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 problems of bubble dynamics
International Nuclear Information System (INIS)
Recently, an asymptotic solution of the Rayleigh equation for an empty bubble in N dimensions has been obtained. Here we give the closed-form general analytical solution of this equation. We also find the general solution of the Rayleigh equation in N dimensions for the case of a gas-filled hyperspherical bubble. In addition, we include a surface tension into consideration. - Highlights: • The Rayleigh equation for bubble's dynamics is considered. • General analytical solutions of the Rayleigh equation are obtained. • Various types of analytical solutions of the Rayleigh equation are studied
Analytic anisotropic solution for holography
Ren, Jie
2016-01-01
An exact solution to Einstein's equations for holographic models is presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution's appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined in detail. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimension reduction.
Analytical solutions for problems of bubble dynamics
Kudryashov, Nikolai A
2016-01-01
Recently, an asymptotic solution of the Rayleigh equation for an empty bubble in $N$ dimensions has been obtained. Here we give the closed--from general analytical solution of this equation. We also find the general solution of the Rayleigh equation in $N$ dimensions for the case of a gas--filled hyperspherical bubble. In addition, we include a surface tension into consideration.
Analytical solution methods for geodesic motion
Hackmann, Eva
2015-01-01
The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole solutions of the Einstein equations the gravitational field is characterized by a small number of parameters which can be read off from the observables related to the orbits of test particles and light rays. Here we review the state of the art of analytical solutions of geodesic equations in various space--times. In particular we consider the four dimensional black hole space--times of Pleba\\'nski--Demia\\'nski type as far as the geodesic equation separates, as well as solutions in higher dimensions, and also solutions with cosmic strings. The mathematical tools used are elliptic and hyperelliptic functions. We present a list of analytic solutions which can be found in the literature.
Analytic vortex solutions on compact hyperbolic surfaces
Maldonado, Rafael; Manton, Nicholas S.
2015-06-01
We construct, for the first time, abelian Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given implicitly in terms of Schwarz triangle functions and analytic solutions are available for certain highly symmetric configurations.
Analytic vortex solutions on compact hyperbolic surfaces
International Nuclear Information System (INIS)
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)
Analytic vortex solutions on compact hyperbolic surfaces
Maldonado, R
2015-01-01
We construct, for the first time, Abelian-Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given implicitly in terms of Schwarz triangle functions and analytic solutions are available for certain highly symmetric configurations.
Analytic Solutions of Elastic Tunneling Problems
Strack, O.E.
2002-01-01
The complex variable method for solving two dimensional linearly elastic problems is used to obtain several fundamental analytical solutions of tunneling problems. The method is used to derive the general mathematical representation of problems involving resultant forces on holes in a half-plane
Analytic solutions of an unclassified artifact /
Energy Technology Data Exchange (ETDEWEB)
Trent, Bruce C.
2012-03-01
This report provides the technical detail for analytic solutions for the inner and outer profiles of the unclassified CMM Test Artifact (LANL Part Number 157Y-700373, 5/03/2001) in terms of radius and polar angle. Furthermore, analytic solutions are derived for the legacy Sheffield measurement hardware, also in terms of radius and polar angle, using part coordinates, i.e., relative to the analytic profile solutions obtained. The purpose of this work is to determine the exact solution for the “cosine correction” term inherent to measurement with the Sheffield hardware. The cosine correction is required in order to interpret the actual measurements taken by the hardware in terms of an actual part definition, or “knot-point spline definition,” that typically accompanies a component drawing. Specifically, there are two portions of the problem: first an analytic solution must be obtained for any point on the part, e.g., given the radii and the straight lines that define the part, it is required to find an exact solution for the inner and outer profile for any arbitrary polar angle. Next, the problem of the inspection of this part must be solved, i.e., given an arbitrary sphere (representing the inspection hardware) that comes in contact with the part (inner and outer profiles) at any arbitrary polar angle, it is required to determine the exact location of that intersection. This is trivial for the case of concentric circles. In the present case, however, the spherical portion of the profiles is offset from the defined center of the part, making the analysis nontrivial. Here, a simultaneous solution of the part profiles and the sphere was obtained.
Analytic Solutions of Elastic Tunneling Problems
Strack, O.E.
2002-01-01
The complex variable method for solving two dimensional linearly elastic problems is used to obtain several fundamental analytical solutions of tunneling problems. The method is used to derive the general mathematical representation of problems involving resultant forces on holes in a half-plane. Such problems are encountered in geomechanics during the excavation of tunnels. When tunnels are excavated the removal of the weighted material inside the tunnel causes the ground under the tunnel to...
Analytical solutions for anomalous dispersion transport
O'Malley, D.; Vesselinov, V. V.
2014-06-01
Groundwater flow and transport often occur in a highly heterogeneous environment (potentially heterogeneous at multiple spatial scales) and is impacted by geochemical reactions, advection, diffusion, and other pore scale processes. All these factors can give rise to large-scale anomalous dispersive behavior that can make complex model representation and prediction of plume concentrations challenging due to difficulties unraveling all the complexities associated with the governing processes, flow medium, and their parameters. An alternative is to use upscaled stochastic models of anomalous dispersion, and this is the approach used here. Within a probabilistic framework, we derive a number of analytical solutions for several anomalous dispersion models. The anomalous dispersion models are allowed to be either non-Gaussian (α-stable Lévy), correlated, or nonstationary from the Lagrangian perspective. A global sensitivity analysis is performed to gain a greater understanding of the extent to which uncertainty in the parameters associated with the anomalous behavior can be narrowed by examining concentration measurements from a network of monitoring wells and to demonstrate the computational speed of the solutions. The developed analytical solutions are encoded and available for use in the open source computational framework MADS (http://mads.lanl.gov).
Analytical Solutions for Sequentially Reactive Transport with Different Retardation Factors
Energy Technology Data Exchange (ETDEWEB)
Sun, Y; Buscheck, T A; Mansoor, K; Lu, X
2001-08-01
Integral transforms have been widely used for deriving analytical solutions for solute transport systems. Often, analytical solutions can only be written in closed form in frequency domains and numerical inverse-transforms have to be involved to obtain semi-analytical solutions in the time domain. For this reason, previously published closed form solutions are restricted either to a small number of species or to the same retardation assumption. In this paper, we applied the solution scheme proposed by Bauer et al. in the time domain. Using available analytical solutions of a single species transport with first-order decay without coupling with its parent species concentration as fundamental solutions, a daughter species concentration can be expressed as a linear function of those fundamental solutions. The implementation of the solution scheme is straight forward and exact analytical solutions are derived for one- and three-dimensional transport systems.
Analytical Solution of Multicompartment Solute Kinetics for Hemodialysis
Directory of Open Access Journals (Sweden)
Przemysław Korohoda
2013-01-01
Full Text Available Objective. To provide an exact solution for variable-volume multicompartment kinetic models with linear volume change, and to apply this solution to a 4-compartment diffusion-adjusted regional blood flow model for both urea and creatinine kinetics in hemodialysis. Methods. A matrix-based approach applicable to linear models encompassing any number of compartments is presented. The procedure requires the inversion of a square matrix and the computation of its eigenvalues λ, assuming they are all distinct. This novel approach bypasses the evaluation of the definite integral to solve the inhomogeneous ordinary differential equation. Results. For urea two out of four eigenvalues describing the changes of concentrations in time are about 105 times larger than the other eigenvalues indicating that the 4-compartment model essentially reduces to the 2-compartment regional blood flow model. In case of creatinine, however, the distribution of eigenvalues is more balanced (a factor of 102 between the largest and the smallest eigenvalue indicating that all four compartments contribute to creatinine kinetics in hemodialysis. Interpretation. Apart from providing an exact analytic solution for practical applications such as the identification of relevant model and treatment parameters, the matrix-based approach reveals characteristic details on model symmetry and complexity for different solutes.
ANALYTIC SOLUTIONS OF SYSTEMS OF FUNCTIONAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
LiuXinhe
2003-01-01
Let r be a given positive number.Denote by D=D the closed disc in the complex plane C whose center is the origin and radius is r.For any subset K of C and any integer m ≥1,write A(Dm,K)={f|f:Dm→Kis a continuous map,and f|(Dm)*is analytic).For H∈A(Dm,C)(m≥2),f∈A(D,D)and z∈D,write ψH(f)(z)=H(z,f(z)……fm=1(x)).Suppose F,G∈A(D2n+1,C),and Hk,Kk∈A(Dk,C),k=2,……,n.In this paper,the system of functional equations {F(z,f(z),f2(ψHz(f)(z))…,fn(ψk2(g)(x))… gn(ψKn(g)(z)))=0 G(z,f(z),f2(ψH2(f)(z))…fn(ψHn(f)(z)),g(z),g2(ψk2(g)(x))…,gn(ψkn(g)(z)))=0(z∈D)is studied and some conditions for the system of equations to have a solution or a unique solution in A(D,D)×A（D，D）are given.
Analytic solutions of a class of nonlinearly dynamic systems
Energy Technology Data Exchange (ETDEWEB)
Wang, M-C [System Engineering Institute of Tianjin University, Tianjin, 300072 (China); Zhao, X-S; Liu, X [Tianjin University of Technology and Education, Tianjin, 300222 (China)], E-mail: mchwang123@163.com.cn, E-mail: xszhao@mail.nwpu.edu.cn, E-mail: liuxinhubei@163.com.cn
2008-02-15
In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently.
Analytical Solution for Stellar Density in Globular Clusters
Indian Academy of Sciences (India)
M. A. Sharaf; A. M. Sendi
2011-09-01
In this paper, four parameters analytical solution will be established for the stellar density function in globular clusters. The solution could be used for any arbitrary order of outward decrease of the cluster’s density.
Analytical chemistry: Sweet solution to sensing
Sia, Samuel K.; Chin, Curtis D.
2011-09-01
Glucose meters allow rapid and quantitative measurement of blood sugar levels for diabetes sufferers worldwide. Now a new method allows this proven technology to be used to quantify a much wider range of analytes.
Analytical solutions of coupled-mode equations for microring resonators
Indian Academy of Sciences (India)
ZHAO C Y
2016-06-01
We present a study on analytical solutions of coupled-mode equations for microring resonators with an emphasis on occurrence of all-optical EIT phenomenon, obtained by using a cofactor. As concrete examples, analytical solutions for a $3 \\times 3$ linearly distributed coupler and a circularly distributed coupler are obtained. The former corresponds to a non-degenerate eigenvalue problem and the latter corresponds to a degenerate eigenvalue problem. For comparison and without loss of generality, analytical solution for a $4 \\times 4$ linearly distributed coupler is also obtained. This paper may be of interest to optical physics and integrated photonics communities.
Analytical solutions of the extended Boussinesq equation
International Nuclear Information System (INIS)
The extended Boussinesq equation for the description of the Fermi-Pasta-Ulam problem has been studied and analyzed with the Painleve test. It has been shown that the equation does not pass the Painleve test, but the necessary condition for the existence of meromorphic solutions is satisfied
Analyticity of solutions of the Korteweg-de Vries equation
Tarama, Shigeo
2004-01-01
We consider the analytic smoothing effect for the KdV equation. That is to say, if the initial data given at $t = 0$ decays very rapidly, the solution to the Cauchy problem becomes analytic with respect to the space variable for $t > 0$. In this paper we show this effect by using the inverse scattering method which transforms the KdV equation to a linear dispersive equation whose analytic smoothing effect is shown through the properties of the Airy function.
Analytical r-mode solution with gravitational radiation reaction force
Dias, O J C; S\\'a, Paulo M.
2005-01-01
We present and discuss the analytical r-mode solution to the linearized hydrodynamic equations of a slowly rotating, Newtonian, barotropic, non-magnetized, perfect-fluid star in which the gravitational radiation reaction force is present.
False Vacuum Transitions - Analytical Solutions and Decay Rate Values
Correa, R A C; da Rocha, Roldao
2015-01-01
In this work we show a class of oscillating configurations for the evolution of the domain walls in Euclidean space. The solutions are obtained analytically. We also find the decay rate of the false vacuum.
New software solutions for analytical spectroscopists
Davies, Antony N.
1999-05-01
Analytical spectroscopists must be computer literate to effectively carry out the tasks assigned to them. This has often been resisted within organizations with insufficient funds to equip their staff properly, a lack of desire to deliver the essential training and a basic resistance amongst staff to learn the new techniques required for computer assisted analysis. In the past these problems were compounded by seriously flawed software which was being sold for spectroscopic applications. Owing to the limited market for such complex products the analytical spectroscopist often was faced with buying incomplete and unstable tools if the price was to remain reasonable. Long product lead times meant spectrometer manufacturers often ended up offering systems running under outdated and sometimes obscure operating systems. Not only did this mean special staff training for each instrument where the knowledge gained on one system could not be transferred to the neighbouring system but these spectrometers were often only capable of running in a stand-alone mode, cut-off from the rest of the laboratory environment. Fortunately a number of developments in recent years have substantially changed this depressing picture. A true multi-tasking operating system with a simple graphical user interface, Microsoft Windows NT4, has now been widely introduced into the spectroscopic computing environment which has provided a desktop operating system which has proved to be more stable and robust as well as requiring better programming techniques of software vendors. The opening up of the Internet has provided an easy way to access new tools for data handling and has forced a substantial re-think about results delivery (for example Chemical MIME types, IUPAC spectroscopic data exchange standards). Improved computing power and cheaper hardware now allows large spectroscopic data sets to be handled without too many problems. This includes the ability to carry out chemometric operations in
Analytic solutions for marginal deformations in open superstring field theory
International Nuclear Information System (INIS)
We extend the calculable analytic approach to marginal deformations recently developed in open bosonic string field theory to open superstring field theory formulated by Berkovits. We construct analytic solutions to all orders in the deformation parameter when operator products made of the marginal operator and the associated superconformal primary field are regular. (orig.)
A hybrid ICT-solution for smart meter data analytics
DEFF Research Database (Denmark)
Liu, Xiufeng; Nielsen, Per Sieverts
2016-01-01
analytics. The proposed solution offers an information integration pipeline for ingesting data from smart meters, a scalable platform for processing and mining big data sets, and a web portal for visualizing analytics results. The implemented system has a hybrid architecture of using Spark or Hive for big...
Analytical solutions for the Rabi model
Yu, Lixian; Liang, Qifeng; Chen, Gang; Jia, Suotang
2012-01-01
The Rabi model that describes the fundamental interaction between a two-level system with a quantized harmonic oscillator is one of the simplest and most ubiquitous models in modern physics. However, this model has not been solved exactly because it is hard to find a second conserved quantity besides the energy. Here we present a unitary transformation to map this unsolvable Rabi model into a solvable Jaynes-Cummings-like model by choosing a proper variation parameter. As a result, the analytical energy spectrums and wavefunctions including both the ground and the excited states can be obtained easily. Moreover, these explicit results agree well with the direct numerical simulations in a wide range of the experimental parameters. In addition, based on our obtained energy spectrums, the recent experimental observation of Bloch-Siegert in the circuit quantum electrodynamics with the ultrastrong coupling can be explained perfectly. Our results have the potential application in the solid-state quantum information...
Analytical Solution for the Current Distribution in Multistrand Superconducting Cables
Bottura, L; Fabbri, M G
2002-01-01
Current distribution in multistrand superconducting cables can be a major concern for stability in superconducting magnets and for field quality in particle accelerator magnets. In this paper we describe multistrand superconducting cables by means of a distributed parameters circuit model. We derive a system of partial differential equations governing current distribution in the cable and we give the analytical solution of the general system. We then specialize the general solution to the particular case of uniform cable properties. In the particular case of a two-strand cable, we show that the analytical solution presented here is identical to the one already available in the literature. For a cable made of N equal strands we give a closed form solution that to our knowledge was never presented before. We finally validate the analytical solution by comparison to numerical results in the case of a step-like spatial distribution of the magnetic field over a short Rutherford cable, both in transient and steady ...
Analytical solutions to SSC coil end design
International Nuclear Information System (INIS)
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.
Analytic solution of simplified Cardan's shaft model
Directory of Open Access Journals (Sweden)
Zajíček M.
2014-12-01
Full Text Available Torsional oscillations and stability assessment of the homokinetic Cardan shaft with a small misalignment angle is described in this paper. The simplified mathematical model of this system leads to the linearized equation of the Mathieu's type. This equation with and without a stationary damping parameter is considered. The solution of the original differential equation is identical with those one of the Fredholm’s integral equation with degenerated kernel assembled by means of a periodic Green's function. The conditions of solvability of such problem enable the identification of the borders between stability and instability regions. These results are presented in the form of stability charts and they are verified using the Floquet theory. The correctness of oscillation results for the system with periodic stiffness is then validated by means of the Runge-Kutta integration method.
Analytical solution to one-dimensional consolidation in unsaturated soils
Institute of Scientific and Technical Information of China (English)
QIN Ai-fang; CHEN Guang-jing; TAN Yong-wei; SUN Dean
2008-01-01
This paper presents an analytical solution of the one-dimensional consolidation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. The analytical solution is for Fredlund's one-dimensionai consolidation equation in unsaturated soils. The transfer relationship between the state vectors at top surface and any depth is obtained by using the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy's law and Fick's law. Excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and boundary conditions. By performing inverse Laplace transforms, the analytical solutions are obtained in the time domain. A typical example illustrates the consolidation characteristics of unsaturated soft from analytical results. Finally, comparisons between the analytical solutions and results of the finite difference method indicate that the analytical solution is correct.
Analytical Solution of the Time Fractional Fokker-Planck Equation
Directory of Open Access Journals (Sweden)
Sutradhar T.
2014-05-01
Full Text Available A nonperturbative approximate analytic solution is derived for the time fractional Fokker-Planck (F-P equation by using Adomian’s Decomposition Method (ADM. The solution is expressed in terms of Mittag- Leffler function. The present method performs extremely well in terms of accuracy, efficiency and simplicity.
AN ANALYTICAL SOLUTION FOR CALCULATING THE INITIATION OF SEDIMENT MOTION
Institute of Scientific and Technical Information of China (English)
Thomas LUCKNER; Ulrich ZANKE
2007-01-01
This paper presents an analytical solution for calculating the initiation of sediment motion and the risk of river bed movement. It thus deals with a fundamental problem in sediment transport, for which no complete analytical solution has yet been found. The analytical solution presented here is based on forces acting on a single grain in state of initiation of sediment motion. The previous procedures for calculating the initiation of sediment motion are complemented by an innovative combination of optical surface measurement technology for determining geometrical parameters and their statistical derivation as well as a novel approach for determining the turbulence effects of velocity fluctuations. This two aspects and the comparison of the solution functions presented here with the well known data and functions of different authors mainly differ the presented solution model for calculating the initiation of sediment motion from previous approaches. The defined values of required geometrical parameters are based on hydraulically laboratory tests with spheres. With this limitations the derivated solution functions permit the calculation of the effective critical transport parameters of a single grain, the calculation of averaged critical parameters for describing the state of initiation of sediment motion on the river bed, the calculation of the probability density of the effective critical velocity as well as the calculation of the risk of river bed movement. The main advantage of the presented model is the closed analytical solution from the equilibrium of forces on a single grain to the solution functions describing the initiation of sediment motion.
Constructing analytic approximate solutions to the Lane–Emden equation
International Nuclear Information System (INIS)
We derive analytic approximations to the solutions of the Lane–Emden equation, a basic equation in Astrophysics that describes the Newtonian equilibrium structure of a self-gravitating polytropic fluid sphere. After recalling some basic results, we focus on the construction of rational approximations, discussing the limitations of previous attempts, and providing new accurate approximate solutions. - Highlights: • We make a critical survey of the literature concerning the Lane–Emden equation. • We discuss problems in the construction of accurate rational approximate solutions. • We derive new analytic approximations of interest for star and cluster dynamics
An analytical solution for improved HIFU SAR estimation
International Nuclear Information System (INIS)
Accurate determination of the specific absorption rates (SARs) present during high intensity focused ultrasound (HIFU) experiments and treatments provides a solid physical basis for scientific comparison of results among HIFU studies and is necessary to validate and improve SAR predictive software, which will improve patient treatment planning, control and evaluation. This study develops and tests an analytical solution that significantly improves the accuracy of SAR values obtained from HIFU temperature data. SAR estimates are obtained by fitting the analytical temperature solution for a one-dimensional radial Gaussian heating pattern to the temperature versus time data following a step in applied power and evaluating the initial slope of the analytical solution. The analytical method is evaluated in multiple parametric simulations for which it consistently (except at high perfusions) yields maximum errors of less than 10% at the center of the focal zone compared with errors up to 90% and 55% for the commonly used linear method and an exponential method, respectively. For high perfusion, an extension of the analytical method estimates SAR with less than 10% error. The analytical method is validated experimentally by showing that the temperature elevations predicted using the analytical method's SAR values determined for the entire 3D focal region agree well with the experimental temperature elevations in a HIFU-heated tissue-mimicking phantom. (paper)
Analytical Solution of Smoluchowski Equation in Harmonic Oscillator Potential
Institute of Scientific and Technical Information of China (English)
SUN Xiao-Jun; LU Xiao-Xia; YAN Yu-Liang; DUAN Jun-Feng; ZHANG Jing-Shang
2005-01-01
Non-equilibrium fission has been described by diffusion model. In order to describe the diffusion process analytically, the analytical solution of Smoluchowski equation in harmonic oscillator potential is obtained. This analytical solution is able to describe the probability distribution and the diffusive current with the variable x and t. The results indicate that the probability distribution and the diffusive current are relevant to the initial distribution shape, initial position, and the nuclear temperature T; the time to reach the quasi-stationary state is proportional to friction coefficient β, but is independent of the initial distribution status and the nuclear temperature T. The prerequisites of negative diffusive current are justified. This method provides an approach to describe the diffusion process for fissile process in complicated potentials analytically.
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.
Analytical solution for a coaxial plasma gun: Weak coupling limit
International Nuclear Information System (INIS)
The analytical solution of the system of coupled ODE's which describes the time evolution of an ideal (i.e., zero resistance) coaxial plasma gun operating in the snowplow mode is obtained in the weak coupling limit, i.e, when the gun is fully influenced by the driving (RLC) circuit in which it resides but the circuit is negligibly influenced by the gun. Criteria for the validity of this limit are derived and numerical examples are presented. Although others have obtained approximate, asymptotic and numerical solutions of the equations, the present analytical results seem not to have appeared previously in the literature
Comparison of Web Analytics : Hosted Solutions vs Server-side Analytics
Mutai, Dominic
2015-01-01
The ratability of websites allows the aggregation of detailed data about the behavior and characteristics of website visitors. This thesis examines the value of different web metrics based on the analytics tools used and the behavior of website visitors. The objective is to test and identify key metrics and discuss how they compare between hosted solutions and server-side analytics. The value of the web metrics is evaluated by examining the relationships of the metrics to website conversions....
Analytic solution for the propagation velocity in superconducting composities
International Nuclear Information System (INIS)
The propagation velocity of normal zones in composite superconductors has been calculated analytically for the case of constant thermophysical properties, including the effects of current sharing. The solution is compared with that of a more elementary theory in which current sharing is neglected, i.e., in which there is a sharp transition from the superconducting to the normal state. The solution is also compared with experiment. This comparison demonstrates the important influence of transient heat transfer on the propagation velocity
Efficient analytical solutions for heated, pressurized multi-layered cylinders
2013-01-01
Two independent sets of analytical solutions, one based on matrix inversion and one based on iteration, are derived for the displacement field and corresponding stress state in multi-layer cylinders subjected to pressure and thermal loading. Solutions are developed for cylinders that are axially free with no friction between layers (plane stress), for cylinders that are fully restrained axially (plane strain) and for axially loaded and spring-mounted cylinders, assuming that the combined two-...
General analytical shakedown solution for structures with kinematic hardening materials
Guo, Baofeng; Zou, Zongyuan; Jin, Miao
2016-04-01
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.
Analytic Solutions for Tachyon Condensation with General Projectors
Okawa, Y; Zwiebach, B; Okawa, Yuji; Rastelli, Leonardo; Zwiebach, Barton
2006-01-01
The tachyon vacuum solution of Schnabl is based on the wedge states, which close under the star product and interpolate between the identity state and the sliver projector. We use reparameterizations to solve the long-standing problem of finding an analogous family of states for arbitrary projectors and to construct analytic solutions based on them. The solutions simplify for special projectors and allow explicit calculations in the level expansion. We test the solutions in detail for a one-parameter family of special projectors that includes the sliver and the butterfly. Reparameterizations further allow a one-parameter deformation of the solution for a given projector, and in a certain limit the solution takes the form of an operator insertion on the projector. We discuss implications of our work for vacuum string field theory.
Analytic solutions for tachyon condensation with general projectors
Energy Technology Data Exchange (ETDEWEB)
Okawa, Y. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Rastelli, L. [C.N. Yang Institute for Theoretical Physics, Stony Brook, NY (United States); Zwiebach, B. [Massachusetts Inst. of Tech., Cambridge, MA (United States). Center for Theoretical Physics
2006-11-15
The tachyon vacuum solution of Schnabl is based on the wedge states, which close under the star product and interpolate between the identity state and the sliver projector. We use reparameterizations to solve the long-standing problem of finding an analogous family of states for arbitrary projectors and to construct analytic solutions based on them. The solutions simplify for special projectors and allow explicit calculations in the level expansion. We test the solutions in detail for a one-parameter family of special projectors that includes the sliver and the butterfly. Reparameterizations further allow a one-parameter deformation of the solution for a given projector, and in a certain limit the solution takes the form of an operator insertion on the projector. We discuss implications of our work for vacuum string field theory. (orig.)
Mathematical Model of Suspension Filtering and Its Analytical Solution
Directory of Open Access Journals (Sweden)
Normahmad Ravshanov
2013-01-01
Full Text Available The work develops mathematical model and computing algorithm to analyze, project and identify the basic parameters of filter units operation and their variation range. On their basis, numerical analytic solution of the problem of ionized liquid solutions filtering was obtained. Computing experiments, resulting in graphic format were presented. Analysis of calculation results enables to determine the optimum modes of filter units operation, used in liquid ionized solutions filtration technology, in food preparation, in drug production and for drinking water purification. Selection of the most suitable parameters contributes to the improvement of economic and technologic efficiency of production and filter units operability.
The big bang and inflation united by an analytic solution
International Nuclear Information System (INIS)
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.
Analytical Solutions for Beams Passing Apertures with Sharp Boundaries
Luz, Eitam; Malomed, Boris A
2016-01-01
An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the condition that the thickness of its edges is much smaller than any other length scale in the beam's initial profile. The approximation can be easily generalized for any beam whose initial profile has several sharp features. Therefore, this method can be used as a tool to investigate the diffraction of beams on complex obstacles. The analytical results are compared to numerical solutions and experimental findings, which demonstrates high accuracy of the approximation. For an initially uniform field confined by sharp boundaries, this solution becomes exact for any propagation distance and any sharpness of the edges. Thus, it can be used as an efficient tool to represent the beams, produced by series of slits with a complex structure, by a simple but exact analytical solution.
Exact Analytical Solution of Alfven Waves in Nonuniform Plasmas
International Nuclear Information System (INIS)
Full text: The propagation of Alfven waves in non-uniform plasmas is described through linear second-order differential equations, governing the total pressure and radial plasma velocity. In general, these two differential equations only admit numerical solutions, whose behavior is very much complicated especially near resonance surfaces which encompass essential degeneracies. It is well-known that most existing analytical methods, including the famous Wentzel-Karmers-Brillouin (WKB) approximation fail near such singularities. In this paper, a power analytical method, which is recently developed and named the Differential Transfer Matrix Method (DTMM), is applied to find a rigorously exact solution to the problem of interest. We also present an approximate solution based on the Airy functions. (author)
Analytical solutions to flexural vibration of slender piezoelectric multilayer cantilevers
International Nuclear Information System (INIS)
The modeling of vibration of piezoelectric cantilevers has often been based on passive cantilevers of a homogeneous material. Although piezoelectric cantilevers and passive cantilevers share certain characteristics, this method has caused confusion in incorporating the piezoelectric moment into the differential equation of motion. The extended Hamilton’s principle is a fundamental approach to modeling flexural vibration of multilayer piezoelectric cantilevers. Previous works demonstrated derivation of the differential equation of motion using this approach; however, proper analytical solutions were not reported. This was partly due to the fact that the differential equation derived by the extended Hamilton’s principle is a boundary-value problem with nonhomogeneous boundary conditions which cannot be solved by modal analysis. In the present study, an analytical solution to the boundary-value problem was obtained by transforming it into a new problem with homogeneous boundary conditions. After the transformation, modal analysis was used to solve the new boundary-value problem. The analytical solutions for unimorphs and bimorphs were verified with three-dimensional finite element analysis (FEA). Deflection profiles and frequency response functions under voltage, uniform pressure and tip force were compared. Discrepancies between the analytical results and FEA results were within 3.5%. Following model validation, parametric studies were conducted to investigate the effects of thickness of electrodes and piezoelectric layers, and the piezoelectric coupling coefficient d 31 on the performance of piezoelectric cantilever actuators. (paper)
Institute of Scientific and Technical Information of China (English)
熊岳山; 韦永康
2001-01-01
The sediment reaction and diffusion equation with generalized initial and boundary condition is studied. By using Laplace transform and Jordan lemma , an analytical solution is got, which is an extension of analytical solution provided by Cheng Kwokming James ( only diffusion was considered in analytical solution of Cheng ). Some problems arisen in the computation of analytical solution formula are also analysed.
Phononic heat transport in the transient regime: An analytic solution
Tuovinen, Riku; Säkkinen, Niko; Karlsson, Daniel; Stefanucci, Gianluca; van Leeuwen, Robert
2016-06-01
We investigate the time-resolved quantum transport properties of phonons in arbitrary harmonic systems connected to phonon baths at different temperatures. We obtain a closed analytic expression of the time-dependent one-particle reduced density matrix by explicitly solving the equations of motion for the nonequilibrium Green's function. This is achieved through a well-controlled approximation of the frequency-dependent bath self-energy. Our result allows for exploring transient oscillations and relaxation times of local heat currents, and correctly reduces to an earlier known result in the steady-state limit. We apply the formalism to atomic chains, and benchmark the validity of the approximation against full numerical solutions of the bosonic Kadanoff-Baym equations for the Green's function. We find good agreement between the analytic and numerical solutions for weak contacts and baths with a wide energy dispersion. We further analyze relaxation times from low to high temperature gradients.
