-z^{2}/4D_{ISM}(p)t], where p is the momentum of CR particle, and z is directed along the field. The core of the cloud expands as z_{dif}\\propto \\sqrt{D_{NL}\\left(p\\right)t} and decays in time as {P}\\propto 2z_{dif}^{-1}\\left(t\\right). The diffusion coefficient D NL is strongly suppressed compared to its background ISM value D ISM: D NL ~ D ISMexp (- Π) Lt D ISM for sufficiently high field-line-integrated CR partial pressure, Π. When Π Gt 1, the CRs drive Alfvén waves efficiently enough to build a transport barrier ( {P}\\approx 2/\\left|z\\right|—"pedestal") that strongly reduces the leakage. The solution has a spectral break at p = p br, where p br satisfies the equation D NL(p br) ~= z 2/t.
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
Analytic solution of a relativistic two-dimensional hydrogen-like atom in a constant magnetic field
International Nuclear Information System (INIS)
Villalba, V.M.
1998-01-01
We obtain exact solutions of the Klein-Gordon and Pauli-Schroedinger equations for a two-dimensional hydrogen-like atom in the presence of a constant magnetic field. Analytic solutions for the energy spectrum are obtained for particular values of the magnetic field strength. The results are compared to those obtained in the non-relativistic and spinless case. We obtain that the relativistic spectrum does not present s states. (orig.)
Analytic Review as a Solution to the Misreporting of Statistical Results in Psychological Science.
Sakaluk, John; Williams, Alexander; Biernat, Monica
2014-11-01
In this article, we propose analytic review (AR) as a solution to the problem of misreporting statistical results in psychological science. AR requires authors submitting manuscripts for publication to also submit the data file and syntax used during analyses. Regular reviewers or statistical experts then review reported analyses in order to verify that the analyses reported were actually conducted and that the statistical values are accurately reported. We begin by describing the problem of misreporting in psychology and introduce the basic AR process. We then highlight both primary and secondary benefits of adopting AR and describe different permutations of the AR system, each of which has its own strengths and limitations. We conclude by attempting to dispel three anticipated concerns about AR: that it will increase the workload placed on scholars, that it will infringe on the traditional peer-review process, and that it will hurt the image of the discipline of psychology. Although implementing AR will add one more step to the bureaucratic publication process, we believe it can be implemented in an efficient manner that would greatly assist in decreasing the frequency and impact of misreporting while also providing secondary benefits in other domains of scientific integrity. © The Author(s) 2014.
Xu, C.; Mudunuru, M. K.; Nakshatrala, K. B.
2016-11-01
The mechanical response, serviceability, and load-bearing capacity of materials and structural components can be adversely affected due to external stimuli, which include exposure to a corrosive chemical species, high temperatures, temperature fluctuations (i.e., freezing-thawing), cyclic mechanical loading, just to name a few. It is, therefore, of paramount importance in several branches of engineering—ranging from aerospace engineering, civil engineering to biomedical engineering—to have a fundamental understanding of degradation of materials, as the materials in these applications are often subjected to adverse environments. As a result of recent advancements in material science, new materials such as fiber-reinforced polymers and multi-functional materials that exhibit high ductility have been developed and widely used, for example, as infrastructural materials or in medical devices (e.g., stents). The traditional small-strain approaches of modeling these materials will not be adequate. In this paper, we study degradation of materials due to an exposure to chemical species and temperature under large strain and large deformations. In the first part of our research work, we present a consistent mathematical model with firm thermodynamic underpinning. We then obtain semi-analytical solutions of several canonical problems to illustrate the nature of the quasi-static and unsteady behaviors of degrading hyperelastic solids.
Analytical solutions for the invariant spin field for model storage rings
International Nuclear Information System (INIS)
Mane, S.R.
2002-01-01
We present nonperturbative analytical expressions for the invariant spin field for several storage ring models. In particular, we solve the important models of a ring with one Snake and a single resonance driving term, and a ring with two Snakes and a single resonance driving term. We also treat several other models, all of which contain Siberian Snakes. Our solutions contain some novel features, e.g. in some cases the polarization does not point along the direction of the closed-orbit spin quantization axis. We also include vertical resonance driving terms, and consider the contributions of sextupoles and higher order multipoles to the resonance driving terms, and argue that these can play a significant role in some circumstances. We offer some brief remarks on the so-called Snake resonances. We relate our results to observations of higher-order depolarizing spin resonances for polarized proton beams in a real ring, and offer some suggestions as to how our ideas might be verified
Sound energy decay in coupled spaces using a parametric analytical solution of a diffusion equation.
Luizard, Paul; Polack, Jean-Dominique; Katz, Brian F G
2014-05-01
Sound field behavior in performance spaces is a complex phenomenon. Issues regarding coupled spaces present additional concerns due to sound energy exchanges. Coupled volume concert halls have been of increasing interest in recent decades because this architectural principle offers the possibility to modify the hall's acoustical environment in a passive way by modifying the coupling area. Under specific conditions, the use of coupled reverberation chambers can provide non-exponential sound energy decay in the main room, resulting in both high clarity and long reverberation which are antagonistic parameters in a single volume room. Previous studies have proposed various sound energy decay models based on statistical acoustics and diffusion theory. Statistical acoustics assumes a perfectly uniform sound field within a given room whereas measurements show an attenuation of energy with increasing source-receiver distance. While previously proposed models based on diffusion theory use numerical solvers, the present study proposes a heuristic model of sound energy behavior based on an analytical solution of the commonly used diffusion equation and physically justified approximations. This model is validated by means of comparisons to scale model measurements and numerical geometrical acoustics simulations, both applied to the same simple concert hall geometry.
Uncoupled continuous-time random walk model: Analytical and numerical solutions
Fa, Kwok Sau
2014-05-01
Solutions for the continuous-time random walk (CTRW) model are known in few cases. In this work, the uncoupled CTRW model is investigated analytically and numerically. In particular, the probability density function (PDF) and n-moment are obtained and analyzed. Exponential and Gaussian functions are used for the jump length PDF, whereas the Mittag-Leffler function and a combination of exponential and power-laws function is used for the waiting time PDF. The exponential and Gaussian jump length PDFs have finite jump length variances and they give the same second moment; however, their distribution functions present different behaviors near the origin. The combination of exponential and power-law function for the waiting time PDF can generate a crossover from anomalous regime to normal regime. Moreover, the parameter of the exponential jump length PDF does not change the behavior of the n-moment for all time intervals, and for the Gaussian jump length PDF the n-moment also indicates a similar behavior.
Applying Big Data solutions for log analytics in the PanDA infrastructure
Alekseev, Aleksandr; The ATLAS collaboration
2017-01-01
PanDA is the workflow management system of the ATLAS experiment at the LHC and is responsible for generating, brokering and monitoring up to two million jobs per day across 150 computing centers in the Worldwide LHC Computing Grid. The PanDA core consists of several components deployed centrally on around 20 servers. The daily log volume is around 400GB per day. In certain cases, troubleshooting a particular issue on the raw log files can be compared to searching for a needle in a haystack and requires a high level of expertise. Therefore we decided to build on trending Big Data solutions and utilize the ELK infrastructure (Filebeat, Logstash, Elastic Search and Kibana) to process, index and analyze our log files. This allows to overcome troubleshooting complexity, provides a better interface to the operations team and generates advanced analytics to understand our system. This paper will describe the features of the ELK stack, our infrastructure, optimal configuration settings and filters. We will provide ex...
Directory of Open Access Journals (Sweden)
Zeng-hui Zhao
2014-01-01
Full Text Available According to the special combined structure of surrounding rock in western mining area of China, a micromechanical model with variable parameters containing contact interface was proposed firstly. Then, the derived stresses in coal and rock near the interface were analyzed on the basis of the harmonized strain relation, and the analytical solutions with respect to stress states near the interface were drawn up. The triaxial compressive strength of coal and rock was further determined in case the contact interface was in the horizontal position. Moreover, effects of stiffness ratio, interface angle, and stress level on the strength of two bodies near the contact area were expounded in detail. Results indicate that additional stresses which have significant effect on the strength of combined model are derived due to the adhesive effect of contact interface and lithological differences between geologic bodies located on both sides. The interface effect on the strength of combined body is most associated with the stiffness, interface angle, and the stress level. These conclusions are also basically valid for three-body model and even for the multibody model and lay important theory foundation to guide the stability study of soft strata composed of different geologic bodies.
Khan, Farman U; Qamar, Shamsul
2017-05-01
A set of analytical solutions are presented for a model describing the transport of a solute in a fixed-bed reactor of cylindrical geometry subjected to the first (Dirichlet) and third (Danckwerts) type inlet boundary conditions. Linear sorption kinetic process and first-order decay are considered. Cylindrical geometry allows the use of large columns to investigate dispersion, adsorption/desorption and reaction kinetic mechanisms. The finite Hankel and Laplace transform techniques are adopted to solve the model equations. For further analysis, statistical temporal moments are derived from the Laplace-transformed solutions. The developed analytical solutions are compared with the numerical solutions of high-resolution finite volume scheme. Different case studies are presented and discussed for a series of numerical values corresponding to a wide range of mass transfer and reaction kinetics. A good agreement was observed in the analytical and numerical concentration profiles and moments. The developed solutions are efficient tools for analyzing numerical algorithms, sensitivity analysis and simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Analytic Solution to the Problem of Aircraft Electric Field Mill Calibration
Koshak, W. J.
2003-12-01
It is by no means a simple task to retrieve storm electric fields from an aircraft instrumented with electric field mill sensors. The presence of the aircraft distorts the ambient field in a complicated way. Before retrievals of the storm field can be made, the field mill measurement system must be "calibrated". In other words, a relationship between impressed (i.e., ambient) electric field and mill output must be established. If this relationship can be determined, it is mathematically inverted so that ambient field can be inferred from the mill outputs. Previous studies have primarily focused on linear theories where the "relationship" between ambient field and mill output is described by a "calibration matrix" M. Each element of the matrix describes how a particular component of the ambient field is enhanced by the aircraft. For example the product MixEx is the contribution of the Ex field to the ith mill output. Similarly, net aircraft charge (described by a "charge field component" Eq) contributes an amount MiqEq to the output of the ith sensor. The central difficulty in obtaining M stems from the fact that the impressed field (Ex, Ey, Ez, Eq) is not known but is instead estimated. Typically, the aircraft is flown through a series of roll and pitch maneuvers in fair weather, and the values of the fair weather field and aircraft charge are estimated at each point along the aircraft trajectory. These initial estimates are often highly inadequate, but several investigators have improved the estimates by implementing various (ad hoc) iterative methods. Though numerical tests show that some of the iterative methods do improve the initial estimates, none of the iterative methods guarantee absolute convergence to the true values, or even to values reasonably close to the true values when measurement errors are present. In this work, the mathematical problem is solved directly by analytic means. For m mills installed on an arbitrary aircraft, it is shown that it is
Analytic solution to leading order coupled DGLAP evolution equations: A new perturbative QCD tool
International Nuclear Information System (INIS)
Block, Martin M.; Durand, Loyal; Ha, Phuoc; McKay, Douglas W.
2011-01-01
We have analytically solved the LO perturbative QCD singlet DGLAP equations [V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972)][G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977)][Y. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977)] using Laplace transform techniques. Newly developed, highly accurate, numerical inverse Laplace transform algorithms [M. M. Block, Eur. Phys. J. C 65, 1 (2010)][M. M. Block, Eur. Phys. J. C 68, 683 (2010)] allow us to write fully decoupled solutions for the singlet structure function F s (x,Q 2 ) and G(x,Q 2 ) as F s (x,Q 2 )=F s (F s0 (x 0 ),G 0 (x 0 )) and G(x,Q 2 )=G(F s0 (x 0 ),G 0 (x 0 )), where the x 0 are the Bjorken x values at Q 0 2 . Here F s and G are known functions--found using LO DGLAP splitting functions--of the initial boundary conditions F s0 (x)≡F s (x,Q 0 2 ) and G 0 (x)≡G(x,Q 0 2 ), i.e., the chosen starting functions at the virtuality Q 0 2 . For both G(x) and F s (x), we are able to either devolve or evolve each separately and rapidly, with very high numerical accuracy--a computational fractional precision of O(10 -9 ). Armed with this powerful new tool in the perturbative QCD arsenal, we compare our numerical results from the above equations with the published MSTW2008 and CTEQ6L LO gluon and singlet F s distributions [A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, Eur. Phys. J. C 63, 189 (2009)], starting from their initial values at Q 0 2 =1 GeV 2 and 1.69 GeV 2 , respectively, using their choice of α s (Q 2 ). This allows an important independent check on the accuracies of their evolution codes and, therefore, the computational accuracies of their published parton distributions. Our method completely decouples the two LO distributions, at the same time guaranteeing that both G and F s satisfy the singlet coupled DGLAP equations. It also allows one to easily obtain the effects of the starting functions on the evolved gluon and singlet structure functions, as functions of both Q
Neng, N R; Silva, A R M; Nogueira, J M F
2010-11-19
A novel enrichment technique, adsorptive μ-extraction (AμE), is proposed for trace analysis of polar solutes in aqueous media. The preparation, stability tests and development of the analytical devices using two geometrical configurations, i.e. bar adsorptive μ-extraction (BAμE) and multi-spheres adsorptive μ-extraction (MSAμE) is fully discussed. From the several sorbent materials tested, activated carbons and polystyrene divinylbenzene phases demonstrated the best stability, robustness and to be the most suitable for analytical purposes. The application of both BAμE and MSAμE devices proved remarkable performance for the determination of trace levels of polar solutes and metabolites (e.g. pesticides, disinfection by-products, drugs of abuse and pharmaceuticals) in water matrices and biological fluids. By comparing AμE techniques with stir bar sorptive extraction based on polydimethylsiloxane phase, great effectiveness is attained overcoming the limitations of the latter enrichment approach regarding the more polar solutes. Furthermore, convenient sensitivity and selectivity is reached through AμE techniques, since the great advantage of this new analytical technology is the possibility to choose the most suitable sorbent to each particular type of application. The enrichment techniques proposed are cost-effective, easy to prepare and work-up, demonstrating robustness and to be a remarkable analytical tool for trace analysis of priority solutes in areas of recognized importance such as environment, forensic and other related life sciences. Copyright © 2010 Elsevier B.V. All rights reserved.
Snellings, RJM; Hulsbergen, W; Prendergast, EP; van den Brink, A; de Haas, AP; Habets, JJLM; Kamermans, R; Koopmans, M; Kuijer, PG; de Laat, CTAM; Ostendorf, RW; Peghaire, A; Rossewij, M
1999-01-01
Particle identification in intermediate heavy-ion collisions, using a modern 4 pi detector which contains several active layers, relies on a parametrisation or numerical integration of the energy loss in thick layers of detector material for different ions. Here an analytical solution applicable
Czech Academy of Sciences Publication Activity Database
Adámek, V.; Valeš, František
2012-01-01
Roč. 85, NOV 2012 (2012), s. 34-44 ISSN 0378-4754 R&D Projects: GA ČR(CZ) GAP101/11/0288 Institutional support: RVO:61388998 Keywords : transient vibration * viscoelastic disc * analytical solution Subject RIV: BI - Acoustics Impact factor: 0.836, year: 2012 http://www.sciencedirect.com/science/article/pii/S037847541200225X
WINKELMAN, JGM; BEENACKERS, AACM
The problem of ps absorption accompanied by a first-order reversible reaction, producing a volatile reaction product, is considered. A general analytical solution is developed for the film model, resulting in explicit relations for the concentration profiles in the film and for the mass transfer
Time-domain analytic solutions of two-wire transmission line excited by a plane-wave field
International Nuclear Information System (INIS)
Ni Guyan; Yan Li; Yuan Naichang
2008-01-01
This paper reports that an analytic method is used to calculate the load responses of the two-wire transmission line excited by a plane-wave directly in the time domain. By the frequency-domain Baum–Liu–Tesche (BLT) equation, the time-domain analytic solutions are obtained and expressed in an infinite geometric series. Moreover, it is shown that there exist only finite nonzero terms in the infinite geometric series if the time variate is at a finite interval. In other word, the time-domain analytic solutions are expanded in a finite geometric series indeed if the time variate is at a finite interval. The computed results are subsequently compared with transient responses obtained by using the frequency-domain BLT equation via a fast Fourier transform, and the agreement is excellent. (the physics of elementary particles and fields)
Zhou, X.; Nenna, F. A.; Aydin, A.
2009-12-01
the FE method is shown by comparing with a classic analytical solution (Jaswon & Bhargava, 1961) for two-dimensional elastic elliptical inclusion problems. For a single LVRS, it is found that the normal stresses at the tip of the elliptical body is compressive and significantly amplified with respect to the remote stresses, whereas on the flanks they are slightly reduced, similar to those shown by previous investigators (e.g. Katsman et al., 2006). We have also calculated stresses associated with parallel and echelon LVRSs in order to investigate the role of interaction in the stress amplification. We found that, in respect to a single LVRS, the normal stresses at the tip areas of two LVRSs are further increased and the normal stresses on their flanks can also increase depending on their relative locations. If the mechanical models represent significant factors in the growth processes of PSSs, then the tip stresses should enhance the in-plane propagation and the lateral linkage of neighboring PSS segments and the flank stresses may contribute to the transverse coalescence of the seams. In this respect, incorporating a creep model into the FE model, which is underway, can help with the transverse propagation and coalescence of LVRSs by accounting for the rate factor.
Developing Semi-Analytical solutions for Saint-Venant Equations in the Uniform Flow Region
Directory of Open Access Journals (Sweden)
M.M. Heidari
2016-09-01
Full Text Available Introduction: Unsteady flow in irrigation systems is the result of operations in response to changes in water demand that affect the hydraulic performance networks. The increased hydraulic performance needed to recognize unsteady flow and quantify the factors affecting it. Unsteady flow in open channels is governed by the fully dynamic Saint Venant equation, which express the principles of conservation of mass and momentum. Unsteady flow in open channels can be classified into two types: routing and operation-type problems. In the routing problems, The Saint Venant equations are solved to get the discharge and water level in the time series. Also, they are used in the operation problem to compute the inflow at the upstream section of the channel according to the prescribed downstream flow hydrographs. The Saint Venant equation has no analytical solution and in the majority cases of such methods use numerical integration of continuity and momentum equations, and are characterized by complicated numerical procedures that are not always convenient for carrying out practical engineering calculations. Therefore, approximate methods deserve attention since they would allow the solution of dynamic problems in analytical form with enough exactness. There are effective methods for automatic controller synthesis in control theory that provide the required performance optimization. It is therefore important to get simplified models of irrigation canals for control design. It would be even more interesting to have linear models that explicitly depend on physical parameters. Such models would allow one to, handle the dynamics of the system with fewer parameters, understand the impact of physical parameters on the dynamics, and facilitate the development a systematic design method. Many analytical models have been proposed in the literature, Most of them have been obtained in the frequency domain by applying Laplace transform to linearized Saint
International Nuclear Information System (INIS)
Wang, R; Han, Q; Pan, E
2010-01-01
We derive, in this paper, the analytical solution for a three-dimensional transversely isotropic axisymmetric multilayered magneto-electro-elastic (MEE) circular plate under simply supported boundary conditions. The state space vector, the finite Hankel transform and propagating matrix methods are utilized together to obtain the full-field solutions for the MEE plate made of piezoelectric (PE) and piezomagnetic (PM) layers. Numerical examples for three-layered and five-layered PE/PM composites with different stacking sequences and under different loading conditions are presented and discussed. These results can serve as benchmark solutions for future numerical analyses of layered MEE plates
International Nuclear Information System (INIS)
Hu Xianquan; Luo Guang; Cui Lipeng; Niu Lianbin; Li Fangyu
2009-01-01
The analytic solution of the radial Schroedinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schroedinger equation is V(r) = α 1 r 8 + α 2 r 3 + α 3 r 2 + β 3 r -1 + β 2 r -3 + β 1 r -4 . Generally speaking, there is only an approximate solution, but not analytic solution for Schroedinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schroedinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → and r → 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schroedinger equation; and lastly, they discuss the solutions and make conclusions. (general)
Deng, Baoqing; Si, Yinbing; Wang, Jia
2017-12-01
Transient storages may vary along the stream due to stream hydraulic conditions and the characteristics of storage. Analytical solutions of transient storage models in literature didn't cover the spatially non-uniform storage. A novel integral transform strategy is presented that simultaneously performs integral transforms to the concentrations in the stream and in storage zones by using the single set of eigenfunctions derived from the advection-diffusion equation of the stream. The semi-analytical solution of the multiple-zone transient storage model with the spatially non-uniform storage is obtained by applying the generalized integral transform technique to all partial differential equations in the multiple-zone transient storage model. The derived semi-analytical solution is validated against the field data in literature. Good agreement between the computed data and the field data is obtained. Some illustrative examples are formulated to demonstrate the applications of the present solution. It is shown that solute transport can be greatly affected by the variation of mass exchange coefficient and the ratio of cross-sectional areas. When the ratio of cross-sectional areas is big or the mass exchange coefficient is small, more reaches are recommended to calibrate the parameter.
Directory of Open Access Journals (Sweden)
Feng Zhou
2018-01-01
Full Text Available Developing an analytical solution for the consolidation of unsaturated soils remains a challenging task due to the complexity of coupled governing equations for air and water phases. This paper presents an equal-strain model for the radial consolidation of unsaturated soils by vertical drains, and the effect of drain resistance is also considered. Simplified governing equations are established, and an analytical solution to calculate the excess pore-air and pore-water pressures is derived by using the methods of matrix analysis and eigenfunction expansion. The average degrees of consolidation for air and water phases and the ground surface settlement are also given. The solutions of the equal-strain model are verified by comparing the proposed free-strain model with the equal-strain model, and reasonably good agreement is obtained. Moreover, parametric studies regarding the drain resistance effect are graphically presented.
Directory of Open Access Journals (Sweden)
Moradi Amir
2013-01-01
Full Text Available In this article, the simultaneous convection-radiation heat transfer of a moving fin of variable thermal conductivity is studied. The differential transformation method (DTM is applied for an analytic solution for heat transfer in fin with two different profiles. Fin profiles are rectangular and exponential. The accuracy of analytic solution is validated by comparing it with the numerical solution that is obtained by fourth-order Runge-Kutta method. The analytical and numerical results are shown for different values of the embedding parameters. DTM results show that series converge rapidly with high accuracy. The results indicate that the fin tip temperature increases when ambient temperature increases. Conversely, the fin tip temperature decreases with an increase in the Peclet number, convection-conduction and radiation-conduction parameters. It is shown that the fin tip temperature of the exponential profile is higher than the rectangular one. The results indicate that the numerical data and analytical method are in a good agreement with each other.
McCormick, Keith; Wei, Bowen
2017-01-01
IBM SPSS Modeler allows quick, efficient predictive analytics and insight building from your data, and is a popularly used data mining tool. This book will guide you through the data mining process, and presents relevant statistical methods which are used to build predictive models and conduct other analytic tasks using IBM SPSS Modeler. From ...
McCormick, Keith; Wei, Bowen
2017-01-01
IBM SPSS Modeler allows quick, efficient predictive analytics and insight building from your data, and is a popularly used data mining tool. This book will guide you through the data mining process, and presents relevant statistical methods which are used to build predictive models and conduct other analytic tasks using IBM SPSS Modeler. From ...
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
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...
International Nuclear Information System (INIS)
Gonis, Antonios; Daene, Markus W.; Nicholson, Don M.; Stocks, George Malcolm
2012-01-01
We have developed and tested in terms of atomic calculations an exact, analytic and computationally simple procedure for determining the functional derivative of the exchange energy with respect to the density in the implementation of the Kohn Sham formulation of density functional theory (KS-DFT), providing an analytic, closed-form solution of the self-interaction problem in KS-DFT. We demonstrate the efficacy of our method through ground-state calculations of the exchange potential and energy for atomic He and Be atoms, and comparisons with experiment and the results obtained within the optimized effective potential (OEP) method.
Analytical Solutions for the Surface States of Bi1-xSbx (0 ≤ x ≲ 0.1)
Fuseya, Yuki; Fukuyama, Hidetoshi
2018-04-01
Analytical solutions for the surface state (SS) of an extended Wolff Hamiltonian, which is a common Hamiltonian for strongly spin-orbit coupled systems, are obtained both for semi-infinite and finite-thickness boundary conditions. For the semi-infinite system, there are two types of SS solutions: (I-a) linearly crossing SSs in the direct bulk band gap, and (I-b) SSs with linear dispersions entering the bulk conduction or valence bands away from the band edge. For the finite-thickness system, a gap opens in the SS of solution I-a. Numerical solutions for the SS are also obtained based on the tight-binding model of Liu and Allen [https://doi.org/10.1103/PhysRevB.52.1566, Phys. Rev. B 52, 1566 (1995)] for Bi1-xSbx (0 ≤ x ≤ 0.1). A perfect correspondence between the analytic and numerical solutions is obtained around the \\bar{M} point including their thickness dependence. This is the first time that the character of the SS numerically obtained is identified with the help of analytical solutions. The size of the gap for I-a SS can be larger than that of bulk band gap even for a "thick" films ( ≲ 200 bilayers ≃ 80 nm) of pure bismuth. Consequently, in such a film of Bi1-xSbx, there is no apparent change in the SSs through the band inversion at x ≃ 0.04, even though the nature of the SS is changed from solution I-a to I-b. Based on our theoretical results, the experimental results on the SS of Bi1-xSbx (0 ≤ x ≲ 0.1) are discussed.
Directory of Open Access Journals (Sweden)
Heung-Ryoul Noh
2016-03-01
Full Text Available We present an analytical calculation of temporal evolution of populations for optically pumped atoms under the influence of weak, circularly polarized light. The differential equations for the populations of magnetic sublevels in the excited state, derived from rate equations, are expressed in the form of inhomogeneous second-order differential equations with constant coefficients. We present a general method of analytically solving these differential equations, and obtain explicit analytical forms of the populations of the ground state at the lowest order in the saturation parameter. The obtained populations can be used to calculate lineshapes in various laser spectroscopies, considering transit time relaxation.
Directory of Open Access Journals (Sweden)
Tohru Morita
2016-03-01
Full Text Available In a series of papers, we discussed the solution of Laplace’s differential equation (DE by using fractional calculus, operational calculus in the framework of distribution theory, and Laplace transform. The solutions of Kummer’s DE, which are expressed by the confluent hypergeometric functions, are obtained with the aid of the analytic continuation (AC of Riemann–Liouville fractional derivative (fD and the distribution theory in the space D′R or the AC of Laplace transform. We now obtain the solutions of the hypergeometric DE, which are expressed by the hypergeometric functions, with the aid of the AC of Riemann–Liouville fD, and the distribution theory in the space D′r,R, which is introduced in this paper, or by the term-by-term inverse Laplace transform of AC of Laplace transform of the solution expressed by a series.
Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics
Kakhktsyan, V. M.; Khachatryan, A. Kh.
2013-07-01
A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.
DEFF Research Database (Denmark)
Khan, Sanaullah; Birch, Johnny; Van Calsteren, Marie-Rose
2018-01-01
Despite a very large number of bacterial exopolysaccharides have been reported, detailed knowledge on their molecular structures and associative interactions with proteins is lacking. Small-angle X-ray scattering, dynamic light scattering and analytical ultracentrifugation (AUC) were used...
Big data analytics as a service infrastructure: challenges, desired properties and solutions
Martín-Márquez, Manuel
2015-01-01
CERN's accelerator complex generates a very large amount of data. A large volumen of heterogeneous data is constantly generated from control equipment and monitoring agents. These data must be stored and analysed. Over the decades, CERN's researching and engineering teams have applied different approaches, techniques and technologies for this purpose. This situation has minimised the necessary collaboration and, more relevantly, the cross data analytics over different domains. These two factors are essential to unlock hidden insights and correlations between the underlying processes, which enable better and more efficient daily-based accelerator operations and more informed decisions. The proposed Big Data Analytics as a Service Infrastructure aims to: (1) integrate the existing developments, (2) centralise and standardise the complex data analytics needs for CERN's research and engineering community, (3) deliver real-time, batch data analytics and information discovery capabilities, and (4) provide transpare...
NUMERICAL AND ANALYTIC SOLUTION OF PRANDTL’S EQUATION FOR SOLID BODIES WITH AGREED CONTACT SURFACES
Directory of Open Access Journals (Sweden)
A. Chigarev
2013-01-01
Full Text Available The paper considers a method for problem solution pertaining to compression of elastic bodies bounded by cylindrical surfaces whose radii are almost equal. The objective aim does not allow to apply the Hertz theory and reduces to finding approximate solutions of the Prandtl’s equation. The resulting solution is compared with the solution in the ANSYS system.
Benhammouda, Brahim; Vazquez-Leal, Hector
2016-01-01
This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.
Validation of the analytical methodology for evaluation of lapachol in solution by HPCL
Fonseca, Said G. C.; Silva, Leila B. L. da; Castro, Rebeka F.; Santana, Davi P. de
2004-01-01
Lapachol is a naphthoquinone found in several species of the Bignoniaceae family possessing mainly anticancer activity. The present work consists of the development and validation of analytical methodology for lapachol and its preparations. The results here obtained show that lapachol has a low quantification limit, that the analytical methodology is accurate, reproducible, robust and linear over the concentration range 0.5-100 µg/mL of lapachol.
Fring, Andreas; Frith, Thomas
2017-01-01
We propose a procedure to obtain exact analytical solutions to the time-dependent Schrödinger equations involving explicit time-dependent Hermitian Hamiltonians from solutions to time-independent non-Hermitian Hamiltonian systems and the time-dependent Dyson relation, together with the time-dependent quasi-Hermiticity relation. We illustrate the working of this method for a simple Hermitian Rabi-type model by relating it to a non-Hermitian time-independent system corresponding to the one-site lattice Yang-Lee model.
International Nuclear Information System (INIS)
Barros, R. C.; Filho, H. A.; Platt, G. M.; Oliveira, F. B. S.; Militao, D. S.
2009-01-01
Coarse-mesh numerical methods are very efficient in the sense that they generate accurate results in short computational time, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points. On the other hand, they generate numerical solutions that do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. In this paper we describe two analytical reconstruction schemes for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates (S N ) transport model in slab geometry. The first scheme we describe is based on the analytical reconstruction of the coarse-mesh solution within each discretization cell of the spatial grid set up on the slab. The second scheme is based on the angular reconstruction of the discrete ordinates solution between two contiguous ordinates of the angular quadrature set used in the S N model. Numerical results are given so we can illustrate the accuracy of the two reconstruction schemes, as described in this paper. (authors)
International Nuclear Information System (INIS)
Sudicky, E.A.; Frind, E.O.
1984-01-01
An analytical solution is presented for the problem of radionuclide chain decay during transport through a discrete fracture situated in a porous rock matrix. The solution takes into account advection along the fracture, molecular diffusion from the fracture to the porous matrix, adsorption on the fracture face, adsorption in the rock matrix, and radioactive decay. The solution for the daughter product is in the form of a double integral which is evaluated by Gauss-Legendre quadrature. Results show that the daughter product tends to advance ahead of the parent nuclide even when the half-life of the parent is larger. This is attributed to the effect of chain decay in the matrix, which tends to reduce the diffusive loss of the daughter along the fracture. The examples also demonstrate that neglecting the parent nuclide and modeling its daughter as a single species can result in significant overestimation of arrival times at some point along the fracture. Although the analytical solution is restricted to a two-member chain for practical reasons, it represents a more realistic description of nuclide transport along a fracture than available single-species models. The solution may be of use for application to other contaminants undergoing different types of first-order transformation reactions
Ford Versypt, Ashlee N; Arendt, Paul D; Pack, Daniel W; Braatz, Richard D
2015-01-01
A mathematical reaction-diffusion model is defined to describe the gradual decomposition of polymer microspheres composed of poly(D,L-lactic-co-glycolic acid) (PLGA) that are used for pharmaceutical drug delivery over extended periods of time. The partial differential equation (PDE) model treats simultaneous first-order generation due to chemical reaction and diffusion of reaction products in spherical geometry to capture the microsphere-size-dependent effects of autocatalysis on PLGA erosion that occurs when the microspheres are exposed to aqueous media such as biological fluids. The model is solved analytically for the concentration of the autocatalytic carboxylic acid end groups of the polymer chains that comprise the microspheres as a function of radial position and time. The analytical solution for the reaction and transport of the autocatalytic chemical species is useful for predicting the conditions under which drug release from PLGA microspheres transitions from diffusion-controlled to erosion-controlled release, for understanding the dynamic coupling between the PLGA degradation and erosion mechanisms, and for designing drug release particles. The model is the first to provide an analytical prediction for the dynamics and spatial heterogeneities of PLGA degradation and erosion within a spherical particle. The analytical solution is applicable to other spherical systems with simultaneous diffusive transport and first-order generation by reaction.
H. Saberi-Nik; S. Effati; R. Buzhabadi
2010-01-01
In this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The homotopy analysis method (HAM) is used for solving this equation. Several examples are given to reconfirm the efficiency of these algorithms. The results of applying this procedure to the integro-differential equation with time-periodic coefficients show the high accuracy, simpli...
Directory of Open Access Journals (Sweden)
H. Saberi-Nik
2013-07-01
Full Text Available In this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The homotopy analysis method (HAM is used for solving this equation. Several examples are given to reconfirm the efficiency of these algorithms. The results of applying this procedure to the integro-differential equation with time-periodic coefficients show the high accuracy, simplicity and efficiency of this method.
Directory of Open Access Journals (Sweden)
H. Saberi-Nik
2010-06-01
Full Text Available In this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The homotopy analysis method (HAM is used for solving this equation. Several examples are given to reconfirm the efficiency of these algorithms. The results of applying this procedure to the integro-differential equation with time-periodic coefficients show the high accuracy, simplicity and efficiency of this method.
Zhoujin Cui; Zisen Mao; Sujuan Yang; Pinneng Yu
2013-01-01
The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is ...