Analytical representation of a black hole puncture solution
International Nuclear Information System (INIS)
The 'moving-puncture' technique has led to dramatic advancements in the numerical simulations of binary black holes. Hannam et al. have recently demonstrated that, for suitable gauge conditions commonly employed in moving-puncture simulations, the evolution of a single black hole leads to a well-known, time-independent, maximal slicing of Schwarzschild spacetime. They construct the corresponding solution in isotropic coordinates numerically and demonstrate its usefulness, for example, for testing and calibrating numerical codes that employ moving-puncture techniques. In this brief report we point out that this solution can also be constructed analytically, making it even more useful as a test case for numerical codes
Barrierless Electronic Relaxation in Solution: An Analytically Solvable Model
Chakraborty, Aniruddha
2013-01-01
We propose an analytical method for understanding the problem of electronic relaxation in solution, modeled by a particle undergoing diffusive motion under the influence of two potentials. The coupling between the two potentials is assumed to be represented by a Dirac Delta function. The diffusive motion in this paper is described by the Smoluchowskii equation. Our solution requires the knowledge of the Laplace transform of the Green's function for the motion in both the uncoupled potentials. Our model is more general than all the earlier models, because we are the first one to consider the effect of ground state potential energy surface explicitly.
An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders
DEFF Research Database (Denmark)
Larsen, Niels Vesterdal; Breinbjerg, Olav
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...
Analytical Analysis and Numerical Solution of Two Flavours Skyrmion
Hadi, Miftachul; Hermawanto, Denny
2010-01-01
Two flavours Skyrmion will be analyzed analytically, in case of static and rotational Skyrme equations. Numerical solution of a nonlinear scalar field equation, i.e. the Skyrme equation, will be worked with finite difference method. This article is a more comprehensive version of \\textit{SU(2) Skyrme Model for Hadron} which have been published at Journal of Theoretical and Computational Studies, Volume \\textbf{3} (2004) 0407.
Analytic solution of certain second-order functional differential equation
Directory of Open Access Journals (Sweden)
Theeradach Kaewong
2006-09-01
Full Text Available We consider the existence of analytic solutions of a certain class of iterative second-order functional differential equation of the form xÃ¢Â€Â³(x[r](z=c0z2+c1(x(z2+(c2x[2](z2+Ã¢Â‹Â¯+cm(x[m](z2, m,rÃ¢Â‰Â¥0.
Semi-analytical solution for soliton propagation in colloidal suspension
Directory of Open Access Journals (Sweden)
Senthilkumar Selvaraj
2013-04-01
Full Text Available We consider the propagation of soliton in colloidal nano-suspension. We derive the semi analytical solution for soliton propagation in colloidal nano-suspensions for both one and two spatial dimensions using variational method. This Variational method uses both Averaged Lagrangian and suitable trial functions. Finally we analyse about Rayleigh scattering loss in the soliton propagation through the colloidal nano-suspensions.
Approximate analytical solutions of the baby Skyrme model
Ioannidou, T. A.; Kopeliovich, V. B.; Zakrzewski, W. J.
2002-01-01
In present paper we show that many properties of the baby skyrmions, which have been determined numerically, can be understood in terms of an analytic approximation. In particular, we show that this approximation captures properties of the multiskyrmion solutions (derived numerically) such as their stability towards decay into various channels, and that it is more accurate for the "new baby Skyrme model" which describes anisotropic physical systems in terms of multiskyrmion fields with axial ...
Analyticity of solutions for quasilinear wave equations and other quasilinear systems
Kuksin, Sergei; Nadirashvili, Nikolai
2012-01-01
We prove the persistence of analyticity for classical solution of the Cauchy problem for quasilinear wave equations with analytic data. Our results show that the analyticity of solutions, stated by the Cauchy-Kowalewski and Ovsiannikov-Nirenberg theorems, lasts till a classical solution exists. Moreover, they show that if the equation and the Cauchy data are analytic only in a part of space-variables, then a classical solution also is analytic in these variables. The approach applies to other...
Analytic solution of pseudocolloid migration in fractured rock
International Nuclear Information System (INIS)
A form of colloid migration that can enhance or retard the migration of a dissolved contaminant in ground water is the sorption of the contaminant on the moving colloidal particulate to form pseudocolloids. In this paper we develop analytical solutions for the interactive migration of radioactive species dissolved in ground water and sorbed as pseudocolloids. The solute and pseudocolloids are assumed to undergo advection and dispersion in a one-dimensional flow field in planar fractures in porous rock. Interaction between pseudocolloid and dissolved species is described by equilibrium sorption. Sorbed species on the pseudocolloids undergo radioactive decay, and pseudocolloids can sorb on fracture surfaces and sediments. Filtration is neglected. The solute can decay and sorb on pseudocolloids, on the fracture surfaces, and on sediments and can diffuse into the porous rock matrix. 1 fig
JOVIAN STRATOSPHERE AS A CHEMICAL TRANSPORT SYSTEM: BENCHMARK ANALYTICAL SOLUTIONS
International Nuclear Information System (INIS)
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 CH4 and C2H6 are mainly in diffusive equilibrium, and the C2H2 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 C2H2) is dominated by the local chemical sources and sinks, while that of a long-lived species (such as C2H6) 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.
JOVIAN STRATOSPHERE AS A CHEMICAL TRANSPORT SYSTEM: BENCHMARK ANALYTICAL SOLUTIONS
Energy Technology Data Exchange (ETDEWEB)
Zhang Xi; Shia Runlie; Yung, Yuk L., E-mail: xiz@gps.caltech.edu [Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125 (United States)
2013-04-20
We systematically investigated the solvable analytical benchmark cases in both one- and two-dimensional (1D and 2D) chemical-advective-diffusive systems. We use the stratosphere of Jupiter as an example but the results can be applied to other planetary atmospheres and exoplanetary atmospheres. In the 1D system, we show that CH{sub 4} and C{sub 2}H{sub 6} are mainly in diffusive equilibrium, and the C{sub 2}H{sub 2} profile can be approximated by modified Bessel functions. In the 2D system in the meridional plane, analytical solutions for two typical circulation patterns are derived. Simple tracer transport modeling demonstrates that the distribution of a short-lived species (such as C{sub 2}H{sub 2}) is dominated by the local chemical sources and sinks, while that of a long-lived species (such as C{sub 2}H{sub 6}) is significantly influenced by the circulation pattern. We find that an equator-to-pole circulation could qualitatively explain the Cassini observations, but a pure diffusive transport process could not. For slowly rotating planets like the close-in extrasolar planets, the interaction between the advection by the zonal wind and chemistry might cause a phase lag between the final tracer distribution and the original source distribution. The numerical simulation results from the 2D Caltech/JPL chemistry-transport model agree well with the analytical solutions for various cases.
Approximate analytical solutions to the condensation-coagulation equation of aerosols
DEFF Research Database (Denmark)
Smith, Naftali R.; Shaviv, Nir J.; Svensmark, Henrik
2016-01-01
We present analytical solutions to the steady state nucleation-condensation-coagulation equation of aerosols in the atmosphere. These solutions are appropriate under different limits but more general than previously derived analytical solutions. For example, we provide an analytic solution to the...
Analytical solutions of transport problems in anisotropic media
International Nuclear Information System (INIS)
Recently, the problem of neutron transport in anisotropic media has received new attention in connection with safety studies of water reactors and design of gas-cooled systems. In situations presenting large voided regions, as the axial streaming is dominating with respect to the transverse one, the average properties of the homogenized material should physically account for such macroscopic anisotropy. Hence, it is suggested that cell calculations produce anisotropic average cross sections, e.g., axial (σA) and transverse (σT) values. Since material anisotropy is due to leakage, as a first-step approximation, the medium can be considered isotropic with respect to scattering phenomena. Transport codes are currently being adapted to include anisotropic cross sections. An important aspect of code development is the validation of algorithms by analytical benchmarks. For that purpose, the present work is devoted to the fully analytical solution of transport problems in slab geometry
ANALYTICAL SOLUTION OF GROUNDWATER FLUCTUATIONS IN ESTUARINE AQUIFER
Institute of Scientific and Technical Information of China (English)
CHEN Jing; ZHOU Zhi-fang; JIA Suo-bao
2005-01-01
As a basic factor in the environment of estuary, tidal effects in the coastal aquifer have recently attracted much attention because tidal dynamic also greatly influences the solute transport in the coastal aquifer. Previous studies on tidal dynamic of coastal aquifers have focused on the inland propagation of oceanic tides in the cross-shore direction, a configuration that is essentially one-dimensional. Two-dimensional analytical solutions for groundwater level fluctuation in recent papers are localized in presenting the effect of both oceanic tides and estuarine tides in quadrantal aquifer. A two-dimensional model of groundwater fluctuations in estuarine zone in proposed in this paper. Using complex transform, the two-dimensional flow equation subject to periodic boundary condition is changed into time-independent elliptic problem. Based on Green function method, an analytical solution for groundwater fluctuations in fan-shaped aquifer is derived. The response to of groundwater tidal loading in an estuary and ocean is discussed. The result show that its more extensive application than recent studies.
Cooling and warming laws: an exact analytical solution
International Nuclear Information System (INIS)
This paper deals with temperature variations over time of objects placed in a constant-temperature environment in the presence of thermal radiation. After a historical introduction, the paper discusses cooling and warming laws, by taking into account first solely object-environment energy exchange by thermal radiation, and then adding object-environment heat exchange by convection. These processes are usually evaluated by approximating the law of exchange of thermal radiation by a linear relationship between power exchange and temperature difference. In contrast, in this paper an exact analytical solution considering Stefan's fourth power law is provided, under some general hypotheses, for both cases. A comparison with exponential approximations and with a historical law proposed by Dulong and Petit in 1817 is presented. Data of an experiment are used to test the analytical solution: the test has allowed evaluating the heat transfer coefficient h of the experiment and has shown that our solution provides a better fit with the measured values than any exponential function. The topic is developed in a way which can be suitable both for undergraduate students and for general physicists.
Comparison between analytical and numerical solution of mathematical drying model
Shahari, N.; Rasmani, K.; Jamil, N.
2016-02-01
Drying is often related to the food industry as a process of shifting heat and mass inside food, which helps in preserving food. Previous research using a mass transfer equation showed that the results were mostly concerned with the comparison between the simulation model and the experimental data. In this paper, the finite difference method was used to solve a mass equation during drying using different kinds of boundary condition, which are equilibrium and convective boundary conditions. The results of these two models provide a comparison between the analytical and the numerical solution. The result shows a close match between the two solution curves. It is concluded that the two proposed models produce an accurate solution to describe the moisture distribution content during the drying process. This analysis indicates that we have confidence in the behaviour of moisture in the numerical simulation. This result demonstrated that a combined analytical and numerical approach prove that the system is behaving physically. Based on this assumption, the model of mass transfer was extended to include the temperature transfer, and the result shows a similar trend to those presented in the simpler case.
Numerical and analytical solutions for problems relevant for quantum computers
International Nuclear Information System (INIS)
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.)
Analytical Solution of the Bosonic Three-Body Problem
International Nuclear Information System (INIS)
We revisit the problem of three identical bosons in free space, which exhibits a universal hierarchy of bound states (Efimov trimers). Modeling a narrow Feshbach resonance within a two-channel description, we map the integral equation for the three-body scattering amplitude to a one-dimensional Schroedinger-type single-particle equation, where an analytical solution of exponential accuracy is obtained. We give exact results for the trimer binding energies, the three-body parameter, the threshold to the three-atom continuum, and the recombination rate
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 Two-Qubit Quantum Rabi Model
Abo-Kahla, Doaa A M; Abdel-Aty, Mahmoud
2015-01-01
In this paper, an analytical solution of the two-qubit Rabi model for the general case is presented. Furthermore, a comparison between the information entropies and the Von Neumann entropy $(\\rho_{A})$ is given for some special values of the qubit-photon coupling constants in case of the detuning parameters. It is demonstrated that oscillations of the occupation probabilities $\\rho_{11}, \\rho_{22}, \\rho_{33}$ and $\\rho_{44}$ are equivalent to the case of the spontaneous emission. The occupation probability $\\rho_{11}$ reaches the case of sudden death, when the detuning parameters $\\Delta_{2}$ equals zero.
Regression techniques and analytical solutions to demonstrate intrinsic bioremediation
International Nuclear Information System (INIS)
It is now generally recognized that a major factor responsible for the attenuation and mass reduction of benzene, toluene, ethylbenzene, and xylenes (BTEX) in groundwater plumes is hydrocarbon biodegradation by indigenous microorganisms in aquifer material. Their objective is to apply well-known regression techniques and analytical solutions to estimate the contribution of advection, dispersion, sorption, and biodecay to the overall attenuation of petroleum hydrocarbons. These calculations yield an apparent biodecay rate based on field data. This biodecay rate is a significant portion of the overall attenuation in stable, dissolved hydrocarbon plumes
Approximate analytical solutions of the baby Skyrme model
Ioannidou, T A; Zakrzewski, W J
2002-01-01
In present paper we show that many properties of the baby skyrmions, which have been determined numerically, can be understood in terms of an analytic approximation. In particular, we show that this approximation captures properties of the multiskyrmion solutions (derived numerically) such as their stability towards decay into various channels, and that it is more accurate for the "new baby Skyrme model" which describes anisotropic physical systems in terms of multiskyrmion fields with axial symmetry. Some universal characteristics of configurations of this kind are demonstrated, which do not depend on their topological number.
Analytical dynamic solution of a flexible cable-suspended manipulator
Bamdad, Mahdi
2013-12-01
Cable-suspended manipulators are used in large scale applications with, heavy in weight and long in span cables. It seems impractical to maintain cable assumptions of smaller robots for large scale manipulators. The interactions among the cables, platforms and actuators can fully evaluate the coupled dynamic analysis. The structural flexibility of the cables becomes more pronounced in large manipulators. In this paper, an analytic solution is provided to solve cable vibration. Also, a closed form solution can be adopted to improve the dynamic response to flexibility. The output is provided by the optimal torque generation subject to the actuator limitations in a mechatronic sense. Finally, the performance of the proposed algorithm is examined through simulations.
New chemical evolution analytical solutions including environment effects
Spitoni, E
2015-01-01
In the last years, more and more interest has been devoted to analytical solutions, including inflow and outflow, to study the metallicity enrichment in galaxies. In this framework, we assume a star formation rate which follows a linear Schmidt law, and we present new analytical solutions for the evolution of the metallicity (Z) in galaxies. In particular, we take into account environmental effects including primordial and enriched gas infall, outflow, different star formation efficiencies, and galactic fountains. The enriched infall is included to take into account galaxy-galaxy interactions. Our main results can be summarized as: i) when a linear Schmidt law of star formation is assumed, the resulting time evolution of the metallicity Z is the same either for a closed-box model or for an outflow model. ii) The mass-metallicity relation for galaxies which suffer a chemically enriched infall, originating from another evolved galaxy with no pre-enriched gas, is shifted down in parallel at lower Z values, if co...
Analytic solutions of tunneling time through smooth barriers
Xiao, Zhi; Huang, Hai
2016-03-01
In the discussion of temporary behaviors of quantum tunneling, people usually like to focus their attention on rectangular barrier with steep edges, or to deal with smooth barrier with semi-classical or even numerical calculations. Very few discussions on analytic solutions of tunneling through smooth barrier appear in the literature. In this paper, we provide two such examples, a semi-infinite long barrier V ( x ) = /A 2 [ 1 + tanh ( x / a ) ] and a finite barrier V(x) = A sech2(x/a). To each barrier, we calculate the associated phase time and dwell time after obtaining the analytic solution. The results show that, different from rectangular barrier, phase time or dwell time does increase with the length parameter a controlling the effective extension of the barrier. More interestingly, for the finite barrier, phase time or dwell time exhibits a peak in k-space. A detailed analysis shows that this interesting behavior can be attributed to the strange tunneling probability Ts(k), i.e., Ts(k) displays a unit step function-like profile Θ(k - k0), especially when a is large, say, a ≫ 1/κ, 1/k. And k 0 ≡ √{ m A } / ħ is exactly where the peak appears in phase or dwell time k-spectrum. Thus only those particles with k in a very narrow interval around k0 are capable to dwell in the central region of the barrier sufficiently long.
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. PMID:24051763
Creation of the CMB blackbody spectrum: precise analytic solutions
Khatri, Rishi
2012-01-01
The blackbody spectrum of CMB was created behind the blackbody surface at redshifts $z\\gtrsim 2\\times 10^6$. At earlier times, the Universe was dense and hot enough that complete thermal equilibrium between baryonic matter (electrons and ions) and photons could be established. Any perturbation away from the blackbody spectrum was suppressed exponentially. New physics, for example annihilation and decay of dark matter, can add energy and photons to CMB at redshifts $z\\gtrsim 10^5$ and result in a non-zero chemical potential ($\\mu$) of CMB. Precise evolution of the CMB spectrum around the critical redshift of $z\\gtrsim 2\\times 10^6$ is required in order to calculate the $\\mu$-type spectral distortion. Although numerical calculation of important processes involved (double Compton process, comptonization and bremsstrahlung) is not difficult, analytic solutions are much faster and easier to calculate and provide valuable physical insights. We provide precise (better than 1%) analytic solutions for the decay of $\\m...
Analytical Solution of Projectile Motion with Quadratic Resistance and Generalisations
Ray, Shouryya
2013-01-01
The paper considers the motion of a body under the influence of gravity and drag of the surrounding fluid. Depending on the fluid mechanical regime, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body relative to the fluid. The case of quadratic drag is substantially more complex than the linear case, as it nonlinearly couples both components of the momentum equation, and no explicit analytic solution is known for a general trajectory. After a detailed account of the literature, the paper provides such a solution in form of a series expansion. This result is discussed in detail and related to other approaches previously proposed. In particular, it is shown to yield certain approximate solutions proposed in the literature as limiting cases. The solution technique employs a strategy to reduce systems of ordinary differential equations with a triangular dependence of the right-hand side on the vector of unknowns to a single equation in an auxiliary variable....
Bondi-Hoyle-Lyttleton accretion flow revisited: Analytic solution
Matsuda, Takuya; Isaka, Hiromu; Ohsugi, Yukimasa
2015-11-01
The time-steady equation for a 1D wind accretion flow, i.e. the Bondi-Hoyle-Lyttleton (BHL) equation, is investigated analytically. The BHL equation is well known to have infinitely many solutions. Traditionally, the accretion radius has been assumed to be 2textit {GM}/v_{infty }2, but its mathematical foundation has not been clarified because of the non-uniqueness of the solution. Here, we assume that the solution curves possess physically nice characteristics, i.e. velocity and line mass-density increase monotonically with radial distance. This condition restricts the accretion radius to the range left (0.71 - 1.0right ) × 2textit {GM}/v_{infty }2. Further assumptions, specifically, that the solution curves for velocity and line mass-density are convex upward, restrict the accretion radius to (0.84 - 0.94) × 2textit {GM}/v_{infty }2, and 0.90 × 2textit {GM}/v_{infty }2, respectively. Therefore, we conclude that the accretion radius is almost uniquely determined to be 0.90 × 2textit {GM}/v_{infty }2.
A non-grey analytical model for irradiated atmospheres. II: Analytical vs. numerical solutions
Parmentier, Vivien; Fortney, Jonathan J; Marley, Mark S
2013-01-01
The recent discovery and characterization of the diversity of the atmospheres of exoplanets and brown dwarfs calls for the development of fast and accurate analytical models. In this paper we first quantify the accuracy of the analytical solution derived in paper I for an irradiated, non-grey atmosphere by comparing it to a state-of-the-art radiative transfer model. Then, using a grid of numerical models, we calibrate the different coefficients of our analytical model for irradiated solar-composition atmospheres of giant exoplanets and brown dwarfs. We show that the so-called Eddington approximation used to solve the angular dependency of the radiation field leads to relative errors of up to 5% on the temperature profile. For grey or semi-grey atmospheres we show that the presence of a convective zone has a limited effect on the radiative atmosphere above it and leads to modifications of the radiative temperature profile of order 2%. However, for realistic non-grey planetary atmospheres, the presence of a con...
Analytic solution of Hubbell's model of local community dynamics
McKane, A; Sole, R; Kane, Alan Mc; Alonso, David; Sole, Ricard
2003-01-01
Recent theoretical approaches to community structure and dynamics reveal that many large-scale features of community structure (such as species-rank distributions and species-area relations) can be explained by a so-called neutral model. Using this approach, species are taken to be equivalent and trophic relations are not taken into account explicitly. Here we provide a general analytic solution to the local community model of Hubbell's neutral theory of biodiversity by recasting it as an urn model i.e.a Markovian description of states and their transitions. Both stationary and time-dependent distributions are analysed. The stationary distribution -- also called the zero-sum multinomial -- is given in closed form. An approximate form for the time-dependence is obtained by using an expansion of the master equation. The temporal evolution of the approximate distribution is shown to be a good representation for the true temporal evolution for a large range of parameter values.
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.
General analytical solutions for DC/AC circuit network analysis
Rubido, Nicolás; Baptista, Murilo S
2014-01-01
In this work, we present novel general analytical solutions for the currents that are developed in the edges of network-like circuits when some nodes of the network act as sources/sinks of DC or AC current. We assume that Ohm's law is valid at every edge and that charge at every node is conserved (with the exception of the source/sink nodes). The resistive, capacitive, and/or inductive properties of the lines in the circuit define a complex network structure with given impedances for each edge. Our solution for the currents at each edge is derived in terms of the eigenvalues and eigenvectors of the Laplacian matrix of the network defined from the impedances. This derivation also allows us to compute the equivalent impedance between any two nodes of the circuit and relate it to currents in a closed circuit which has a single voltage generator instead of many input/output source/sink nodes. Contrary to solving Kirchhoff's equations, our derivation allows to easily calculate the redistribution of currents that o...
POLYNOMIAL SOLUTIONS TO PIEZOELECTRIC BEAMS(Ⅱ)--ANALYTICAL SOLUTIONS TO TYPICAL PROBLEMS
Institute of Scientific and Technical Information of China (English)
DING Hao-jiang; JIANG Ai-min
2005-01-01
For the orthotropic piezoelectric plane problem, a series of piezoelectric beams is solved and the corresponding analytical solutions are obtained with the trialand-error method on the basis of the general solution in the case of three distinct eigenvalues, in which all displacements, electrical potential, stresses and electrical displacements are expressed by three displacement functions in terms of harmonic polynomials. These problems are cantilever beam with cross force and point charge at free end, cantilever beam and simply-supported beam subjected to uniform loads on the upper and lower surfaces, and cantilever beam subjected to linear electrical potential.
Concerning an analytical solution of some families of Kepler’s transcendental equation
Directory of Open Access Journals (Sweden)
Slavica M. Perovich
2016-03-01
Full Text Available The problem of finding an analytical solution of some families of Kepler transcendental equation is studied in some detail, by the Special Trans Functions Theory – STFT. Thus, the STFT mathematical approach in the form of STFT iterative methods with a novel analytical solutions are presented. Structure of the STFT solutions, numerical results and graphical simulations confirm the validity of the basic principle of the STFT. In addition, the obtained analytical results are compared with the calculated values of other analytical methods for alternative proving its significance. Undoubtedly, the proposed novel analytical approach implies qualitative improvement in comparison with conventional numerical and analytical methods.
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. PMID:27198809
Analytical Solution and Physics of a Propellant Damping Device
Yang, H. Q.; Peugeot, John
2011-01-01
NASA design teams have been investigating options for "detuning" Ares I to prevent oscillations originating in the vehicle solid-rocket main stage from synching up with the natural resonance of the rest of the vehicle. An experimental work started at NASA MSFC center in 2008 using a damping device showed great promise in damping the vibration level of an 8 resonant tank. However, the mechanisms of the vibration damping were not well understood and there were many unknowns such as the physics, scalability, technology readiness level (TRL), and applicability for the Ares I vehicle. The objectives of this study are to understand the physics of intriguing slosh damping observed in the experiments, to further validate a Computational Fluid Dynamics (CFD) software in propellant sloshing against experiments with water, and to study the applicability and efficiency of the slosh damper to a full scale propellant tank and to cryogenic fluids. First a 2D fluid-structure interaction model is built to model the system resonance of liquid sloshing and structure vibration. A damper is then added into the above model to simulate experimentally observed system damping phenomena. Qualitative agreement is found. An analytical solution is then derived from the Newtonian dynamics for the thrust oscillation damper frequency, and a slave mass concept is introduced in deriving the damper and tank interaction dynamics. The paper will elucidate the fundamental physics behind the LOX damper success from the derivation of the above analytical equation of the lumped Newtonian dynamics. Discussion of simulation results using high fidelity multi-phase, multi-physics, fully coupled CFD structure interaction model will show why the LOX damper is unique and superior compared to other proposed mitigation techniques.
New analytic solutions for modeling vertical gravity gradient anomalies
Kim, Seung-Sep; Wessel, Paul
2016-05-01
Modern processing of satellite altimetry for use in marine gravimetry involves computing the along-track slopes of observed sea-surface heights, projecting them into east-west and north-south deflection of the vertical grids, and using Laplace's equation to algebraically obtain a grid of the vertical gravity gradient (VGG). The VGG grid is then integrated via overlapping, flat Earth Fourier transforms to yield a free-air anomaly grid. Because of this integration and associated edge effects, the VGG grid retains more short-wavelength information (e.g., fracture zone and seamount signatures) that is of particular importance for plate tectonic investigations. While modeling of gravity anomalies over arbitrary bodies has long been a standard undertaking, similar modeling of VGG anomalies over oceanic features is not commonplace yet. Here we derive analytic solutions for VGG anomalies over simple bodies and arbitrary 2-D and 3-D sources. We demonstrate their usability in determining mass excess and deficiency across the Mendocino fracture zone (a 2-D feature) and find the best bulk density estimate for Jasper seamount (a 3-D feature). The methodologies used herein are implemented in the Generic Mapping Tools, available from gmt.soest.hawaii.edu.
Analytical solutions for peak and residual uplift resistance of pipelines
Energy Technology Data Exchange (ETDEWEB)
Nixon, J.F. [Nixon Geotech Ltd., Calgary, AB (Canada); Oswell, J.M. [Naviq Consulting Inc., Calgary, AB (Canada)
2010-07-01
Frost heave can occur on cold pipelines that traverse unfrozen, non permafrost terrain. The stresses experienced by the pipeline are partly a function of the strength of the soil on the non heaving side of the frozen-unfrozen interface. This paper proposed three analytical solutions to estimate the soil uplift resistance by considering the pipeline and soil to act similar to a strip footing, a punching shear failure, and by considering the formation of horizontal crack emanating from the spring line of the pipe. Peak uplift resistance and residual uplift resistance were discussed. Results for full scale pipe and for laboratory scale model pipes were presented, with particular reference to cover depth, temperature and crack width; and limits to residual uplift resistance. It was concluded that the peak uplift resistance and the residual uplift resistance are generally independent and controlled by different factors. The peak resistance is related directly to pipe diameter, and less strongly dependent on springline depth. It is also strongly dependent on soil temperature. However, the residual uplift resistance is strongly dependent on burial depth, weakly dependent on pipe displacement rate and also on soil temperature. 15 refs., 19 figs.
Approximate analytic solutions to the NPDD: Short exposure approximations
Close, Ciara E.; Sheridan, John T.
2014-04-01
There have been many attempts to accurately describe the photochemical processes that take places in photopolymer materials. As the models have become more accurate, solving them has become more numerically intensive and more 'opaque'. Recent models incorporate the major photochemical reactions taking place as well as the diffusion effects resulting from the photo-polymerisation process, and have accurately described these processes in a number of different materials. It is our aim to develop accessible mathematical expressions which provide physical insights and simple quantitative predictions of practical value to material designers and users. In this paper, starting with the Non-Local Photo-Polymerisation Driven Diffusion (NPDD) model coupled integro-differential equations, we first simplify these equations and validate the accuracy of the resulting approximate model. This new set of governing equations are then used to produce accurate analytic solutions (polynomials) describing the evolution of the monomer and polymer concentrations, and the grating refractive index modulation, in the case of short low intensity sinusoidal exposures. The physical significance of the results and their consequences for holographic data storage (HDS) are then discussed.
An analytical solution of non-Fourier Chen-Holmes bioheat transfer equation
Institute of Scientific and Technical Information of China (English)
GOU Chenhua; CAI Ruixian
2005-01-01
An algebraically explicit analytical solution with heat wave effect is derived for the non-Fourier bioheat transfer Chen-Holmes model. Besides its important theoretical meaning (for example, to expand the understanding of heat wave phenomena in living tissues), this analytical solution is also valuable as the benchmark solution to check the numerical calculation and to develop various numerical computational approaches.
Approximate analytical solutions to the condensation-coagulation equation of aerosols
Smith, Naftali; Svensmark, Henrik
2015-01-01
We present analytical solutions to the steady state injection-condensation-coagulation equation of aerosols in the atmosphere. These solutions are appropriate under different limits but more general than previously derived analytical solutions. For example, we provide an analytic solution to the coagulation limit plus a condensation correction. Our solutions are then compared with numerical results. We show that the solutions can be used to estimate the sensitivity of the cloud condensation nuclei number density to the nucleation rate of small condensation nuclei and to changes in the formation rate of sulfuric acid.
An analytical solution for the Marangoni mixed convection boundary layer flow
DEFF Research Database (Denmark)
Moghimi, M. A.; Kimiaeifar, Amin; Rahimpour, M.; Bagheri, G. H.