Kolář, Michal
2014-01-01
The work is focused on the analysis of the service process in the company Analytical Medical Instruments Ltd. (hereinafter the firm AMI, Ltd.), and subsequent optimization of the service process . The main objective is service process to analyze and propose a solution that would optimize the service process . The first part is theoretical , includes a search of the sources and methodologies. Then I described the company AMI, Ltd. The second part is based on a brief description of the organiza...
Hilliard, Mark; Alley, William R; McManus, Ciara A; Yu, Ying Qing; Hallinan, Sinead; Gebler, John; Rudd, Pauline M
Glycosylation is an important attribute of biopharmaceutical products to monitor from development through production. However, glycosylation analysis has traditionally been a time-consuming process with long sample preparation protocols and manual interpretation of the data. To address the challenges associated with glycan analysis, we developed a streamlined analytical solution that covers the entire process from sample preparation to data analysis. In this communication, we describe the complete analytical solution that begins with a simplified and fast N-linked glycan sample preparation protocol that can be completed in less than 1 hr. The sample preparation includes labelling with RapiFluor-MS tag to improve both fluorescence (FLR) and mass spectral (MS) sensitivities. Following HILIC-UPLC/FLR/MS analyses, the data are processed and a library search based on glucose units has been included to expedite the task of structural assignment. We then applied this total analytical solution to characterize the glycosylation of the NIST Reference Material mAb 8761. For this glycoprotein, we confidently identified 35 N-linked glycans and all three major classes, high mannose, complex, and hybrid, were present. The majority of the glycans were neutral and fucosylated; glycans featuring N-glycolylneuraminic acid and those with two galactoses connected via an α1,3-linkage were also identified.
Directory of Open Access Journals (Sweden)
S.V. Bystrov
2016-05-01
Full Text Available Subject of Research.We present research results for the signal uncertainty problem that naturally arises for the developers of servomechanisms, including analytical design of serial compensators, delivering the required quality indexes for servomechanisms. Method. The problem was solved with the use of Besekerskiy engineering approach, formulated in 1958. This gave the possibility to reduce requirements for input signal composition of servomechanisms by using only two of their quantitative characteristics, such as maximum speed and acceleration. Information about input signal maximum speed and acceleration allows entering into consideration the equivalent harmonic input signal with calculated amplitude and frequency. In combination with requirements for maximum tracking error, the amplitude and frequency of the equivalent harmonic effects make it possible to estimate analytically the value of the amplitude characteristics of the system by error and then convert it to amplitude characteristic of open-loop system transfer function. While previously Besekerskiy approach was mainly used in relation to the apparatus of logarithmic characteristics, we use this approach for analytical synthesis of consecutive compensators. Main Results. Proposed technique is used to create analytical representation of "input–output" and "error–output" polynomial dynamic models of the designed system. In turn, the desired model of the designed system in the "error–output" form of analytical representation of transfer functions is the basis for the design of consecutive compensator, that delivers the desired placement of state matrix eigenvalues and, consequently, the necessary set of dynamic indexes for the designed system. The given procedure of consecutive compensator analytical design on the basis of Besekerskiy engineering approach under conditions of signal uncertainty is illustrated by an example. Practical Relevance. The obtained theoretical results are
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R. K.
of the problem, i.e. the number of state variables of the dynamical systems. In contrast, the application of the simulation techniques is not limited to Markov problems, nor is it dependent on the mean rate of impulses. Moreover their use is straightforward for a large class of point processes, at least......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically......-numerical techniques suitable for Markov response problems such as moments equation, Petrov-Galerkin and cell-to-cell mapping techniques are briefly discussed. Usefulness of these techniques is limited by the fact that effectiveness of each of them depends on the mean rate of impulses. Another limitation is the size...
Directory of Open Access Journals (Sweden)
Hua Yang
2012-01-01
Full Text Available We are concerned with the stochastic differential delay equations with Poisson jump and Markovian switching (SDDEsPJMSs. Most SDDEsPJMSs cannot be solved explicitly as stochastic differential equations. Therefore, numerical solutions have become an important issue in the study of SDDEsPJMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEsPJMSs when the drift and diffusion coefficients are Taylor approximations.
Directory of Open Access Journals (Sweden)
Tiago A. Morgado
2015-06-01
Full Text Available We derive closed analytical formulae for the power emitted by moving charged particles in a uniaxial wire medium by means of an eigenfunction expansion. Our analytical expressions demonstrate that, in the absence of material dispersion, the stopping power of the uniaxial wire medium is proportional to the charge velocity, and that there is no velocity threshold for the Cherenkov emission. It is shown that the eigenfunction expansion formalism can be extended to the case of dispersive lossless media. Furthermore, in the presence of material dispersion, the optimal charge velocity that maximizes the emitted Cherenkov power may be less than the speed of light in a vacuum.
Hedayati, R; Sadighi, M; Mohammadi-Aghdam, M; Zadpoor, A A
2016-03-01
Additive manufacturing (AM) has enabled fabrication of open-cell porous biomaterials based on repeating unit cells. The micro-architecture of the porous biomaterials and, thus, their physical properties could then be precisely controlled. Due to their many favorable properties, porous biomaterials manufactured using AM are considered as promising candidates for bone substitution as well as for several other applications in orthopedic surgery. The mechanical properties of such porous structures including static and fatigue properties are shown to be strongly dependent on the type of the repeating unit cell based on which the porous biomaterial is built. In this paper, we study the mechanical properties of porous biomaterials made from a relatively new unit cell, namely truncated cube. We present analytical solutions that relate the dimensions of the repeating unit cell to the elastic modulus, Poisson's ratio, yield stress, and buckling load of those porous structures. We also performed finite element modeling to predict the mechanical properties of the porous structures. The analytical solution and computational results were found to be in agreement with each other. The mechanical properties estimated using both the analytical and computational techniques were somewhat higher than the experimental data reported in one of our recent studies on selective laser melted Ti-6Al-4V porous biomaterials. In addition to porosity, the elastic modulus and Poisson's ratio of the porous structures were found to be strongly dependent on the ratio of the length of the inclined struts to that of the uninclined (i.e. vertical or horizontal) struts, α, in the truncated cube unit cell. The geometry of the truncated cube unit cell approaches the octahedral and cube unit cells when α respectively approaches zero and infinity. Consistent with those geometrical observations, the analytical solutions presented in this study approached those of the octahedral and cube unit cells when
Energy Technology Data Exchange (ETDEWEB)
Claesson, J.; Probert, T. [Lund Univ. (Sweden). Dept. of Building Physics and Mathematical Physics
1996-01-01
The temperature field in rock due to a large rectangular grid of heat releasing canisters containing nuclear waste is studied. The solution is by superposition divided into different parts. There is a global temperature field due to the large rectangular canister area, while a local field accounts for the remaining heat source problem. The global field is reduced to a single integral. The local field is also solved analytically using solutions for a finite line heat source and for an infinite grid of point sources. The local solution is reduced to three parts, each of which depends on two spatial coordinates only. The temperatures at the envelope of a canister are given by a single thermal resistance, which is given by an explicit formula. The results are illustrated by a few numerical examples dealing with the KBS-3 concept for storage of nuclear waste. 8 refs.
Zhang, Bo; Chen, Tianning; Zhao, Yuyuan; Zhang, Weiyong; Zhu, Jian
2012-09-01
On the basis of the work of Wilson et al. [J. Acoust. Soc. Am. 84, 350-359 (1988)], a more exact numerical approach was constructed for predicting the nonlinear sound propagation and absorption properties of rigid porous media at high sound pressure levels. The numerical solution was validated by the experimental results for sintered fibrous porous steel samples and its predictions were compared with the numerical solution of Wilson et al. An approximate analytical solution was further put forward for the normalized surface acoustic admittance of rigid air-saturated porous materials with infinite thickness, based on the wave perturbation method developed by Lambert and McIntosh [J. Acoust. Soc. Am. 88, 1950-1959 (1990)]. Comparisons were made with the numerical results.
Wetterneck, Chad T.; Hart, John M.
2012-01-01
Problems with intimacy and interpersonal issues are exhibited across most psychiatric disorders. However, most of the targets in Cognitive Behavioral Therapy are primarily intrapersonal in nature, with few directly involved in interpersonal functioning and effective intimacy. Functional Analytic Psychotherapy (FAP) provides a behavioral basis for…
An analytical solution for contact resistance of staggered organic field-effect transistors
Karimi-Alavijeh, Hamidreza; Katebi-Jahromi, Alireza
2017-03-01
We have developed analytical models for bias dependent contact resistance (RC) and output characteristics of staggered organic field-effect transistors (OFETS) based on a bulk resistance-approximated and mobility-modified current-crowding method. Numerical evaluations of RC and its resistive components show that the bias dependency of the bulk resistance is negligible. Consequently, the properties of the active layer interfaces determine RC and its characteristics. Effective parameters include a normally constant charge injection barrier at the organic-metal interface (Eb) and a gate induced surface carrier-concentration (PS0) at the organic-insulator boundary. The energy barrier pertains to the fabrication process, and its related resistance (rc) can be determined as the fitting parameter of the theoretical model. However, PS0 is strongly gate bias dependent and the results of the numerical model indicate that the resulting component (rch) is dominant and has a considerable effect on RC and its characteristics. More importantly, PS0 as the key parameter of the contact resistance is analytically expressible and by using a proposed mobility-modified current-crowding model, the contact resistance can be analytically formulated. Accordingly, the output characteristics of the OFETs in the triode region can be also analytically modeled using the developed relation of RC.
Semi-analytical solution to plane strain loading of elastic layered ...
Indian Academy of Sciences (India)
Abstract. The plane strain loading of a linear elastic layered coating halfspace is solved semi-analytically through a combination of Airy stress function and Fourier transforms and highly simplified and compact expressions for displacement and stresses in layer and substrate are presented in terms of pressure distribution in ...
The analytical solution of wake-fields in an elliptical pillbox cavity
International Nuclear Information System (INIS)
Yang, J.S.; Chen, K.W.
1991-01-01
The wake potential of a bunch of relativistic charged particles traversing an elliptical pillbox cavity is derived analytically in the limit of vanishing aperture. It is found that the resonant modes of an elliptical cavity can be expressed in terms of Mathieu functions. Calculation results are presented and compared with numerical ones. (author) 10 refs., 10 figs., 2 tabs
Czech Academy of Sciences Publication Activity Database
Křížek, T.; Kubíčková, A.; Hladílková, Jana; Coufal, P.; Heyda, J.; Jungwirth, Pavel
2014-01-01
Roč. 35, č. 5 (2014), s. 617-624 ISSN 0173-0835 R&D Projects: GA ČR GBP208/12/G016 Institutional support: RVO:61388963 Keywords : EOF markers * ion-specific effects * ion-specific mobilization * molecular dynamics simulations * neutral analytes Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.028, year: 2014
Czech Academy of Sciences Publication Activity Database
Rontó, András; Rontó, M.; Holubová, G.; Nečesal, P.
-, - (2011), s. 58 ISSN 1687-2770 Institutional research plan: CEZ:AV0Z10190503 Keywords : nonlinear boundary value problem * numerical-analytic method * Chebyshev interpolation polynomials Subject RIV: BA - General Mathematics Impact factor: 0.911, year: 2011 http://www.boundaryvalueproblems.com/content/2011/1/58/abstract
Gómez-Aguilar, J. F.
2018-03-01
In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.
Directory of Open Access Journals (Sweden)
A. Beléndez
2012-01-01
Full Text Available Accurate approximate closed-form solutions for the cubic-quintic Duffing oscillator are obtained in terms of elementary functions. To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation. Explicit approximate solutions are then expressed as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function cn. Then we obtain other approximate expressions for these solutions, which are expressed in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean is used and the rational harmonic balance method is applied to obtain the periodic solution of the original nonlinear oscillator.
International Nuclear Information System (INIS)
Moraes, Pedro Gabriel B.; Leite, Michel C.A.; Barros, Ricardo C.
2013-01-01
In this work we developed a software to model and generate results in tables and graphs of one-dimensional neutron transport problems in multi-group formulation of energy. The numerical method we use to solve the problem of neutron diffusion is analytic, thus eliminating the truncation errors that appear in classical numerical methods, e.g., the method of finite differences. This numerical analytical method increases the computational efficiency, since they are not refined spatial discretization necessary because for any spatial discretization grids used, the numerical result generated for the same point of the domain remains unchanged unless the rounding errors of computational finite arithmetic. We chose to develop a computational application in MatLab platform for numerical computation and program interface is simple and easy with knobs. We consider important to model this neutron transport problem with a fixed source in the context of shielding calculations of radiation that protects the biosphere, and could be sensitive to ionizing radiation
International Nuclear Information System (INIS)
Shooshtari, Alireza; Marzieh Hoseini, Seyedeh; Kalhori, Hamed; Nima Mahmoodi, S
2012-01-01
Nonlinear vibrations of viscoelastic microcantilevers with a piezoelectric actuator layer on the top surface are investigated. In this work, the microcantilever follows a classical linear viscoelastic model, i.e., Kelvin–Voigt. In addition, it is assumed that the microcantilever complies with Euler–Bernoulli beam theory. The Hamilton principle is used to obtain the equations of motion for the microcantilever oscillations. Then, the Galerkin approximation is utilized for separation of time and displacement variables, thus the time function is obtained as a second order nonlinear ordinary differential equation with quadratic and cubic nonlinear terms. Nonlinearities appear in stiffness, inertia and damping terms. Using the method of multiple scales, the analytical relations for nonlinear natural frequency and amplitude of the vibration are derived. Using the obtained analytical relations, the effects of geometric factors and material properties on the free nonlinear behavior of this beam are investigated. The results are also verified by numerical analysis of the equations. (paper)
Analytical solution for the free vibration analysis of delaminated Timoshenko beams.
Jafari-Talookolaei, Ramazan-Ali; Abedi, Maryam
2014-01-01
This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. Natural frequencies and mode shapes of various Timoshenko beams are presented to demonstrate the efficiency of the methodology.
Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams
Directory of Open Access Journals (Sweden)
Ramazan-Ali Jafari-Talookolaei
2014-01-01
Full Text Available This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. Natural frequencies and mode shapes of various Timoshenko beams are presented to demonstrate the efficiency of the methodology.
Makoveeva, Eugenya V.; Alexandrov, Dmitri V.
2018-01-01
This article is concerned with a new analytical description of nucleation and growth of crystals in a metastable mushy layer (supercooled liquid or supersaturated solution) at the intermediate stage of phase transition. The model under consideration consisting of the non-stationary integro-differential system of governing equations for the distribution function and metastability level is analytically solved by means of the saddle-point technique for the Laplace-type integral in the case of arbitrary nucleation kinetics and time-dependent heat or mass sources in the balance equation. We demonstrate that the time-dependent distribution function approaches the stationary profile in course of time. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.
Energy Technology Data Exchange (ETDEWEB)
Hoang-Do, Ngoc-Tram; Hoang, Van-Hung; Le, Van-Hoang [Department of Physics, Ho Chi Minh City University of Pedagogy, 280 An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)
2013-05-15
The Feranchuk-Komarov operator method is developed by combining with the Levi-Civita transformation in order to construct analytical solutions of the Schroedinger equation for a two-dimensional exciton in a uniform magnetic field of arbitrary strength. As a result, analytical expressions for the energy of the ground and excited states are obtained with a very high precision of up to four decimal places. Especially, the precision is uniformly stable for the whole range of the magnetic field. This advantage appears due to the consideration of the asymptotic behaviour of the wave-functions in strong magnetic field. The results could be used for various physical analyses and the method used here could also be applied to other atomic systems.
Avilés, L.; Canfora, F.; Dimakis, N.; Hidalgo, D.
2017-12-01
We construct the first analytic examples of topologically nontrivial solutions of the (3 +1 )-dimensional U (1 ) gauged Skyrme model within a finite box in (3 +1 )-dimensional flat space-time. There are two types of gauged solitons. The first type corresponds to gauged Skyrmions living within a finite volume. The second corresponds to gauged time crystals (smooth solutions of the U (1 ) gauged Skyrme model whose periodic time dependence is protected by a winding number). The notion of electromagnetic duality can be extended for these two types of configurations in the sense that the electric and one of the magnetic components can be interchanged. These analytic solutions show very explicitly the Callan-Witten mechanism (according to which magnetic monopoles may "swallow" part of the topological charge of the Skyrmion) since the electromagnetic field contributes directly to the conserved topological charge of the gauged Skyrmions. As it happens in superconductors, the magnetic field is suppressed in the core of the gauged Skyrmions. On the other hand, the electric field is strongly suppresed in the core of gauged time crystals.
Analytical solution for the anisotropic Rabi model: effects of counter-rotating terms.
Zhang, Guofeng; Zhu, Hanjie
2015-03-04
The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.
Directory of Open Access Journals (Sweden)
Marwan Fahs
2018-02-01
Full Text Available The Henry problem (HP continues to play a useful role in theoretical and practical studies related to seawater intrusion (SWI into coastal aquifers. The popularity of this problem is attributed to its simplicity and precision to the existence of semi-analytical (SA solutions. The first SA solution has been developed for a high uniform diffusion coefficient. Several further studies have contributed more realistic solutions with lower diffusion coefficients or velocity-dependent dispersion. All the existing SA solutions are limited to homogenous and isotropic domains. This work attempts to improve the realism of the SA solution of the dispersive HP by extending it to heterogeneous and anisotropic coastal aquifers. The solution is obtained using the Fourier series method. A special hydraulic conductivity–depth model describing stratified heterogeneity is used for mathematical convenience. An efficient technique is developed to solve the flow and transport equations in the spectral space. With this technique, we show that the HP can be solved in the spectral space with the salt concentration as primary unknown. Several examples are generated, and the SA solutions are compared against an in-house finite element code. The results provide high-quality data assessed by quantitative indicators that can be effectively used for code verification in realistic configurations of heterogeneity and anisotropy. The SA solution is used to explain contradictory results stated in the previous works about the effect of anisotropy on the saltwater wedge. It is also used to investigate the combined influence of stratification and anisotropy on relevant metrics characterizing SWI. At a constant gravity number, anisotropy leads to landward migration of the saltwater wedge, more intense saltwater flux, a wider mixing zone and shallower groundwater discharge zone to the sea. The influence of stratified heterogeneity is more pronounced in highly anisotropic aquifers. The
Alshaery, Aisha; Ebaid, Abdelhalim
2017-11-01
Kepler's equation is one of the fundamental equations in orbital mechanics. It is a transcendental equation in terms of the eccentric anomaly of a planet which orbits the Sun. Determining the position of a planet in its orbit around the Sun at a given time depends upon the solution of Kepler's equation, which we will solve in this paper by the Adomian decomposition method (ADM). Several properties of the periodicity of the obtained approximate solutions have been proved in lemmas. Our calculations demonstrated a rapid convergence of the obtained approximate solutions which are displayed in tables and graphs. Also, it has been shown in this paper that only a few terms of the Adomian decomposition series are sufficient to achieve highly accurate numerical results for any number of revolutions of the Earth around the Sun as a consequence of the periodicity property. Numerically, the four-term approximate solution coincides with the Bessel-Fourier series solution in the literature up to seven decimal places at some values of the time parameter and nine decimal places at other values. Moreover, the absolute error approaches zero using the nine term approximate Adomian solution. In addition, the approximate Adomian solutions for the eccentric anomaly have been used to show the convergence of the approximate radial distances of the Earth from the Sun for any number of revolutions. The minimal distance (perihelion) and maximal distance (aphelion) approach 147 million kilometers and 152.505 million kilometers, respectively, and these coincide with the well known results in astronomical physics. Therefore, the Adomian decomposition method is validated as an effective tool to solve Kepler's equation for elliptical orbits.
Energy Technology Data Exchange (ETDEWEB)
Spoerl, Andreas
2008-06-05
Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria to identify systems with dynamics which are invertible under local operations. Finally, a full quantum algorithm to distinguish between two knots was implemented on a spin(1)/(2) system. All operations for this experiment were calculated analytically. The experimental results coincide with the theoretical expectations. (orig.)
The focusing effect of P-wave in the Moon's and Earth's low-velocity core. Analytical solution
Fatyanov, A. G.; Burmin, V. Yu
2018-04-01
The important aspect in the study of the structure of the interiors of planets is the question of the presence and state of core inside them. While for the Earth this task was solved long ago, the question of whether the core of the Moon is in a liquid or solid state up to the present is debatable up to present. If the core of the Moon is liquid, then the velocity of longitudinal waves in it should be lower than in the surrounding mantle. If the core is solid, then most likely, the velocity of longitudinal waves in it is higher than in the mantle. Numerical calculations of the wave field allow us to identify the criteria for drawing conclusions about the state of the lunar core. In this paper we consider the problem of constructing an analytical solution for wave fields in a layered sphere of arbitrary radius. A stable analytic solution is obtained for the wave fields of longitudinal waves in a three-layer sphere. Calculations of the total wave fields and rays for simplified models of the Earth and the Moon with real parameters are presented. The analytical solution and the ray pattern showed that the low-velocity cores of the Earth and the Moon possess the properties of a collecting lens. This leads to the emergence of a wave field focusing area. As a result, focused waves of considerable amplitude appear on the surface of the Earth and the Moon. In the Earth case, they appear before the first PKP-wave arrival. These are so-called "precursors", which continue in the subsequent arrivals of waves. At the same time, for the simplified model of the Earth, the maximum amplitude growth is observed in the 147-degree region. For the Moon model, the maximum amplitude growth is around 180°.
Energy Technology Data Exchange (ETDEWEB)
Ikhdair, Sameer M., E-mail: sikhdair@neu.edu.tr [Department of Electrical and Electronic Engineering, Near East University, 922022 Nicosia, Northern Cyprus (Turkey); Department of Physics, Faculty of Science, An-Najah National University, New Campus, Nablus, West Bank, Palestine (Country Unknown); Falaye, Babatunde J., E-mail: fbjames11@physicist.net [Theoretical Physics Section, Department of Physics, University of Ilorin, P.M.B. 1515, Ilorin (Nigeria)
2013-06-27
Highlights: • Solutions of Schrödinger equation in the presence of Pöschl–Teller potential is obtained. • Solutions of Dirac equation in the presence of Pöschl–Teller potential is obtained. • Rotational and vibrational energy eigenvalues of some diatomic molecules are calculated. • Thermodynamics properties of some diatomic molecules are obtained. - Abstract: We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrödinger equation in the presence of Pöschl–Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of spin and pseudospin (p-spin) symmetries. We show that in the nonrelativistic limits, the solution of Dirac system converges to that of Schrödinger system. Rotational and vibrational energy eigenvalues of some diatomic molecules are calculated. Some special cases of interest are studied such as S-wave case, reflectionless-type potential and symmetric hyperbolic PT potential. Furthermore, we present a high temperature partition function in order to study the behavior of the thermodynamic functions such as the vibrational mean energy U, specific heat C, free energy F and entropy S.
International Nuclear Information System (INIS)
Bhattar, S.L.; Kolekar, G.B.; Patil, S.R.
2008-01-01
Fluorescence resonance energy transfer (FRET) between perylene and riboflavin is studied in micellar solution of sodium dodecyl sulfate. The fluorescence of perylene is quenched by riboflavin and quenching is in accordance with Stern-Volmer relation. The efficiency of energy transfer is found to depend on the concentration of riboflavin. The value of critical energy transfer distance (R 0 ) calculated by using Foster relation is 32.13 A, and as it is less than 50 A, it indicates efficient energy transfer in the present system. The analytical relation was established between extent of sensitization and concentration of riboflavin, which helped to estimate vitamin B 2 directly from pharmaceutical tablets
Digital Repository Service at National Institute of Oceanography (India)
Shankar, D.; McCreary, J.P.; Han, W.; Shetye, S.R.
linear, continuously stratified model is used to investigate how forcing by interior Ekman pumping and local alongshore winds affects the East India Coastal Current (EICC). Solutions are found analytically to an approximate version of the equations...) by f_ D n(z')dz', and integrate over the water column. After a few integrations by parts and the use of (2)-(4c), it follows that O + u. - fv. + p. - F. + V u , ( a) O + v, + fu, + p,. = G, + V v , (6b) 0 + - = 0 + ( ) Cn 2 P ( e...
International Nuclear Information System (INIS)
Montan, D.N.
1987-02-01
This report is intended to describe, document and provide instructions for the use of new versions of a set of computer programs commonly referred to as the PLUS family. These programs were originally designed to numerically evaluate simple analytical solutions of the diffusion equation. The new versions include linear thermo-elastic effects from thermal fields calculated by the diffusion equation. After the older versions of the PLUS family were documented a year ago, it was realized that the techniques employed in the programs were well suited to the addition of linear thermo-elastic phenomena. This has been implemented and this report describes the additions. 3 refs., 14 figs
International Nuclear Information System (INIS)
Barrachina, M.; Sauvagnac, R.
1962-01-01
In this paper we go on with our study of the heterogeneous ion-isotopic exchange in column. At present, we apply it to determine the radiochemical composition of the raw solutions used in the industrial recuperation of the long-lived fission products. The separation of the radioelements contained in these solutions is carried out mainly by making use of small columns, 1-3 cm height, of BaSO 4 or SrSO 4 , under selected experimental conditions. These columns behave like a special type of inorganic exchangers, working by absorption or by ion-isotopic exchange depending on the cases,a nd they provide the means for the selective separation of several important fission products employing very small volumes of fixing and eluting solutions. (Author) 11 refs
Construction of exact solutions to the modified forms of DP and CH equations by analytical methods
Directory of Open Access Journals (Sweden)
Jalil Manafian Heris
2015-11-01
Full Text Available In this work, we establish the exact solutions to the modified forms of Degasperis–Procesi (DP and Camassa–Holm (CH equations. The generalized (G’/G-expansion and generalized tanh-coth methods were used to construct solitary wave solutions of nonlinear evolution equations. The generalized (G’/G-expansion method presents a wider applicability for handling nonlinear wave equations. It is shown that the (G’/G-expansion method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
Analytic Solution of the Electromagnetic Eigenvalues Problem in a Cylindrical Resonator
Energy Technology Data Exchange (ETDEWEB)
Checchin, Mattia [Fermilab; Martinello, Martina [Fermilab
2016-10-06
Resonant accelerating cavities are key components in modern particles accelerating facilities. These take advantage of electromagnetic fields resonating at microwave frequencies to accelerate charged particles. Particles gain finite energy at each passage through a cavity if in phase with the resonating field, reaching energies even of the order of $TeV$ when a cascade of accelerating resonators are present. In order to understand how a resonant accelerating cavity transfers energy to charged particles, it is important to determine how the electromagnetic modes are exited into such resonators. In this paper we present a complete analytical calculation of the resonating fields for a simple cylindrical-shaped cavity.
Analytical Chemistry Developmental Work Using a ^{243}Am Solution
Energy Technology Data Exchange (ETDEWEB)
Spencer, Khalil J. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Stanley, Floyd E. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Porterfield, Donivan R. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Castro, Alonso [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-02-24
This project seeks to reestablish our analytical capability to characterize Am bulk material and develop a reference material suitable to characterizing the purity and assay of ^{241}Am oxide for industrial use. The tasks associated with this phase of the project included conducting initial separations experiments, developing thermal ionization mass spectrometry capability using the ^{243}Am isotope as an isotope dilution spike , optimizing the spike for the determination of ^{241}Pu-^{241} Am radiochemistry, and, additionally, developing and testing a methodology which can detect trace to ultra- trace levels of Pu (both assay and isotopics) in bulk Am samples .
International Nuclear Information System (INIS)
Abreu Alvarez, Maikel; Garcia Penna, Caridad Margarita; Martinez Miranda, Lissette
2010-01-01
A validated analytical method by high-performance liquid chromatography (HPLC) was applicable to study of 1 mg/mL Risperidone oral solution stability. The above method was linear, accurate, specific and exact. A stability study of the 1 mg/mL Risperidone oral solution was developed determining its expiry date. The shelf life study was conducted for 24 months at room temperature; whereas the accelerated stability study was conducted with product under influence of humidity and temperature; analysis was made during 3 months. Formula fulfilled the quality specifications described in Pharmacopeia. The results of stability according to shelf life after 24 months showed that the product maintains the parameters determining its quality during this time and in accelerated studies there was not significant degradation (p> 0.05) in the product. Under mentioned conditions expiry date was of 2 years
International Nuclear Information System (INIS)
Garcia, R.D.M.
2015-01-01
Highlights: • An improved 1-D model of 3-D particle transport in ducts is studied. • The cases of isotropic and directional incidence are treated with the ADO method. • Accurate numerical results are reported for ducts of circular cross section. • A comparison with results of other authors is included. • The ADO method is found to be very efficient. - Abstract: An analytical discrete-ordinates solution is developed for the problem of particle transport in ducts, as described by a one-dimensional model constructed with two basis functions. Two types of particle incidence are considered: isotropic incidence and incidence described by the Dirac delta distribution. Accurate numerical results are tabulated for the reflection probabilities of semi-infinite ducts and the reflection and transmission probabilities of finite ducts. It is concluded that the developed solution is more efficient than commonly used numerical implementations of the discrete-ordinates method.
Snellings, R; Prendergast, E P; Brink, A V D; Haas, A P D; Habets, J J L; Kamermans, R; Koopmans, M; Kuijer, P G; Laat, C T A; Ostendorf, R W; Peghaire, A; Rossewij, M
1999-01-01
Particle identification in intermediate heavy-ion collisions, using a modern 4 pi detector which contains several active layers, relies on a parametrisation or numerical integration of the energy loss in thick layers of detector material for different ions. Here an analytical solution applicable over an energy range of a few MeV up to a 100A MeV and for ions up to at least Z=8 is presented. Also, the consequences for time-of-flight measurements (TOF) in detectors behind several thick layers of detector material are discussed. The solution is applied to the data of the Huygens detector, which uses a TPC (dE/dx) and plastic scintillators for particle identification (E and TOF or dE/dx and TOF).
International Nuclear Information System (INIS)
Agashe, Janhavi S; Arnold, David P
2008-01-01
Kelvin's formula is used to calculate forces acting on a permanent magnet in the presence of an external magnetic field from a second permanent magnet. This approach is used to derive explicit analytical solutions for the axial and lateral forces between cuboidal and cylindrical permanent magnets as functions of magnet dimensions and separation. While exact solutions can be found for cuboidal magnets, a hypergeometric expansion is used to approximate the elliptic integrals in solving for the fields and forces for the cylindrical magnets. The resulting equations are applied over a range of magnet sizes and geometries to explore scaling laws and other geometrical effects. It is shown that cuboidal magnets provide larger forces than equivalently sized cylindrical magnets. Also, the aspect ratio of the magnets significantly affects the forces. These results are intended to benefit the design and optimization of sensors, actuators and systems that rely on magnetic forces, particularly at the microscale
Li, Ping; Li, Xin-zhou; Xi, Ping
2016-06-01
We present a detailed study of the spherically symmetric solutions in Lorentz-breaking massive gravity. There is an undetermined function { F }(X,{w}1,{w}2,{w}3) in the action of Stückelberg fields {S}φ ={{{Λ }}}4\\int {{{d}}}4x\\sqrt{-g}{ F }, which should be resolved through physical means. In general relativity, the spherically symmetric solution to the Einstein equation is a benchmark and its massive deformation also plays a crucial role in Lorentz-breaking massive gravity. { F } will satisfy the constraint equation {T}01=0 from the spherically symmetric Einstein tensor {G}01=0, if we maintain that any reasonable physical theory should possess the spherically symmetric solutions. The Stückelberg field {φ }i is taken as a ‘hedgehog’ configuration {φ }i=φ (r){x}i/r, whose stability is guaranteed by the topological one. Under this ansätz, {T}01=0 is reduced to d{ F }=0. The functions { F } for d{ F }=0 form a commutative ring {R}{ F }. We obtain an expression of the solution to the functional differential equation with spherical symmetry if { F }\\in {R}{ F }. If { F }\\in {R}{ F } and \\partial { F }/\\partial X=0, the functions { F } form a subring {S}{ F }\\subset {R}{ F }. We show that the metric is Schwarzschild, Schwarzschild-AdS or Schwarzschild-dS if { F }\\in {S}{ F }. When { F }\\in {R}{ F } but { F }\
Andrei, R.M.; Smith, C.S.; Fraanje, P.R.; Verhaegen, M.; Korkiakoski, V.A.; Keller, C.U.; Doelman, N.J.
2012-01-01
In this paper we give a new wavefront estimation technique that overcomes the main disadvantages of the phase diversity (PD) algorithms, namely the large computational complexity and the fact that the solutions can get stuck in a local minima. Our approach gives a good starting point for an
Analytical Approximation Methods for the Stabilizing Solution of the Hamilton-Jacobi Equation
Sakamoto, Noboru; van der Schaft, Arjan J.
2008-01-01
In this paper, two methods for approximating the stabilizing solution of the Hamilton-Jacobi equation are proposed using symplectic geometry and a Hamiltonian perturbation technique as well as stable manifold theory. The first method uses the fact that the Hamiltonian lifted system of an integrable
Analytical Approximation Methods for the Stabilizing Solution of the Hamilton–Jacobi Equation
Sakamoto, Noboru; Schaft, Arjan J. van der
2008-01-01
In this paper, two methods for approximating the stabilizing solution of the Hamilton–Jacobi equation are proposed using symplectic geometry and a Hamiltonian perturbation technique as well as stable manifold theory. The first method uses the fact that the Hamiltonian lifted system of an integrable
Analytical and numerical solutions of the Schrödinger–KdV equation
Indian Academy of Sciences (India)
The Schrödinger–KdV equation with power-law nonlinearity is studied in this paper. The solitary wave ansatz method is used to carry out the integration of the equation and obtain one-soliton solution. The ′/ method is also used to integrate this equation. Subsequently, the variational iteration method and homotopy ...
Analytical and numerical solutions of the Schrödinger–KdV equation
Indian Academy of Sciences (India)
solitary wave ansatz method is used to carry out the integration of the equation and obtain one-soliton solution. The G /G method is also used to integrate this equation. Subsequently, the variational iteration method and homotopy perturbation method are also applied to solve this equation. The numerical simulations are ...