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...... control the convergence of the solution. The numerical solution of the similarity equations is developed and the results are in good agreement with the analytical results based on the HAM....
Analytical solution of a model for complex food webs
Camacho Castro, Juan; Guimerà, Roger; Amaral, Luís A. Nunes
2002-01-01
We investigate numerically and analytically a recently proposed model for food webs [Nature {\\bf 404}, 180 (2000)] in the limit of large web sizes and sparse interaction matrices. We obtain analytical expressions for several quantities with ecological interest, in particular the probability distributions for the number of prey and the number of predators. We find that these distributions have fast-decaying exponential and Gaussian tails, respectively. We also find that our analytical expressi...
On analytical solutions for the nonlinear diffusion equation
Directory of Open Access Journals (Sweden)
Ulrich Olivier Dangui-Mbani
2014-09-01
Full Text Available The nonlinear diffusion equation arises in many important areas of nonlinear problems of heat and mass transfer, biological systems and processes involving fluid flow and most of the known exact solutions turn out to be approximate solutions in the form of a series which is the exact solution in the closed form. The approximate results obtained by using Homotopy perturbation transform method (HPTM and have been compared with the exact solutions by using software “mathematica” to show the stability of the solutions of nonlinear equation. The comparisons indicate that there is a very good agreement between the HPTM solutions and exact solutions in terms of accuracy
Analytic Solution for Magnetohydrodynamic Stagnation Point Flow towards a Stretching Sheet
Institute of Scientific and Technical Information of China (English)
DING Qi; ZHANG Hong-Qing
2009-01-01
A steady two-dimensional magnetohydrodynamic stagnation point flow towards a stretching sheet with variable surface temperature is investigated. The analytic solution is obtained by homotopy analysis method. Theconvergence region is computed and the feature of the solution is discussed.
Analytical 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
Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-w...
Analytic solution for bending-compression/tension members with different moduli
International Nuclear Information System (INIS)
In this paper, based on elastic theory of different tension-compression moduli, formulas for calculation of stress and displacement are obtained for bending-compression/tension members under complex stress and subject to combined loadings. An example is given and the obtained analytical solution is compared with numerical results, showing high accuracy of the obtained analytic solution
An analytical solution for quantum size effects on Seebeck coefficient
Karabetoglu, S.; Sisman, A.; Ozturk, Z. F.
2016-03-01
There are numerous experimental and numerical studies about quantum size effects on Seebeck coefficient. In contrast, in this study, we obtain analytical expressions for Seebeck coefficient under quantum size effects. Seebeck coefficient of a Fermi gas confined in a rectangular domain is considered. Analytical expressions, which represent the size dependency of Seebeck coefficient explicitly, are derived in terms of confinement parameters. A fundamental form of Seebeck coefficient based on infinite summations is used under relaxation time approximation. To obtain analytical results, summations are calculated using the first two terms of Poisson summation formula. It is shown that they are in good agreement with the exact results based on direct calculation of summations as long as confinement parameters are less than unity. The analytical results are also in good agreement with experimental and numerical ones in literature. Maximum relative errors of analytical expressions are less than 3% and 4% for 2D and 1D cases, respectively. Dimensional transitions of Seebeck coefficient are also examined. Furthermore, a detailed physical explanation for the oscillations in Seebeck coefficient is proposed by considering the relative standard deviation of total variance of particle number in Fermi shell.
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.
Can We Remove Secular Terms for Analytical Solution of Groundwater Response under Tidal Influence?
Munusamy, Selva Balaji
2016-01-01
This paper presents a secular term removal methodology based on the homotopy perturbation method for analytical solutions of nonlinear problems with periodic boundary condition. The analytical solution for groundwater response to tidal fluctuation in a coastal unconfined aquifer system with the vertical beach is provided as an example. The non-linear one-dimensional Boussinesq's equation is considered as the governing equation for the groundwater flow. An analytical solution is provided for non-dimensional Boussinesq's equation with cosine harmonic boundary condition representing tidal boundary condition. The analytical solution is obtained by using homotopy perturbation method with a virtual embedding parameter. The present approach does not require pre-specified perturbation parameter and also facilitates secular terms elimination in the perturbation solution. The solutions starting from zeroth-order up to third-order are obtained. The non-dimensional expression, $A/D_{\\infty}$ emerges as an implicit parame...
Indian Academy of Sciences (India)
Zehra Pinar; Abhishek Dutta; Guido Bény; Turgut Öziş
2015-01-01
This paper presents an effective analytical simulation to solve population balance equation (PBE), involving particulate aggregation and breakage, by making use of appropriate solution(s) of associated complementary equation via auxiliary equation method (AEM). Travelling wave solutions of the complementary equation of a nonlinear PBE with appropriately chosen parameters is taken to be analogous to the description of the dynamic behaviour of the particulate processes. For an initial proof-of-concept, a general case when the number of particles varies with respect to time is chosen. Three cases, i.e. (1) balanced aggregation and breakage, (2) when aggregation can dominate and (3) breakage can dominate, are selected and solved for their corresponding analytical solutions. The results are then compared with the available analytical solution, based on Laplace transform obtained from literature. In this communication, it is shown that the solution approach proposed via AEM is flexible and therefore more efficient than the analytical approach used in the literature.
Application of a two energy group analytical solution to the Yalina experiment SC3A
International Nuclear Information System (INIS)
The SC3A experiment in the YALINA-Booster facility is described and investigated. For this investigation the very special configuration of YALINA-Booster is analyzed based on HELIOS calculations. To improve the representation to this special configuration a new analytical solution for two energy groups with two sources (central external and boundary source) has been developed starting form the Green's function solution. Very good agreement has been found for these improved analytical solutions. (author)
On analytical solution of the Navier-Stokes equations
International Nuclear Information System (INIS)
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
Analytic solution for a class of turbulence problems
Vlad, M.; Spineanu, F.; Misguich, J. H.; Balescu, R.
2001-01-01
An exact analytical method for determining the Lagrangian velocity correlation and the diffusion coefficient for particles moving in a stochastic velocity field is derived. It applies to divergence-free 2-dimensional Gaussian stochastic fields which are stationary, homogeneous and have factorized Eulerian correlations.
Analytical solution based on stream-aquifer interactions in partially penetrating streams
Directory of Open Access Journals (Sweden)
Yong Huang
2010-09-01
Full Text Available An analytical solution of drawdown caused by pumping is developed in an aquifer hydraulically connected to a finite-width stream on the condition of two streams. The proposed analytical solution modified Hunt’s analytical solution and not only considers the effect of stream width on drawdown, but also takes the distribution of drawdown on the interaction of two streams into account. Advantages of the solution include its simple structure, consisting of the Theis well function, parameters of aquifer and streambed semipervious material. The calculated results show that the proposed analytical solution agrees well with the previous solution and the errors between the two solutions are equal to zero on the condition of a stream without considering the effect of stream width. Also, deviations between the two analytical solutions increase with the increase of stream width. Furthermore, four cases are studied to discuss the effect of two streams on drawdown. It assumes that some parameters are changeable, and other parameters are constant, such as stream width, the distance between stream and pumping well, stream recharge rate, and the leakance coefficient of streambed semipervious material, etc. The analytical solution may provide estimates for parameters of aquifer and streambed semipervious material using the Type Curve Method through the data of field test.
Institute of Scientific and Technical Information of China (English)
CAI; Ruixian; GOU; Chenhua; ZHANG; Na
2005-01-01
Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media. Besides their important theoretical meaning (for example, in analyzing the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer. Some solutions considering the anisotropic effect of permeability have been given previously by the authors, and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.
Analytic Solution of Strongly Coupling Schr(o)dinger Equations
Institute of Scientific and Technical Information of China (English)
LIAO Jin-Feng; ZHUANG Peng-Fei
2004-01-01
A recently developed expansion method for analytically solving the ground states of strongly coupling Schrodinger equations by Friedberg,Lee,and Zhao is extended to excited states and applied to power-law central forces for which scaling properties are proposed.As examples for application of the extended method,the Hydrogen atom problem is resolved and the low-lying states of Yukawa potential are approximately obtained.
Analytical 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 solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subj...
Analytical solutions of simply supported magnetoelectroelastic circular plate under uniform loads
Institute of Scientific and Technical Information of China (English)
陈江瑛; 丁皓江; 侯鹏飞
2003-01-01
In this paper, the axisymmetric general solutions of transversely isotropic magnetoelectroelastic media are expressed with four harmonic displacement functions at first. Then, based on the solutions, the analytical three-dimensional solutions are provided for a simply supported magnetoelectroelastic circular plate subjected to uniform loads. Finally, the example of circular plate is presented.
Analytical Solution of a Tapering Cable Equation for Dendrites and Conformal Symmetry
Romero, Juan M.; Trenado, Carlos
2015-09-01
Progress towards detailed characterization of structural and biophysical properties of dendrites emphasizes the importance of finding analytical solutions for more realistic dendrite models with circular cross-section and varying diameter. In this regard, we employ symmetry methods and the passive cable theory to deduce a generalized analytical solution for electric propagation in a family of tapering dendrites. In particular, we study the effect of such tapering geometries on the obtained electric voltage. Simulations using the deduced analytical solution indicate that for a subfamily of tapering profiles neural integration is better than in the stereotypical profile given by a cylinder.
Editorial: Special Issue on Analytical and Approximate Solutions for Numerical Problems
Directory of Open Access Journals (Sweden)
Walailak Journal of Science and Technology
2014-08-01
Full Text Available Though methods and algorithms in numerical analysis are not new, they have become increasingly popular with the development of high speed computing capabilities. Indeed, the ready availability of high speed modern digital computers and easy-to-employ powerful software packages has had a major impact on science, engineering education and practice in the recent past. Researchers in the past had to depend on analytical skills to solve significant engineering problems but, nowadays, researchers have access to tremendous amount of computation power under their fingertips, and they mostly require understanding the physical nature of the problem and interpreting the results. For some problems, several approximate analytical solutions already exist for simple cases but finding new solution to complex problems by designing and developing novel techniques and algorithms are indeed a great challenging task to give approximate solutions and sufficient accuracy especially for engineering purposes. In particular, it is frequently assumed that deriving an analytical solution for any problem is simpler than obtaining a numerical solution for the same problem. But in most of the cases relationships between numerical and analytical solutions complexities are exactly opposite to each other. In addition, analytical solutions are limited to relatively simple problems while numerical ones can be obtained for complex realistic situations. Indeed, analytical solutions are very useful for testing (benchmarking numerical codes and for understanding principal physical controls of complex processes that are modeled numerically. During the recent past, in order to overcome some numerical difficulties a variety of numerical approaches were introduced, such as the finite difference methods (FDM, the finite element methods (FEM, and other alternative methods. Numerical methods typically include material on such topics as computer precision, root finding techniques, solving
Analytical solution for multilayer plates using general layerwise plate theory
Directory of Open Access Journals (Sweden)
Vuksanović Đorđe M.
2005-01-01
Full Text Available This paper deals with closed-form solution for static analysis of simply supported composite plate, based on generalized laminate plate theory (GLPT. The mathematical model assumes piece-wise linear variation of in-plane displacement components and a constant transverse displacement through the thickness. It also include discrete transverse shear effect into the assumed displacement field, thus providing accurate prediction of transverse shear stresses. Namely, transverse stresses satisfy Hook's law, 3D equilibrium equations and traction free boundary conditions. With assumed displacement field, linear strain-displacement relation, and constitutive equations of the lamina, equilibrium equations are derived using principle of virtual displacements. Navier-type closed form solution of GLPT, is derived for simply supported plate, made of orthotropic laminae, loaded by harmonic and uniform distribution of transverse pressure. Results are compared with 3D elasticity solutions and excellent agreement is found.
General Analytical Solutions of Scalar Field Cosmology with Arbitrary Potential
Dimakis, N; Zampeli, Adamantia; Paliathanasis, Andronikos; Christodoulakis, T; Terzis, Petros A
2016-01-01
We present the solution space for the case of a minimally coupled scalar field with arbitrary potential in a FLRW metric. This is made possible due to the existence of a nonlocal integral of motion corresponding to the conformal Killing field of the two-dimensional minisuperspace metric. The case for both spatially flat and non flat are studied first in the presence of only the scalar field and subsequently with the addition of non interacting perfect fluids. It is verified that this addition does not change the general form of the solution, but only the particular expressions of the scalar field and the potential. The results are applied in the case of parametric dark energy models where we derive the scalar field equivalence solution for some proposed models in the literature.
Visual analytics : towards intelligent interactive internet and security solutions
Davey, James; Mansmann, Florian; Kohlhammer, Jörn; Keim, Daniel
2012-01-01
In the Future Internet, Big Data can not only be found in the amount of traffic, logs or alerts of the network infrastructure, but also on the content side. While the term Big Data refers to the increase in available data, this implicitly means that we must deal with problems at a larger scale and thus hints at scalability issues in the analysis of such data sets. Visual Analytics is an enabling technology, that offers new ways of extracting information from Big Data through intelligent, inte...
Analytical solution of a system of two coupled Schroedinger equations
International Nuclear Information System (INIS)
The problem of solving analytically a system of two coupled Schroedinger equations is examined from the methodological point of view. First, the proof of a theorem on the separability of the equations is given, followed by application to a few examples of interest in physics. Particularly, it will be seen that the exact resonance as well as the constant coupling case are merely special cases of this theorem. When the separation of the equations is not possible, i.e. in the non-resonance case, a new formulation of the problem will be introduced in the frame of a modified resonance distortion approximation
Analytical solution of a stochastic content-based network model
International Nuclear Information System (INIS)
We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behaviour to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show any scaling behaviour
Analytic solution for relativistic transverse flow at the softest point
Biro, T S
2000-01-01
We obtain an extension of Bjorken's 1+1 dimensional scaling relativistic flow solution to relativistic transverse velocities with cylindrical symmetry in 1+3 dimensions at constant, homogeneous pressure (vanishing sound velocity). This can be the situation during a first order phase transition converting quark matter into hadron matter in relativistic heavy ion collisions.
Analytical solutions for ozone generation by point to plane corona discharge
International Nuclear Information System (INIS)
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
Analytical solution for 1D consolidation of unsaturated soil with mixed boundary condition
Institute of Scientific and Technical Information of China (English)
Zhen-dong SHAN; Dao-sheng LING; Hao-jiang DING
2013-01-01
Based on consolidation equations proposed for unsaturated soil,an analytical solution for 1D consolidation of an unsaturated single-layer soil with nonhomogeneous mixed boundary condition is developed.The mixed boundary condition can be used for special applications,such as tests occur in laboratory.The analytical solution is obtained by assuming all material parameters remain constant during consolidation.In the derivation of the analytical solution,the nonhomogeneous boundary condition is first transformed into a homogeneous boundary condition.Then,the eigenfunction and eigenvalue are derived according to the consolidation equations and the new boundary condition.Finally,using the method of undetermined coefficients and the orthogonal relation of the eigenfunction,the analytical solution for the new boundary condition is obtained.The present method is applicable to various types of boundary conditions.Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with mixed boundary condition.
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.
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.
Analytical Solution of Boundary Integral Equations for 2-D Steady Linear Wave Problems
Institute of Scientific and Technical Information of China (English)
J.M. Chuang
2005-01-01
Based on the Fourier transform, the analytical solution of boundary integral equations formulated for the complex velocity of a 2-D steady linear surface flow is derived. It has been found that before the radiation condition is imposed,free waves appear both far upstream and downstream. In order to cancel the free waves in far upstream regions, the eigensolution of a specific eigenvalue, which satisfies the homogeneous boundary integral equation, is found and superposed to the analytical solution. An example, a submerged vortex, is used to demonstrate the derived analytical solution. Furthermore,an analytical approach to imposing the radiation condition in the numerical solution of boundary integral equations for 2-D steady linear wave problems is proposed.
The analyticity of solutions to a class of degenerate elliptic equations
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In the present paper,the analyticity of solutions to a class of degenerate elliptic equations is obtained.A kind of weighted norms are introduced and under such norms some degenerate elliptic operators are of weak coerciveness.
Institute of Scientific and Technical Information of China (English)
侯进军
2007-01-01
@@ 1 Seed Selection Genetic Programming In Genetic Programming, each tree in population shows an algebraic or surmounting expression, and each algebraic or surmounting expression shows an approximate analytic solution to differential equations.
Directory of Open Access Journals (Sweden)
Xiao-Ying Qin
2014-01-01
Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.
Analytic solution of an initial-value problem from Stokes flow with free boundary
Xuming Xie
2008-01-01
We study an initial-value problem arising from Stokes flow with free boundary. If the initial data is analytic in disk $mathcal{R}_r$ containing the unit disk, it is proved that unique solution, which is analytic in $mathcal{R}_s$ for $sin (1,r)$, exists locally in time.
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.
Analytic Solutions of Three-Level Dressed-Atom Model
Institute of Scientific and Technical Information of China (English)
WANG Zheng-Ling; YIN Jian-Ping
2004-01-01
On the basis of the dressed-atom model, the general analytic expressions for the eigenenergies, eigenstates and their optical potentials of the A-configuration three-level atom system are derived and analysed. From the calculation of dipole matrix element of different dressed states, we obtain the spontaneous-emission rates in the dressed-atom picture. We find that our general expressions of optical potentials for the three-level dressed atom can be reduced to the same as ones in previous references under the approximation of a small saturation parameter. We also analyse the dependences of the optical potentials of a three-level 85Rb atom on the laser detuning and the dependences of spontaneous-emission rates on the radial position in the dark hollow beam, and discuss the probability (population) evolutions of dressed-atomic eigenstates in three levels in the hollow beam.
Analytic Asymptotic Solution to Spherical Relativistic Shock Breakout
Yalinewich, Almog
2016-01-01
We investigate the relativistic breakout of a shock wave from the surface of a star. In this process, each fluid shell is endowed with some kinetic and thermal energy by the shock, and then continues to accelerate adiabatically by converting thermal energy into kinetic energy. This problem has been previously studied for a mildly relativistic breakout, where the acceleration ends close to the surface of the star. The current work focuses on the case where the acceleration ends at distances much greater than the radius of the star. We derive an analytic description for the hydrodynamic evolution of the ejecta in this regime, and validate it using a numerical simulation. We also provide predictions for the expected light curves and spectra from such an explosion. The relevance to astrophysical explosions is discussed, and it is shown that such events require more energy than is currently believed to result from astrophysical explosions.
A New Analytical Solution to the Relativistic Polytropic Fluid Spheres
Nouh, Mohamed
2014-01-01
This paper introduces an accelerated power series solution for Tolman-Oppenheimer-Volkoff (TOV) equation, which represents the relativistic polytropic fluid spheres. We constructed a recurrence relation for the series coefficients in the power series expansion of the solution of TOV equation. For the range of the polytropic index 01.5, the series diverges except for some values of sigma. To improve the convergence radii of the series, we used a combination of two techniques Euler-Abel transformation and Pad\\'e approximation. The new transformed series converges everywhere for the range of the polytropic index 0<=n<=3. Comparison between the results obtained by the proposed accelerating scheme presented here and the numerical one, revealed good agreement with maximum relative error is of order 0.001.
New Analytical Solutions of a Modified Black-Scholes Equation with the European Put Option
Juan Ospina
2015-01-01
Using Maple, we compute some analytical solutions of a modified Black-Scholes equation, recently proposed, in the case of the European put option. We show that the modified Black-Scholes equation with the European put option is exactly solvable in terms of associated Laguerre polynomials. We make some numerical experiments with the analytical solutions and we compare our results with the results derived from numerical experiments using the standard Black-Scholes equation.
Analytical solutions for the slow neutron capture process of heavy element nucleosynthesis
Institute of Scientific and Technical Information of China (English)
Wu Kai-Su
2009-01-01
In this paper,the network equation for the slow neutron capture process (s-process) of heavy element nucleosynthesis is investigated. Dividing the s-process network reaction chains into two standard forms and using the technique of matrix decomposition,a group of analytical solutions for the network equation are obtained. With the analytical solutions,a calculation for heavy element abundance of the solar system is carried out and the results are in good agreement with the astrophysical measurements.
Approximate Analytical Solutions for a Class of Laminar Boundary-Layer Equations
Institute of Scientific and Technical Information of China (English)
Seripah Awang Kechil; Ishak Hashim; Sim Siaw Jiet
2007-01-01
A simple and efficient approximate analytical technique is presented to obtain solutions to a class of two-point boundary value similarity problems in fluid mechanics. This technique is based on the decomposition method which yields a general analytic solution in the form of a convergent infinite series with easily computable terms. Comparative study is carried out to show the accuracy and effectiveness of the technique.
Mustafa, M. T.; Arif, A. F. M.; Khalid Masood
2014-01-01
A new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented. It is based on an effective combination of Lie symmetry method, homotopy perturbation method, finite element method, and simulation based error reduction techniques. Implementation of the proposed approach is demonstrated by applying it to determine approximate analytic solutions of real life problems consisting of transient nonlinear heat conduction in semi-infinite bars...
Directory of Open Access Journals (Sweden)
Jalil Manafian Heris
2014-02-01
Full Text Available In this article, we establish exact travelling wave solutions of the symmetric regularized long wave (SRLW by using analytical methods. The analytical methods are: the tanh-coth method and the sech^2 method which used to construct solitary wave solutions of nonlinear evolution equations. With the help of symbolic computation, we show that aforementioned methods provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.
Analytic electrostatic solution of an axisymmetric accelerator gap
International Nuclear Information System (INIS)
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
Analytical solutions of the problem of violent explosions in a plasma of varying density
International Nuclear Information System (INIS)
Analytical solutions of the non-linear problem of violent explosions in a plasma of varying density under power law have been obtained. A critical law for a medium of decreasing density from the source of explosion is determined for which the problem admits a very simple solution but beyond this critical line analytical solutions admit another discontinuity automatically occuring inside a blast wave region. It is assumed that a disturbance caused by violent explosion due to sudden release of immense amount of energy is expanding very rapidly and is headed by a strong MHD shock wave. It is found that the discontinuity appearing inside a blast wave region causes a violation of continuum theory in the physical plane and consequently a cavity is formed. Analytical solutions predict that just before a discontinuity appears, the gas pressure falls to zero and the solution breaks down and can not be extended further. (Auth.)
Analysing an Analytical Solution Model for Simultaneous Mobility
Directory of Open Access Journals (Sweden)
Md. Ibrahim Chowdhury
2013-12-01
Full Text Available Current mobility models for simultaneous mobility h ave their convolution in designing simultaneous movement where mobile nodes (MNs travel randomly f rom the two adjacent cells at the same time and also have their complexity in the measurement of th e occurrences of simultaneous handover. Simultaneou s mobility problem incurs when two of the MNs start h andover approximately at the same time. As Simultaneous mobility is different for the other mo bility pattern, generally occurs less number of tim es in real time; we analyze that a simplified simultaneou s mobility model can be considered by taking only symmetric positions of MNs with random steps. In ad dition to that, we simulated the model using mSCTP and compare the simulation results in different sce narios with customized cell ranges. The analytical results shows that with the bigger the cell sizes, simultaneous handover with random steps occurrences become lees and for the sequential mobility (where initial positions of MNs is predetermined with ran dom steps, simultaneous handover is more frequent.
Analytic solutions for degenerate Raman-coupled model
Institute of Scientific and Technical Information of China (English)
Zhang Zhi-Ming; Yu Ya-Fei
2008-01-01
The Raman-coupled interaction between an atom and a single mode of a cavity field is studied. For the cases in which a light field is initially in a coherent state and in a thermal state separately, we have derived the analytic expressions for the time evolutions of atomic population difference W, modulus B of the Bloch vector, and entropy E. We find that the time evolutions of these quantities are periodic with a period of e. The maxima of W and B appear at the scaled interaction time points (τ) = κπ(κ =0, 1, 2,...). At these time points, E = 0, which shows that the atom and the field are not entangled. Between these time points, E ≠ 0, which means that the atom and the field are entangled. When the field is initially in a coherent state, near the maxima, the envelope of W is a Gaussian function with a variance of 1/(4(-n)) ((-n) is the mean number of photons). Under the envelope, W oscillates at a frequency of (-n)/e.When the field is initially in a thermal state, near the maxima, W is a Lorentz function with a width of 1/(-n).
Approximate analytical solutions for excitation and propagation in cardiac tissue
Greene, D'Artagnan; Shiferaw, Yohannes
2015-04-01
It is well known that a variety of cardiac arrhythmias are initiated by a focal excitation in heart tissue. At the single cell level these currents are typically induced by intracellular processes such as spontaneous calcium release (SCR). However, it is not understood how the size and morphology of these focal excitations are related to the electrophysiological properties of cardiac cells. In this paper a detailed physiologically based ionic model is analyzed by projecting the excitation dynamics to a reduced one-dimensional parameter space. Based on this analysis we show that the inward current required for an excitation to occur is largely dictated by the voltage dependence of the inward rectifier potassium current (IK 1) , and is insensitive to the detailed properties of the sodium current. We derive an analytical expression relating the size of a stimulus and the critical current required to induce a propagating action potential (AP), and argue that this relationship determines the necessary number of cells that must undergo SCR in order to induce ectopic activity in cardiac tissue. Finally, we show that, once a focal excitation begins to propagate, its propagation characteristics, such as the conduction velocity and the critical radius for propagation, are largely determined by the sodium and gap junction currents with a substantially lesser effect due to repolarizing potassium currents. These results reveal the relationship between ion channel properties and important tissue scale processes such as excitation and propagation.
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.
Analytical solutions for sensitivity contribution in nuclear imaging
DiPirro, Joseph Christopher
The use of slit-slat collimation in diagnostic medical nuclear imaging is analyzed for the purpose of finding background sensitivity. A general derivation of sensitivity contribution is expressed for various camera positions outside particular radioactive objects. These objects can represent possible human or animal organs for different clinical imaging tasks. Rectangular, circular, elliptical, and parabolic cross-sections are analyzed for a given set of variables to represent the total background contribution within any particular shape for any given detector location, whether it is a point, line, or area sensitivity contribution. The sensitivity of a point source is calculated for any location inside the slit-slat's field-of-view as a function of the following constraints: (i) object shape, (ii) slit distance, (iii) depth within the object, (iv) acceptance angle, and if necessary (v) attenuation coefficient of the medium, and (vi) lateral displacement of the detector. The analysis is split into parts for all shapes to find the line or area contribution within an object. The sum of the point sources can be performed digitally to find a solution in terms of the provided situation; in some cases, an exact solution was found. The line sensitivity contributions can be applied to slit-slat cameras to reduce noise and fluctuation in imaging system design and analysis.
Analyticity of solutions for randomly forced two-dimensional Navier-Stokes equations
International Nuclear Information System (INIS)
A study is made of randomly forced two-dimensional Navier-Stokes equations with periodic boundary conditions. Under the assumption that the random forcing is analytic in the spatial variables and is a white noise in the time, it is proved that a large class of solutions, which contains all stationary solutions with finite energy, admits analytic continuation to a small complex neighbourhood of the torus. Moreover, a lower bound is obtained for the radius of analyticity in terms of the viscosity ν, and it is shown that the Kolmogorov dissipation scale can be asymptotically estimated below by ν2+δ for any δ>0
Analytical solutions for Dirac and Klein-Gordon equations using Backlund transformations
Energy Technology Data Exchange (ETDEWEB)
Zabadal, Jorge R.; Borges, Volnei, E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio, E-mail: marciophd@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Centro de Estudos Interdisciplinares
2015-07-01
This work presents a new analytical method for solving Klein-Gordon type equations via Backlund transformations. The method consists in mapping the Klein-Gordon model into a first order system of partial differential equations, which contains a generalized velocity field instead of the Dirac matrices. This system is a tensor model for quantum field theory whose space solution is wider than the Dirac model in the original form. Thus, after finding analytical expressions for the wave functions, the Maxwell field can be readily obtained from the Dirac equations, furnishing a self-consistent field solution for the Maxwell-Dirac system. Analytical and numerical results are reported. (author)
Analytic solutions and Singularity formation for the Peakon b--Family equations
Coclite, Giuseppe Maria; Gargano, Francesco; Sciacca, Vincenzo
2012-01-01
Using the Abstract Cauchy-Kowalewski Theorem we prove that the $b$-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to $H^s$ with $s > 3/2$, and the momentum density $u_0 - u_{0,{xx}}$ does not change sign, we prove that the solution stays analytic globally in time, for $b\\geq 1$. Using pseudospectral numerical methods, we study, also, the singularity formation for the $b$-family equations with the singularity t...
Analytical solution for laser evaporative heating process: time exponentially decaying pulse case
International Nuclear Information System (INIS)
The modelling of the laser heating process gives insight into the laser workpiece interaction and minimizes the experimental cost. In the present study, analytical solution for the laser pulse heating process is considered and the closed form solution for the temperature rise due to time exponentially varying pulse is obtained. In the analysis, evaporation of the surface is taken into account. A Laplace transformation method was used when formulating the closed form solution for the temperature profiles. The effect of pulse parameters 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 surface recession velocity is set to zero in the closed form solution. Moreover, the predictions of numerical simulation and closed form solution are found to be in good agreement. (author)
Super stellar clusters with a bimodal hydrodynamic solution: an Approximate Analytic Approach
Wünsch, R; Palous, J; Tenorio-Tagle, G
2007-01-01
We look for a simple analytic model to distinguish between stellar clusters undergoing a bimodal hydrodynamic solution from those able to drive only a stationary wind. Clusters in the bimodal regime undergo strong radiative cooling within their densest inner regions, which results in the accumulation of the matter injected by supernovae and stellar winds and eventually in the formation of further stellar generations, while their outer regions sustain a stationary wind. The analytic formulae are derived from the basic hydrodynamic equations. Our main assumption, that the density at the star cluster surface scales almost linearly with that at the stagnation radius, is based on results from semi-analytic and full numerical calculations. The analytic formulation allows for the determination of the threshold mechanical luminosity that separates clusters evolving in either of the two solutions. It is possible to fix the stagnation radius by simple analytic expressions and thus to determine the fractions of the depo...