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...
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.
Directory of Open Access Journals (Sweden)
Shymaa S. Medany
2012-07-01
Full Text Available Poly 1-amino-9, 10-anthraquinone (PAAQ films were prepared by the electropolymerization of 1-amino-9,10-anthraquinone (AAQ on platinum substrate from aqueous media, where 5.0 × 10−3 mol L−1 AAQ and 6.0 mol L−1 H2SO4 were used. The kinetics of the electropolymerization process was investigated by determining the change of the charge consumed during the polymerization process with time at different concentrations of both monomer and electrolyte. The results have shown that the process follows first order kinetics with respect to the monomer concentration. The order of the reaction with respect to the aqueous solvent i.e. H2SO4 was found to be negative. The polymer films were successfully used as sensors for the electroanalytical determination of many hazardous compounds, e.g. phenols, and biologically important materials like dopamine. The electroanalytical determination was based on the measurements of the oxidation current peak of the material in the cyclic voltammetric measurements. The cyclic voltammograms were recorded at a scan rate of 100 mV s−1 and different analyte concentrations. A calibration curve was constructed for each analyte, from which the determination of low concentrations of catechol and hydroquinone (HQ as examples of hazardous compounds present in waste water and also for ascorbic acid and dopamine as examples of valuable biological materials can be achieved.
Otero-Espinar, M. V.; Seoane, L. F.; Nieto, J. J.; Mira, J.
2013-12-01
An in-depth analytic study of a model of language dynamics is presented: a model which tackles the problem of the coexistence of two languages within a closed community of speakers taking into account bilingualism and incorporating a parameter to measure the distance between languages. After previous numerical simulations, the model yielded that coexistence might lead to survival of both languages within monolingual speakers along with a bilingual community or to extinction of the weakest tongue depending on different parameters. In this paper, such study is closed with thorough analytical calculations to settle the results in a robust way and previous results are refined with some modifications. From the present analysis it is possible to almost completely assay the number and nature of the equilibrium points of the model, which depend on its parameters, as well as to build a phase space based on them. Also, we obtain conclusions on the way the languages evolve with time. Our rigorous considerations also suggest ways to further improve the model and facilitate the comparison of its consequences with those from other approaches or with real data.
Analytical solutions and particle simulations of cross-field plasma sheaths
International Nuclear Information System (INIS)
Gerver, M.J.; Parker, S.E.; Theilhaber, K.
1989-01-01
Particles simulations have been made of an infinite plasma slab, bounded by absorbing conducting walls, with a magnetic field parallel to the walls. The simulations have been either 1-D, or 2-D, with the magnetic field normal to the simulation plane. Initially, the plasma has a uniform density between the walls, and there is a uniform source of ions and electrons to replace particles lost to the walls. In the 1-D case, there is no diffusion of the particle guiding centers, and the plasma remains uniform in density and potential over most of the slab, with sheaths about a Debye length wide where the potential rises to the wall potential. In the 2-D case, the density profile becomes parabolic, going almost to zero at the walls, and there is a quasineutral presheath in the bulk of the plasma, in addition to sheaths near the walls. Analytic expressions are found for the density and potential profiles in both cases, including, in the 2-D case, the magnetic presheath due to finite ion Larmor radius, and the effects of the guiding center diffusion rate being either much less than or much grater than the energy diffusion rate. These analytic expressions are shown to agree with the simulations. A 1-D simulation with Monte Carlo guiding center diffusion included gives results that are good agreement with the much more expensive 2-D simulation. 17 refs., 10 figs
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.
Dalarsson, Mariana; Tassin, Philippe
2009-04-13
We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results obtained by accurate numerical simulations. Our model straightforwardly allows for arbitrary spectral dispersion.
Dalarsson, Mariana; Tassin, Philippe
2012-01-01
We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results o...
Schwartz, Andrew J.; Ray, Steven J.; Chan, George C.-Y.; Hieftje, Gary M.
2016-11-01
Past studies of the solution-cathode glow discharge (SCGD) revealed that elemental and molecular emission are not spatially homogenous throughout the source, but rather conform to specific zones within the discharge. Exploiting this inhomogeneity can lead to improved analytical performance if emission is collected only from regions of the discharge where analyte species emit strongly and background emission (from continuum, elemental and/or molecular sources) is lower. Effects of this form of spatial discrimination on the analytical performance of SCGD optical emission spectrometry (OES) have been investigated with an imaging spectrograph for fourteen atomic lines, with emphasis on detection limits and precision. Vertical profiles of the emission intensity, signal-to-background ratio, and signal-to-noise ratio were collected and used to determine the optimal region to view the SCGD on a per-element basis. With optimized spatial filtering, detection limits ranged from 0.09-360 ppb, a 1.4-13.6 fold improvement over those obtained when emission is collected from the full vertical profile (1.1-840 ppb), with a 4.2-fold average improvement. Precision was found to be unaffected by spatial filtering, ranging from 0.5-2.6% relative standard deviation (RSD) for all elements investigated, closely comparable to the 0.4-2.4% RSD observed when no spatial filtering is used. Spatial profiles also appear useful for identifying optimal line pairs for internal standardization and for flagging the presence of matrix interferences in SCGD-OES.
International Nuclear Information System (INIS)
Alonso-Vargas, G.
1991-01-01
A computer program has been developed which uses a technique of synthetic acceleration by diffusion by analytical schemes. Both in the diffusion equation as in that of transport, analytical schemes were used which allowed a substantial time saving in the number of iterations required by source iteration method to obtain the K e ff. The program developed ASD (Synthetic Diffusion Acceleration) by diffusion was written in FORTRAN and can be executed on a personal computer with a hard disc and mathematical O-processor. The program is unlimited as to the number of regions and energy groups. The results obtained by the ASD program for K e ff is nearly completely concordant with those of obtained utilizing the ANISN-PC code for different analytical type problems in this work. The ASD program allowed obtention of an approximate solution of the neutron transport equation with a relatively low number of internal reiterations with good precision. One of its applications would be in the direct determinations of axial distribution neutronic flow in a fuel assembly as well as in the obtention of the effective multiplication factor. (Author)
Sazykina, Tatiana G; Kryshev, Alexander I
2016-01-01
A dynamic mathematical model is formulated, predicting the development of radiation effects in a generic animal population, inhabiting an elemental ecosystem 'population-limiting resource'. Differential equations of the model describe the dynamic responses to radiation damage of the following population characteristics: gross biomass; intrinsic fractions of healthy and reversibly damaged tissues in biomass; intrinsic concentrations of the self-repairing pool and the growth factor; and amount of the limiting resource available in the environment. Analytical formulae are found for the steady states of model variables as non-linear functions of the dose rate of chronic radiation exposure. Analytical solutions make it possible to predict the expected severity of radiation effects in a model ecosystem, including such endpoints as morbidity, mortality, life shortening, biosynthesis, and population biomass. Model parameters are selected from species data on lifespan, physiological growth and mortality rates, and individual radiosensitivity. Thresholds for population extinction can be analytically calculated for different animal species, examples are provided for generic mice and wolf populations. The ecosystem model demonstrates a compensatory effect of the environment on the development of radiation effects in wildlife. The model can be employed to construct a preliminary scale 'radiation exposure-population effects' for different animal species; species can be identified, which are vulnerable at a population level to chronic radiation exposure. Copyright © 2015. Published by Elsevier Ltd.
Simon, Laurent; Ospina, Juan
2016-07-25
Three-dimensional solute transport was investigated for a spherical device with a release hole. The governing equation was derived using the Fick's second law. A mixed Neumann-Dirichlet condition was imposed at the boundary to represent diffusion through a small region on the surface of the device. The cumulative percentage of drug released was calculated in the Laplace domain and represented by the first term of an infinite series of Legendre and modified Bessel functions of the first kind. Application of the Zakian algorithm yielded the time-domain closed-form expression. The first-order solution closely matched a numerical solution generated by Mathematica(®). The proposed method allowed computation of the characteristic time. A larger surface pore resulted in a smaller effective time constant. The agreement between the numerical solution and the semi-analytical method improved noticeably as the size of the orifice increased. It took four time constants for the device to release approximately ninety-eight of its drug content. Copyright © 2016 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Liu, Yongbao; Wang, Qiang; Xu, Huidong
2017-01-01
The smooth bifurcation and non-smooth grazing bifurcation of periodic solution of three-degree-of-freedom vibro-impact systems with clearance are studied in this paper. Firstly, six-dimensional Poincaré maps are established through choosing suitable Poincaré section and solving periodic solutions of vibro-impact system. Then, as the analytic expressions of all eigenvalues of Jacobi matrix of six-dimensional map are unavailable, the numerical calculations to search for the critical bifurcation values point by point is a laborious job based on the classical critical criterion described by the properties of eigenvalues. To overcome the difficulty from the classical bifurcation criteria, the explicit critical criterion without using eigenvalues calculation of high-dimensional map is applied to determine bifurcation points of Co-dimension-one bifurcations and Co-dimension-two bifurcations, and then local dynamical behaviors of these bifurcations are further analyzed. Finally, the existence of the grazing periodic solution of the vibro-impact system and grazing bifurcation point are analyzed, the discontinuous grazing bifurcation behavior is studied based on the compound normal form map near the grazing point, the discontinuous jumping phenomenon and the co-existing multiple solutions near the grazing bifurcation point are revealed.
Directory of Open Access Journals (Sweden)
S. Benić
2014-11-01
Full Text Available The Witten–Veneziano relation, or, alternatively, its generalization proposed by Shore, facilitates understanding and describing the complex of η and η′ mesons. We present an analytic, closed-form solution to Shore's equations which gives results on the η–η′ complex in full agreement with results previously obtained numerically. Although the Witten–Veneziano relation and Shore's equations are related, the ways they were previously used in the context of dynamical models to calculate η and η′ properties, were rather different. However, with the analytic solution, the calculation can be formulated similarly to the approach through the Witten–Veneziano relation, and with some conceptual improvements. In the process, one strengthens the arguments in favor of a possible relation between the UA(1 and SUA(3 chiral symmetry breaking and restoration. To test this scenario, the experiments such as those at RHIC, NICA and FAIR, which extend the RHIC (and LHC high-temperature scans also to the finite-density parts of the QCD phase diagram, should pay particular attention to the signatures from the η′–η complex indicating the symmetry restoration.
Fast Single Image Super-Resolution Using a New Analytical Solution for l2 - l2 Problems.
Zhao, Ningning; Wei, Qi; Basarab, Adrian; Dobigeon, Nicolas; Kouame, Denis; Tourneret, Jean-Yves
2016-08-01
This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high-resolution image from its blurred, decimated, and noisy version. The existing algorithms for single image SR use different strategies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution is derived and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an l2 -regularized quadratic model, i.e., an l2 - l2 optimization problem. The flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded into traditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with existing techniques.
Fast Single Image Super-resolution using a New Analytical Solution for l2-l2 Problems.
Zhao, Ningning; Wei, Qi; Basarab, Adrian; Dobigeon, Nicolas; Kouame, Denis; Tourneret, Jean-Yves
2016-05-11
This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high resolution image from its blurred, decimated and noisy version. The existing algorithms for single image SR use different strategies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution can be obtained and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an `2-regularized quadratic model, i.e., an `2-`2 optimization problem. Furthermore, the flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded into traditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with the existing techniques.
International Nuclear Information System (INIS)
Alvarez, Gustavo; Concepcion Univ.; Cvetic, Gorazd; Kniehl, Bernd A.; Kondrashuk, Igor; Univ. del Bio-Bio, Chillan; Parra-Ferrada, Ivan
2016-11-01
We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be N=4 supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of transfer momentum and of Bjorken x. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behaviour in the vicinity of the point x=0 and a smooth behaviour in the vicinity of the point x=1.
Yan, Shaomin; Li, Zhenchong; Wu, Guang
2010-04-01
The understanding of evolutionary mechanism is important, and equally important is to describe the evolutionary process. If so, we would know where the biological evolution will go. At species level, we would know whether and when a species will extinct or be prosperous. At protein level, we would know when a protein family will mutate more. In our previous study, we explored the possibility of using the differential equation to describe the evolution of protein family from influenza A virus based on the assumption that the mutation process is the exchange of entropy between protein family and its environment. In this study, we use the analytical solution of system of differential equations to fit the evolution of matrix protein 1 family from influenza A virus. Because the evolutionary process goes along the time course, it can be described by differential equation. The results show that the evolution of a protein family can be fitted by the analytical solution. With the obtained fitted parameters, we may predict the evolution of matrix protein 1 family from influenza A virus. Our model would be the first step towards the systematical modeling of biological evolution and paves the way for further modeling.
International Nuclear Information System (INIS)
Geng, X Y; Indraratna, B; Rujikiatkamjorn, C
2010-01-01
Vertical drains combined with vacuum pressure and surcharge preloading are widely used to accelerate the consolidation process of soft clay in order to decrease the pore pressure as well as to increase the effective stress. Currently there are two types of vacuum preloading systems commercially available; (a) membrane system with an airtight membrane over the drainage layer and, (b) membraneless system where a vacuum system is connected to individual drain. Their effectiveness varies from site to site depending on the type of soil treated and the characteristics of the drain-vacuum system. This study presents the analytical solutions of vertical drains with vacuum preloading for both membrane and membraneless systems. According to the field and laboratory observations, the vacuum in both of the membraneless and membrane system was assumed to be decreasing along the drain whereas in the membrane system, it was maintained at a constant level. This model was verified by using the measured settlements and excess pore pressures obtained from large-scale laboratory testing and case studies in Australia. The analytical solutions improved the accuracy of predicting the dissipation of pore water pressure and the associated settlement. The effects of the permeability of the sand blanket in a membrane system and the possible loss of vacuum were also discussed.
Sarmah, Ratan; Tiwari, Shubham
2018-03-01
An analytical solution is developed for predicting two-dimensional transient seepage into ditch drainage network receiving water from a non-uniform steady ponding field from the surface of the soil under the influence of source/sink in the flow domain. The flow domain is assumed to be saturated, homogeneous and anisotropic in nature and have finite extends in horizontal and vertical directions. The drains are assumed to be standing vertical and penetrating up to impervious layer. The water levels in the drains are unequal and invariant with time. The flow field is also assumed to be under the continuous influence of time-space dependent arbitrary source/sink term. The correctness of the proposed model is checked by developing a numerical code and also with the existing analytical solution for the simplified case. The study highlights the significance of source/sink influence in the subsurface flow. With the imposition of the source and sink term in the flow domain, the pathline and travel time of water particles started deviating from their original position and above that the side and top discharge to the drains were also observed to have a strong influence of the source/sink terms. The travel time and pathline of water particles are also observed to have a dependency on the height of water in the ditches and on the location of source/sink activation area.
Energy Technology Data Exchange (ETDEWEB)
Alvarez, Gustavo [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Concepcion Univ. (Chile). Dept. de Fisica; Cvetic, Gorazd [Univ. Tecnica Federico Santa Maria, Valparaiso (Chile). Dept. de Fisica; Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kondrashuk, Igor [Univ. del Bio-Bio, Chillan (Chile). Grupo de Matematica Aplicada; Univ. del Bio-Bio, Chillan (Chile). Grupo de Fisica de Altas Energias; Parra-Ferrada, Ivan [Talca Univ. (Chile). Inst. de Matematica y Fisica
2016-11-15
We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be N=4 supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of transfer momentum and of Bjorken x. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behaviour in the vicinity of the point x=0 and a smooth behaviour in the vicinity of the point x=1.
Busemann, A.; Vinh, N. X.; Culp, R. D.
1974-01-01
The general solution for the optimum three-dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere is developed. A set of dimensionless variables, modified Chapman variables, is introduced. The resulting exact equations of motion, referred to as Chapman's exact equations, have the advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a completely general lift-drag relationship is used in the derivation. The results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary drag polar, and entering any planetary atmosphere. The aerodynamic controls chosen are the lift coefficient and the bank angle. General optimum control laws for these controls are developed. Several earlier particular solutions are shown to be special cases of this general result. Results are valid for both free and constrained terminal position.
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Sumit Gupta
2015-09-01
Full Text Available The aim of this paper was to present a user friendly numerical algorithm based on homotopy perturbation transform method for solving various linear and nonlinear convection-diffusion problems arising in physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. The homotopy perturbation transform method is a combined form of the homotopy perturbation method and Laplace transform method. The nonlinear terms can be easily obtained by the use of He’s polynomials. The technique presents an accurate methodology to solve many types of partial differential equations The approximate solutions obtained by proposed scheme in a wide range of the problem’s domain were compared with those results obtained from the actual solutions. The comparison shows a precise agreement between the results.
International Nuclear Information System (INIS)
Imhof, Armando Luis; Calvo, Carlos Adolfo; Moyano, Amalia; Sanchez, Manuel
2015-01-01
A determined curve path is followed by the propagation of seismic waves generated in emitters and detected in receivers by the principle of minimum time of Fermat. An ordinary differential equation is derived from the application of the calculation of variations. Due to the compaction of the terrain, the speed usually increases with depth. The experimental laws for each soil have led to this variation leading to a numerical resolution. The adjustment of experimental speed data by an exponential function; the analytical integration of the differential equation and the numerical determination of the integration constants are studied. A geophysical method such as up-hole or down-hole has determined the experimental data. Its main application is centered in the validation of numerical models of curved trajectories. Then time of first arrivals through tomographic algorithms for detection and modeling of anomalies in the first 12 m depth. (author) [es
Analytical and numerical solution of one- and two-dimensional steady heat transfer in a coldplate
International Nuclear Information System (INIS)
Jones, G.F.; Bennett, G.A.; Bultman, D.H.