Institute of Scientific and Technical Information of China (English)
2008-01-01
Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical solutions, and even to develop various numerical methods such as their differencing schemes and grid generation skills as well. A hybrid method of separating variables for simultaneous partial differential equation sets is presented. It is proposed that different methods of separating variables for different independent variables in the simultaneous equa-tion set may be used to improve the solution derivation procedure, for example, using the ordinary separating method for some variables and using extraordinary methods of separating variables, such as the separating variables with addition promoted by the first author, for some other variables. In order to prove the ability of the above-mentioned hybrid method, a lot of analytical exact solutions of two-buoyancy convection in porous media are successfully derived with such a method. The physical features of these solutions are given.
Institute of Scientific and Technical Information of China (English)
CAI RuiXian; LIU QiBin
2008-01-01
Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical solutions, and even to develop various numerical methods such as their differencing schemes and grid generation skills as well. A hybrid method of separating variables for simultaneous partial differential equation sets is presented. It is proposed that different methods of separating variables for different independent variables in the simultaneous equa-tion set may be used to improve the solution derivation procedure, for example, using the ordinary separating method for some variables and using extraordinary methods of separating variables, such as the separating variables with addition promoted by the first author, for some other variables. In order to prove the ability of the above-mentioned hybrid method, a lot of analytical exact solutions of two-buoyancy convection in porous media are successfully derived with such a method. The physical features of these solutions are given.
Analytical Solution to the MHD Flow of Micropolar Fluid Over a Linear Stretching Sheet
Directory of Open Access Journals (Sweden)
Siddheshwar P.G.
2015-05-01
Full Text Available The flow due to a linear stretching sheet in a fluid with suspended particles, modeled as a micropolar fluid, is considered. All reported works on the problem use numerical methods of solution or a regular perturbation technique. An analytical solution is presented in the paper for the coupled non-linear differential equations with inhomogeneous boundary conditions.
Analytical Solution to the MHD Flow of Micropolar Fluid Over a Linear Stretching Sheet
Siddheshwar P.G.; Mahabaleshwar U.S.
2015-01-01
The flow due to a linear stretching sheet in a fluid with suspended particles, modeled as a micropolar fluid, is considered. All reported works on the problem use numerical methods of solution or a regular perturbation technique. An analytical solution is presented in the paper for the coupled non-linear differential equations with inhomogeneous boundary conditions.
Analytical Solution to the MHD Flow of Micropolar Fluid Over a Linear Stretching Sheet
Siddheshwar, P. G.; Mahabaleshwar, U. S.
2015-05-01
The flow due to a linear stretching sheet in a fluid with suspended particles, modeled as a micropolar fluid, is considered. All reported works on the problem use numerical methods of solution or a regular perturbation technique. An analytical solution is presented in the paper for the coupled non-linear differential equations with inhomogeneous boundary conditions.
An analytic solution of the non-stationary Navier-Stokes equation in three dimensions
Thambynayagam, R. K. Michael
2014-01-01
In this paper we describe a method to derive classical solutions of the Navier-Stokes equations for non-stationary initial value problems in domain R^n (n = 2, 3 or higher). A new closed-form analytic solution of the incompressible Navier-Stokes equations on the decay of vortices in a viscous fluid in R3 is presented.
Analytical solution of a class of coupled second order differential-difference equations
Directory of Open Access Journals (Sweden)
J. A. Martin Alustiza
1993-06-01
Full Text Available In this paper coupled systems of second order differential-difference equations are considered. By means of the concept of co-solution of certain algebraic equations associated to the problem, an analytical solution of initial value problems for coupled systems of second order differential-difference equations is constructed.
Analytic solutions and universal properties of sugar loading models in Münch phloem flow
DEFF Research Database (Denmark)
Jensen, Kåre Hartvig; Berg-Sørensen, Kirstine; Friis, Søren Michael Mørk;
2012-01-01
relied on numerical solutions, which makes it difficult to draw general conclusions. Here, we present analytic solutions to the Münch–Horwitz flow equations when the loading and unloading rates are assumed to be linear functions of the concentration, thus allowing them to depend on the local osmotic...
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
equation is solved analytically by Homotopy Analysis Methods. Present solution gives an expression which can be used in wide range of time for all domain of response. Comparisons of the obtained solutions with numerical results show that this method is effective and convenient for solving this problem....
Hemker, K.; Bakker, M.
2006-01-01
Analytical solutions are derived for steady state groundwater flow in a heterogeneous, anisotropic, semiconfined aquifer. The aquifer consists of a number of horizontal layers, while each layer consists of a number of homogeneous cells with different hydraulic conductivity tensors. An exact solution
Afanas'ev, A. P.; Dzyuba, S. M.
2015-10-01
A method for constructing approximate analytic solutions of systems of ordinary differential equations with a polynomial right-hand side is proposed. The implementation of the method is based on the Picard method of successive approximations and a procedure of continuation of local solutions. As an application, the problem of constructing the minimal sets of the Lorenz system is considered.
Analytic solutions to dynamic equations of plasma armature railguns
Energy Technology Data Exchange (ETDEWEB)
Shahinpoor, M.; Hawke, R.S.
1988-01-01
General governing nonlinear differential equations pertaining to the dynamic behavior of a plasma armature electromagnetic railgun are first derived. Three different cases are then considered and the corresponding governing equations are then solved exactly by means of a set of nonlinear transformations. These cases correspond to (1) no-ablation, (2) continuous-ablation, and (3) partial-ablation for which an ablation threshold velocity v/sub t/ plays a fundamental role. Corresponding to each case, a nonlinear transformation is employed to reduce the nonlinear differential equations to their equivalent linear ones and subsequently allow solution of the pertinent linear differential equations, which are second order, by means of the transition matrix technique. It is concluded that in order to achieve very high projectile velocities the projectile should be injected into the railgun at velocities higher than the ablation threshold velocity. Thus, the ablation may be completely alleviated and the ensuing turbulent drag may be significantly diminished. It is shown that under these conditions one may typically accelerate projectiles up to 30 km/s or more while without hypervelocity injection, for the same railgun and typical operating conditions, one might severely limit the maximum projectile velocity.
Analytic solutions to dynamic equations of plasma armature railguns
Energy Technology Data Exchange (ETDEWEB)
Shahinpoor, M. (New Mexico Univ., Albuquerque, NM (USA). Dept. of Mechanical Engineering); Hawke, R.S. (Lawrence Livermore National Lab., CA (USA))
1989-01-01
General governing nonlinear differential equations pertaining to the dynamic behavior of a plasma armature electromagnetic railgun are first derived. Three different cases are then considered and the corresponding governing equations are then solved exactly by means of a set of nonlinear transformations. These cases correspond to (1) no-ablation, (2) continuous-ablation, and (3) partial-ablation for which an ablation threshold velocity {nu}/sub tau/ plays a fundamental role. Corresponding to each case, a nonlinear transformation is employed to reduce the nonlinear differential equations to their equivalent linear ones and subsequently allow solution of the pertinent linear differential equations, which are second order, by means of the transition matrix technique. It is concluded that in order to achieve very high projectile velocities the projectile should be injected into the railgun at velocities higher than the ablation threshold velocity. Thus, the ablation may be completely alleviated and the ensuing turbulent drag may be significantly diminished. It is shown that under these conditions one may typically accelerate projectiles up to 30 km/s or more while without hypervelocity injection, for the same railgun and typical operating conditions, one might severely limit the maximum projectile velocity.
Analytical solutions of cracks emanating from an elliptical hole under shear
Institute of Scientific and Technical Information of China (English)
Liu Shuhong; Duan Shijie
2014-01-01
Based on the complex variable method, the analytical solutions of stress functions and stress intensity factors (SIFs) are provided for the plane problem of two collinear edge cracks emanating from an elliptical hole in an infinite plate under shear. The stress distribution along the horizontal axis is given in graphical forms, which conforms to Saint-Venant’s principle. The influences of crack length and ellipse shape on the stress intensity factors are evaluated. Comparing the analytical solutions with finite element method (FEM) results shows good coincidence. These numerical examples show that the present solutions are accurate.
An approximate analytical solution for interlaminar stresses in angle-ply laminates
Rose, Cheryl A.; Herakovich, Carl T.
1991-01-01
An improved approximate analytical solution for interlaminar stresses in finite width, symmetric, angle-ply laminated coupons subjected to axial loading is presented. The solution is based upon statically admissible stress fields which take into consideration local property mismatch effects and global equilibrium requirements. Unknown constants in the admissible stress states are determined through minimization of the complementary energy. Typical results are presented for through-the-thickness and interlaminar stress distributions for angle-ply laminates. It is shown that the results represent an improved approximate analytical solution for interlaminar stresses.
Nonlinear analytical solution for one-dimensional consolidation of soft soil under cyclic loading
Institute of Scientific and Technical Information of China (English)
XIE Kang-he; QI Tian; DONG Ya-qin
2006-01-01
This paper presents an analytical solution for one-dimensional consolidation of soft soil under some common types of cyclic loading such as trapezoidal cyclic loading, based on the assumptions proposed by Davis and Raymond (1965) that the decrease in permeability is proportional to the decrease in compressibility during the consolidation process of the soil and that the distribution of initial effective stress is constant with depth. It is verified by the existing analytical solutions in special cases. Using the solution obtained, some diagrams are prepared and the relevant consolidation behavior is investigated.
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.
Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models
Luther, K.; Haitjema, H. M.
2000-04-01
We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.
Approximate analytical solution of two-dimensional multigroup P-3 equations
International Nuclear Information System (INIS)
Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (orig./RW)
Approximate analytical solution of two-dimensional multigroup P-3 equations
International Nuclear Information System (INIS)
Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (author)
Grants, Ilmārs; Bojarevičs, Andris; Gerbeth, Gunter
2016-06-01
Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.
Institute of Scientific and Technical Information of China (English)
CAI; Ruixian; GOU; Chenhua
2006-01-01
This paper presents two algebraically explicit analytical solutions for the incompressible unsteady rotational flow of Oldroyd-B type in an annular pipe. The first solution is derived with the common method of separation of variables. The second one is deduced with the method of separation of variables with addition developed in recent years. The first analytical solution is of clear physical meaning and both of them are fairly simple and valuable for the newly developing computational fluid dynamics. They can be used as the benchmark solutions to verify the applicability of the existing numerical computational methods and to inspire new differencing schemes, grid generation ways, etc. Moreover, a steady solution for the generalized second grade rheologic fluid flow is also presented. The correctness of these solutions can be easily proven by substituting them into the original governing equation.
Properties of the exact analytic solution of the growth factor and its applications
International Nuclear Information System (INIS)
There have been the approximate analytic solution [V. Silveira and I. Waga, Phys. Rev. D 50, 4890 (1994).] and several approximate analytic forms [W. J. Percival, Astron. Astrophys. 443, 819 (2005).][S. M. Carroll, W. H. Press, and E. L. Turner, Annu. Rev. Astron. Astrophys. 30, 499 (1992).][S. Basilakos, Astrophys. J. 590, 636 (2003).] of the growth factor Dg for the general dark energy models with the constant values of its equation of state ωde after Heath found the exact integral form of the solution of Dg for the Universe including the cosmological constant or the curvature term. Recently, we obtained the exact analytic solutions of the growth factor for both ωde=-1 or -(1/3)[S. Lee and K.-W. Ng, arXiv:0905.1522.] and the general dark energy models with the constant equation of state ωde[S. Lee and K.-W. Ng, Phys. Lett. B 688, 1 (2010).] independently. We compare the exact analytic solution of Dg with the other well known approximate solutions. We also prove that the analytic solutions for ωde=-1 or -(1/3) in [S. Lee and K.-W. Ng, arXiv:0905.1522.] are the specific solutions of the exact solutions of the growth factor for general ωde models in [S. Lee and K.-W. Ng, Phys. Lett. B 688, 1 (2010).] even though they look quite different. Comparison with the numerical solution obtained from the public code is done. We also investigate the possible extensions of the exact solution of Dg to the time-varying ωde for the comparison with observations.
International Nuclear Information System (INIS)
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
An analytical dynamo solution for large-scale magnetic fields of galaxies
Chamandy, Luke
2016-01-01
We present an effectively global analytical asymptotic galactic dynamo solution for the regular magnetic field of an axisymmetric thin disc in the saturated state. This solution is constructed by combining two well-known types of local galactic dynamo solution, parameterized by the disc radius. Namely, the critical (zero growth) solution obtained by treating the dynamo equation as a perturbed diffusion equation is normalized using a non-linear solution that makes use of the `no-$z$' approximation and the dynamical $\\alpha$-quenching non-linearity. This overall solution is found to be reasonably accurate when compared with detailed numerical solutions. It is thus potentially useful as a tool for predicting observational signatures of magnetic fields of galaxies. In particular, such solutions could be painted onto galaxies in cosmological simulations to enable the construction of synthetic polarized synchrotron and Faraday rotation measure (RM) datasets. Further, we explore the properties of our numerical solut...
Analytical Solution for the SU(2) Hedgehog Skyrmion and Static Properties of Nucleons
Jia, Duojie; Liu, Feng
2009-01-01
An analytical solution for symmetric Skyrmion was proposed for the SU(2) Skyrme model, which take the form of the hybrid form of a kink-like solution and that given by the instanton method. The static properties of nucleons was then computed within the framework of collective quantization of the Skyrme model, with a good agreement with that given by the exact numeric solution. The comparisons with the previous results as well as the experimental values are also given.
Santosh Soni
2011-01-01
OnTARGET and MAP are examples of analytics-based solutions that were designed from the outset to address specific business challenges in the broad area of sales force productivity. Although they address different underlying issues, these solutions implement a common approach that is generally applicable to a broad class of operational challenges. Both solutions rely on rigorously defined data models that integrate all relevant data into a common database. Choices of the data to be included in...
Abrupt PN junctions: Analytical solutions under equilibrium and non-equilibrium
Khorasani, Sina
2016-08-01
We present an explicit solution of carrier and field distributions in abrupt PN junctions under equilibrium. An accurate logarithmic numerical method is implemented and results are compared to the analytical solutions. Analysis of results shows reasonable agreement with numerical solution as well as the depletion layer approximation. We discuss extensions to the asymmetric junctions. Approximate relations for differential capacitance C-V and current-voltage I-V characteristics are also found under non-zero external bias.
Kurylyk, Barret L.; Irvine, Dylan J.
2016-02-01
This study details the derivation and application of a new analytical solution to the one-dimensional, transient conduction-advection equation that is applied to trace vertical subsurface fluid fluxes. The solution employs a flexible initial condition that allows for nonlinear temperature-depth profiles, providing a key improvement over most previous solutions. The boundary condition is composed of any number of superimposed step changes in surface temperature, and thus it accommodates intermittent warming and cooling periods due to long-term changes in climate or land cover. The solution is verified using an established numerical model of coupled groundwater flow and heat transport. A new computer program FAST (Flexible Analytical Solution using Temperature) is also presented to facilitate the inversion of this analytical solution to estimate vertical groundwater flow. The program requires surface temperature history (which can be estimated from historic climate data), subsurface thermal properties, a present-day temperature-depth profile, and reasonable initial conditions. FAST is written in the Python computing language and can be run using a free graphical user interface. Herein, we demonstrate the utility of the analytical solution and FAST using measured subsurface temperature and climate data from the Sendia Plain, Japan. Results from these illustrative examples highlight the influence of the chosen initial and boundary conditions on estimated vertical flow rates.
Yang, Yong; Liu, Yongzhong; Yu, Bo; Ding, Tian
2016-06-01
Volatile contaminants may migrate with carbon dioxide (CO2) injection or leakage in subsurface formations, which leads to the risk of the CO2 storage and the ecological environment. This study aims to develop an analytical model that could predict the contaminant migration process induced by CO2 storage. The analytical model with two moving boundaries is obtained through the simplification of the fully coupled model for the CO2-aqueous phase -stagnant phase displacement system. The analytical solutions are confirmed and assessed through the comparison with the numerical simulations of the fully coupled model. Then, some key variables in the analytical solutions, including the critical time, the locations of the dual moving boundaries and the advance velocity, are discussed to present the characteristics of contaminant migration in the multi-phase displacement system. The results show that these key variables are determined by four dimensionless numbers, Pe, RD, Sh and RF, which represent the effects of the convection, the dispersion, the interphase mass transfer and the retention factor of contaminant, respectively. The proposed analytical solutions could be used for tracking the migration of the injected CO2 and the contaminants in subsurface formations, and also provide an analytical tool for other solute transport in multi-phase displacement system.
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.
Analytical solutions for non-linear differential equations with the help of a digital computer
Cromwell, P. C.
1964-01-01
A technique was developed with the help of a digital computer for analytic (algebraic) solutions of autonomous and nonautonomous equations. Two operational transform techniques have been programmed for the solution of these equations. Only relatively simple nonlinear differential equations have been considered. In the cases considered it has been possible to assimilate the secular terms into the solutions. For cases where f(t) is not a bounded function, a direct series solution is developed which can be shown to be an analytic function. All solutions have been checked against results obtained by numerical integration for given initial conditions and constants. It is evident that certain nonlinear differential equations can be solved with the help of a digital computer.
Latyshev, A. V.; Yushkanov, A. A.
2012-01-01
Analytical solution of second Stokes problem of behaviour of rarefied gas with Cercignani boundary accomodation conditions The second Stokes problem about behaviour of rarefied gas filling half-space is analytically solved. A plane, limiting half-space, makes harmonious fluctuations in the plane. The kinetic BGK-equation (Bhatnagar, Gross, Krook) is used. The boundary accomodation conditions of Cercignani of reflexion gaseous molecules from a wall are considered. Distribution function of the ...
A comment on the importance of numerical evaluation of analytic solutions involving approximations.
Overall, J E; Starbuck, R R; Doyle, S R
1994-07-01
An analytic solution proposed by Senn (1) for removing the effects of covariate imbalance in controlled clinical trials was subjected to Monte Carlo evaluation. For practical applications of his derivation, Senn proposed substitution of sample statistics for parameters of the bivariate normal model. Unfortunately, that substitution produces severe distortion in the size of tests of significance for treatment effects when covariate imbalance is present. Numerical verification of proposed substitutions into analytic models is recommended as a prudent approach. PMID:7951276
An Approximate Analytical Solution of Sloshing Frequencies for a Liquid in Various Shape Aqueducts
Yuchun Li; Zhuang Wang
2014-01-01
An approximate analytical solution of sloshing frequencies for a liquid in the various shape aqueducts is formulated by using the Ritz method. The present approximate method is, respectively, applied to find the sloshing frequencies of the liquid in rectangular, trapezoid, oval, circular, U-shaped tanks (aqueducts), and various shape tuned liquid dampers (TLD). The first three antisymmetric and symmetric frequencies by the present approach are within 5% accuracy compared to the other analytic...
Analytical Solution of the Blast Wave Problem in a Non-Ideal Gas
International Nuclear Information System (INIS)
An analytical approach is used to construct the exact solution of the blast wave problem with generalized geometries in a non-ideal medium. It is assumed that the density ahead of the shock front varies according to a power of distance from the source of the blast wave. Also, an analytical expression for the total energy in a non-ideal medium is derived. (fundamental areas of phenomenology(including applications))
An Analytical Solution for Transient Thermal Response of an Insulated Structure
Blosser, Max L.
2012-01-01
An analytical solution was derived for the transient response of an insulated aerospace vehicle structure subjected to a simplified heat pulse. This simplified problem approximates the thermal response of a thermal protection system of an atmospheric entry vehicle. The exact analytical solution is solely a function of two non-dimensional parameters. A simpler function of these two parameters was developed to approximate the maximum structural temperature over a wide range of parameter values. Techniques were developed to choose constant, effective properties to represent the relevant temperature and pressure-dependent properties for the insulator and structure. A technique was also developed to map a time-varying surface temperature history to an equivalent square heat pulse. Using these techniques, the maximum structural temperature rise was calculated using the analytical solutions and shown to typically agree with finite element simulations within 10 to 20 percent over the relevant range of parameters studied.
Some analytic solutions for stochastic reactor models based on the joint composition PDF
Kraft, Markus; Fey, Harald
1999-06-01
The stochastic reactor models, partially stirred reactor (PaSR) and partially stirred plug flow reactor (PaSPFR) have been investigated. These models are based on a simplified joint composition PDF transport equation. Analytic solutions for five different Cauchy problems for the PDF transport equation as given by the stochastic reactor models are presented. In all cases, molecular mixing in the stochastic reactor models is described by the linear mean-square estimation (LMSE) mixing model for turbulent diffusion. The analytic solutions have been found by combining the method of characteristics with a set of ordinary differential equations for the statistical moments to account for the functional dependence of the coefficients in the corresponding PDF transport equation. For each case an example problem is discussed to illustrate the behaviour of the analytic solution.
Analytic Solutions of a Second-Order Iterative Functional Differential Equations
Liu, Lingxia
In this paper, the existence of analytic solutions of an iterative functional differential equation is studied. We reduce this problem to finding analytic solutions of a functional differential equation without iteration of the unknown function. For technical reasons, in previous work the constant α given in Schröder transformation is required to fulfill that α is off the unit circle or lies on the circle with the Diophantine condition. In this paper, we break the restraint of the Diophantine condition and obtain results of analytic solutions in the case of α at resonance, i.e., at a root of the unity and the case of α near resonance under the Brjuno condition.
Energy Technology Data Exchange (ETDEWEB)
Zou Mingqing; Zhang Duanming; Yu Boming [Department of Physics and the State Key Laboratory of Laser, Huazhong University of Science and Technology, Wuhan (China)]. E-mail: yu3838@public.wh.hb.cn
2002-08-07
In this paper, an analytical expression for transverse thermal conductivities of unidirectional fibre composites with thermal barrier is derived based on the electrical analogy technique and on the cylindrical filament-square packing array unit cell model (C-S model). The present analytical expressions both with and without thermal barrier between fibre and matrix are presented. The present theoretical predictions without thermal barrier are found to be in excellent agreement with the existing analytical model and nomogram from the finite difference method (FDM), and in good agreement with existing experimental data. Furthermore, the present analytical predictions with thermal barrier can best fit the experimental data and can provide a higher accuracy than the finite element method (FEM). The validity of the present analytical solution is thus verified for transverse thermal conductivities of unidirectional fibre composites with thermal barrier. (author)
International Nuclear Information System (INIS)
In this paper, an analytical expression for transverse thermal conductivities of unidirectional fibre composites with thermal barrier is derived based on the electrical analogy technique and on the cylindrical filament-square packing array unit cell model (C-S model). The present analytical expressions both with and without thermal barrier between fibre and matrix are presented. The present theoretical predictions without thermal barrier are found to be in excellent agreement with the existing analytical model and nomogram from the finite difference method (FDM), and in good agreement with existing experimental data. Furthermore, the present analytical predictions with thermal barrier can best fit the experimental data and can provide a higher accuracy than the finite element method (FEM). The validity of the present analytical solution is thus verified for transverse thermal conductivities of unidirectional fibre composites with thermal barrier. (author)
An analytical solution to a simplified EDXRF model for Monte Carlo code verification
International Nuclear Information System (INIS)
The objective of this study is to obtain an analytical solution to the scalar photon transport equation that can be used to obtain benchmark results for the verification of energy dispersive X-Ray fluorescence (EDXRF) Monte Carlo simulation codes. The multi-collided flux method (multiple scattering method) is implemented to obtain analytical expressions for the space-, energy-, and angle-dependent scalar photon flux for a one dimensional EDXRF model problem. In order to obtain benchmark results, higher-order multiple scattering terms are included in the multi-collided flux method. The details of the analytical solution and of the proposed EDXRF model problem are presented. Analytical expressions obtained are then used to calculate the energy-dependent current. The analytically-calculated energy-dependent current is compared with Monte Carlo code results. The findings of this study show that analytical solutions to the scalar photon transport equation with the proposed model problem can be used as a verification tool in EDXRF Monte Carlo code development.
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; Arabsolghar, A. R.; Rahimpour, M.
2011-01-01
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......An analytical solution for non-orthogonal stagnation point for the steady flow of a viscous and incompressible fluid is presented. The governing nonlinear partial differential equations for the flow field are reduced to ordinary differential equations by using similarity transformations existed in...
Corrected Analytical Solution of the Generalized Woods-Saxon Potential for Arbitrary $\\ell$ States
Bayrak, O
2015-01-01
The bound state solution of the radial Schr\\"{o}dinger equation with the generalized Woods-Saxon potential is carefully examined by using the Pekeris approximation for arbitrary $\\ell$ states. The energy eigenvalues and the corresponding eigenfunctions are analytically obtained for different $n$ and $\\ell$ quantum numbers. The obtained closed forms are applied to calculate the single particle energy levels of neutron orbiting around $^{56}$Fe nucleus in order to check consistency between the analytical and Gamow code results. The analytical results are in good agreement with the results obtained by Gamow code for $\\ell=0$.
Corrected analytical solution of the generalized Woods–Saxon potential for arbitrary ℓ states
International Nuclear Information System (INIS)
The bound state solution of the radial Schrödinger equation with the generalized Woods–Saxon potential is carefully examined using the Pekeris approximation for arbitrary ℓ states. The energy eigenvalues and the corresponding eigenfunctions are analytically obtained for different n and ℓ quantum numbers. The closed forms obtained are applied to calculate the single particle energy levels of a neutron orbiting around 56Fe nucleus in order to check the consistency between the analytical and the Gamow code results. The analytical results are in good agreement with the results obtained using Gamow code for ℓ=0. (paper)
Institute of Scientific and Technical Information of China (English)
冯君; 巫锡勇; 朱宝龙; 杨期祥
2015-01-01
An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund’s one-dimensional consolidation equation for unsaturated soil. The transfer relationship between the state vectors at the top surface and any depth was gained by applying the Laplace transform and Cayley−Hamilton mathematical methods to the governing equations of water and air, Darcy’s law and Fick’s law. The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain were obtained by using the Laplace transform with the initial and boundary conditions. The analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement were obtained in the time domain by performing the inverse Laplace transforms. A typical example illustrates the consolidation characteristics of unsaturated soil under sinusoidal loading from analytical results. Finally, comparisons between the analytical solutions and results of the numerical method indicate that the analytical solution is correct.
Analytic solution and pulse area theorem for three-level atoms
Shchedrin, Gavriil; O'Brien, Chris; Rostovtsev, Yuri; Scully, Marlan O.
2015-12-01
We report an analytic solution for a three-level atom driven by arbitrary time-dependent electromagnetic pulses. In particular, we consider far-detuned driving pulses and show an excellent match between our analytic result and the numerical simulations. We use our solution to derive a pulse area theorem for three-level V and Λ systems without making the rotating wave approximation. Formulated as an energy conservation law, this pulse area theorem can be used to understand pulse propagation through three-level media.
Domains of analyticity for response solutions in strongly dissipative forced systems
International Nuclear Information System (INIS)
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 c0∈R is such that g(c0) equals the average of f and g′(c0) ≠ 0, under very mild assumptions on ω there exists a quasi-periodic solution close to c0 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 of nonlinear Schrödinger equation with distributed coefficients
International Nuclear Information System (INIS)
We combine the F-expansion method with the homogeneous balance principle to build a strategy to find analytical solitonic and periodic wave solutions to a generalized nonlinear Schrödinger equation with distributed coefficients, linear gain/loss, and nonlinear gain/absorption. In the case of a dimensionless effective Gross–Pitaevskii equation which describes the evolution of the wave function of a quasi-one-dimensional cigar-shaped Bose–Einstein condensate, the building strategy is applied to generate analytical solutions
An exact analytical solution for the interstellar magnetic field in the vicinity of the heliosphere
Röken, Christian; Fichtner, Horst
2014-01-01
An analytical representation of the interstellar magnetic field in the vicinity of the heliosphere is derived. The three-dimensional field structure close to the heliopause is calculated as a solution of the induction equation under the assumption that it is frozen into a prescribed plasma flow resembling the characteristic interaction of the solar wind with the local interstellar medium. The usefulness of this analytical solution as an approximation to self-consistent magnetic field configurations obtained numerically from the full MHD equations is illustrated by quantitative comparisons.
Institute of Scientific and Technical Information of China (English)
WANG Chun-ling; HUANG Yi; JIA Ji-hong
2007-01-01
The method of double Fourier transform was employed in the analysis of the semi-infinite elastic foundation with vertical load. And an integral representations for the displacements of the semi-infinite elastic foundation was presented. The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semiinfinite elastic foundation. Some computational results and the analysis on the influence of parameters were presented.
An Approximate Analytical Solution of Sloshing Frequencies for a Liquid in Various Shape Aqueducts
Directory of Open Access Journals (Sweden)
Yuchun Li
2014-01-01
Full Text Available An approximate analytical solution of sloshing frequencies for a liquid in the various shape aqueducts is formulated by using the Ritz method. The present approximate method is, respectively, applied to find the sloshing frequencies of the liquid in rectangular, trapezoid, oval, circular, U-shaped tanks (aqueducts, and various shape tuned liquid dampers (TLD. The first three antisymmetric and symmetric frequencies by the present approach are within 5% accuracy compared to the other analytical, numerical, and experimental values. The approximate solutions of this paper for the various shape aqueducts are acceptable to the engineering applications.
Institute of Scientific and Technical Information of China (English)
CAI Ruixian; ZHANG Na
2004-01-01
The analytical solutions of unsteady heat conduction with variable thermal properties(thermal conductivity,density and specific heat are functions of temperature or coordinates)are meaningful in theory.In addition,they are very useful to the computational heat conduction to check the numerical solutions and to develop numerical schemes,grid generation methods and so forth.Such solutions in rectangular coordinates have been derived by the authors.Some other solutions for 1-D and 2-D axisymmetrical heat conduction in cylin drical coordinates are given in this paper to promote the heat conduction theory and to develop the relative computational heat conduction.
Analytically-derived sensitivities in one-dimensional models of solute transport in porous media
Knopman, D.S.