1987-01-01
We develop analytical models for steady-state, one- and two-dimensional heat transfer in a single-material, flat-plate coldplate. Discrete heat sources are mounted on one side of the plate and heat transfer to a flowing fluid occurs on the other. The models are validated numerically using finite differences. We propose a simple procedure for estimating maximum coldplate temperature at the location of each heat source which includes thermal interaction among the sources. Results from one model are compared with data obtained for a composite coldplate operated in the laboratory. We demonstrate the utility of the models as diagnostic tools to be used for predicting the existence and extent of void volumes and delaminations in the composite material that can occur with coldplates of this type. Based on our findings, recommendations for effective coldplate design are given
Analytic solution for American strangle options using Laplace-Carson transforms
Kang, Myungjoo; Jeon, Junkee; Han, Heejae; Lee, Somin
2017-06-01
A strangle has been important strategy for options when the trader believes there will be a large movement in the underlying asset but are uncertain of which way the movement will be. In this paper, we derive analytic formula for the price of American strangle options. American strangle options can be mathematically formulated into the free boundary problems involving two early exercise boundaries. By using Laplace-Carson Transform(LCT), we can derive the nonlinear system of equations satisfied by the transformed value of two free boundaries. We then solve this nonlinear system using Newton's method and finally get the free boundaries and option values using numerical Laplace inversion techniques. We also derive the Greeks for the American strangle options as well as the value of perpetual American strangle options. Furthermore, we present various graphs for the free boundaries and option values according to the change of parameters.
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.
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Hasan Bulut
2013-01-01
Full Text Available We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM to some interesting nonhomogeneous fractional ordinary differential equations (FODEs. Finally, we use the solutions to form two-dimensional (2D graphs, by using the symbolic algebra package Mathematica Program 7.
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.
A new analytical solution of the hyperbolic Kepler equation using the Adomian decomposition method
Ebaid, Abdelhalim; Rach, Randolph; El-Zahar, Essam
2017-09-01
In this paper, the Adomian decomposition method (ADM) is proposed to solve the hyperbolic Kepler equation which is often used to describe the eccentric anomaly of a comet of extrasolar origin in its hyperbolic trajectory past the Sun. A convenient method is therefore needed to solve this equation to accurately determine the radial distance and/or the Cartesian coordinates of the comet. It has been shown that Adomian's series using a few terms are sufficient to achieve extremely accurate numerical results even for much higher values of eccentricity than those in the literature. Besides, an exceptionally rapid rate of convergence of the sequence of the obtained approximate solutions has been demonstrated. Such approximate solutions possess the odd property in the mean anomaly which are illustrated through several plots. Moreover, the absolute remainder error, using only three components of Adomian's solution decreases across a specified domain, approaches zero as the eccentric anomaly tends to infinity. Also, the absolute remainder error decreases by increasing the number of components of the Adomian decomposition series. In view of the obtained results, the present method may be the most effective approach to treat the hyperbolic Kepler equation.
International Nuclear Information System (INIS)
Sazykina, Tatiana G.; Kryshev, Alexander I.
2016-01-01
A dynamic mathematical model is formulated, predicting the development of radiation effects in a generic animal population, inhabiting an elemental ecosystem ‘population-limiting resource’. Differential equations of the model describe the dynamic responses to radiation damage of the following population characteristics: gross biomass; intrinsic fractions of healthy and reversibly damaged tissues in biomass; intrinsic concentrations of the self-repairing pool and the growth factor; and amount of the limiting resource available in the environment. Analytical formulae are found for the steady states of model variables as non-linear functions of the dose rate of chronic radiation exposure. Analytical solutions make it possible to predict the expected severity of radiation effects in a model ecosystem, including such endpoints as morbidity, mortality, life shortening, biosynthesis, and population biomass. Model parameters are selected from species data on lifespan, physiological growth and mortality rates, and individual radiosensitivity. Thresholds for population extinction can be analytically calculated for different animal species, examples are provided for generic mice and wolf populations. The ecosystem model demonstrates a compensatory effect of the environment on the development of radiation effects in wildlife. The model can be employed to construct a preliminary scale ‘radiation exposure-population effects’ for different animal species; species can be identified, which are vulnerable at a population level to chronic radiation exposure. - Highlights: • Mathematical model is formulated predicting radiation effects in elemental ecosystem. • Analytical formulae are found for steady states of variables as functions of exposure. • Severity of radiation effects are calculated, including population extinction. • Model parameterization is made for generic mice and wolf populations.
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A. L. Lapikov
2014-01-01
Full Text Available The paper concerns the solution of direct kinematic problem for the Stewart-Gough platform of the type 6-3. The article represents a detailed analysis of methods of direct kinematic problem solution for platform mechanisms based on the parallel structures. The complexity of the problem solution is estimated for the mechanisms of parallel kinematics in comparison with the classic manipulators, characterized by the open kinematic chain.The method for the solution of this problem is suggested. It consists in setting up the correspondence between the functional dependence of Cartesian coordinates and the orientation of the moving platform centre on the values of generalized coordinates of the manipulator, which may be represented, in the case of platform manipulators, by the lengths of extensible arms to connect the foundation and the moving platform of the manipulator. The method is constructed in such a way that the solution of the direct kinematic problem reduces to solution of the analytical equation of plane where the moving platform is situated. The equation of the required plane is built according to three points which in this case are attachment points of moving platform joints. To define joints coordinates values it is necessary to generate a system of nine nonlinear equations. It ought to be noted that in generating a system of equation are used the equations with the same type of nonlinearity. The physical meaning of all nine equations of the system is Euclidean distance between the points of the manipulator. The location and orientation of the moving platform is represented as a homogeneous transformation matrix. The components of translation and rotation of this matrix can be defined through the required plane.The obtained theoretical results are supposed to be used in the decision support system during the complex research of multi-sectional manipulators of parallel kinematics to describe the geometrically similar 3D-prototype of the
Shan, Zhendong; Ling, Daosheng
2018-02-01
This article develops an analytical solution for the transient wave propagation of a cylindrical P-wave line source in a semi-infinite elastic solid with a fluid layer. The analytical solution is presented in a simple closed form in which each term represents a transient physical wave. The Scholte equation is derived, through which the Scholte wave velocity can be determined. The Scholte wave is the wave that propagates along the interface between the fluid and solid. To develop the analytical solution, the wave fields in the fluid and solid are defined, their analytical solutions in the Laplace domain are derived using the boundary and interface conditions, and the solutions are then decomposed into series form according to the power series expansion method. Each item of the series solution has a clear physical meaning and represents a transient wave path. Finally, by applying Cagniard's method and the convolution theorem, the analytical solutions are transformed into the time domain. Numerical examples are provided to illustrate some interesting features in the fluid layer, the interface and the semi-infinite solid. When the P-wave velocity in the fluid is higher than that in the solid, two head waves in the solid, one head wave in the fluid and a Scholte wave at the interface are observed for the cylindrical P-wave line source.
Henclik, Sławomir
2018-03-01
The influence of dynamic fluid-structure interaction (FSI) onto the course of water hammer (WH) can be significant in non-rigid pipeline systems. The essence of this effect is the dynamic transfer of liquid energy to the pipeline structure and back, which is important for elastic structures and can be negligible for rigid ones. In the paper a special model of such behavior is analyzed. A straight pipeline with a steady flow, fixed to the floor with several rigid supports is assumed. The transient is generated by a quickly closed valve installed at the end of the pipeline. FSI effects are assumed to be present mainly at the valve which is fixed with a spring dash-pot attachment. Analysis of WH runs, especially transient pressure changes, for various stiffness and damping parameters of the spring dash-pot valve attachment is presented in the paper. The solutions are found analytically and numerically. Numerical results have been computed with the use of an own computer program developed on the basis of the four equation model of WH-FSI and the specific boundary conditions formulated at the valve. Analytical solutions have been found with the separation of variables method for slightly simplified assumptions. Damping at the dash-pot is taken into account within the numerical study. The influence of valve attachment parameters onto the WH courses was discovered and it was found the transient amplitudes can be reduced. Such a system, elastically attached shut-off valve in a pipeline or other, equivalent design can be a real solution applicable in practice.
Analytical solution of the optimal three dimensional reentry problem using Chapman's exact equations
Vinh, N. X.; Busemann, A.; Culp, R. D.
1974-01-01
This paper presents the general solution for the optimal three dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere. A set of dimensionless variables is introduced, and the resulting exact equations of motion have the distinctive advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a general lift-drag polar is used to define the aerodynamic control. Hence, the results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary polar and entering any planetary atmosphere.
Wen-Yu, Luo; Xiao-Lin, Yu; Xue-Feng, Yang; Ren-He, Zhang
2016-04-01
An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a line source in plane geometry. Besides, an unconditionally stable numerical solution is also presented, which entirely resolves the stability problem in previous methods. Generally the branch line integral contributes to the total field only at short ranges, and hence is usually ignored in traditional normal mode models. However, for the special case where a mode lies near the branch cut, the branch line integral can contribute to the total field significantly at all ranges. The wavenumber integration method is well-suited for such problems. Numerical results are also provided, which show that the present model can serve as a benchmark for sound propagation in a Pekeris waveguide. Project supported by the National Natural Science Foundation of China (Grant No. 11125420), the Knowledge Innovation Program of the Chinese Academy of Sciences, the China Postdoctoral Science Foundation (Grant No. 2014M561882), and the Doctoral Fund of Shandong Province, China (Grant No. BS2012HZ015).
International Nuclear Information System (INIS)
Kazi, Tasneem G.; Khan, Sumaira; Baig, Jameel A.; Kolachi, Nida F.; Afridi, Hassan I.; Kandhro, Ghulam A.; Kumar, Sham; Shah, Abdul Q.
2009-01-01
A new method is reported for the separation of aluminum ions [Al(III)] from interfering elements in parenteral and pharmaceutical solutions (PS) and bottled mineral water (BMW) samples, through solid-phase extraction with 2-methyl-8-hydroxyquinoline (quinaldine) adsorbed onto activated silica gel. While the enrichment step of separated Al(III) was carried out by cloud point extraction (CPE) using 8-hydroxyquinoline as complexing reagent, the resulted complex was entrapped in a non-ionic surfactant octylphenoxypolyethoxyethanol (Triton X-114). The enriched Al(III) in sample solutions were determined by spectrofluorometry (SPF) at λ excitation 370 nm and λ emission 510 nm, and flame atomic absorption spectrometry (FAAS) for comparative purpose. The variables affecting the complexation and extraction steps were studied and optimized. The validity of methodology was checked with certified reference material of water and standard addition method. The enrichment factor and detection limit of Al(III) for the preconcentration of 50 ml of PS and BMW were found to be 100 and 0.25 μg/L, respectively. The proposed method has been applied for the determination of trace amount of Al(III) in PS and BMW samples with satisfactory results. In PS the levels of Al(III) are above than permissible limit (25 μg/L).
Poznanski, R R
2010-09-01
A reaction-diffusion model is presented to encapsulate calcium-induced calcium release (CICR) as a potential mechanism for somatofugal bias of dendritic calcium movement in starburst amacrine cells. Calcium dynamics involves a simple calcium extrusion (pump) and a buffering mechanism of calcium binding proteins homogeneously distributed over the plasma membrane of the endoplasmic reticulum within starburst amacrine cells. The system of reaction-diffusion equations in the excess buffer (or low calcium concentration) approximation are reformulated as a nonlinear Volterra integral equation which is solved analytically via a regular perturbation series expansion in response to calcium feedback from a continuously and uniformly distributed calcium sources. Calculation of luminal calcium diffusion in the absence of buffering enables a wave to travel at distances of 120 μm from the soma to distal tips of a starburst amacrine cell dendrite in 100 msec, yet in the presence of discretely distributed calcium-binding proteins it is unknown whether the propagating calcium wave-front in the somatofugal direction is further impeded by endogenous buffers. If so, this would indicate CICR to be an unlikely mechanism of retinal direction selectivity in starburst amacrine cells.
Colaiori, Francesca; Castellano, Claudio; Cuskley, Christine F; Loreto, Vittorio; Pugliese, Martina; Tria, Francesca
2015-01-01
Empirical evidence shows that the rate of irregular usage of English verbs exhibits discontinuity as a function of their frequency: the most frequent verbs tend to be totally irregular. We aim to qualitatively understand the origin of this feature by studying simple agent-based models of language dynamics, where each agent adopts an inflectional state for a verb and may change it upon interaction with other agents. At the same time, agents are replaced at some rate by new agents adopting the regular form. In models with only two inflectional states (regular and irregular), we observe that either all verbs regularize irrespective of their frequency, or a continuous transition occurs between a low-frequency state, where the lemma becomes fully regular, and a high-frequency one, where both forms coexist. Introducing a third (mixed) state, wherein agents may use either form, we find that a third, qualitatively different behavior may emerge, namely, a discontinuous transition in frequency. We introduce and solve analytically a very general class of three-state models that allows us to fully understand these behaviors in a unified framework. Realistic sets of interaction rules, including the well-known naming game (NG) model, result in a discontinuous transition, in agreement with recent empirical findings. We also point out that the distinction between speaker and hearer in the interaction has no effect on the collective behavior. The results for the general three-state model, although discussed in terms of language dynamics, are widely applicable.
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Frunza, T; Susan-Resiga, R [Department of Hydraulic Machinery, ' Politehnica' University of Timisoara Bv. Mihai Viteazu 1, RO-300222, Timisoara (Romania); Muntean, S; Bernad, S, E-mail: tfrunza@yahoo.co [Centre of Advanced Research in Engineering Sciences, Romanian Academy - Timisoara Branch, Bv. Mihai Viteazu 24, RO-300223, Timisoara (Romania)
2010-08-15
The paper presents the authors ongoing efforts to develop a robust and efficient numerical methodology, and the associated expert software, for analysis, design and optimization of hydrofoil cascades. We developed, so far, a Finite Element solver with streamfunction formulation for incompressible, inviscid and irrotational cascade flow, using a modern software infrastructure, and efficient implementation. Two test cases will be presented to evaluate the accuracy of our CASCADExpert code. In the first case, our code is tested for a thin hydrofoil cascade designed with the quasi-analytical approach. Second, the blade loading and thickness distributions obtain with our code from a given hydrofoil shape are used in an inverse design method. As a result, an optimized hydrofoil cascade is obtained. The pressure distribution on the original and optimized hydrofoil cascades is compared. We have applied the method in order to optimize the turbine and pump hydrofoil cascades, respectively. Consequently, a new method is developed in order to generate the optimized hydrofoil cascade geometry for hydraulic machinery.
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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.
Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur
2018-03-01
Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.
Veling, E.J.M.
2012-01-01
The analytical solution is presented to the convection–diffusion equation describing the concentration of solutes in a radial velocity field due to extracting groundwater from or injecting water into an aquifer with arbitrary initial concentration data F(r), with r the radial distance, and an
An analytical solution of the Navier-Stokes equation for internal flows
International Nuclear Information System (INIS)
Lyberg, Mats D; Tryggeson, Henrik
2007-01-01
This paper derives a solution to the Navier-Stokes equation by considering vorticity generated at system boundaries. The result is an explicit expression for the velocity. The Navier-Stokes equation is reformulated as a divergence and integrated, giving a tensor equation that splits into a symmetric and a skew-symmetric part. One equation gives an algebraic system of quadratic equations involving velocity components. A system of nonlinear partial differential equations is reduced to algebra. The velocity is then explicitly calculated and shown to depend on boundary conditions only. This removes the need to solve the Navier-Stokes equation by a 3D numerical computation, replacing it by computation of 2D surface integrals over the boundary. (fast track communication)
Feng, Lian-Li; Tian, Shou-Fu; Zhang, Tian-Tian; Zhou, Jun
2017-07-01
Under investigation in this paper is the variant Boussinesq system, which describes the propagation of surface long wave towards two directions in a certain deep trough. With the help of the truncated Painlevé expansion, we construct its nonlocal symmetry, Bäcklund transformation, and Schwarzian form, respectively. The nonlocal symmetries can be localised to provide the corresponding nonlocal group, and finite symmetry transformations and similarity reductions are computed. Furthermore, we verify that the variant Boussinesq system is solvable via the consistent Riccati expansion (CRE). By considering the consistent tan-function expansion (CTE), which is a special form of CRE, the interaction solutions between soliton and cnoidal periodic wave are explicitly studied.
Kauranen, P. S.