1987-01-01
Analytically-derived sensitivities are presented for parameters in one-dimensional models of solute transport in porous media. Sensitivities were derived by direct differentiation of closed form solutions for each of the odel, and by a time integral method for two of the models. Models are based on the advection-dispersion equation and include adsorption and first-order chemical decay. Boundary conditions considered are: a constant step input of solute, constant flux input of solute, and exponentially decaying input of solute at the upstream boundary. A zero flux is assumed at the downstream boundary. Initial conditions include a constant and spatially varying distribution of solute. One model simulates the mixing of solute in an observation well from individual layers in a multilayer aquifer system. Computer programs produce output files compatible with graphics software in which sensitivities are plotted as a function of either time or space. (USGS)
Approximate analytical solution of MHD flow of an Oldroyd 8-constant fluid in a porous medium
Directory of Open Access Journals (Sweden)
Faisal Salah
2014-12-01
Full Text Available The steady flow in an incompressible, magnetohydrodynamic (MHD Oldroyd 8-constant fluid in a porous medium with the motion of an infinite plate is investigated. Using modified Darcy’s law of an Oldroyd 8-constant fluid, the equations governing the flow are modelled. The resulting nonlinear boundary value problem is solved using the homotopy analysis method (HAM. The obtained approximate analytical solutions clearly satisfy the governing nonlinear equations and all the imposed initial and boundary conditions. The convergence of the HAM solutions for different orders of approximation is demonstrated. For the Newtonian case, the approximate analytical solution via HAM is shown to be in close agreement with the exact solution. Finally, the variations of velocity field with respect to the magnetic field, porosity and non-Newtonian fluid parameters are graphically shown and discussed.
International Nuclear Information System (INIS)
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.
Axially symmetric static sources: A general framework and some analytical solutions
Herrera, L.; Di Prisco, A.; J. Ibañez; Ospino, J.
2013-01-01
We provide all basic equations and concepts required to carry out a general study on axially symmetric static sources. The Einstein equations and the conservation equations are written down for a general anisotropic static fluid endowed with axial symmetry. The structure scalars are calculated and the inhomogeneity factors are identified. Finally some exact analytical solutions were found. One of these solutions describes an incompressible spheroid with isotropic pressure and becomes the well...
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.
Mathematic Model and Analytic Solution for a Cylinder Subject to Exponential Function
Institute of Scientific and Technical Information of China (English)
LIU Wen; SHAN Rui
2009-01-01
Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lamè solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.
Analytical solution of point kinetic equations for sub-critical systems
International Nuclear Information System (INIS)
This article presents an analytical solution for the set of point kinetic equations for sub-critical reactors. This solution stems from the ordinary, non-homogeneous differential equation that rules the neutron density and that presents the incomplete Gamma function in its functional form. The method used proved advantageous and allowed practical applications such as the linear insertion of reactivity, considering an external constant source or with both varying linearly. (author)
Masoud, Hassan; James D. Felske
2008-01-01
Exact analytical solutions are derived for the Stokes flows within evaporating sessile drops of spherical and cylindrical cap shapes. The results are valid for arbitrary contact angle. Solutions are obtained for arbitrary evaporative flux distributions along the free surface as long as the flux is bounded at the contact line. The field equations, E^4(Psi)=0 and Del^4(Phi)=0, are solved for the spherical and cylindrical cap cases, respectively. Specific results and computations are presented f...
On the analytical solution of Fornberg–Whitham equation with the new fractional derivative
Indian Academy of Sciences (India)
Olaniyi Samuel Iyiola; Gbenga Olayinka Ojo
2015-10-01
Motivated by the simplicity, natural and efficient nature of the new fractional derivative introduced by R Khalil et al in J. Comput. Appl. Math. 264, 65 (2014), analytical solution of space-time fractional Fornberg–Whitham equation is obtained in series form using the relatively new method called q-homotopy analysis method (q-HAM). The new fractional derivative makes it possible to introduce fractional order in space to the Fornberg–Whitham equation and be able to obtain its solution. This work displays the elegant nature of the application of q-HAM to solve strongly nonlinear fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for nonlinear differential equations. Comparisons are made on the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.
International Nuclear Information System (INIS)
The objective of this work is to describe the new analytical solution of the neutron slowing down equation for infinite monoatomic media with arbitrary energy dependence of cross section. The solution is obtained by introducing Green slowing down functions instead of starting from slowing down equations directly. The previously used methods for calculation of fission neutron spectra in the reactor cell were numerical. The proposed analytical method was used for calculating the space-energy distribution of fast neutrons and number of neutron reactions in a thermal reactor cell. The role of analytical method in solving the neutron slowing down in reactor physics is to enable understating of the slowing down process and neutron transport. The obtained results could be used as standards for testing the accuracy od approximative and practical methods
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.
Institute of Scientific and Technical Information of China (English)
LI Zhi-Bing; WANG Wei-Liang
2006-01-01
We derive the analytic solution of induced electrostatic potential along single wall carbon nanotubes. Under the hypothesis of constant density of states in the charge-neutral level, we are able to obtain the linear density of excess charge in an external Geld parallel to the tube axis.
Li, Zhibing; Wang, Weiliang
2006-01-01
We derived the analytic solution of induced electrostatic potential along single wall carbon nanotubes. Under the hypothesis of constant density of states in the charge-neutral level, we are able to obtain the linear density of excess charge in an external field parallel to the tube axis.
Ouwersloot, H.G.; Arellano, de J.V.G.
2013-01-01
In Ouwersloot and Vila-Guerau de Arellano (Boundary-Layer Meteorol. doi: 10. 1007/s10546-013-9816-z, 2013, this issue), the analytical solutions for the boundary-layer height and scalar evolutions are derived for the convective boundary layer, based on the prognostic equations of mixed-layer slab mo
International Nuclear Information System (INIS)
In this work, the analytical solution of the radial Schroedinger equation for the Woods–Saxon potential is presented. In our calculations, we have applied the Nikiforov–Uvarov method by using the Pekeris approximation to the centrifugal potential for arbitrary l states. The bound state energy eigenvalues and corresponding eigenfunctions are obtained for various values of n and l quantum numbers. (author)
Analytical solution for the advection-dispersion transport equation in layered media
The advection-dispersion transport equation with first-order decay was solved analytically for multi-layered media using the classic integral transform technique (CITT). The solution procedure used an associated non-self-adjoint advection-diffusion eigenvalue problem that had the same form and coef...
Bibi, Sameena; Qamar, Shamsul; Seidel-Morgenstern, Andreas
2015-03-13
This work is concerned with the analysis of models for linear reactive chromatography describing irreversible A→B and reversible A↔B reactions. In contrast to previously published results rectangular reactant pulses are injected into initially empty or pre-equilibrated columns assuming both Dirichlet and Danckwerts boundary conditions. The models consist of two partial differential equations, accounting for convection, longitudinal dispersion and first order chemical reactions. Due to the effect of involved mechanisms on solute transport, analytical and numerical solutions of the models could be helpful to understand, design and optimize chromatographic reactors. The Laplace transformation is applied to solve the model equations analytically for linear adsorption isotherms. Statistical temporal moments are derived from solutions in the Laplace domain. Analytical results are compared with numerical predictions generated using a high-resolution finite volume scheme for two sets of boundary conditions. Several case studies are carried out to analyze reactive liquid chromatographic processes for a wide range of mass transfer and reaction kinetics. Good agreements in the results validate the correctness of the analytical solutions and accuracy of the proposed numerical algorithm. PMID:25670415
International Nuclear Information System (INIS)
An exact analytical solution, based on the method of characteristics, has been obtained for the spatial and temporal variation of vapor volumetric (void) fraction in a depressurizing pool. Numerical evaluations have shown that the axial void profile is strongly dependent on the drift velocity formulation, and that wall heat flux plays only a minor role in the pool swell transient. (Auth.)
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.
Wijnant, Ysbrand; Spiering, Ruud; Blijderveen, van Maarten; Boer, de André
2006-01-01
Previous research has shown that viscothermal wave propagation in narrow gaps can efficiently be described by means of the low reduced frequency model. For simple geometries and boundary conditions, analytical solutions are available. For example, Beltman [4] gives the acoustic pressure in the gap b
Several numerical and analytical solutions of the radiative transfer equation (RTE) for plane albedo were compared for solar light reflection by sea water. The study incorporated the simplest case, that being a semi-infinite one-dimensional plane-parallel absorbing and scattering...
Real analytic quasi-periodic solutions for the derivative nonlinear Schrödinger equations
Geng, Jiansheng; Wu, Jian
2012-10-01
In this paper, we show that one dimension derivative nonlinear Schrödinger equation admits a whitney smooth family of small amplitude, real analytic quasi-periodic solutions with two Diophantine frequencies. The proof is based on a partial Birkhoff normal form reduction and an abstract infinite dimensional Kolmogorov-Arnold-Moser (KAM) theorem.
Analytical solution of the linear transport equation AN approach with plane symmetry
International Nuclear Information System (INIS)
This work presents a new derivation of the AN approximation of the one-dimensional linear transport equation. The Kuznetsov transformation and Gaussian Quadrature scheme are employed. An analytical solution of the AN equations are also obtained using the Laplace transform. Numerical simulations are presented. (author). 8 refs, 3 tabs
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.
Quick analytical method for the determination of iodide and iodate ions in aqueous solutions
International Nuclear Information System (INIS)
An analytical quick-test method was developed to determine iodide and iodate ions in aqueous solutions using solid phase extraction cartridges for sample preparation. Work was focussed on finding simple, but efficient conditions for quantitative separation of iodate and iodide. Iodine amounts were then determined by standard methods. Ion-exchange absorbers in cartridge form were used. Selectivity and yield of the species separation were studied at pH value of 5-10 and various solution compositions using 131I radioactive tracer. The electrolytes used were diluted alkaline, nitrate and boric acid-borate solutions. Application to nuclear reactor cooling water analysis or environmental investigations and monitoring is proposed. (author)
Institute of Scientific and Technical Information of China (English)
刘林; C.K.Shum
2000-01-01
The analytic perturbation solutions to the motions of a planetary orbiter given in this paper are effective for0< e< 1, where e is the orbital eccentricity of the orbiter. in the solution, it is as-sumed that the rotation of the central body is slow, and its astronomical background is clear. Examples for such planets in the solar system are Ven黶 and Mercury. The perturbation solution is tested numer-ically on two Venusian orbiters with eccentric orbits, PVO and Magellan, and found to be effective.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The analytic perturbation solutions to the motions of a planetary orbiter given in this paper are effective for 0＜e＜1,where e is the orbital eccentricity of the orbiter.In the solution,it is assumed that the rotation of the central body is slow,and its astronomical background is clear.Examples for such planets in the solar system are Venus and Mercury.The perturbation solution is tested numerically on two Venusian orbiters with eccentric orbits,PVO and Magellan,and found to be effective.
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Lund, Erik; Thomsen, Ole Thybo; Barari, Amin
2010-01-01
In this work, an analytical method, which is referred to as Parameter-expansion Method is used to obtain the exact solution for the problem of nonlinear vibrations of an inextensible beam. It is shown that one term in the series expansion is sufficient to obtain a highly accurate solution, which is...... valid for the whole domain of the problem. A comparison of the obtained the numerical solution demonstrates that PEM is effective and convenient for solving such problems. After validation of the obtained results, the system response and stability are also discussed....
A New Homotopy Analysis Method for Approximating the Analytic Solution of KdV Equation
Directory of Open Access Journals (Sweden)
Vahid Barati
2014-01-01
Full Text Available In this study a new technique of the Homotopy Analysis Method (nHAM is applied to obtain an approximate analytic solution of the well-known Korteweg-de Vries (KdV equation. This method removes the extra terms and decreases the time taken in the original HAM by converting the KdV equation to a system of first order differential equations. The resulted nHAM solution at third order approximation is then compared with that of the exact soliton solution of the KdV equation and found to be in excellent agreement.
A class of blowup and global analytical solutions of the viscoelastic Burgers' equations
Energy Technology Data Exchange (ETDEWEB)
An, Hongli, E-mail: hongli.an@connect.polyu.hk [College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Cheung, Ka-Luen, E-mail: kaluen@ied.edu.hk [Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Po Ling Road, Tai Po, New Territories (Hong Kong); Yuen, Manwai, E-mail: nevetsyuen@hotmail.com [Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Po Ling Road, Tai Po, New Territories (Hong Kong)
2013-11-08
In this Letter, by employing the perturbational method, we obtain a class of analytical self-similar solutions of the viscoelastic Burgers' equations. These solutions are of polynomial-type whose forms, remarkably, coincide with that given by Yuen for the other physical models, such as the compressible Euler or Navier–Stokes equations and two-component Camassa–Holm equations. Furthermore, we classify the initial conditions into several groups and then discuss the properties on blowup and global existence of the corresponding solutions, which may be readily seen from the phase diagram.
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.
Energy Technology Data Exchange (ETDEWEB)
Moawad, S. M., E-mail: smmoawad@hotmail.com [Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef (Egypt)
2015-02-15
In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics.
Moawad, S. M.
2015-02-01
In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics.
International Nuclear Information System (INIS)
In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics
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.
International Nuclear Information System (INIS)
Different current and planned experiments are designed to study the zero power neutron physical behavior of accelerator driven systems (ADS). However, the analysis of these experiments is mostly based on point kinetics. To improve this situation and to overcome the limitations resulting from the separation of space and time, the paper presents a fully analytical approximation solution for a space-time dependent neutron transport problem in a one dimensional system consisting of a homogenized medium with a central neutron source. The basic solution without delayed neutrons is derived with Green's functions without separation of space and time. The delayed neutron production is later on implemented by means of the multiple scale expansion method. This way of separating the different time scales avoids the stiff problem arising in a closed form solution. Finally, a fully analytic approximation solution is generated for the switch on of a localized external neutron source in the center of the homogenized subcritical system. Space time dependent results based on a cross section set for a light water reactor configuration are presented to demonstrate the potential of the developed analytical approximation solution. The development is the first step towards improving the methods for the analysis of kinetic ADS experiments. It is the final goal to provide an improved tool for on site analysis of kinetics ADS experiments. (authors)
International Nuclear Information System (INIS)
The quasistationary derivatives method is applied in the paper to improve efficiency of numerical algorithms used for calculating analytical solutions of spatial kinetics problems. A one-dimensional problem (BSS-6) published in the ANL Benchmark Problem Book is considered. According to the approach used by the authors of BSS-6, the system of reactor kinetics equations is presented by a system of ordinary differential equations (ODE) obtained after approximation of the diffusion operator by a finite-difference scheme, thus the analytical solution is calculated on the basis of the solution of the full eigenvalue problem. The difficulty is that the matrix of this stiff system is ill-conditioned, therefore standard subroutines for solving problems of linear algebra appear to be unstable numerically here because of the round-off error. The quasistationary derivatives method is used as a preconditioning procedure to diminish the condition number of the system matrix. (author)
Analytical Solutions of a Fractional Diffusion-advection Equation for Solar Cosmic-Ray Transport
Litvinenko, Yuri E.; Effenberger, Frederic
2014-12-01
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.
Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport
Litvinenko, Yuri E
2014-01-01
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we solve analytically a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.
International Nuclear Information System (INIS)
We present an analytical solution to the collisionless Boltzmann equation for describing the distribution function of molecular ensembles subject to an external periodic traveling force of pulsed optical fields. We apply our solution to study a pulsed standing wave mirror for neutral molecules, recently proposed [P. Ryytty et al., Phys. Rev. Lett. 84, 5074 (2000)]. Using our analytical solution we study the effects of the anharmonicity of optical potential on the reflectivity of the molecular mirror and the corresponding optimal pulse duration. We demonstrate that the reflectivity of the molecular mirror can be significantly improved by optimizing the pulse duration of the external optical fields when taking into account the anharmonicity of molecular motion
Modelling stellar jets with magnetospheres using as initial states analytical MHD solutions
Todorov, P; Cayatte, V; Sauty, C; Lima, J J G; Tsinganos, K
2016-01-01
In this paper we focus on the construction of stellar outflow models emerging from a polar coronal hole-type region surrounded by a magnetosphere in the equatorial regions during phases of quiescent accretion. The models are based on initial analytical solutions. We adopt a meridionally self-similar solution of the time-independent and axisymmetric MHD equations which describes effectively a jet originating from the corona of a star. We modify appropriately this solution in order to incorporate a physically consistent stellar magnetosphere. We find that the closed fieldline region may exhibit different behaviour depending on the associated boundary conditions and the distribution of the heat flux. However, the stellar jet in all final equilibrium states is very similar to the analytical one prescribed in the initial conditions. When the initial net heat flux is maintained, the magnetosphere takes the form of a dynamical helmet streamer with a quasi steady state slow magnetospheric wind. With no heat flux, a s...
MATHEMATIC MODEL AND ANALYTIC SOLUTION FOR CYLINDER SUBJECT TO UNEVEN PRESSURES
Institute of Scientific and Technical Information of China (English)
LIU Wen
2006-01-01
According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surfaces of cylinder. When borderline condition that is predigested according to the Saint-Venant's theory is joined, an equation suit is constructed which meets both the biharmonic equations and the boundary conditions. Furthermore, its analytic solution is deduced with Matlab.When this theory is applied to hydraulic bulging rollers, the experimental results inosculate with the theoretic calculation. Simultaneously, the limit along the axis invariable direction is given and the model building of hollow cylinder and for the analytic solution of hollow cylinder with randomly uneven pressure.
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.
Analytical Solutions of a Nonlinear Convection-Diﬀusion Equation With Polynomial Sources
Directory of Open Access Journals (Sweden)
N. A. Kudryashov
2016-01-01
Full Text Available Nonlinear convection–diﬀusion equations are widely used for the description of various processes and phenomena in physics, mechanics and biology. In this work we consider a family of nonlinear ordinary diﬀerential equations which is a traveling wave reduction of a nonlinear convection–diﬀusion equation with a polynomial source. We study a question about integrability of this family of nonlinear ordinary diﬀerential equations. We consider both stationary and non–stationary cases of this equation with and without convection. In order to construct general analytical solutions of equations from this family we use an approach based on nonlocal transformations which generalize the Sundman transformations. We show that in the stationary case without convection the general analytical solution of the considered family of equations can be constructed without any constraints on its parameters and can be expressed via the Weierstrass elliptic function. Since in the general case this solution has a cumbersome form we ﬁnd some correlations on the parameters which allow us to construct the general solution in the explicit form. We show that in the non–stationary case both with and without convection we can ﬁnd a general analytical solution of the considered equation only imposing some correlation on the parameters. To this aim we use criteria for the integrability of the Lienard equation which have recently been obtained. We ﬁnd explicit expressions in terms of exponential and elliptic functions for the corresponding analytical solutions.
Entry guidance with real-time planning of reference based on analytical solutions
Yu, Wenbin; Chen, Wanchun
2015-05-01
In this paper, first, we develop new analytical solutions to hypersonic gliding problem. In the derivation of these solutions, we propose an innovative method based on spectral decomposition for solving a special type of linear system with variable coefficients, where the system matrix can be expressed as the product of a scale function and a constant matrix. Next, we design an entry guidance based on these analytical solutions. In the guidance, the downrange analytical expression is used to plan the longitudinal reference profile satisfying the downrange requirement in real time. Two bank reversals are needed to eliminate the crossrange error. The first is planned by the crossrange analytical expression such that the second is at a specified point near the end of the flight. After the first bank reversal is performed, the second is slightly corrected using the trajectory simulation. Because the longitudinal reference profile and bank reversals are planned onboard, the entry guidance can handle various urgent tasks and deal well with large dispersions in the initial conditions, aerodynamic model and atmospheric model.
International Nuclear Information System (INIS)
Acids and corrosion products in used perchloroethylene scrubber solutions collected from HTGR fuel preparation processes have been analyzed by several analytical methods to determine the source and possible remedy of the corrosion caused by these solutions. Hydrochloric acid was found to be concentrated on the carbon particles suspended in perchloroethylene. Filtration of carbon from the scrubber solutions removed the acid corrosion source in the process equipment. Corrosion products chemisorbed on the carbon particles were identified. Filtered perchloroethylene from used scrubber solutions contained practically no acid. It is recommended that carbon particles be separated from the scrubber solutions immediately after the scrubbing process to remove the source of acid and that an inhibitor be used to prevent the hydrolysis of perchloroethylene and the formation of acids
A semi-analytical solution for slug tests in an unconfined aquifer considering unsaturated flow
Sun, Hongbing
2016-01-01
A semi-analytical solution considering the vertical unsaturated flow is developed for groundwater flow in response to a slug test in an unconfined aquifer in Laplace space. The new solution incorporates the effects of partial penetrating, anisotropy, vertical unsaturated flow, and a moving water table boundary. Compared to the Kansas Geological Survey (KGS) model, the new solution can significantly improve the fittings of the modeled to the measured hydraulic heads at the late stage of slug tests in an unconfined aquifer, particularly when the slug well has a partially submerged screen and moisture drainage above the water table is significant. The radial hydraulic conductivities estimated with the new solution are comparable to those from the KGS, Bouwer and Rice, and Hvorslev methods. In addition, the new solution also can be used to examine the vertical conductivity, specific storage, specific yield, and the moisture retention parameters in an unconfined aquifer based on slug test data.
Over-reflection of slow magnetosonic waves by homogeneous shear flow: Analytical solution
International Nuclear Information System (INIS)
We have analyzed the amplification of slow magnetosonic (or pseudo-Alfvenic) waves (SMW) in incompressible shear flow. As found here, the amplification depends on the component of the wave-vector perpendicular to the direction of the shear flow. Earlier numerical results are consistent with the general analytic solution for the linearized magnetohydrodynamic equations, derived here for the model case of pure homogeneous shear (without Coriolis force). An asymptotically exact analytical formula for the amplification coefficient is derived for the case when the amplification is sufficiently large.
A Hybrid Analytical-Numerical Solution to the Laminar Flow inside Biconical Ducts
Directory of Open Access Journals (Sweden)
Thiago Antonini Alves
2015-10-01
Full Text Available In this work was presented a hybrid analytical-numerical solution to hydrodynamic problem of fully developed Newtonian laminar flow inside biconical ducts employing the Generalized Integral Transform Technique (GITT. In order to facilitate the analytical treatment and the application of the boundary conditions, a Conformal Transform was used to change the domain into a more suitable coordinate system. Thereafter, the GITT was applied on the momentum equation to obtain the velocity field. Numerical results were obtained for quantities of practical interest, such as maximum and minimum velocity, Fanning friction factor, Poiseuille number, Hagenbach factor and hydrodynamic entry length.
International Nuclear Information System (INIS)
In AC electrokinetics, the application of an AC electric field to a suspension of particles results in the manipulation and separation of the particles also the movement of the fluid. One application is dielectrophoresis (DEP). The second effect is travelling wave dielectrophoresis (twDEP). This paper presents the analytical solutions of the dielectrophoretic and travelling wave forces for the interdigitated electrode arrays energised with either a two- or four-phase signal, respectively. The torque that rotates the particle in the four-phase travelling wave arrays is also analytically solved.
Effects of variable viscosity in a third grade fluid with porous medium: An analytic solution
Ellahi, R.; Afzal, S.
2009-05-01
This study extends the analysis of ref. [Hayat T, Ellahi R, Asghar S. The influence of variable viscosity and viscous dissipation on the non-Newtonian flow: An analytic solution, Commun Nonlinear Sci Numer Simul 2007;12:300-313] in a porous medium by employing modified Darcy's law. Beside this Reynolds and Vogels models of temperature dependent viscosity are considered. The problem is solved using homotopy analysis method (HAM). Expressions of velocity and temperature profiles are constructed analytically and explained with the help of graphs.
Approximate Analytical Solutions for Primary Chatter in the Non-Linear Metal Cutting Model
Warmiński, J.; Litak, G.; Cartmell, M. P.; Khanin, R.; Wiercigroch, M.
2003-01-01
This paper considers an accepted model of the metal cutting process dynamics in the context of an approximate analysis of the resulting non-linear differential equations of motion. The process model is based upon the established mechanics of orthogonal cutting and results in a pair of non-linear ordinary differential equations which are then restated in a form suitable for approximate analytical solution. The chosen solution technique is the perturbation method of multiple time scales and approximate closed-form solutions are generated for the most important non-resonant case. Numerical data are then substituted into the analytical solutions and key results are obtained and presented. Some comparisons between the exact numerical calculations for the forces involved and their reduced and simplified analytical counterparts are given. It is shown that there is almost no discernible difference between the two thus confirming the validity of the excitation functions adopted in the analysis for the data sets used, these being chosen to represent a real orthogonal cutting process. In an attempt to provide guidance for the selection of technological parameters for the avoidance of primary chatter, this paper determines for the first time the stability regions in terms of the depth of cut and the cutting speed co-ordinates.
International Nuclear Information System (INIS)
Analytical solutions based on the Laplace and Fourier transformation techniques are presented for the two- and three-dimensional space-time-dependent convective-dispersive transport of a four-member radionuclide decay chain in homogeneous porous media. The longitudinal dispersion-free solution is also reported. The computation was executed using the MASCOT model on a VAX/VMS-Version 4.1. The solutions are designed for an unbounded medium flow field assumed to be semi-infinite in the direction normal to the source, and infinite orthogonal to the source, with a variety of boundary conditions (single or multiple finite line source or a Gaussian distributed source in the two-dimensional case; single or multiple patch source or bivariate normally distributed source in the three-dimensional case). Radionuclide release modes of the constant and nuclide-dependent type are taken into account. An optimization of the convergence of the integration required by these solutions is achieved after operating a transformation of the infinite interval into the sum of two finite ones. The efficiency of two quadrature formulas (Gauss-Legendre and a fourth-order Newton-Cotes based on an iterative approach) was investigated. Solution accuracy was verified against available one- and two-dimensional analytical solutions. 15 refs
Energy Technology Data Exchange (ETDEWEB)
Dobranskis, R. R.; Zharkova, V. V., E-mail: valentina.zharkova@northumbria.ac.uk [Department of Mathematics and Information Sciences, University of Northumbria, Newcastle upon Tyne NE1 2XP (United Kingdom)
2014-06-10
The original continuity equation (CE) used for the interpretation of the power law energy spectra of beam electrons in flares was written and solved for an electron beam flux while ignoring an additional free term with an electron density. In order to remedy this omission, the original CE for electron flux, considering beam's energy losses in Coulomb collisions, was first differentiated by the two independent variables: depth and energy leading to partial differential equation for an electron beam density instead of flux with the additional free term. The analytical solution of this partial differential continuity equation (PDCE) is obtained by using the method of characteristics. This solution is further used to derive analytical expressions for mean electron spectra for Coulomb collisions and to carry out numeric calculations of hard X-ray (HXR) photon spectra for beams with different parameters. The solutions revealed a significant departure of electron densities at lower energies from the original results derived from the CE for the flux obtained for Coulomb collisions. This departure is caused by the additional exponential term that appeared in the updated solutions for electron differential density leading to its faster decrease at lower energies (below 100 keV) with every precipitation depth similar to the results obtained with numerical Fokker-Planck solutions. The effects of these updated solutions for electron densities on mean electron spectra and HXR photon spectra are also discussed.
International Nuclear Information System (INIS)
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)
New Analytic Solution to the Lane-Emden Equation of Index 2
Directory of Open Access Journals (Sweden)
S. S. Motsa
2012-01-01
Full Text Available We present two new analytic methods that are used for solving initial value problems that model polytropic and stellar structures in astrophysics and mathematical physics. The applicability, effectiveness, and reliability of the methods are assessed on the Lane-Emden equation which is described by a second-order nonlinear differential equation. The results obtained in this work are also compared with numerical results of Horedt (1986 which are widely used as a benchmark for testing new methods of solution. Good agreement is observed between the present results and the numerical results. Comparison is also made between the proposed new methods and existing analytical methods and it is found that the new methods are more efficient and have several advantages over some of the existing analytical methods.
Analytic solutions for links and triangles distributions in finite Barab\\'asi-Albert networks
Ferreira, Ricardo M; Brunnet, Leonardo G
2016-01-01
Barab\\'asi-Albert model describes many different natural networks, often yielding sensible explanations to the subjacent dynamics. However, finite size effects may prevent from discerning among different underlying physical mechanisms and from determining whether a particular finite system is driven by Barab\\'asi-Albert dynamics. Here we propose master equations for the evolution of the degrees, links and triangles distributions, solve them both analytically and by numerical iteration, and compare with numerical simulations. The analytic solutions for all these distributions predict the network evolution for systems as small as 100 nodes. The analytic method we developed is applicable for other classes of networks, representing a powerful tool to investigate the evolution of natural networks.
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.
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
Plane strain analytical solutions for a functionally graded elastic-plastic pressurized tube
International Nuclear Information System (INIS)
Plane strain analytical solutions to functionally graded elastic and elastic-plastic pressurized tube problems are obtained in the framework of small deformation theory. The modulus of elasticity and the uniaxial yield limit of the tube material are assumed to vary radially according to two parametric parabolic forms. The analytical plastic model is based on Tresca's yield criterion, its associated flow rule and ideally plastic material behaviour. Elastic, partially plastic and fully plastic stress states are investigated. It is shown that the elastoplastic response of the functionally graded pressurized tube is affected significantly by the material nonhomogeneity. Different modes of plasticization may take place unlike the homogeneous case. It is also shown mathematically that the nonhomogeneous elastoplastic solution presented here reduces to that of a homogeneous one by appropriate choice of the material parameters
International Nuclear Information System (INIS)
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)
A new analytical solution to axisymmetric Blot's consolidation of a finite soil layer
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A new analytical method is presented to study the axisymmetric Blot's consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot's consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface (z= 0) and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.
Closed-form analytical solutions of high-temperature heat pipe startup and frozen startup limitation
Cao, Y.; Faghri, A.