1993-04-01
In the solid state concept of a direct methanol fuel cell (DMFC), methanol is directly oxidized at the anode of a solid polymer electrolyte fuel cell (SPEFC). Mathematical modelling of the transport and reaction phenomena within the electrodes and the electrolyte membrane is needed in order to get a closer insight into the operation of the fuel cell. In the work, macro-homogenous porous electrode and dilute solution theories are used to derive the phenomenological equations describing the transport and reaction mechanisms in a SPEFC single cell. The equations are first derived for a conventional H2/air SPEFC, and then extended for a DMFC. The basic model is derived in a one dimensional form in which it is assumed that species transport take place only in the direction crossing the cell sandwich. In addition, two dimensional descriptions of the catalyst layer are reviewed.
Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder
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Morteza Eskandari-Ghadi
2013-12-01
Full Text Available An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are used to derive the solution for the potential functions, and then the displacements-, stresses- and temperature-potential relationships are used to determine the displacements, stresses and temperature fields. It is shown that the formulation presented here are identically collapsed on the solution existed in the literature for simpler case of axissymetric configuration. A numerical procedure is needed to evaluate the displacements, stresses and temperature at any point and any time. The numerical inversion method proposed by Durbin is applied to evaluate the inverse Laplace transforms of different functions involved in this paper. For numerical inversion, there exist many difficulties such as singular points in the integrand functions, infinite limit of the integral and the time step of integration. With a very precise attention, the desired functions have been numerically evaluated and shown that the boundary conditions have been satisfied very accurately. The numerical evaluations are graphically shown to make engineering sense for the problem involved in this paper for different case of boundary conditions. The results show the wave velocity and the time lack of receiving stress waves. The effect of temperature boundary conditions are shown to be somehow oscillatory, which is used in designing of such an elements.
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Quitschke Wolfgang W
2008-11-01
Full Text Available Abstract Background Commercially available curcumin preparations contain a mixture of related polyphenols, collectively referred to as curcuminoids. These encompass the primary component curcumin along with its co-purified derivatives demethoxycurcumin and bisdemethoxycurcumin. Curcuminoids have numerous biological activities, including inhibition of cancer related cell proliferation and reduction of amyloid plaque formation associated with Alzheimer disease. Unfortunately, the solubility of curcuminoids in aqueous solutions is exceedingly low. This restricts their systemic availability in orally administered formulations and limits their therapeutic potential. Results Methods are described that achieve high concentrations of soluble curcuminoids in serum. Solid curcuminoids were either mixed directly with serum, or they were predissolved in dimethyl sulfoxide and added as aliquots to serum. Both methods resulted in high levels of curcuminoid-solubility in mammalian sera from different species. However, adding aliquots of dimethyl sulfoxide-dissolved curcuminoids to serum proved to be more efficient, producing soluble curcuminoid concentrations of at least 3 mM in human serum. The methods also resulted in the differential solubility of individual curcuminoids in serum. The addition of dimethyl sulfoxide-dissolved curcuminoids to serum preferentially solubilized curcumin, whereas adding solid curcuminoids predominantly solubilized bisdemethoxycurcumin. Either method of solubilization was equally effective in inhibiting dose-dependent HeLa cell proliferation in culture. The maximum concentration of curcuminoids achieved in serum was at least 100-fold higher than that required for inhibiting cell proliferation in culture and 1000-fold higher than the concentration that has been reported to prevent amyloid plaque formation associated with Alzheimer disease. Curcuminoids were also highly soluble in solutions of purified albumin, a major component of
An analytical solution to proton Bragg peak deflection in a magnetic field
International Nuclear Information System (INIS)
Wolf, Russell; Bortfeld, Thomas
2012-01-01
The role of MR imaging for image-guided radiation therapy (IGRT) is becoming more and more important thanks to the excellent soft tissue contrast offered by MRI. Hybrid therapy devices with integrated MRI scanners are under active development for x-ray therapy. The combination of proton therapy with MRI imaging has only been investigated at the theoretical or conceptual level. Of concern is the deflection of the proton beam in the homogeneous magnetic field. A previous publication has come to the conclusion that the impact of a 0.5 T magnetic field on the dose distribution for proton therapy is very small and lateral deflections stay well below 2 mm. The purpose of this study is to provide new insights into the effects of magnetic fields on a proton beam coming to rest in a patient. We performed an analytical calculation of the lateral deflection of protons with initial energies between 50 MeV and 250 MeV, perpendicular to the beam direction and the magnetic field. We used a power-law range-energy relationship and the Lorentz force in both relativistic and non-relativistic conditions. Calculations were done for protons coming to rest in water or soft tissue, and generalized to other uniform and non-uniform media. Results were verified by comparisons with numerical calculations and Monte Carlo simulations. A key result of our calculations is that the maximum lateral deflection at the end of range is proportional to the third power of the initial energy. Accordingly, due to the strong dependence on the energy, even a relatively small magnetic field of 0.5 T will cause a deflection of the proton beam by 1 cm at the end of range of a 200 MeV beam. The maximum deflection at 200 MeV is more than 10 times larger than that of a 90 MeV beam. Relativistic corrections of the deflection are generally small but they can become non-negligible at higher energies around 200 MeV and above. Contrary to previous findings, the lateral deflection of a proton beam can be significant (1
International Nuclear Information System (INIS)
Saez, D.G.; Hernandez, L.; Borroto, M.; Figueredo, M.
1996-01-01
A semiempirical equation of polynomial-exponential type is presented to describe the transmission data of Co-60 gamma radiation in finite materials of concrete and lead. This equation and the expression obtained for the relationship of scatter-to-incident exposure made easy the developing in computer of an analytical solution for shielding calculations of Co 60 teletherapy rooms, based on the procedures of the NCRP 49 and Simpkin's method. The standard error in the estimation of parameters is less than 1.7 % except for the attenuation of 150 'o' scattered radiation in concrete that resulted in 6.3 % for one of them. The shielding calculations were compared with the data in NCRP 49 for the same conditions with a correlation better than 99 %
Directory of Open Access Journals (Sweden)
Zhoujin Cui
2013-01-01
Full Text Available The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM and the homotopy perturbation method (HPM. RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM with some known technique (HPM shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The two different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance.
Shukla, Nisha; Rana, Puneet; Beg, O. A.; Singh, Bani
2017-01-01
An analytical study of the MHD boundary layer flow of electrically conducting nanofluid over a horizontal cylinder with the effects of chemical reaction and viscous dissipation is presented. Similarity transformations have been applied to transform the cylindrical form of the governing equations into the system of coupled ordinary differential equations and then homotopy analysis method has been implemented to solve the system. Homotopy analysis method (HAM) does not contain any small or large parameter like perturbation technique and also provides an easiest approach to ensure the convergence of the series of solution. The effects of chemical reaction parameter, magnetic parameter and other important governing parameters with no flux nanoparticles concentration is carried out to describe important physical quantities.
Khan, Junaid Ahmad; Mustafa, Meraj; Hayat, Tasawar; Alsaedi, Ahmed
2014-01-01
This article studies the viscous flow and heat transfer over a plane horizontal surface stretched non-linearly in two lateral directions. Appropriate wall conditions characterizing the non-linear variation in the velocity and temperature of the sheet are employed for the first time. A new set of similarity variables is introduced to reduce the boundary layer equations into self-similar forms. The velocity and temperature distributions are determined by two methods, namely (i) optimal homotopy analysis method (OHAM) and (ii) fourth-fifth-order Runge-Kutta integration based shooting technique. The analytic and numerical solutions are compared and these are found in excellent agreement. Influences of embedded parameters on momentum and thermal boundary layers are sketched and discussed.
Directory of Open Access Journals (Sweden)
S. Sreenadh
2016-06-01
Full Text Available The Peristaltic transport of conducting nanofluids under the effect of slip condition in an asymmetric channel is reported in the present work. The mathematical modelling has been carried out under long wavelength and low Reynolds number approximations. The analytical solutions are obtained for pressure rise, nanoparticle concentration, temperature distribution, velocity profiles and stream function. Influence of various parameters on the flow characteristics has been discussed with the help of graphs. The results showed that the pressure rise increases with increasing magnetic effect and decreases with increasing slip parameter. The effects of thermophoresis parameter and Brownian motion parameter on the nanoparticle concentration and temperature distribution are studied. It is observed that the pressure gradient increases with increasing slip parameter and magnetic effect. The trapping phenomenon for different parameters is presented.
Doe, T.; McLaren, R.; Finilla, A.
2017-12-01
An enduring legacy of Paul Witherspoon and his students and colleagues has been both the development of geothermal energy and the bases of modern fractured-rock hydrogeology. One of the seminal contributions to the geothermal field was Gringarten, Witherspoon, and Ohnishi's analytical models for enhanced geothermal systems. Although discrete fracture network (DFN) modeling developed somewhat independently in the late 1970s, Paul Witherspoon's foresight in promoting underground in situ testing at the Stripa Mine in Sweden was a major driver in Lawrence Berkeley Laboratory's contributions to its development.This presentation looks extensions of Gringarten's analytical model into discrete fracture network modeling as a basis for providing further insights into the challenges and opportunities of engineered geothermal systems. The analytical solution itself has many insightful applications beyond those presented in the original paper. The definition of dimensionless time by itself shows that thermal breakthrough has a second power dependence on surface area and on flow rate. The fracture intensity also plays a strong role, as it both increases the surface area and decrease his flow rate per fracture. The improvement of EGS performance with fracture intensity reaches a limit where thermal depletion of the rock lags only slightly behind the thermal breakthrough of cold water in the fracture network.Simple network models, which couple a DFN generator (FracMan) with a hydrothermally coupled flow solver (HydroGeoSphere) expand on Gringarten's concepts to show that realistic heterogeneity of spacing and transmissivity significantly degrades EGS performance. EGS production in networks of stimulated fractures initially follows Gringarten's type curves, with a later deviation is the smaller rock blocks thermally deplete and the entire stimulated volume acts as a single sink. Three-dimensional models of EGS performance show the critical importance of the relative magnitudes of
Application of novel analytical ultracentrifuge analysis to solutions of fungal mannans
Gillis, Richard B.
2016-07-21
Polysaccharides, the most abundant biopolymers, are required for a host of activities in lower organisms, animals, and plants. Their solution characterization is challenging due to their complex shape, heterogeneity, and size. Here, recently developed data analysis approaches were applied for traditional sedimentation equilibrium and velocity methods in order to investigate the molar mass distribution(s) of a subtype of polysaccharide, namely, mannans from four Candida spp. The molecular weight distributions of these mannans were studied using two recently developed equilibrium approaches: SEDFIT-MSTAR and MULTISIG, resulting in corroboratory distribution profiles. Additionally, sedimentation velocity data for all four mannans, analyzed using ls-g*(s) and Extended Fujita approaches, suggest that two of the fungal mannans (FM-1 and FM-3) have a unimodal distribution of molecular species whereas two others (FM-2 and FM-4) displayed bi-modal and broad distributions, respectively: this demonstrates considerable molecular heterogeneity in these polysaccharides, consistent with previous observations of mannans and polysaccharides in general. These methods not only have applications for the characterization of mannans but for other biopolymers such as polysaccharides, DNA, and proteins (including intrinsically disordered proteins).
DataCare: Big Data Analytics Solution for Intelligent Healthcare Management
Directory of Open Access Journals (Sweden)
Alejandro Baldominos Gómez
2018-03-01
Full Text Available This paper presents DataCare, a solution for intelligent healthcare management. This product is able not only to retrieve and aggregate data from different key performance indicators in healthcare centers, but also to estimate future values for these key performance indicators and, as a result, fire early alerts when undesirable values are about to occur or provide recommendations to improve the quality of service. DataCare’s core processes are built over a free and open-source cross-platform document-oriented database (MongoDB, and Apache Spark, an open-source cluster-computing framework. This architecture ensures high scalability capable of processing very high data volumes coming at fast speed from a large set of sources. This article describes the architecture designed for this project and the results obtained after conducting a pilot in a healthcare center. Useful conclusions have been drawn regarding how key performance indicators change based on different situations, and how they affect patients’ satisfaction.
Analytical solution of the problem of a shock wave in the collapsing gas in Lagrangian coordinates
Kuropatenko, V. F.; Shestakovskaya, E. S.
2016-10-01
It is proposed the exact solution of the problem of a convergent shock wave and gas dynamic compression in a spherical vessel with an impermeable wall in Lagrangian coordinates. At the initial time the speed of cold ideal gas is equal to zero, and a negative velocity is set on boundary of the sphere. When t > t0 the shock wave spreads from this point into the gas. The boundary of the sphere will move under the certain law correlated with the motion of the shock wave. The trajectories of the gas particles in Lagrangian coordinates are straight lines. The equations determining the structure of the gas flow between the shock front and gas border have been found as a function of time and Lagrangian coordinate. The dependence of the entropy on the velocity of the shock wave has been found too. For Lagrangian coordinates the problem is first solved. It is fundamentally different from previously known formulations of the problem of the self-convergence of the self-similar shock wave to the center of symmetry and its reflection from the center, which was built up for the infinite area in Euler coordinates.
Analytical Solution for Stress Field and Intensity Factor in CSTBD under Mixed Mode Conditions
Directory of Open Access Journals (Sweden)
Najaf Ali Ghavidel
2014-06-01
Full Text Available Considering the fact that rocks fail faster under tensile stress, rock tensile strength is of greatimportance in applications such as blasting, rock fragmentation, slope stability, hydraulic fracturing,caprock integrity, and geothermal energy extraction. There are two direct and indirect methods tomeasure tensile strength. Since direct methods always encompass difficulties in test setup, indirectmethods, specifically the Brazilian test, have often been employed for tensile strength measurement.Tensile failure is technically attributed to crack propagation in rock. Fracture mechanics hassignificant potential for the determination of crack behaviour as well as propagation pattern. To applyBrazilian tests, cracked disc geometry has been suggested by the International Society for RockMechanics ISRM. Accordingly, a comprehensive study is necessary to evaluate stress field and stressintensity factor (SIF around the crack in the centre of the specimen. In this paper, superpositionprinciple is employed to solve the problem of cracked straight-through Brazilian disc (CSTBD, usingtwo methods of dislocation and complex stress function. Stress field and SIF in the vicinity of thecrack tip are then calculated. With the proposed method, the magnitude of critical load for crackinitiation in structures can be predicted. This method is valid for any crack of any arbitrary length andangle. In addition, numerical modelling has been carried out for the Brazilian disc. Finally, theanalytical solution has been compared with numerical modelling results showing the same outcomefor both methods.
Directory of Open Access Journals (Sweden)
R. T. Al-Khairy
2009-01-01
source, whose capacity is given by (,=((1−− while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discussion of solutions for different time characteristics of heat sources capacity (constant, instantaneous, and exponential is presented. The effect of absorption coefficients on the temperature profiles is examined in detail. It is found that the closed form solution derived from the present study reduces to the previously obtained analytical solution when the medium velocity is set to zero in the closed form solution.
Hajrahimi, Nafiseh; Dehaghani, Sayed Mehdi Hejazi; Hajrahimi, Nargess; Sarmadi, Sima
2014-01-01
Implementing information technology in the best possible way can bring many advantages such as applying electronic services and facilitating tasks. Therefore, assessment of service providing systems is a way to improve the quality and elevate these systems including e-commerce, e-government, e-banking, and e-learning. This study was aimed to evaluate the electronic services in the website of Isfahan University of Medical Sciences in order to propose solutions to improve them. Furthermore, we aim to rank the solutions based on the factors that enhance the quality of electronic services by using analytic hierarchy process (AHP) method. Non-parametric test was used to assess the quality of electronic services. The assessment of propositions was based on Aqual model and they were prioritized using AHP approach. The AHP approach was used because it directly applies experts' deductions in the model, and lead to more objective results in the analysis and prioritizing the risks. After evaluating the quality of the electronic services, a multi-criteria decision making frame-work was used to prioritize the proposed solutions. Non-parametric tests and AHP approach using Expert Choice software. The results showed that students were satisfied in most of the indicators. Only a few indicators received low satisfaction from students including, design attractiveness, the amount of explanation and details of information, honesty and responsiveness of authorities, and the role of e-services in the user's relationship with university. After interviewing with Information and Communications Technology (ICT) experts at the university, measurement criteria, and solutions to improve the quality were collected. The best solutions were selected by EC software. According to the results, the solution "controlling and improving the process in handling users complaints" is of the utmost importance and authorities have to have it on the website and place great importance on updating this process
Dobrinskaya, Tatiana
2015-01-01
This paper presents a new method for optimizing yaw maneuvers, which are the most common large maneuvers on the International Space Station (ISS). The goal of the maneuver optimization is to find a maneuver trajectory with minimal torques acting on the vehicle during the maneuver. Therefore, the thruster firings necessary to perform the maneuver are minimized. Reduction of thruster firings saves propellant and decreases structural loads and contamination of the vehicle critical elements, thus saving the service life of the thrusters and the vehicle itself. Equations describing the pitch and roll motion needed to counteract the major torques during a yaw maneuver are obtained. Also, a yaw rate profile is suggested. In the obtained optimized case, the torques are significantly reduced. The proposed approximate analytical solution does not require extensive computer resources and, therefore, can be implemented using software onboard the ISS. As a result, the maneuver execution will be automatic. This is one of the major benefits of the simplified solution presented in this paper with respect to existing computational approaches. The suggested maneuver optimization method can be used not only for the ISS, but for other space vehicles as well.