1992-01-01
Previous numerical and experimental studies indicate that the high-temperature heat pipe startup process is characterized by a moving hot zone with relatively sharp fronts. Based on the above observation, a flat-front model for an approximate analytical solution is proposed. A closed-form solution related to the temperature distribution in the hot zone and the hot zone length as a function of time are obtained. The analytical results agree well with the corresponding experimental data, and provide a quick prediction method for the heat pipe startup performance. Finally, a heat pipe limitation related to the frozen startup process is identified, and an explicit criterion for the high-temperature heat pipe startup is derived. The frozen startup limit identified in this paper provides a fundamental guidance for high-temperature heat pipe design.
An analytic cosmological solution of Poincare gauge gravity with a pseudoscalar torsion
Lu, Jianbo
2016-01-01
A cosmology of Poincare gauge theory is developed, and its analytic solution is obtained. The calculation results agree with observational data and can be compared with the $\\Lambda $CDM model. The cosmological constant puzzle, the coincidence and fine tuning problem are relieved naturally at the same time. The cosmological constant turns out to be the intrinsic torsion and curvature of the vacuum universe and is derived from the theory naturally rather than added artificially. The dark energy originates from geometry, includes the cosmological constant but differs from it. The analytic expression of the state equations of the dark energy and the density parameters of the matter and the geometric dark energy are derived. The full equations of linear cosmological perturbations and the solutions are obtained.
Analytical Solution for the Size of the Minimum Dominating Set in Complex Networks
Nacher, Jose C
2016-01-01
Domination is the fastest-growing field within graph theory with a profound diversity and impact in real-world applications, such as the recent breakthrough approach that identifies optimized subsets of proteins enriched with cancer-related genes. Despite its conceptual simplicity, domination is a classical NP-complete decision problem which makes analytical solutions elusive and poses difficulties to design optimization algorithms for finding a dominating set of minimum cardinality in a large network. Here we derive for the first time an approximate analytical solution for the density of the minimum dominating set (MDS) by using a combination of cavity method and Ultra-Discretization (UD) procedure. The derived equation allows us to compute the size of MDS by only using as an input the information of the degree distribution of a given network.
Indian Academy of Sciences (India)
Jianping Shi; Jibin Li; Shumin Li
2013-11-01
By using dynamical system method, this paper considers the (2+1)-dimensional Davey–Stewartson-type equations. The analytical parametric representations of solitary wave solutions, periodic wave solutions as well as unbounded wave solutions are obtained under different parameter conditions. A few diagrams corresponding to certain solutions illustrate some dynamical properties of the equations.
Analytical solutions for the flow of Carreau and Cross fluids in circular pipes and thin slits
Sochi, Taha
2015-01-01
In this paper, analytical expressions correlating the volumetric flow rate to the pressure drop are derived for the flow of Carreau and Cross fluids through straight rigid circular uniform pipes and long thin slits. The derivation is based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield method to obtain flow solutions for generalized Newtonian fluids through pipes and our adaptation of this method to the flow through slits. The derived expressions are validated by comparing their solutions to the solutions obtained from direct numerical integration. They are also validated by comparison to the solutions obtained from the variational method which we proposed previously. In all the investigated cases, the three methods agree very well. The agreement with the variational method also lends more support to this method and to the variational principle which the method is based upon.
Unified Analytical Solution for Radial Flow to a Well in a Confined Aquifer
Mishra, Phoolendra Kumar
2011-01-01
Drawdowns generated by extracting water from a large diameter (e.g. water supply) well are affected by wellbore storage. We present an analytical solution in Laplace transformed space for drawdown in a uniform anisotropic aquifer caused by withdrawing water at a constant rate from a partially penetrating well with storage. The solution is back transformed into the time domain numerically. When the pumping well is fully penetrating our solution reduces to that of Papadopulos and Cooper [1967]; Hantush [1964] when the pumping well has no wellbore storage; Theis [1935] when both conditions are fulfilled and Yang et.al. [2006] when the pumping well is partially penetrating, has finite radius but lacks storage. We use our solution to explore graphically the effects of partial penetration, wellbore storage and anisotropy on time evolutions of drawdown in the pumping well and in observation wells.
A semi-analytical solution for frost heave prediction of clay soil
Institute of Scientific and Technical Information of China (English)
Hui Bing; Ying Zhang; GuoYu Li
2014-01-01
Frost heave is one of the main freezing problems for construction in permafrost regions. The Konrad-Morgenstern seg-regation potential (SP) model is being used in practice for frost heave using numerical techniques. However, the heat re-lease from in-situ and migrated water in the freezing zone could result in some numerical instability, so the simulation of frost fringe is not ideal. In this study, a semi-analytical solution is developed for frost heave prediction of clay soil. The prediction results to the two tests with different freezing mode with clay soil agree well with the tested behavior, which indicates the feasibility of the solution.
A three-dimensional analytical solution for radioactive contaminant dispersion in the atmosphere
International Nuclear Information System (INIS)
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)
An analytical solution for the two-group kinetic neutron diffusion equation in cylindrical geometry
International Nuclear Information System (INIS)
Recently the two-group Kinetic Neutron Diffusion Equation with six groups of delay neutron precursor in a rectangle was solved by the Laplace Transform Technique. In this work, we report on an analytical solution for this sort of problem but in cylindrical geometry, assuming a homogeneous and infinite height cylinder. The solution is obtained applying the Hankel Transform to the Kinetic Diffusion equation and solving the transformed problem by the same procedure used in the rectangle. We also present numerical simulations and comparisons against results available in literature. (author)
Analytical solution for a class of linear quadratic open-loop Nash game with multiple players
Institute of Scientific and Technical Information of China (English)
Xiaohong NIAN; Zhisheng DUAN; Wenyan TANG
2006-01-01
In this paper, the Nash equilibria for differential games with multiple players is studied. A method for solving the Riccati-type matrix differential equations for open-loop Nash strategy in linear quadratic game with multiple players is presented and analytical solution is given for a type of differential games in which the system matrixcan be diagonalizable. As the special cases, the Nash equilibria for some type of differential games with particular structure is studied also, and some results in previous literatures are extended. Finally, a numerical example is given to illustrate the effectiveness of the solution procedure.
Lancaster, H.
1982-02-01
Although the SUPERFISH program is used for calculating the design parameters of an radio frequency quadrupole (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 (5), electric field (E), magnetic field (H), stored energy (U), power dissipation (P), and quality factor (Q).
An analytical solution for the two-group kinetic neutron diffusion equation in cylindrical geometry
Energy Technology Data Exchange (ETDEWEB)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio, E-mail: julio.lombaldo@ufrgs.br, E-mail: vilhena@pq.cnpq.br [Programa de Pos Graduacao em Matematica Aplicada (DMPA/UFRGS), Universidade Federal do Rio Grande do Sul Porto Alegre, RS (Brazil); Bodmann, Bardo Ernst, E-mail: bardo.bodmann@ufrgs.br [Programa de Pos-Graduacao em Engenharia Mecanica (PROMEC/UFRGS), Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil)
2011-07-01
Recently the two-group Kinetic Neutron Diffusion Equation with six groups of delay neutron precursor in a rectangle was solved by the Laplace Transform Technique. In this work, we report on an analytical solution for this sort of problem but in cylindrical geometry, assuming a homogeneous and infinite height cylinder. The solution is obtained applying the Hankel Transform to the Kinetic Diffusion equation and solving the transformed problem by the same procedure used in the rectangle. We also present numerical simulations and comparisons against results available in literature. (author)
Analytical solution of the Schr\\"odinger equation for the hydrogen molecular ion $H_2^+$
Mitin, A V
2015-01-01
The analytical solution of the Schr\\"{o}dinger equation for the hydrogen molecular ion $H_2^+$ (special case of the quantum tree-body problem with the Coulomb interaction) is obtained first. The solution shows that the total wave function is a two-component function in the sense that it is a linear combination of the two linear independent wave functions. The two-component character of the total wave function was visualized in calculations of the total electron density of $H_2^+$ at different internuclear separations.
Functions of diffraction correction and analytical solutions in nonlinear acoustic measurement
Alliès, Laurent; Nadi, M
2008-01-01
This paper presents an analytical formulation for correcting the diffraction associated to the second harmonic of an acoustic wave, more compact than that usually used. This new formulation, resulting from an approximation of the correction applied to fundamental, makes it possible to obtain simple solutions for the second harmonic of the average acoustic pressure, but sufficiently precise for measuring the parameter of nonlinearity B/A in a finite amplitude method. Comparison with other expressions requiring numerical integration, show the solutions are precise in the nearfield.
Indian Academy of Sciences (India)
Ali S Wadi; Mourad F Dimian; Fayez N Ibrahim
2014-08-01
We present simple analytical solutions for the unsteady advection–dispersion equations describing the pollutant concentration (, ) in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions ≤ 0 and ≥0 and the origin at = 0. The variation of (, ) with the time from = 0 up to → ∞ (the steady state case) is taken into account in our study. The special case for which the dispersion coefficient = 0 is studied in detail. The parameters controlling the pollutant concentration along the river are determined.
Analytical solution to the Riemann problem of 1D elastodynamics with general constitutive laws
Berjamin, H; Chiavassa, G; Favrie, N
2016-01-01
Under the hypothesis of small deformations, the equations of 1D elastodynamics write as a 2 x 2 hyperbolic system of conservation laws. Here, we study the Riemann problem for convex and nonconvex constitutive laws. In the convex case, the solution can include shock waves or rarefaction waves. In the nonconvex case, compound waves must also be considered. In both convex and nonconvex cases, a new existence criterion for the initial velocity jump is obtained. Also, admissibility regions are determined. Lastly, analytical solutions are completely detailed for various constitutive laws (hyperbola, tanh and polynomial), and reference test cases are proposed.
Directory of Open Access Journals (Sweden)
Eskandari Jam Jafar
2014-12-01
Full Text Available In this paper, by using a semi-analytical solution based on multi-layered approach, the authors present the solutions of temperature, displacements, and transient thermal stresses in functionally graded circular hollow cylinders subjected to transient thermal boundary conditions. The cylinder has finite length and is subjected to axisymmetric thermal loads. It is assumed that the functionally graded circular hollow cylinder is composed of N fictitious layers and the properties of each layer are assumed to be homogeneous and isotropic. Time variations of the temperature, displacements, and stresses are obtained by employing series solving method for ordinary differential equation, Laplace transform techniques and a numerical Laplace inversion.
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.
Directory of Open Access Journals (Sweden)
Anastasia S. Lermontova
2015-09-01
Full Text Available The article describes a method yielding approximate analytical solutions under the theory of elasticity for a set of interacting arbitrarily spaced shear fractures. Accurate analytical solutions of this problem are now available only for the simplest individual cases, such as a single fracture or two collinear fractures. A large amount of computation is required to yield a numerical solution for a case considering arbitrary numbers and locations of fractures, while this problem has important practical applications, such as assessment of the state of stress in seismically active regions, forecasts of secondary destruction impacts near systems of large faults, studies of reservoir properties of the territories comprising oil and gas provinces.In this study, an approximate estimation is obtained with the following simplification assumptions: (1 functions showing shear of fractures’ borders are determined similar to the shear function for a single fracture, and (2 boundary conditions for the fractures are specified in the integrated form as mean values along each fracture. Upon simplification, the solution is obtained through the system of linear algebraic equations for unknown values of tangential stress drop. With this approach, the accuracy of approximate solutions is consistent with the accuracy of the available data on real fractures.The reviewed examples of estimations show that the resultant stress field is dependent on the number, size and location of fractures and the sequence of displacements of the fractures’ borders.
An analytical solution to contaminant transport through composite liners with geomembrane defects
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
To investigate the performance of landfill composite liner system,a one-dimensional model was developed for solute transport through composite liners containing geomembrane defects.An analytical solution to the model was obtained by the method of Laplace transformation.The results obtained by the presented solution agree well with those obtained by the numerical method.Results show that leachate head and construction quality of geomembrane(GM) have significant influences on the performance of the composite liners for heavy metal ions.The breakthrough time of lead decreases from 50 a to 19 a when the leachate head increases from 0.3 m to 10 m.It is also indicated that the contaminant mass flux of volatile organic compounds(VOCs) induced by leakage can not be neglected in case of poor construction quality of the landfill barrier system.It is shown that diffusion coefficient and partition coefficient of GM have great influences on solute transport through composite liners for VOCs.The breakthrough time of heavy metal ions will be greatly overestimated if the effects of diffusion and adsorption of clay and geosynthetic clay liner(GCL) are neglected.The composite liner consisting of a geomembrane and a GCL provides a poor barrier for VOCs.The presented analytical solution is relatively simple to apply and can be used for preliminary design of composite liners,evaluating experimental results,and verifying more complex numerical models.
Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model
Directory of Open Access Journals (Sweden)
Houyu Zhao
2012-01-01
Full Text Available We study the existence of analytic solutions of a functional differential equation (z(s+α2z'(s=β(z(s+z(s-z(s which comes from traffic flow model. By reducing the equation with the Schröder transformation to an auxiliary equation, the author discusses not only that the constant λ at resonance, that is, at a root of the unity, but also those λ near resonance under the Brjuno condition.
Two-phase bounded acceleration traffic flow model: Analytical solutions and applications
LEBACQUE, JP
2003-01-01
The present paper describes a two phase traffic flow model. One phase is traffic equilibrium: flow and speed are functions of density, and traffic acceleration is low. The second phase is characterized by constant acceleration. This model extends first order traffic flow models and recaptures the fact that traffic acceleration is bounded. The paper show how to calculate analytical solutions of the two-phase model for dynamic traffic situations, provides a set of calculation rules, and analyze...
Zeng-hui Zhao; Wei-ming Wang; Li-hua Wang; Ji-xing Yan
2014-01-01
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 ...
Ryll, Christopher; Löber, Jakob; Martens, Steffen; Engel, Harald; Tröltzsch, Fredi
2015-01-01
This work deals with the position control of selected patterns in reaction-diffusion systems. Exemplarily, the Schl\\"{o}gl and FitzHugh-Nagumo model are discussed using three different approaches. First, an analytical solution is proposed. Second, the standard optimal control procedure is applied. The third approach extends standard optimal control to so-called sparse optimal control that results in very localized control signals and allows the analysis of second order optimality conditions.
Analytical Solutions for Some Simple Flows of a Binary Mixture of Incompressible Newtonian Fluids
BARIŞ, Serdar
2002-01-01
The problems dealing with some simple flows of a mixture of two incompressible Newtonian fluids have been analysed. By using the theory of binary mixtures of Newtonian fluids, the equations governing the velocity fields are reduced to a system of coupled ordinary differential equations. In the case of non-inertial flow the analytical solutions of these equations have been obtained for the following three problems: (i) the parallel flow with a free surface; (ii) the flow between inter...
Benchmarking the invariant embedding method against analytical solutions in model transport problems
Wahlberg Malin; Pázsit Imre
2006-01-01
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 ...
Human Capital as an Asset Mix and Optimal Life-Cycle Portfolio: An Analytical Solution
Takao Kobayashi; Risa Sai; Kazuya Shibata
2008-01-01
This study examines life-cycle optimal consumption and asset allocation in the presence of human capital. Labor income seems like a "money market mutual fund" whose balance in one or two years is predictable but a wide dispersion results after many years, reflecting fluctuations in economic conditions. We use the Martingale method to derive an analytical solution, finding that Merton's well-known " constant-mix strategy" is still true after incorporating human capital from the perspective of ...
Bars, Itzhak; Chen, Shih-Hung; Steinhardt, Paul J.; Turok, Neil
2012-01-01
We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions...
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.
Analytical Solution of Flow and Heat Transfer over a Permeable Stretching Wall in a Porous Medium
M. Dayyan; Seyyedi, S. M.; G. G. Domairry; M. Gorji Bandpy
2013-01-01
Boundary layer flow through a porous medium over a stretching porous wall has seen solved with analytical solution. It has been considered two wall boundary conditions which are power-law distribution of either wall temperature or heat flux. These are general enough to cover the isothermal and isoflux cases. In addition to momentum, both first and second laws of thermodynamics analyses of the problem are investigated. The governing equations are transformed into a system of ordinary differen...
Directory of Open Access Journals (Sweden)
Santosh Soni
2011-12-01
Full Text Available OnTARGET and MAP are examples of analytics-based solutions that were designed from the outset to address specific business challenges in the broad area of sales force productivity. Although they address different underlying issues, these solutions implement a common approach that is generally applicable to a broad class of operational challenges. Both solutions rely on rigorously defined data models that integrate all relevant data into a common database. Choices of the data to be included in the data model are driven both by end-user requirements as well as the need for relevant inputs to analytical models. Both business problems have a natural mapping to applications of predictive modeling: predicting the probability to purchase in the case of OnTARGET, and estimating the realistic revenue opportunity in the case of MAP. Delivering the underlying data and the analytic insights directly to frontline decision makers (sales representatives for OnTARGET and sales executives for MAP is crucial to driving business impact, and a significant effort has been invested in developing efficient web-based tools with the necessary supporting infrastructure. In this paper we discuss several aspects and analyze them.
Directory of Open Access Journals (Sweden)
Santosh Soni
2011-09-01
Full Text Available OnTARGET and MAP are examples of analytics-based solutions that were designed from the outset to address specific business challenges in the broad area of sales force productivity. Although they address different underlying issues, these solutions implement a common approach that is generally applicable to a broad class of operational challenges. Both solutions rely on rigorously defined data models that integrate all relevant data into a common database. Choices of the data to be included in the data model are driven both by end-user requirements as well as the need for relevant inputs to analytical models. Both business problems have a natural mapping to applications of predictive modeling: predicting the probability to purchase in the case of OnTARGET, and estimating the realistic revenue opportunity in the case of MAP. Delivering the underlying data and the analytic insights directly to frontline decision makers (sales representatives for OnTARGET and sales executives for MAP is crucial to driving business impact, and a significant effort has been invested in developing efficient web-based tools with the necessary supporting infrastructure. In this paper we discuss several aspects and analyze them.
International Nuclear Information System (INIS)
We describe a method 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 in the direction away from the surface. Thus this paper is a supplement to Williams [Williams, M.M.R., 2009, Three-dimensional transport theory: an analytical solution for the internal beam searchlight problem I. Annals of Nuclear Energy 36, 767-783]. For example, we consider a point source, a ring source and a disk source, and calculate the surface scalar flux as a function of the radial co-ordinate when the source is at a fixed distance from the surface. The results are in full agreement with the work of Ganapol and Kornreich [Ganapol, B.D., Kornreich, D.E., this issue. Three-dimensional transport theory: an analytical solution for the internal beam searchlight problem II. Annals of Nuclear Energy]. Diffusion theory results are also included.
Big data analytics as a service infrastructure: challenges, desired properties and solutions
Martín-Márquez, Manuel
2015-12-01
CERN's accelerator complex generates a very large amount of data. A large volumen of heterogeneous data is constantly generated from control equipment and monitoring agents. These data must be stored and analysed. Over the decades, CERN's researching and engineering teams have applied different approaches, techniques and technologies for this purpose. This situation has minimised the necessary collaboration and, more relevantly, the cross data analytics over different domains. These two factors are essential to unlock hidden insights and correlations between the underlying processes, which enable better and more efficient daily-based accelerator operations and more informed decisions. The proposed Big Data Analytics as a Service Infrastructure aims to: (1) integrate the existing developments; (2) centralise and standardise the complex data analytics needs for CERN's research and engineering community; (3) deliver real-time, batch data analytics and information discovery capabilities; and (4) provide transparent access and Extract, Transform and Load (ETL), mechanisms to the various and mission-critical existing data repositories. This paper presents the desired objectives and properties resulting from the analysis of CERN's data analytics requirements; the main challenges: technological, collaborative and educational and; potential solutions.
Starn, J. J.
2013-12-01
Particle tracking often is used to generate particle-age distributions that are used as impulse-response functions in convolution. A typical application is to produce groundwater solute breakthrough curves (BTC) at endpoint receptors such as pumping wells or streams. The commonly used semi-analytical particle-tracking algorithm based on the assumption of linear velocity gradients between opposing cell faces is computationally very fast when used in combination with finite-difference models. However, large gradients near pumping wells in regional-scale groundwater-flow models often are not well represented because of cell-size limitations. This leads to inaccurate velocity fields, especially at weak sinks. Accurate analytical solutions for velocity near a pumping well are available, and various boundary conditions can be imposed using image-well theory. Python can be used to embed these solutions into existing semi-analytical particle-tracking codes, thereby maintaining the integrity and quality-assurance of the existing code. Python (and associated scientific computational packages NumPy, SciPy, and Matplotlib) is an effective tool because of its wide ranging capability. Python text processing allows complex and database-like manipulation of model input and output files, including binary and HDF5 files. High-level functions in the language include ODE solvers to solve first-order particle-location ODEs, Gaussian kernel density estimation to compute smooth particle-age distributions, and convolution. The highly vectorized nature of NumPy arrays and functions minimizes the need for computationally expensive loops. A modular Python code base has been developed to compute BTCs using embedded analytical solutions at pumping wells based on an existing well-documented finite-difference groundwater-flow simulation code (MODFLOW) and a semi-analytical particle-tracking code (MODPATH). The Python code base is tested by comparing BTCs with highly discretized synthetic steady
Bars, Itzhak; Chen, Shih-Hung; Steinhardt, Paul J.; Turok, Neil
2012-10-01
We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the Universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the Universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null-energy condition. There is a special subset of geodesically complete nongeneric solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine-tuning the initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained.
International Nuclear Information System (INIS)
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)
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.
Popov, I. Yu.; Lobanov, I. S.; POPOV S.I.; Popov, A. I.; Gerya, T. V.
2014-01-01
Geodynamic modeling is often related with challenging computations involving solution of the Stokes and continuity equations under the condition of highly variable viscosity. Based on a new analytical approach we have developed particular analytical solutions for 2-D and 3-D incompressible Stokes flows with both linearly and exponentially variable viscosity. We demonstrate how these particular solutions can be converted into 2-D and 3-D test problems suitable for...
Calculation of initial elevation in tsunami source making use of exact analytical solutions
Sementsov, Kirill A.; Nosov, Mikhail A.
2013-04-01
Strong bottom earthquakes are the most prevailing cause for the rise of tsunamis. As a rule, numerical simulation of tsunamis is based on the equations of hydrodynamics, averaged over the vertical coordinate. As for the description of tsunami generation, an earthquake is considered to instantly cause residual deformations of the ocean bottom. Then, the assumption is made that the displacement of the bottom is simultaneously accompanied by formation at the surface of the ocean of a perturbation (initial elevation), the shape of which is fully similar to the vertical residual deformations of the bottom. The initial elevation thus obtained is then applied as the initial condition in resolving the problem of tsunami propagation. The initial field of flow velocities is assumed to be zero. This traditional approach is not accurate due to at least the following two reasons. First, direct transfer of bottom deformations up to the water surface artificially enriches the spectrum of the tsunami at the expense of unrealistically short waves. Second, the horizontal deformation of a sloping bottom can also contribute significantly to the initial elevation. Improved method of calculation of initial elevation in tsunami source was suggested in [1, 2]. This method takes into account both the "smoothing effect" of water layer and contribution of vertical and horizontal components of bottom deformation. The method requires the solution of 3D Laplace's equation. Numerical solution to the 3D problem is computationally expensive, besides there are some difficulties in specification of a static free-pass condition at ocean-crossing outer borders. Analytic-Numerical Algorithm (ANA) [2] is a good alternative to the numerical solution. ANA is based on the analytical solution to the problem in case of the ocean of constant depth. The first purpose of this study is to verify ANA making use of the newly derived exact analytical solution to the problem in case of inclined flat bottom. The
Real analytic solutions for marginal deformations in open superstring field theory
International Nuclear Information System (INIS)
We construct analytic solutions for marginal deformations satisfying the reality condition in open superstring field theory formulated by Berkovits when operator products made of the marginal operator and the associated superconformal primary field are regular. Our strategy is based on the recent observation by Erler that the problem of finding solutions for marginal deformations in open superstring field theory can be reduced to a problem in the bosonic theory of finding a finite gauge parameter for a certain pure-gauge configuration labeled by the parameter of the marginal deformation. We find a gauge transformation generated by a real gauge parameter which infinitesimally changes the deformation parameter and construct a finite gauge parameter by its path-ordered exponential. The resulting solution satisfies the reality condition by construction. (orig.)
Bychkov, Vladimir; Kurianovych, Evgeniy
2016-01-01
We further discuss properties of a simple model, which allows existence of domain walls with orientational moduli, localized on them. We review an analytic solution of such a model and discuss properties of that solution in a context of previous results. We discuss an existence of one-dimensional domain walls, localized on two-dimensional ones, and construct a corresponding effective action. Then in low-energy limit, which is $O(3)$ sigma-model, we discuss existence of skyrmions, localized on domain walls, and provide a solution for a skyrmion configuration, based on the analogy with instantons. We perform a symmetry analysis of the initial model and low-energy theory on the domain wall world volume.
Latunde-Dada, Seyi; Bott, Rachel; Hampton, Karl; Leszczyszyn, Oksana Iryna
2015-08-21
Taylor Dispersion Analysis (TDA) in the presence of interactions between solutes and capillary walls yields inaccurate results for the diffusion coefficients of the solutes because the resulting concentration profiles are broadened and asymmetric. Whilst there are practical ways of mitigating these interactions, it is not always possible to eradicate them completely. In this paper, an analytical method of mitigating the effects of the adsorptions is presented. By observing the dispersion of the solute molecules at two detection points and using the expected relations between measured parameters, such as the standard deviations and peak amplitudes, the dispersive components of the profiles were isolated with a constrained fitting algorithm. The method was successfully applied to lysozyme and cytochrome C which adsorb onto fused silica capillary walls. Furthermore, this illustrates an advantage of using the fitting method for Taylor Dispersion Analysis. PMID:26189206
Dai, Hui-Hui
2011-01-01
A polymer network can imbibe water, forming an aggregate called hydrogel, and undergo large and inhomogeneous deformation with external mechanical constraint. Due to the large deformation, nonlinearity plays a crucial role, which also causes the mathematical difficulty for obtaining analytical solutions. Based on an existing model for equilibrium states of a swollen hydrogel with a core-shell structure, this paper seeks analytical solutions of the deformations by perturbation methods for three cases, i.e. free-swelling, nearly free-swelling and general inhomogeneous swelling. Particularly for the general inhomogeneous swelling, we introduce an extended method of matched asymptotics to construct the analytical solution of the governing nonlinear second-order variable-coefficient differential equation. The analytical solution captures the boundary layer behavior of the deformation. Also, analytical formulas for the radial and hoop stretches and stresses are obtained at the two boundary surfaces of the shell, ma...
DEFF Research Database (Denmark)
Larsen, Niels Vesterdal; Breinbjerg, Olav
2004-01-01
To facilitate the validation of the numerical Method of Auxiliary Sources an analytical Method of Auxiliary Sources solution is derived in this paper. The Analytical solution is valid for transverse magnetic, and electric, plane wave scattering by circular impedance Cylinders, and it is derived by...... 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 of the...... numerical Method of Auxiliary Sources for a range of scattering configurations....
Analytical solutions for some defect problems in 1D hexagonal and 2D octagonal quasicrystals
Indian Academy of Sciences (India)
X Wang; E Pan
2008-05-01
We study some typical defect problems in one-dimensional (1D) hexagonal and two-dimensional (2D) octagonal quasicrystals. The first part of this investigation addresses in detail a uniformly moving screw dislocation in a 1D hexagonal piezoelectric quasicrystal with point group 6. A general solution is derived in terms of two functions 1, 2, which satisfy wave equations, and another harmonic function 3. Elementary expressions for the phonon and phason displacements, strains, stresses, electric potential, electric fields and electric displacements induced by the moving screw dislocation are then arrived at by employing the obtained general solution. The derived solution is verified by comparison with existing solutions. Also obtained in this part of the investigation is the total energy of the moving screw dislocation. The second part of this investigation is devoted to the study of the interaction of a straight dislocation with a semi-infinite crack in an octagonal quasicrystal. Here the crack penetrates through the solid along the period direction and the dislocation line is parallel to the period direction. We first derive a general solution in terms of four analytic functions for plane strain problem in octagonal quasicrystals by means of differential operator theory and the complex variable method. All the phonon and phason displacements and stresses can be expressed in terms of the four analytic functions. Then we derive the exact solution for a straight dislocation near a semi-infinite crack in an octagonal quasicrystal, and also present the phonon and phason stress intensity factors induced by the straight dislocation and remote loads.
Benchmarking the invariant embedding method against analytical solutions in model transport problems
International Nuclear Information System (INIS)
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)
Multidimensional self-similar analytical solutions of two-phase flow in porous media
Fučík, Radek; Illangasekare, Tissa H.; Beneš, Michal
2016-04-01
In general, analytical solutions serve a useful purpose to obtain better insights and to verify numerical codes. For flow of two incompressible and immiscible phases in homogeneous porous media without gravity, one such method that neglects capillary pressure in the solution was first developed by Buckley and Leverett (1942). Subsequently, McWhorter and Sunada (1990) derived an exact solution for the one and two dimensional cases that factored in capillary effects. This solution used a similarity transform that allowed to reduce the governing equations into a single ordinary differential equation (ODE) that can be further integrated into an equivalent integral equation. We present a revision to McWhorter and Sunada solution by extending the self-similar solution into a general multidimensional space. Inspired by the derivation proposed by McWhorter and Sunada (1990), we integrate the resulting ODE in the third and higher dimensions into a new integral equation that can be subsequently solved iteratively by means of numerical integration. We developed implementations of the iterative schemes for one- and higher dimensional cases that can be accessed online on the authors' website.
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.
Yarrow, Maurice; Vastano, John A.; Lomax, Harvard
1992-01-01
Generic shapes are subjected to pulsed plane waves of arbitrary shape. The resulting scattered electromagnetic fields are determined analytically. These fields are then computed efficiently at field locations for which numerically determined EM fields are required. Of particular interest are the pulsed waveform shapes typically utilized by radar systems. The results can be used to validate the accuracy of finite difference time domain Maxwell's equations solvers. A two-dimensional solver which is second- and fourth-order accurate in space and fourth-order accurate in time is examined. Dielectric media properties are modeled by a ramping technique which simplifies the associated gridding of body shapes. The attributes of the ramping technique are evaluated by comparison with the analytic solutions.
Latyshev, A V
2012-01-01
Analytical solution of second Stokes problem of behaviour of rarefied gas with Cercignani boundary accomodation conditions The second Stokes problem about behaviour of rarefied gas filling half-space is analytically solved. A plane, limiting half-space, makes harmonious fluctuations in the plane. The kinetic BGK-equation (Bhatnagar, Gross, Krook) is used. The boundary accomodation conditions of Cercignani of reflexion gaseous molecules from a wall are considered. Distribution function of the gaseous molecules is constructed. The velocity of gas in half-space is found, also its value direct at a wall is found. The force resistance operating from gas on border is found. Besides, the capacity of dissipation of the energy falling to unit of area of the fluctuating plate limiting gas is obtained.
Analytical solutions and genuine multipartite entanglement of the three-qubit Dicke model
Zhang, Yu-Yu; Chen, Xiang-You; He, Shu; Chen, Qing-Hu
2016-07-01
We present analytical solutions to three qubits and a single-mode cavity coupling system beyond the rotating-wave approximation (RWA). The zeroth-order approximation, equivalent to the adiabatic approximation, works well for arbitrary coupling strength for small qubit frequency. The first-order approximation, called the generalized rotating-wave approximation (GRWA), produces an effective solvable Hamiltonian with the same form as the ordinary RWA one and exhibits substantial improvements of energy levels over the RWA even on resonance. Based on these analytical eigensolutions, we study both the bipartite entanglement and genuine multipartite entanglement (GME). The dynamics of these two kinds of entanglements using the GRWA are consistent with the numerical exact ones. Interestingly, the well-known sudden death of entanglement occurs in the bipartite entanglement dynamics but not in the GME dynamics.
Analytical Solution of Flow and Heat Transfer over a Permeable Stretching Wall in a Porous Medium
Directory of Open Access Journals (Sweden)
M. Dayyan
2013-01-01
Full Text Available Boundary layer flow through a porous medium over a stretching porous wall has seen solved with analytical solution. It has been considered two wall boundary conditions which are power-law distribution of either wall temperature or heat flux. These are general enough to cover the isothermal and isoflux cases. In addition to momentum, both first and second laws of thermodynamics analyses of the problem are investigated. The governing equations are transformed into a system of ordinary differential equations. The transformed ordinary equations are solved analytically using homotopy analysis method. A comprehensive parametric study is presented, and it is shown that the rate of heat transfer increases with Reynolds number, Prandtl number, and suction to the surface.
International Nuclear Information System (INIS)
Analytical solutions based on Laplace transform are developed for the problem of radionuclides transport along a discrete planar fracture in porous rock. The solutions take into account advective transport in the fracture, longitudinal hydrodynamic dispersion along the fracture axis, molecular diffusion from the fracture into the rock matrix, sorption within the rock matrix, sorption onto the surface of the fracture and radioactive decay. The initial concentration in both the fracture and the rock matrix is assumed to be zero. Four boundary conditions, constant concentration, exponentially decaying concentration, exponentially decaying flux and kinetic solubility-limited dissolution are assumed. All these analytical solutions are in a form of a single integral that is evaluated by a Gauss-Legendre quadrature for each point in space and time. A comparison between the concentration profiles with a constant concentration inlet boundary condition and those with a decaying concentration inlet boundary condition shows that the concentration profile is strongly influenced by the inlet boundary condition when the retardation factor of the matrix is high. As the dissolution rate constant approaches infinity, the inlet boundary condition of the kinetic solubility-limited dissolution model can be replaced by the boundary condition of constant concentration
An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem
International Nuclear Information System (INIS)
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
On the propagation of diel signals in river networks using analytic solutions of flow equations
Fonley, M.; Mantilla, R.; Small, S. J.; Curtu, R.
2015-08-01
Two hypotheses have been put forth to explain the magnitude and timing of diel streamflow oscillations during low flow conditions. The first suggests that delays between the peaks and troughs of streamflow and daily evapotranspiration are due to processes occurring in the soil as water moves toward the channels in the river network. The second posits that they are due to the propagation of the signal through the channels as water makes its way to the outlet of the basin. In this paper, we design and implement a theoretical experiment to test these hypotheses. We impose a baseflow signal entering the river network and use a linear transport equation to represent flow along the network. We develop analytic streamflow solutions for two cases: uniform and nonuniform velocities in space over all river links. We then use our analytic solutions to simulate streamflows along a self-similar river network for different flow velocities. Our results show that the amplitude and time delay of the streamflow solution are heavily influenced by transport in the river network. Moreover, our equations show that the geomorphology and topology of the river network play important roles in determining how amplitude and signal delay are reflected in streamflow signals. Finally, our results are consistent with empirical observations that delays are more significant as low flow decreases.
Bars, Itzhak; Steinhardt, Paul J; Turok, Neil
2012-01-01
We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null energy condition. There is a special subset of geodesically complete non-generic solutions which perform zero-size bounces without ever entering the antigravit...
An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem
Milazzo, A.; Orlando, C.; Alaimo, A.
2009-08-01
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.
Vijayaraghavan, A.
1984-01-01
Hill's variational equations are solved analytically for the orbital perturbations of a spacecraft nominally in an elliptic orbit around a non-spherical body. The rotation of the central planet about its spin-axis is not considered in the analysis. The perturbations are restricted to the planetary gravitational harmonics only. An extremely simple algorithm is derived to transform the spherical harmonic potentials to the orbital coordinate system, and the resulting accelerations are shown to be simply trigonometric functions of the true anomaly. With the principal matrix solution for the differential equations of the adjoint system given in closed form, the orthogonality of the trigonometric functions makes it possible to obtain an analytic solution for the non-homogeneous problem, at intervals of 2 pi in true anomaly. The solution for orbital perturbations can be extended over several revolutions by applying well-known results from Floquet's theory. The technique is demonstrated with results presented on the spacecraft periapsis altitude for the forthcoming Venus Radar Mapper Mission.
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.
Fock space, symbolic algebra, and analytical solutions for small stochastic systems.
Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A
2015-12-01
Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics. PMID:26764734
Fock space, symbolic algebra, and analytical solutions for small stochastic systems
Santos, Fernando A. N.; Gadêlha, Hermes; Gaffney, Eamonn A.
2015-12-01
Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.
Approximate analytic transport problem solution of particle reflection from solid target
International Nuclear Information System (INIS)
The first part of thesis deals with the analytic investigation of the energy and time independent particle transport in plane geometry described by a common anisotropic scattering function. Regarding particles with specific diffusion histories in infinite or semi-infinite medium, new particular solutions of the corresponding transport equations are exactly derived by means of the Fourier inversion technique. Aiming at preserving the analytic outcome, the two groups of particles scattered after each successive collision into directions μ0, were considered. Its Fourier transformed transport equations have solutions without logarithmic singular points, in the upper part or the down part of the complex k-plane. Consequently, the Fourier inversion of solutions are carried out analytically and the closing expressions in real space are acquired as a compound of the elementary exponential functions over space coordinate x. Opposite to the exact solution for the whole angular flux density - being a key result of the rigorous transport theory, these particular solutions do not comprise elements with the exponential singular integrals and could be easily applied in subsequent calculations. It has been shown that these formulae represent a valid generalization of the expressions for the flux of once scattered particles. Moreover, they incorporate a great fraction of all particles and, at least in the case of a small multiplication constant c, they closely approach the entire angular flux density. Using the particular solutions previously derived, an approximate analytic method for solving the energy and time independent transport equation in plane geometry is developed. The procedure is based on the particle flux decomposition in two components. The first component is exactly obtained and the second one is determined approximately by the ordinary DPN method of low order. The infinite medium Green's function and the half-space reflection coefficient were calculated. A careful
Zharkova, V. V.; Dobranskis, R. R.
2016-06-01
In this paper we consider simultaneous analytical solutions of continuity equations for electron beam precipitation (a) in collisional losses and (b) in ohmic losses, or mixed energy losses (MEL) by applying the iterative method to calculate the resulting differential densities at given precipitation depth. The differential densities of precipitating electrons derived from the analytical solutions for MELs reveal increased flattening at energies below 10-30 keV compared to a pure collisional case. This flattening becomes stronger with an increasing precipitation depth turning into a positive slope at greater precipitation depths in the chromosphere resulting in a differential density distribution with maximum that shifts towards higher energies with increase in column depth, while the differential densities combining precipitating and returning electrons are higher at lower energies than those for a pure collisional case. The resulting hard X-ray (HXR) emission produced by the beams with different initial energy fluxes and spectral indices is calculated using the MEL approach for different ratios between the differential densities of precipitating and returning electrons. The number of returning electrons can be even further enhanced by a magnetic mirroring, not considered in the present model, while dominating at lower atmospheric depths where the magnetic convergence and magnitude are the highest. The proposed MEL approach provides an opportunity to account simultaneously for both collisional and ohmic losses in flaring events, which can be used for a quick spectral fitting of HXR spectra and evaluation of a fraction of returning electrons versus precipitating ones. The semi-analytical MEL approach is used for spectral fitting to Reuven High Energy Solar Spectroscopic Imager observations of nine C, M and X class flares revealing a close fit to the observations and good resemblance to numerical FP solutions.
Vujević, M; Vidaković-Cifrek, Z; Tkalec, M; Tomíc, M; Regula, I
2000-11-01
Saturated water solutions of calcium chloride, calcium bromide and their 1:1 mixture are commonly used as "high density brines" for pressure control in oil wells. To compare the effect of these chemicals of technical grade with the effect of the chemicals of analytical grade the Lemna test was used. The multiplication rate, fresh weight, dry to fresh weight ratio, area covered by plants and chlorophyll content were measured as toxicity parameters. The concentrations of tested chemicals were 0.025, 0.05. 0.075 and 0.1 mol dm(-3). Generally, the chemicals of both technical and analytical grade in concentrations of 0.025 mol dm(-3) stimulated the Lemna minor growth, while tested chemicals in concentrations of 0.05 mol dm(-3) did not affect the growth significantly. The exceptions were results obtained by measuring fresh weight. Most of tested chemicals in concentrations of 0.075 mol dm(-3) and all chemicals in concentrations of 0.1 mol dm(-3) reduced the growth. No major differences between effects of tested chemicals of technical and analytical grade on plant growth were observed, except that tested chemicals of analytical grade in concentrations of 0.1 mol dm(-3) increased dry to fresh weight ratio much stronger than chemicals of technical grade. All tested chemicals in all concentrations increased chlorophyll content. After treatment with chemicals of analytical grade much higher increase of chlorophyll a concentration in comparison to increase of chlorophyll b was noticed, while chemicals of technical grade caused more prominent increase of chlorophyll b. PMID:11057678
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 tidal groundwater flow in coastal two-aquifer system
Li, Hailong; Jiao, Jiu Jimmy
This paper presents a complete analytical solution to describe tidal groundwater level fluctuations in a coastal subsurface system. The system consists of two aquifers and a leaky layer between them. Previous solutions of Jacob [Flow of groundwater, in: H. Rouse (Ed.), Engineering Hydraulics, Wiley, New York, 1950, pp. 321-386], Jiao and Tang [Water Resour. Res. 35 (3) (1999) 747], Li and Jiao [Adv. Water Resour. 24 (5) (2001a) 565], Li et al. [Water Resour. Res. 37 (2001) 1095] and Jeng et al. [Adv. Water Resour. (in press)] are special cases of the new solution. The present solution differs from previous work in that both the effects of the leaky layer's elastic storage and the tidal wave interference between the two aquifers are considered. If the upper and lower aquifers have the same storativities and transimissivities, the system can be simplified into an equivalent double-layered, aquifer-aquitard system bounded by impermeable layers from up and down. It is found that the leaky layer's elastic storage behaves as a buffer to the tidal wave interference between the two aquifers. The buffer capacity increases with the leaky layer's thickness, specific storage, and decreases with the leaky layer's vertical permeability. Great buffer capacity can result in negligible tidal wave interference between the upper and lower aquifers so that the Li and Jiao (loc. cit.) solution applies.
Analytical solutions to general anti-plane shear problems in finite elasticity
Gao, David Yang
2016-03-01
This paper presents a pure complementary energy variational method for solving a general anti-plane shear problem in finite elasticity. Based on the canonical duality-triality theory developed by the author, the nonlinear/nonconvex partial differential equations for the large deformation problem are converted into an algebraic equation in dual space, which can, in principle, be solved to obtain a complete set of stress solutions. Therefore, a general analytical solution form of the deformation is obtained subjected to a compatibility condition. Applications are illustrated by examples with both convex and nonconvex stored strain energies governed by quadratic-exponential and power-law material models, respectively. Results show that the nonconvex variational problem could have multiple solutions at each material point, the complementary gap function and the triality theory can be used to identify both global and local extremal solutions, while the popular convexity conditions (including rank-one condition) provide mainly local minimal criteria and the Legendre-Hadamard condition (i.e., the so-called strong ellipticity condition) does not guarantee uniqueness of solutions. This paper demonstrates again that the pure complementary energy principle and the triality theory play important roles in finite deformation theory and nonconvex analysis.
Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system
Sedghi, Mohammad M.; Samani, Nozar
2015-09-01
Semi-analytical solutions of flow to a well in an unconfined single porosity aquifer underlain by a fractured double porosity aquifer, both of infinite radial extent, are obtained. The upper aquifer is pumped at a constant rate from a pumping well of infinitesimal radius. The solutions are obtained via Laplace and Hankel transforms and are then numerically inverted to time domain solutions using the de Hoog et al. algorithm and Gaussian quadrature. The results are presented in the form of dimensionless type curves. The solution takes into account the effects of pumping well partial penetration, water table with instantaneous drainage, leakage with storage in the lower aquifer into the upper aquifer, and storativity and hydraulic conductivity of both fractures and matrix blocks. Both spheres and slab-shaped matrix blocks are considered. The effects of the underlying fractured aquifer hydraulic parameters on the dimensionless drawdown produced by the pumping well in the overlying unconfined aquifer are examined. The presented solution can be used to estimate hydraulic parameters of the unconfined and the underlying fractured aquifer by type curve matching techniques or with automated optimization algorithms. Errors arising from ignoring the underlying fractured aquifer in the drawdown distribution in the unconfined aquifer are also investigated.
Energy Technology Data Exchange (ETDEWEB)
Xu, Zhijie; Fang, Yilin; Scheibe, Timothy D.; Bonneville, Alain
2012-05-15
We present a hydro-mechanical model for geological sequestration of carbon dioxide. The model considers the poroelastic effects by taking into account the coupling between the geomechanical response and the fluid flow in greater detail. The simplified hydro-mechanical model includes the geomechanical part that relies on the linear elasticity, while the fluid flow is based on the Darcy’s law. Two parts were coupled using the standard linear poroelasticity. Analytical solutions for pressure field were obtained for a typical geological sequestration scenario. The model predicts the temporal and spatial variation of pressure field and effects of permeability and elastic modulus of formation on the fluid pressure distribution.
The Analytical Solution of the Schr\\"odinger Particle in Multiparameter Potential
Taş, Ahmet
2016-01-01
In this study, we present analytical solutions of the Schr\\"odinger equation with the Multiparameter potential containing the different types of physical potential via the asymptotic iteration method (AIM) by applying a Pekeris-type approximation to the centrifugal potential. For any n and l (states) quantum numbers, we get the bound state energy eigenvalues numerically and the corresponding eigenfunctions.Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.
SWASHES: a library of Shallow Water Analytic Solutions for Hydraulic and Environmental Studies
Delestre, Olivier; Pierre-Antoine, Ksinant; Darboux, Frédéric; Christian, Laguerre; Vo, Thi Ngoc Tuoi; James, Francois; Cordier, Stephane
2013-01-01
A significant number of analytic solutions to the Shallow Water equations is discribed in a unified formalism. They encompass a wide variety of flow conditions (supercritical, subcritical, shock, etc.), in 1 or 2 space dimensions, with or without rain and soil friction, for transitory flow or steady state. An original feature is that the corresponding source codes are made available to the community (http://www.univ-orleans.fr/mapmo/soft/SWASHES), so that users of Shallow Water based models can easily find an adaptable benchmark library to validate numerical methods.
International Nuclear Information System (INIS)
Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed
International Nuclear Information System (INIS)
Under investigation in this paper are two coupled integrable dispersionless (CID) equations modeling the dynamics of the current-fed string within an external magnetic field. Through a set of the dependent variable transformations, the bilinear forms for the CID equations are derived. Based on the Hirota method and symbolic computation, the analytic N-soliton solutions are presented. Infinitely many conservation laws for the CID equations are given through the known spectral problem. Propagation characteristics and interaction behaviors of the solitons are analyzed graphically. (general)
Analytical solution to a fracture problem in a tough layered structure
Hamamoto, Yukari; Okumura, Ko
2008-08-01
Nacre causes the shining beauty of pearl due to its remarkable layered structure, which is also strong. We reconsider a simplified layered model of nacre proposed previously [Okumura and de Gennes, Eur. Phys. J. E 4, 121 (2001)] and obtain an analytical solution to a fundamental crack problem. The result asserts that the fracture toughness is enhanced due to a large displacement around the crack tip (even if the crack-tip stress is not reduced). The derivation offers ideas for solving a number of boundary problems for partial differential equations important in many fields.
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...... 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...
Exact analytical solution of a nonlinear equation arising in heat transfer
Abbasbandy, S.; Shivanian, E.
2010-01-01
This Letter shows that the nonlinear equation arising in heat transfer recently investigated in papers [D.D. Ganji, Phys. Lett. A 355 (2006) 337; S. Abbasbandy, Phys. Lett. A 360 (2006) 109; Hafez Tari, D.D. Ganji, H. Babazadeh, Phys. Lett. A 363 (2007) 213] and [M.S.H. Chowdhury, I. Hashim, Phys. Lett. A 372 (2008) 1240] is exactly solvable, analyses the equation fully and, furthermore, gives analytic exact solution in implicit form for each value of parameters of equation.
Analytical versus discretized solutions of four-group diffusion equations to thermal reactors
International Nuclear Information System (INIS)
This paper presents the application of four-group Diffusion theory to thermal reactor criticality calculation. The four-group diffusion equations are applied to the spherical nucleus and reflector of an example reactor. The neutrons fluxes depend upon the radial coordinate. The simultaneous linear ordinary differential equations are solved given the solutions for the fluxes. The neutron fluxes for the nucleus are functions of the eight functions linearly independent consisting of sin, cos, sinh, cosh, sin sinh, sin cosh, cos sinh, and cos cosh. The analytical and discretized calculations of keff value give excellent agreement, an error around 0,03%. (author)
Spin-Hall effect theory: new analytical solutions of the Pauli equation in a quantum dot
J. L. Cardoso
2012-01-01
In this work, we present the analytical solution of the effective mass Pauli equation, with Rashba and linear Dresselhaus interactions, for an electron gas moving through a semiconductor quantum dot under a longitudinal electric field, which is defined along the $x$-direction. We study the relative influence of the Rashba and Dresselhaus terms on the spin-Hall effect for the first propagating and edge channels, by analyzing the mixing between spin-up and -down states and the zero-field spin s...
Analytical Solutions of Time Periodic Electroosmotic Flow in a Semicircular Microchannel
Directory of Open Access Journals (Sweden)
Shaowei Wang
2015-01-01
Full Text Available The time periodic electroosmotic flow of Newtonian fluids through a semicircular microchannel is studied under the Debye–Hückel approximation. Analytical series of solutions are found, and they consist of a time-dependent oscillating part and a time-dependent generating or transient part. Some new physical phenomena are found. The electroosmotic flow driven by an alternating electric field is not periodic in time, but quasi-periodic. There is a phase shift between voltage and flow, which is only dependent on the frequency of external electric field.
Kazempour, Sobhan; Soroushfar, Saheb
2016-01-01
In this paper we add a compact dimension to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes, which describes (rotating) black string-(anti-) de sitter spacetime. We study the geodesic motion of test particles and light rays in this spacetime. We present the analytical solutions of the geodesic equations in terms of Weierstrass elliptic and Kleinian sigma hyperelliptical functions. We also discuss the possible orbits and classify them according to particle's energy and angular momentum. Moreover, the obtained results, are compared to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes.
Complete Analytic Solutions of the Mie-type Potentials in N-Dimensions
Agboola, D.
2008-01-01
The exact solutions of the N-dimensional Schrodinger equation with the Mie-type potentials are obtained using the conventional Nikiforov-Uvarov method.The expectation values r^{-1} and r^{-2}$ and the virial theorem are also obtained in N-dimensions using the Hellmann-Feynman theorem.The ladder operators are also construct for the Mie-type potentials in N-dimensions and the matrix elements of some operators $r$ and r\\frac{d}{dr} are analytically obtained from the ladder operators.And the gene...
International Nuclear Information System (INIS)
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
An Explicit,Totally Analytic Solution of Laminar Viscous FLow over a Semi—Infinite Flat Plate
Institute of Scientific and Technical Information of China (English)
Shi－JunLIAO
1998-01-01
In this paper,a new kind of analytic technique for nonlinear problems,namely the Homotopy Analysis Method,is applied to give an explicit,totally analytic solution of the Blasius' flow.i.e.,the two dimensional (2D) laminar viscous flow over a semi-infinite flat plate.This analytic solution is valid in the whole region having physical meanings.To our knowledge,it is the first time in history that such a kind of explicit,totally analytic solution is given.This fact well verifies the great potential and validity of the Honmotopy Analysis Method as a kind of powerful analytic tool for nonlinear problems in science and engineering.
Fleming, C H; Hu, B L
2010-01-01
We revisit the model of a quantum Brownian oscillator linearly coupled to an environment of quantum oscillators at finite temperature. By introducing a compact and particularly well-suited formulation, we give a rather quick and direct derivation of the master equation and its solutions for general spectral functions and arbitrary temperatures. The flexibility of our approach allows for an immediate generalization to cases with an external force and with an arbitrary number of Brownian oscillators. More importantly, we point out an important mathematical subtlety concerning boundary-value problems for integro-differential equations which led to incorrect master equation coefficients and impacts on the description of nonlocal dissipation effects in all earlier derivations. Furthermore, we provide explicit, exact analytical results for the master equation coefficients and its solutions in a wide variety of cases, including ohmic, sub-ohmic and supra-ohmic environments with a finite cut-off.
Institute of Scientific and Technical Information of China (English)
Wang Teng; Wang Kuihua; Xie Kanghe
2001-01-01
The vibration problem of a pile of arbitrary segments with variable modulus under exciting force is established, in which the influence of the soil under pile toe and the surroundings is taken into account. With Laplace transforms, the transmit functions for velocity and displacement of pile are derived. Furthermore, in terms of the convolution theorem and inversed Laplace transform, an analytical solution for the time domain response of a pile subjected to a semi-sine impulse is developed,which is the theoretical basis of the sonic method in pile integrity testing. Based on the solution, the vibration properties of pile with sharp or continuous modulus are studied. The validity of this approach is verified through fidd dynamic tests on some engineering piles. It shows that the theoretical prediction and the response of the pile are in good agreement.
Directory of Open Access Journals (Sweden)
Md. Alal Hosen
2015-01-01
Full Text Available In the present paper, a complicated strongly nonlinear oscillator with cubic and harmonic restoring force, has been analysed and solved completely by harmonic balance method (HBM. Investigating analytically such kinds of oscillator is very difficult task and cumbersome. In this study, the offered technique gives desired results and to avoid numerical complexity. An excellent agreement was found between approximate and numerical solutions, which prove that HBM is very efficient and produces high accuracy results. It is remarkably important that, second-order approximate results are almost same with exact solutions. The advantage of this method is its simple procedure and applicable for many other oscillatory problems arising in science and engineering.
A nonlinear model arising in the buckling analysis and its new analytic approximate solution
Energy Technology Data Exchange (ETDEWEB)
Khan, Yasir [Zhejiang Univ., Hangzhou, ZJ (China). Dept. of Mathematics; Al-Hayani, Waleed [Univ. Carlos III de Madrid, Leganes (Spain). Dept. de Matematicas; Mosul Univ. (Iraq). Dept. of Mathematics
2013-05-15
An analytical nonlinear buckling model where the rod is assumed to be an inextensible column and prismatic is studied. The dimensionless parameters reduce the constitutive equation to a nonlinear ordinary differential equation which is solved using the Adomian decomposition method (ADM) through Green's function technique. The nonlinear terms can be easily handled by the use of Adomian polynomials. The ADM technique allows us to obtain an approximate solution in a series form. Results are presented graphically to study the efficiency and accuracy of the method. To the author's knowledge, the current paper represents a new approach to the solution of the buckling of the rod problem. The fact that ADM solves nonlinear problems without using perturbations and small parameters can be judged as a lucid benefit of this technique over the other methods. (orig.)
International Nuclear Information System (INIS)
A novel mathematical model for single-phase fluid flow from unconsolidated formations to a horizontal well with the consideration of stress-sensitive permeability is presented. The model assumes the formation permeability is an exponential function of the pore pressure. Using a perturbation technique, the model is solved for either constant pressure or constant flux or infinite lateral boundary conditions with closed top and bottom boundaries. Through Laplace transformation, finite Fourier transformation and numerical inversion methods, the solutions are obtained and the pressure response curves are analyzed. The agreement between the analytical solutions in this paper and the numerical results from commercial software (Saphir) is excellent, which manifests the accuracy of the results derived in this paper. (paper)
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.
International Nuclear Information System (INIS)
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. (general)
Energy Technology Data Exchange (ETDEWEB)
Ceolin, Celina; Vilhena, Marco T.; Bodmann, Bardo E.J., E-mail: vilhena@pq.cnpq.b, E-mail: bardo.bodmann@ufrgs.b [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Alvim, Antonio Carlos Marques, E-mail: alvim@nuclear.ufrj.b [Universidade Federal do Rio de Janeiro (PEN/COPPE/UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-Graduacao de Engenharia. Programa de Energia Nuclear
2011-07-01
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)
Analytical solution of laminar-laminar stratified two-phase flows with curved interfaces
International Nuclear Information System (INIS)
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
An analytic solution of steady Stokes flow on a rotating polar cap
International Nuclear Information System (INIS)
An analytic solution of two-dimensional, steady, linear, viscous flow on a polar cap-the polar region of a sphere that lies above (or below) a given plane normal to the rotation axis-rotating about its center is obtained. Inflow and outflow on the boundary of the polar cap drive the fluid motion. The solution of the stream function is expressed as the Fourier series in longitudes and the associated Legendre functions of complex degrees in cosines of colatitudes. Fluid particles move almost along lines of constant latitude, some circulate cyclonically and others anticyclonically, in the geostrophic balance everywhere except near the north pole where the flow is relatively slow and the viscous force dominates over the Coriolis force. Our results support the approximation analysis and laboratory experiment studied by Imawaki and Takano (1974 Deep-Sea Res. 21 69-77).
An Analytical Solution Applied to Heat and Mass Transfer in a Vibrated Fluidised Bed Dryer
Energy Technology Data Exchange (ETDEWEB)
Picado, Apolinar
2011-07-01
A mathematical model for the drying of particulate solids in a continuous vibrated fluidised bed dryer was developed and applied to the drying of grain wetted with a single liquid and porous particles containing multicomponent liquid mixtures. Simple equipment and material models were applied to describe the process. In the plug-flow equipment model, a thin layer of particles moving forward and well mixed in the direction of the gas flow was regarded; thus, only the longitudinal changes of particle moisture content and composition as well as temperature along the dryer were considered. Concerning the material model, mass and heat transfer in a single isolated particle was studied. For grain wetted with a single liquid, mass and heat transfer within the particles was described by effective transfer coefficients. Assuming a constant effective mass transport coefficient and effective thermal conductivity of the wet particles, analytical solutions of the mass and energy balances were obtained. The variation of both transport coefficients along the dryer was taken into account by a stepwise application of the analytical solution in space intervals with non-uniform inlet conditions and averaged coefficients from previous locations in the dryer. Calculation results were verified by comparison with experimental data from the literature. There was fairly good agreement between experimental data and simulation but the results depend strongly on the correlation used to calculate heat and mass transfer coefficients. For the case of particles containing a multicomponent liquid mixture dried in the vibrated fluidised bed dryer, interactive diffusion and heat conduction were considered the main mechanisms for mass and heat transfer within the particles. Assuming a constant matrix of effective multicomponent diffusion coefficients and thermal conductivity of the wet particles, analytical solutions of the diffusion and conduction equations were obtained. The equations for mass
Analytical techniques for characterization of cyclodextrin complexes in aqueous solution: a review.
Mura, Paola
2014-12-01
Cyclodextrins are cyclic oligosaccharides endowed with a hydrophilic outer surface and a hydrophobic inner cavity, able to form inclusion complexes with a wide variety of guest molecules, positively affecting their physicochemical properties. In particular, in the pharmaceutical field, cyclodextrin complexation is mainly used to increase the aqueous solubility and dissolution rate of poorly soluble drugs, and to enhance their bioavailability and stability. Analytical characterization of host-guest interactions is of fundamental importance for fully exploiting the potential benefits of complexation, helping in selection of the most appropriate cyclodextrin. The assessment of the actual formation of a drug-cyclodextrin inclusion complex and its full characterization is not a simple task and often requires the use of different analytical methods, whose results have to be combined and examined together. The purpose of the present review is to give, as much as possible, a general overview of the main analytical tools which can be employed for the characterization of drug-cyclodextrin inclusion complexes in solution, with emphasis on their respective potential merits, disadvantages and limits. Further, the applicability of each examined technique is illustrated and discussed by specific examples from literature. PMID:24680374
Directory of Open Access Journals (Sweden)
J.-S. Chen
2011-04-01
Full Text Available This study presents a generalized analytical solution for one-dimensional solute transport in finite spatial domain subject to arbitrary time-dependent inlet boundary condition. The governing equation includes terms accounting for advection, hydrodynamic dispersion, linear equilibrium sorption and first order decay processes. The generalized analytical solution is derived by using the Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate. Several special cases are presented and compared to illustrate the robustness of the derived generalized analytical solution. Result shows an excellent agreement. The analytical solutions of the special cases derived in this study have practical applications. Moreover, the derived generalized solution which consists an integral representation is evaluated by the numerical integration to extend its usage. The developed generalized solution offers a convenient tool for further development of analytical solution of specified time-dependent inlet boundary conditions or numerical evaluation of the concentration field for arbitrary time-dependent inlet boundary problem.