Qian, Youhua; Chen, Shengmin
2010-10-01
In this paper, the homotopy analysis method (HAM) is presented to establish the accurate approximate analytical solutions for multi-degree-of-freedom (MDOF) nonlinear coupled oscillators. The periodic solutions for the three-degree-of-freedom (3DOF) coupled van der Pol-Duffing oscillators are applied to illustrate the validity and great potential of this method. For given physical parameters of nonlinear systems and with different initial conditions, the frequency ω , displacements x1 (t),x2 (t) and x3 (t) can be explicitly obtained. In addition, comparisons are conducted between the results obtained by the HAM and the numerical integration (i.e. Runge-Kutta) method. It is shown that the analytical solutions of the HAM are in excellent agreement with respect to the numerical integration solutions, even if time t progresses to a certain large domain in the time history responses. Finally, the homotopy Pade technique is used to accelerate the convergence of the solutions.
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.
Weldegebreal, Blen; Redi-Abshiro, Mesfin; Chandravanshi, Bhagwan Singh
2017-12-05
This study was conducted to develop fast and cost effective methods for the determination of caffeine in green coffee beans. In the present work direct determination of caffeine in aqueous solution of green coffee bean was performed using FT-IR-ATR and fluorescence spectrophotometry. Caffeine was also directly determined in dimethylformamide solution using NIR spectroscopy with univariate calibration technique. The percentage of caffeine for the same sample of green coffee beans was determined using the three newly developed methods. The caffeine content of the green coffee beans was found to be 1.52 ± 0.09 (% w/w) using FT-IR-ATR, 1.50 ± 0.14 (% w/w) using NIR and 1.50 ± 0.05 (% w/w) using fluorescence spectroscopy. The means of the three methods were compared by applying one way analysis of variance and at p = 0.05 significance level the means were not significantly different. The percentage of caffeine in the same sample of green coffee bean was also determined by using the literature reported UV/Vis spectrophotometric method for comparison and found to be 1.40 ± 0.02 (% w/w). New simple, rapid and inexpensive methods were developed for direct determination of caffeine content in aqueous solution of green coffee beans using FT-IR-ATR and fluorescence spectrophotometries. NIR spectrophotometry can also be used as alternative choice of caffeine determination using reduced amount of organic solvent (dimethylformamide) and univariate calibration technique. These analytical methods may therefore, be recommended for the rapid, simple, safe and cost effective determination of caffeine in green coffee beans.
Czech Academy of Sciences Publication Activity Database
Tichý, V.; Kuběna, Aleš Antonín; Skála, L.
2012-01-01
Roč. 90, č. 6 (2012), s. 503-513 ISSN 0008-4204 Institutional support: RVO:67985556 Keywords : Schroninger equation * partial differential equation * analytic solution * anharmonic oscilator * double-well Subject RIV: BE - Theoretical Physics Impact factor: 0.902, year: 2012 http://library.utia.cas.cz/separaty/2012/E/kubena-analytic energies and wave functions of the two-dimensional schrodinger equation.pdf
International Nuclear Information System (INIS)
Kulich, N.V.; Nemtsev, V.A.
1986-01-01
The analytical solution to the problem on the stationary temperature field in an infinite structural element of rectangular profile characteristic of the conjugation points of a vessel and a tube sheet of a heat exchanger (or of a finned surface) at the third-kind boundary conditions has been obtained by the methods of the complex variable function theory. With the help of the obtained analytical dependences the calculations of the given element of the design and the comparison with the known data have been conducted. The proposed analytical solution can be effectively used in calculations of temperature fields in finned surfaces and structural elements of the power equipment of the considered profile and the method is applied for solution of the like problems
Directory of Open Access Journals (Sweden)
Sorin BERBENTE
2011-12-01
Full Text Available A gas (oxidizer flows between two parallel walls of solid fuel. A combustion is initiated: the solid fuel is vaporized and a diffusive flame occurs. The hot combustion products are submitted both to thermal diffusion and convection. Analytical solutions can be obtained both for the velocity and temperature distributions by considering an equivalent mean temperature where the density and the thermal conductivity are evaluated. The main effects of heat transfer are due to heat convection at the flame. Because the detailed mechanism of the diffusion flame is not introduced the reference chemical reaction is the combustion of premixed fuel with oxidizer in excess. In exchange the analytical solution is used to define an ideal quasi-uniform combustion that could be realized by an n adequate control. The given analytical closed solutions prove themselves flexible enough to adjust the main data of some existing experiments and to suggest new approaches to the problem.
Directory of Open Access Journals (Sweden)
Abdallah Ibrahim A.
2009-01-01
Full Text Available The analytical solution is derived for the steady MHD mixed convection, laminar, heat and mass transfer over an isothermal, inclined permeable stretching sheet, immersed in a uniform porous medium in the presence of chemical reaction, thermal radiation, Dufour and Soret effects, an external transverse magnetic field, and internal heating. The governing equations are transformed into a dimensionless coupled system of non-linear ordinary differential equations and then solved analytically by the homotopy analysis method. A parametric study illustrating the influence of the chemical reaction, magnetic field, porous medium inertia parameter, and the Dufour and Soret numbers on the fluid velocity, temperature, and concentration are investigated through the obtained analytic solution. As well as the local Nusselt and the Sherwood numbers is conducted. The obtained results are presented graphically and the physical aspects of the problem are discussed. The obtained solution has been tested numerically for some values of the system parameters. Comparison with previously reported numerical results is tabulated and agreement is recorded. Analytic form of some characteristic parameters, e. g. the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number, stress at the stretching surface, local mass transfer coefficient, the local wall mass flux, the local heat transfer coefficient and the local heat flux, are given due to the obtained analytic solution.
Shahkarami, Pirouz; Liu, Longcheng; Moreno, Luis; Neretnieks, Ivars
2015-01-01
This study presents an analytical approach to simulate nuclide migration through a channel in a fracture accounting for an arbitrary-length decay chain. The nuclides are retarded as they diffuse in the porous rock matrix and stagnant zones in the fracture. The Laplace transform and similarity transform techniques are applied to solve the model. The analytical solution to the nuclide concentrations at the fracture outlet is governed by nine parameters representing different mechanisms acting on nuclide transport through a fracture, including diffusion into the rock matrices, diffusion into the stagnant water zone, chain decay and hydrodynamic dispersion. Furthermore, to assess how sensitive the results are to parameter uncertainties, the Sobol method is applied in variance-based global sensitivity analyses of the model output. The Sobol indices show how uncertainty in the model output is apportioned to the uncertainty in the model input. This method takes into account both direct effects and interaction effects between input parameters. The simulation results suggest that in the case of pulse injections, ignoring the effect of a stagnant water zone can lead to significant errors in the time of first arrival and the peak value of the nuclides. Likewise, neglecting the parent and modeling its daughter as a single stable species can result in a significant overestimation of the peak value of the daughter nuclide. It is also found that as the dispersion increases, the early arrival time and the peak time of the daughter decrease while the peak value increases. More importantly, the global sensitivity analysis reveals that for time periods greater than a few thousand years, the uncertainty of the model output is more sensitive to the values of the individual parameters than to the interaction between them. Moreover, if one tries to evaluate the true values of the input parameters at the same cost and effort, the determination of priorities should follow a certain
Suk, Heejun
2017-04-01
This paper presents a semi-analytical procedure for solving coupled the multispecies reactive solute transport equations, with a sequential first-order reaction network in arbitrary heterogeneous media using General Integral Transformation Tecgnique(GITT).This proposed approach was developed to describe behavior of reactive multicpecise transport on spatially or temporally varying flow velocities and dispersion coefficients with distinct retardation factors, which might be function of space and time. This proposed approach deals with general initial conditions, and arbitrary temporal variable inlet concentration as well as arbitrary heterogenous media. The proposed approach sequentially calculates the concentration distributions of each species by employing only the generalized integral transform technique (GITT). Because the proposed solutions for each species' concentration distributions have separable forms in space and time, the solution for subsequent species (daughter species) can be obtained using only the GITT without the decomposition by change-of-variables method imposing the limitation of identical retarda- tion values for all the reactive species by directly substituting solutions for the preceding species (parent species) into the transport equation of subsequent species (daughter species). The proposed solutions were compared with previously published analytical solutions or numerical solutions of the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) in all verification examples. In these examples, the proposed solutions were well matched with previous analytical solutions and the numerical solutions obtained by 2DFATMIC model. A hypothetical single-well push-pull test example and a scale-dependent dispersion example were designed to demonstrate the practical application of the proposed solution to a real field problem.
Suk, Heejun
2016-08-01
This paper presents a semi-analytical procedure for solving coupled the multispecies reactive solute transport equations, with a sequential first-order reaction network on spatially or temporally varying flow velocities and dispersion coefficients involving distinct retardation factors. This proposed approach was developed to overcome the limitation reported by Suk (2013) regarding the identical retardation values for all reactive species, while maintaining the extensive capability of the previous Suk method involving spatially variable or temporally variable coefficients of transport, general initial conditions, and arbitrary temporal variable inlet concentration. The proposed approach sequentially calculates the concentration distributions of each species by employing only the generalized integral transform technique (GITT). Because the proposed solutions for each species' concentration distributions have separable forms in space and time, the solution for subsequent species (daughter species) can be obtained using only the GITT without the decomposition by change-of-variables method imposing the limitation of identical retardation values for all the reactive species by directly substituting solutions for the preceding species (parent species) into the transport equation of subsequent species (daughter species). The proposed solutions were compared with previously published analytical solutions or numerical solutions of the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) in three verification examples. In these examples, the proposed solutions were well matched with previous analytical solutions and the numerical solutions obtained by 2DFATMIC model. A hypothetical single-well push-pull test example and a scale-dependent dispersion example were designed to demonstrate the practical application of the proposed solution to a real field problem.
39 (APPROXIMATE ANALYTICAL SOLUTION)
African Journals Online (AJOL)
Rotating machines like motors, turbines, compressors etc. are generally subjected to periodic forces and the system parameters remain more or less constant. ... parameters change and, consequently, the natural frequencies too, due to reasons of changing gyroscopic moments, centrifugal forces, bearing characteristics,.
Heath, Melissa; Woodfield, Peter Lloyd; Hall, Wayne
2017-06-01
Taking the limit of small Reynolds number for a vessel being filled with compressed gas, the energy equation was found to asymptote to the unsteady heat conduction equation with heat generation and variable density. This equation was solved analytically for cylindrical and spherical geometry. Assuming the density changes linearly with time, a solution is obtained which is identical in form to the constant density solution if the Fourier number is defined using the log-mean density rather than the instantaneous density. At steady state conditions, the Nusselt number based on the diameter for cylinders with aspect ratios larger than 1 rapidly approaches an integer solution of NuD = 8. For cylinders with aspect ratios less than 1, the Nusselt number based on the cylinder length (height) characteristic dimension rapidly approaches NuL = 6. It is shown experimentally and numerically that during compression filling, the heat transfer asymptotically approaches this analytical solution at low Reynolds numbers.
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Koulikov, Alexei O.; Meili, Markus
2003-01-01
After the sudden fallout from the Chernobyl nuclear accident in 1986, activities and bioaccumulation factors of radiocaesium ( 137 Cs, 134 Cs) fluctuated strongly over several years before reaching quasi-equilibrium, with patterns significantly differing among organisms. To model these dynamic relaxation processes based on ecological mechanisms we developed mass balance equations for 137 Cs in an aquatic food chain on the following basis: (a) potassium acts as a biogeochemical analogue ('carrier') of caesium; (b) the concentration of potassium in fish and other animals is effectively constant; (c) the main source of potassium in freshwater fish is the dietary uptake. The model is applicable to linear food chains of any number of trophic levels, while solutions evaluated here include the following food chain compartments: water, invertebrates (fish food), non-piscivorous fish, and piscivorous fish. The activity concentration in the water, which is considered as the secondary source of 137 Cs, is described by multi-component first-order decay function, although two components (fast and slow) are often sufficient to provide agreement with empirical data. In every compartment the turnover rate of caesium is considered as a constant over time. The analytical solution of the model equations describes the 137 Cs activity concentration in every compartment as a series of exponential functions, of which some are derived from the source pattern, and the others determined by the 137 Cs turnover rate in each food chain compartment. The model was tested with post-Chernobyl data from several long-term studies in lakes and provided a reasonable description of important radioecological aspects
Bruce, William J; Maxwell, E A; Sneddon, I N
1963-01-01
Analytic Trigonometry details the fundamental concepts and underlying principle of analytic geometry. The title aims to address the shortcomings in the instruction of trigonometry by considering basic theories of learning and pedagogy. The text first covers the essential elements from elementary algebra, plane geometry, and analytic geometry. Next, the selection tackles the trigonometric functions of angles in general, basic identities, and solutions of equations. The text also deals with the trigonometric functions of real numbers. The fifth chapter details the inverse trigonometric functions
Lolli, S.; Demoz, B.; Di Girolamo, P.; Welton, E. J.
2015-12-01
The water cycle describes the fluxes and the continuous circulation of the water inside the earth hydrosphere through its three different phases (liquid, solid and gaseous). It refers to the continuous hydric mass exchanges between the atmosphere, earth, surface and underground waters. Other than water accumulation in different regions, i. e. the oceans, the terrestrial water fulfills multiple cycles including condensation, precipitation and evaporation. The contribution of the rain direct evaporation to the heat and moisture of the clouds and to the atmospheric moisture cycling is fundamental, but very few measurements of those processes are available. Rain evaporation directly influences the induction and mainteinance of the downdrafts under the cloud base both in mesoscale precipitation or convective environment. In the past, different approaches measured and retrieved rain evaporation both through remote sensing (radar) or in-situ measurements, but the different methods came with serious errors in the estimation. We first present with this study a retrieval of the rainfall evaporation using dual-wavelength high-resolution lidar. This already proven technique (Lolli et al., 2013) permits to retrieve the raindrop equivolumetric diameter and then the evaporation at each range bin up to full evaporation. The results are then utilized to assess the discrepancies with an approximate analytical solution model for raindrop evaporation.
International Nuclear Information System (INIS)
Loghman, A.; Abdollahian, M.; Jafarzadeh Jazi, A.; Ghorbanpour Arani, A.
2013-01-01
Time-dependent electro-magneto-thermoelastic creep response of rotating disk made of functionally graded piezoelectric materials (FGPM) is studied. The disk is placed in a uniform magnetic and a distributed temperature field and is subjected to an induced electric potential and a centrifugal body force. The material thermal, mechanical, magnetic and electric properties are represented by power-law distributions in radial direction. The creep constitutive model is Norton's law in which the creep parameters are also power functions of radius. Using equations of equilibrium, strain-displacement and stress-strain relations in conjunction with the potential-displacement equation a non-homogeneous differential equation containing time-dependent creep strains for displacement is derived. A semi-analytical solution followed by a numerical procedure has been developed to obtain history of stresses, strains, electric potential and creep-strain rates by using Prandtl-Reuss relations. History of electric potential, Radial, circumferential and effective stresses and strains as well as the creep stress rates and effective creep strain rate histories are presented. It has been found that tensile radial stress distribution decreases during the life of the FGPM rotating disk which is associated with major electric potential redistributions which can be used as a sensor for condition monitoring of the FGPM rotating disk. (authors)
Kubáň, Pavel; Seip, Knut Fredrik; Gjelstad, Astrid; Pedersen-Bjergaard, Stig
2016-11-02
This work investigated selective micro-electromembrane extractions (μ-EMEs) of the colored indicators metanil yellow and congo red (visual proof-of-principle) and the small drug substances nortriptyline, papaverine, mianserin, and citalopram (model analytes) based on their acid-base strength. With two free liquid membranes (FLMs), the target analytes were extracted from aqueous donor solution, across FLM 1 (1-pentanol, 1-ethyl-2-nitrobenzene (ENB) or 4-nitrocumene (4-NC)), into aqueous acceptor solution 1, further across FLM 2 (1-pentanol, ENB or 4-NC), and finally into aqueous acceptor solution 2. All phases had volumes between 1.0 and 1.5 μL and extractions were promoted by 200-300 V d.c. applied across the five-phase μ-EME system formed in a perfluoroalkoxy capillary tubing. The anode was located in acceptor solution 2 and the cathode was located in donor solution for μ-EMEs of acidic analytes, and locations of the electrodes were vice versa for μ-EMEs of basic analytes. After μ-EME, donor solution and acceptor solution 1 and 2 were analyzed by capillary electrophoresis or liquid chromatography-mass spectrometry. The model analytes migrated efficiently in the proposed μ-EME system, their migration behavior was controlled by pH in aqueous solutions and their selective fractionation into acceptor solution 1 and 2 was demonstrated based on their acid-base strength. Under optimal conditions, acceptor solution 2 contained 60% nortriptyline (pK a = 10.5) and less than 1% papaverine (pK a = 6.0) and acceptor solution 1 contained 17% nortriptyline and 27% papaverine after 15 min of μ-EME. The five-phase μ-EME system was also compatible with human plasma samples. Work is in progress to further increase the fractionation capability, and to implement the concept into microfluidic platforms. Copyright © 2016 Elsevier B.V. All rights reserved.