S.A. Zahedi; M. Fazeli; Tolou, N.
2008-01-01
This study deals with analytical solution of time-dependent partial differential equations. The analyses are carried out by the means of Homotopy Analysis Method (HAM), Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM). The results have been compared and depicted graphically. It is shown that the presented approaches are very effective, straightforward and capable to the analytical solutions of the large classes of linear or nonlinear time-dependent partial diffe...
Application of the homotopy method for analytical solution of non-Newtonian channel flows
International Nuclear Information System (INIS)
This paper presents the homotopy series solution of the Navier-Stokes and energy equations for non-Newtonian flows. Three different problems, Couette flow, Poiseuille flow and Couette-Poiseuille flow have been investigated. For all three cases, the nonlinear momentum and energy equations have been solved using the homotopy method and analytical approximations for the velocity and the temperature distribution have been obtained. The current results agree well with those obtained by the homotopy perturbation method derived by Siddiqui et al (2008 Chaos Solitons Fractals 36 182-92). In addition to providing analytical solutions, this paper draws attention to interesting physical phenomena observed in non-Newtonian channel flows. For example, it is observed that the velocity profile of non-Newtonian Couette flow is indistinctive from the velocity profile of the Newtonian one. Additionally, we observe flow separation in non-Newtonian Couette-Poiseuille flow even though the pressure gradient is negative (favorable). We provide physical reasoning for these unique phenomena.
Application of the homotopy method for analytical solution of non-Newtonian channel flows
Energy Technology Data Exchange (ETDEWEB)
Roohi, Ehsan [Department of Aerospace Engineering, Sharif University of Technology, PO Box 11365-8639, Azadi Avenue, Tehran (Iran, Islamic Republic of); Kharazmi, Shahab [Department of Mechanical Engineering, Sharif University of Technology, PO Box 11365-8639, Azadi Avenue, Tehran (Iran, Islamic Republic of); Farjami, Yaghoub [Department of Computer Engineering, University of Qom, Qom (Iran, Islamic Republic of)], E-mail: roohi@sharif.edu
2009-06-15
This paper presents the homotopy series solution of the Navier-Stokes and energy equations for non-Newtonian flows. Three different problems, Couette flow, Poiseuille flow and Couette-Poiseuille flow have been investigated. For all three cases, the nonlinear momentum and energy equations have been solved using the homotopy method and analytical approximations for the velocity and the temperature distribution have been obtained. The current results agree well with those obtained by the homotopy perturbation method derived by Siddiqui et al (2008 Chaos Solitons Fractals 36 182-92). In addition to providing analytical solutions, this paper draws attention to interesting physical phenomena observed in non-Newtonian channel flows. For example, it is observed that the velocity profile of non-Newtonian Couette flow is indistinctive from the velocity profile of the Newtonian one. Additionally, we observe flow separation in non-Newtonian Couette-Poiseuille flow even though the pressure gradient is negative (favorable). We provide physical reasoning for these unique phenomena.
Sharma, Pankaj; Parashar, Sandeep Kumar
2016-05-01
The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d15 effect. In piezoelectric actuators, the potential use of d15 effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d31 and d33. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton`s principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.
Analytical solutions of heat transfer for laminar flow in rectangular channels
Directory of Open Access Journals (Sweden)
Rybiński Witold
2014-12-01
Full Text Available The paper presents two analytical solutions namely for Fanning friction factor and for Nusselt number of fully developed laminar fluid flow in straight mini channels with rectangular cross-section. This type of channels is common in mini- and microchannel heat exchangers. Analytical formulae, both for velocity and temperature profiles, were obtained in the explicit form of two terms. The first term is an asymptotic solution of laminar flow between parallel plates. The second one is a rapidly convergent series. This series becomes zero as the cross-section aspect ratio goes to infinity. This clear mathematical form is also inherited by the formulae for friction factor and Nusselt number. As the boundary conditions for velocity and temperature profiles no-slip and peripherally constant temperature with axially constant heat flux were assumed (H1 type. The velocity profile is assumed to be independent of the temperature profile. The assumption of constant temperature at the channel’s perimeter is related to the asymptotic case of channel’s wall thermal resistance: infinite in the axial direction and zero in the peripheral one. It represents typical conditions in a minichannel heat exchanger made of metal.
Energy Technology Data Exchange (ETDEWEB)
Silva, Milena W. Da; Vilhena, Marco T. de; Bodmann, Bardo E., E-mail: milena.wollmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardobodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Leite, Sergio B., E-mail: bogado@cnen.gov.br [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RS (Brazil)
2013-07-01
In this work, we report on an analytical representation for the solution of the neutron point kinetics equation, free of stiffness and assuming that the reactivity is a continuous or sectionally continuous function of time. To this end, we cast the point kinetics equation in a first order linear differential equation. Next, we split the corresponding matrix into a diagonal matrix plus a matrix that contains the remaining terms. Expanding the neutron density and the delayed neutron precursors concentrations in a truncated series, allows one to construct a recursive system, in form of a first order matrix differential equation with source. The initialization of the recursion procedure is of diagonal form and has no source, but satisfies the initial conditions. The remaining equations are subject to null initial conditions and include the time dependent diagonal elements together with the off diagonal elements as a source term. The solution is obtained in analytical representation which may be evaluated for any time value, because it is free of stiffness. We present numerical simulations and comparisons against results from the literature, for a constant, a step, a ramp, a quadratic and sine shaped reactivity function. (author)
Analytical solution for beam with time-dependent boundary conditions versus response spectrum
Energy Technology Data Exchange (ETDEWEB)
Gou, P.F.; Panahi, K.K. [GE Nuclear Energy, San Jose, CA (United States)
2001-07-01
This paper studies the responses of a uniform simple beam for which the supports are subjected to time-dependent conditions. Analytical solution in terms of series was presented for two cases: (1) Two supports of a simple beam are subjected to a harmonic motion, and (2) One of the two supports is stationary while the other is subjected to a harmonic motion. The results of the analytical solution were investigated and compared with the results of conventional response spectrum method using the beam finite element model. One of the applications of the results presented in this paper can be used to assess the adequacy and accuracy of the engineering approaches such as response spectra methods. It has been found that, when the excitation frequency equals the fundamental frequency of the beam, the results from response spectrum method are in good agreement with the exact calculation. The effects of initial conditions on the responses are also examined. It seems that the non-zero initial velocity has pronounced effects on the displacement time histories but it has no effect on the maximum accelerations. (author)
Semi-analytical solutions for the effect of well shut down on rock stability
Energy Technology Data Exchange (ETDEWEB)
Han, G.; Ioannidis, M.; Dusseault, M.B. [Waterloo Univ., ON (Canada)
2002-06-01
This paper presents three newly developed models to describe the effect of well shut down (or sharp change of production rate) on rock stress distributions. The methods are particularly useful in poorly consolidated rock around a wellbore which may become unstable after the process of well shut down and restart. Analytical solutions for quasi-static pressure recovery processes in a bounded oil reservoir are combined with a poro-elastic geomechanics model in which pressure fluctuations inside the wellbore provide a boundary condition to the formation outside the wellbore. Analytical solutions explain the direct relationships between fluid properties, rock properties and production parameters. Stress fluctuations are examined in the context of rock stability changes resulting from dynamic loading. Model calculations show that the fluctuations of effective stresses and shear stress could reach several hundred kPa due to pressure waves created by the water hammer effect inside a wellbore. The models can be used to quantify the effects of pressure oscillation, resulting from operation at the surface, on the stability of underground rock. It is noted that more research is needed to obtain accurate information on the dynamic response of unconsolidated sandstones to rapidly oscillating pressures before this method can be widely used. The model can be used to evaluate risks such as rock instability. It can also be used to choose which wells may start sanding if they are shut down or started up abruptly. 13 refs., 1 tab., 7 figs., 1 append.
New analytical exact solutions of time fractional KdV–KZK equation by Kudryashov methods
S Saha, Ray
2016-04-01
In this paper, new exact solutions of the time fractional KdV–Khokhlov–Zabolotskaya–Kuznetsov (KdV–KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann–Liouville derivative is used to convert the nonlinear time fractional KdV–KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV–KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV–KZK equation.
Analytical solution to the circularity problem in the discounted cash flow valuation framework
Directory of Open Access Journals (Sweden)
Felipe Mejía-Peláez
2011-12-01
Full Text Available In this paper we propose an analytical solution to the circularity problem between value and cost of capital. Our solution is derived starting from a central principle of finance that relates value today to value, cash flow, and the discount rate for next period. We present a general formulation without circularity for the equity value (E, cost of levered equity (Ke, levered firm value (V, and the weighted average cost of capital (WACC. We furthermore compare the results obtained from these formulas with the results of the application of the Adjusted Present Value approach (no circularity and the iterative solution of circularity based upon the iteration feature of a spreadsheet, concluding that all methods yield exactly the same answer. The advantage of this solution is that it avoids problems such as using manual methods (i.e., the popular “Rolling WACC” ignoring the circularity issue, setting a target leverage (usually constant with the inconsistencies that result from it, the wrong use of book values, or attributing the discrepancies in values to rounding errors.
Barrett, Steven R. H.; Britter, Rex E.
Predicting long-term mean pollutant concentrations in the vicinity of airports, roads and other industrial sources are frequently of concern in regulatory and public health contexts. Many emissions are represented geometrically as ground-level line or area sources. Well developed modelling tools such as AERMOD and ADMS are able to model dispersion from finite (i.e. non-point) sources with considerable accuracy, drawing upon an up-to-date understanding of boundary layer behaviour. Due to mathematical difficulties associated with line and area sources, computationally expensive numerical integration schemes have been developed. For example, some models decompose area sources into a large number of line sources orthogonal to the mean wind direction, for which an analytical (Gaussian) solution exists. Models also employ a time-series approach, which involves computing mean pollutant concentrations for every hour over one or more years of meteorological data. This can give rise to computer runtimes of several days for assessment of a site. While this may be acceptable for assessment of a single industrial complex, airport, etc., this level of computational cost precludes national or international policy assessments at the level of detail available with dispersion modelling. In this paper, we extend previous work [S.R.H. Barrett, R.E. Britter, 2008. Development of algorithms and approximations for rapid operational air quality modelling. Atmospheric Environment 42 (2008) 8105-8111] to line and area sources. We introduce approximations which allow for the development of new analytical solutions for long-term mean dispersion from line and area sources, based on hypergeometric functions. We describe how these solutions can be parameterized from a single point source run from an existing advanced dispersion model, thereby accounting for all processes modelled in the more costly algorithms. The parameterization method combined with the analytical solutions for long-term mean
Analytical traveling wave solutions for transport with nonlinear and nonequilibrium adsorption
Energy Technology Data Exchange (ETDEWEB)
Van Der Zee, S.E.A.T.M. (Agricultural Univ., Wageningen (Netherlands))
1990-10-01
Transport was modeled for a soil with dual porosity, or with chemical nonequilibrium, assuming first-order kinetics. The equilibrium sorption equation in the immobile region is nonlinear. Two equilibrium equations for sorption were considered, that is, the Langmuir and the Van Bemmelen-Freundlich equations. The sorption equation in the mobile region is assumed to be linear. Analytical solutions were obtained that describe the traveling wave displacement found for initial resident concentrations that are smaller than the feed concentration and for infinite displacement times, neglecting the coupled effects of dispersion and nonequilibrium conditions. These waves travel with a fixed shape and a fixed velocity through the homogeneous flow domain. Besides expressions for the front shape, expressions for the front thickness and the front position were also presented. Differences with respect to the linear sorption case are the smaller front thickness and the non-Fickian type of displacement. The non-Fickian behavior is intrinsic to the traveling wave assumption as the front does not spread with the square root of time. The analytical solutions obtained for the equilibrium and for the nonequilibrium situations are mathematically equivalent. Only the effective diffusion/dispersion coefficient needs to be adapted to account for nonequilibrium effects, as for linear dual-porosity models. Apart from early time behavior, the traveling wave solutions agree well with numerical approximations. The front steepness depends sensitively on the degree of nonlinearity. The sensitivity on the dispersion coefficient and first-order rate coefficient may be large but depends on which mechanism controls front spreading.
Analytical Traveling Wave Solutions for Transport With Nonlinear and Nonequilibrium Adsorption
van der Zee, Sjoerd E. A. T. M.
1990-10-01
Transport was modeled for a soil with dual porosity, or with chemical nonequilibrium, assuming first-order kinetics. The equilibrium sorption equation in the immobile region is nonlinear. Two equilibrium equations for sorption were considered, that is, the Langmuir and the Van Bemmelen-Freundlich equations. The sorption equation in the mobile region is assumed to be linear. Analytical solutions were obtained that describe the traveling wave displacement found for initial resident concentrations that are smaller than the feed concentration and for infinite displacement times, neglecting the coupled effects of dispersion and nonequilibrium conditions. These waves travel with a fixed shape and a fixed velocity through the homogeneous flow domain. Besides expressions for the front shape, expressions for the front thickness and the front position were also presented. Differences with respect to the linear sorption case are the smaller front thickness and the non-Fickian type of displacement. The non-Fickian behavior is intrinsic to the traveling wave assumption as the front does not spread with the square root of time. The analytical solutions obtained for the equilibrium and for the nonequilibrium situations are mathematically equivalent. Only the effective diffusion/dispersion coefficient needs to be adapted to account for nonequilibrium effects, as for linear dual-porosity models. Apart from early time behavior, the traveling wave solutions agree well with numerical approximations. The front steepness depends sensitively on the degree of nonlinearity. The sensitivity on the dispersion coefficient and first-order rate coefficient may be large but depends on which mechanism controls front spreading.
On analytic solutions of wave equations in regular coordinate systems on Schwarzschild background
Philipp, Dennis
2015-01-01
The propagation of (massless) scalar, electromagnetic and gravitational waves on fixed Schwarzschild background spacetime is described by the general time-dependent Regge-Wheeler equation. We transform this wave equation to usual Schwarzschild, Eddington-Finkelstein, Painleve-Gullstrand and Kruskal-Szekeres coordinates. In the first three cases, but not in the last one, it is possible to separate a harmonic time-dependence. Then the resulting radial equations belong to the class of confluent Heun equations, i.e., we can identify one irregular and two regular singularities. Using the generalized Riemann scheme we collect properties of all the singular points and construct analytic (local) solutions in terms of the standard confluent Heun function HeunC, Frobenius and asymptotic Thome series. We study the Eddington-Finkelstein case in detail and obtain a solution that is regular at the black hole horizon. This solution satisfies causal boundary conditions, i.e., it describes purely ingoing radiation at $r=2M$. ...
Decoupling the NLO coupled DGLAP evolution equations: an analytic solution to pQCD
Block, Martin M; Ha, Phuoc; McKay, Douglas W
2010-01-01
Using repeated Laplace transform techniques, along with newly-developed accurate numerical inverse Laplace transform algorithms, we transform the coupled, integral-differential NLO singlet DGLAP equations first into coupled differential equations, then into coupled algebraic equations, which we can solve iteratively. After Laplace inverting the algebraic solution analytically, we numerically invert the solutions of the decoupled differential equations. Finally, we arrive at the decoupled NLO evolved solutions F_s(x,Q^2)=calF_s(F_{s0}(x),G_0(x)) and G(x,Q^2)=calG(F_{s0}(x),G_0(x)), where calF_s and calG are known functions - determined using the DGLAP splitting functions up to NLO in the strong coupling constant alpha_s(Q^2). The functions F_{s0}(x)=F_s(x,Q_0^2) and G_0(x)=G(x,Q_0^2) are the starting functions for the evolution at Q_0^2. This approach furnishes us with a new tool for readily obtaining, independently, the effects of the starting functions on either the evolved gluon or singlet structure functio...
Analytical solutions for two-dimensional soil heat flow with radiation surface boundary conditions
International Nuclear Information System (INIS)
Heat flow add temperature variations in soil are important in agriculture, forestry, and ecology. Nonuniform surface cover and variability in soil properties result in two-dimensional soil heat flow. This study derives analytical solutions for unsteady two-dimensional soil heat transfer problems with standard (constant temperature coefficient) and modified (temperature coefficient varies with position) radiation surface boundary conditions. Solutions are periodic in time and horizontal direction. The structure of the solutions guarantees that soil temperatures are smooth functions of position and time, even if the temperature coefficient or forcing function in the radiation boundary condition are discontinuous. Calculated soil temperature heat flux densities, and surface energy balance components for bare wet strips alternating with strips covered with either chalk, black plastic, or clear plastic were found to vary strongly with time and position. For diurnal variations, lateral heat flow only significantly affected temperatures in the middle of strips narrower than approximately 0.2 m. Sensitivity of soil temperature to changes in soil thermal properties increased as the temperature coefficient in the surface boundary condition decreased. Both cases showed that spatial differences in albedo, surface resistance, and serodynamic resistance spatially alter the surface energy balance and soil thermal regimes, including surface temperature and heat flux density
International Nuclear Information System (INIS)
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
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.
International Nuclear Information System (INIS)
We study the pressureless Navier–Stokes–Poisson equations with density-dependent viscosity. With the extension of the blowup solutions for the Euler–Poisson equations, the analytical blowup solutions, in radial symmetry, in RN (N ≥ 2) are constructed
International Nuclear Information System (INIS)
A variable-coefficient Kadomtsev–Petviashvili equation is investigated. The Painlevé analysis leads to its explicit Painlevé-integrable conditions. An auto-Bäcklund transformation and the bilinear form are presented via the truncated Painlevé expansion and symbolic computation. Several families of new analytic solutions are presented, including the soliton-like and periodic solutions. (general)
Directory of Open Access Journals (Sweden)
J. N. Kapur
1960-04-01
Full Text Available In the present paper, an exact analytical solution of the equation of ballistics, for the specific case of a tubular charge has been given. This solution applies to some particular values, of the pressure-index alpha greater than unity, and for these values, the function G (gamma, alfa of Clemmow has also been explicitly determined.
Directory of Open Access Journals (Sweden)
Andrea Amicarelli
2015-01-01
Full Text Available This study presents 1D analytical solutions for the ensemble variance of reactive scalars in one-dimensional turbulent flows, in case of stationary conditions, homogeneous mean scalar gradient and turbulence, Dirichlet boundary conditions, and first order kinetics reactions. Simplified solutions and sensitivity analysis are also discussed. These solutions represent both analytical tools for preliminary estimations of the concentration variance and upwind spatial reconstruction schemes for CFD (Computational Fluid Dynamics—RANS (Reynolds-Averaged Navier-Stokes codes, which estimate the turbulent fluctuations of reactive scalars.
Analytical solution of the point reactor kinetics equations with temperature feedback
International Nuclear Information System (INIS)
Highlights: ► Supercritical process in a pressurized-water reactor with 235U as fissile materials. ► Solution of the point reactor kinetics equation with a temperature feedback. ► The linear relationship between reactivity and neutron generation time. - Abstract: In this paper the point reactor kinetics equations with one group of averaged delayed neutrons and the adiabatic feedback model are solved analytically. The relations of reactivity, and neutron density with neutron lifetime are calculated. The numerical results of the delayed-supercritical process in a pressurized-water reactor with 235U as a fissile material under constant step reactivity of ρ0 = β/2 are given. Our investigations report one of the most accurate results. However this method is valid and applicable as long as the adiabatic condition of heat transfer from fuel rods to the coolant is met.
A New Efficient Analytical Method for Picolinate Ion Measurements in Complex Aqueous Solutions
Energy Technology Data Exchange (ETDEWEB)
Parazols, M.; Dodi, A. [CEA Cadarache, Lab Anal Radiochim and Chim, DEN, F-13108 St Paul Les Durance (France)
2010-07-01
This study focuses on the development of a new simple but sensitive, fast and quantitative liquid chromatography method for picolinate ion measurement in high ionic strength aqueous solutions. It involves cation separation over a chromatographic CS16 column using methane sulfonic acid as a mobile phase and detection by UV absorbance (254 nm). The CS16 column is a high-capacity stationary phase exhibiting both cation exchange and RP properties. It allows interaction with picolinate ions which are in their zwitterionic form at the pH of the mobile phase (1.3-1.7). Analysis is performed in 30 min with a detection limit of about 0.05 {mu}M and a quantification limit of about 0.15 {mu}M. Moreover, this analytical technique has been tested efficiently on complex aqueous samples from an effluent treatment facility. (authors)
Analytic solutions for the three-dimensional compressible Navier–Stokes equation
International Nuclear Information System (INIS)
We investigate the three-dimensional compressible Navier–Stokes (NS) and the continuity equations in Cartesian coordinates for Newtonian fluids. The problem has an importance in different fields of science and engineering like fluid, aerospace dynamics or transfer processes. Finding an analytic solution may bring considerable progress in understanding the transport phenomena and in the design of different equipments where the NS equation is applicable. For solving the equation the polytropic equation of state is used as a closing condition. The key idea is the three-dimensional generalization of the well-known self-similar ansatz which was already used for non-compressible viscous flow in our former study. The geometrical interpretations of the trial function is also discussed. We compared our recent results to the former non-compressible ones. (paper)
Analytical solutions of the Schroedinger equation with the Woods-Saxon potential for l = 0 states
International Nuclear Information System (INIS)
An analytical solution of the radial Schroedinger equation is of high importance in non relativistic quantum mechanics, because the wave function contains all necessary information for full description of a quantum system. There are only few potentials for which the radial Schroedinger equation can be solved explicitly for all n and l states. Many methods were developed to solve the radial Schroedinger equation exactly for l = 0 within these potentials. The radial Schroedinger equation for the Woods-Saxon potential can not be solved exactly for l ≠ 0. It is well known that the Woods-Saxon potential is one of the important short-range potentials in physics. Furthermore, this potential was applied to numerous problems, in nuclear and particle physics, atomic physics, condensed matter, and chemical physics
UNSTEADY BOUNDARY LAYER FLOW ALONG A STRETCHING CYLINDER AN ANALYTICAL SOLUTION
Directory of Open Access Journals (Sweden)
M. Y. Akl
2014-01-01
Full Text Available The axisymetric laminar boundary layer unsteady flow along a continuously stretching cylinder immersed in a viscous and incompressible fluid is studied. The governing partial boundary layer equations in cylindrical form are first transformed into ordinary differential equations these equations are solved analytically using the optimal modified Homotopy Asymptotic method in order to get a closed form solution for the dimensionless functions f and è. The main object of this study is to investigate the effect of an unsteady motion of a stretching cylinder on the flow and heat transfer characteristics such as surface skin friction and surface heat flux. These characteristics have a direct effect on the quality of the final product of the fiber manufacturing and extrusion processes. Considerable effects were found for the dynamic parameter (γ, the curvature parameter (ρ and the prandtl number (pr on the velocity and the heat transfer.
A comparison between numerical and semi-analytical solutions to the point-dynamics equations
Energy Technology Data Exchange (ETDEWEB)
Silva, Jeronimo J.A.; Alvim, Antonio C.M, E-mail: shaolin.jr@gmail.com, E-mail: alvim@nuclear.ufrj.br [Coordenacao dos Programas de Pos-Graduacao em Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Instituto Alberto Luiz Coimbra; Vilhena, Marco T.M.B.; Bodmann, Bardo E.J., E-mail: vilhena@pq.cnpq.br, E-mail: bardo.bodmann@ufrgs.brb [Univeridade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graducao em Engenharia Mecanica
2013-07-01
This work presents a comparison between purely numerical methods and a semi-analytical model that uses the Adomian polynomial expansion to solve the point dynamics set of equations. The aforementioned set of equations describe the magnitude of the neutron density in a fixed point of a nuclear reactor, as well as the neutron precursors density and the temperature of the temperature results in a nonlinear equation to the neutron behavior. Furthermore, these equations show the stiffness properties, due to the large difference in the time scales of each group of precursors. The decomposition method, in association with the Adomian polynomials results in a powerful toll to solve non-linear equations, and with the right choice of the time step, the obtained solution can be proven to be stable. (author)
Analytical solutions for thermal forcing vortices in boundary layer and its applications
Institute of Scientific and Technical Information of China (English)
LIU Xiao-ran; LI Guo-ping
2007-01-01
Using the Boussinesq approximation, the vortex in the boundary layer is assumed to be axisymmetrical and thermal-wind balanced system forced by diabatic heating and friction, and is solved as an initial-value problem of linearized vortex equation set in cylindrical coordinates. The impacts of thermal forcing on the flow field structure of vortex are analyzed. It is found that thermal forcing has significant impacts on the flow field structure, and the material representative forms of these impacts are closely related to the radial distribution of heating. The discussion for the analytical solutions for the vortex in the boundary layer can explain some main structures of the vortex over the Tibetan Plateau.
Tanaka, Tomiji; Watanabe, Kenjiro
2008-02-20
For holographic data storage, it is necessary to adjust the wavelength and direction of the reading beam if the reading and recording temperature do not match. An analytical solution for this adjustment is derived using first-order approximations in a two-dimensional model. The optimum wavelength is a linear function of the temperature difference between recording and reading, and is independent of the direction of the reference beam. However, the optimum direction of incidence is not only a linear function of the temperature difference, but also depends on the direction of the reference beam. The retrieved image, which is produced by a diffracted beam, shrinks or expands slightly according to the temperature difference. PMID:18288226
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.
International Nuclear Information System (INIS)
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)
International Nuclear Information System (INIS)
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.
Mass inflation in Eddington-inspired Born-Infeld black holes: analytical scaling solutions
Avelino, P P
2016-01-01
We study the inner dynamics of accreting Eddington-inspired Born-Infeld black holes using the homogeneous approximation and taking charge as a surrogate for angular momentum. We show that there is a minimum of the accretion rate below which mass inflation does not occur, and we derive an analytical expression for this threshold as a function of the fundamental scale of the theory, the accretion rate, the mass, and the charge of the black hole. Our result explicitly demonstrates that, no matter how close Eddington-inspired Born-Infeld gravity is to general relativity, there is always a minimum accretion rate below which there is no mass inflation. For larger accretion rates, mass inflation takes place inside the black hole as in general relativity until the extremely rapid density variations bring it to an abrupt end. We derive analytical scaling solutions for the value of the energy density and of the Misner-Sharp mass attained at the end of mass inflation as a function of fundamental scale of the theory, the...
Analytical and Numerical Solutions of Generalized Fokker-Planck Equations - Final Report
International Nuclear Information System (INIS)
The overall goal of this project was to develop advanced theoretical and numerical techniques to quantitatively describe the spreading of a collimated beam of charged particles in space, in angle, and in energy, as a result of small deflection, small energy transfer Coulomb collisions with the target nuclei and electrons. Such beams arise in several applications of great interest in nuclear engineering, and include electron and ion radiotherapy, ion beam modification of materials, accelerator transmutation of waste, and accelerator production of tritium, to name some important candidates. These applications present unique and difficult modeling challenges, but from the outset are amenable to the language of ''transport theory'', which is very familiar to nuclear engineers and considerably less-so to physicists and material scientists. Thus, our approach has been to adopt a fundamental description based on transport equations, but the forward peakedness associated with charged particle interactions precludes a direct application of solution methods developed for neutral particle transport. Unique problem formulations and solution techniques are necessary to describe the transport and interaction of charged particles. In particular, we have developed the Generalized Fokker-Planck (GFP) approach to describe the angular and radial spreading of a collimated beam and a renormalized transport model to describe the energy-loss straggling of an initially monoenergetic distribution. Both analytic and numerical solutions have been investigated and in particular novel finite element numerical methods have been developed. In the first phase of the project, asymptotic methods were used to develop closed form solutions to the GFP equation for different orders of expansion, and was described in a previous progress report. In this final report we present a detailed description of (i) a novel energy straggling model based on a Fokker-Planck approximation but which is adapted for a
Wu, Yang; Kelly, Damien P.
2014-01-01
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 Un and Vn 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 Δρ 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 2πm/Δρ, where m is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system. PMID
Farjas, Jordi; Roura, Pere
2008-01-01
Avrami's model describes the kinetics of phase transformation under the assumption of spatially random nucleation. In this paper we provide a quasi-exact analytical solution of Avrami's model when the transformation takes place under continuous heating. This solution has been obtained with different activation energies for both nucleation and growth rates. The relation obtained is also a solution of the so-called Kolmogorov-Johnson-Mehl-Avrami transformation rate equation. The corresponding n...
Liang, Ching-Ping; Hsu, Shao-Yiu; Chen, Jui-Sheng
2016-09-01
It is recommended that an in-situ infiltration tracer test is considered for simultaneously determining the longitudinal and transverse dispersion coefficients in soil. Analytical solutions have been derived for two-dimensional advective-dispersive transport in a radial geometry in the literature which can be used for interpreting the result of such a tracer test. However, these solutions were developed for a transport domain with an unbounded-radial extent and an infinite thickness of vadose zone which might not be realistically manifested in the actual solute transport during a field infiltration tracer test. Especially, the assumption of infinite thickness of vadose zone should be invalid for infiltration tracer tests conducted in soil with a shallow groundwater table. This paper describes an analytical model for interpreting the results of an infiltration tracer test based on improving the transport domain with a bounded-radial extent and a finite thickness of vadose zone. The analytical model is obtained with the successive application of appropriate integral transforms and their corresponding inverse transforms. A comparison of the newly derived analytical solution against the previous analytical solutions in which two distinct sets of radial extent and thickness of vadose zone are considered is conducted to determine the influence of the radial and exit boundary conditions on the solute transport. The results shows that both the radial and exit boundary conditions substantially affect the trailing segment of the breakthrough curves for a soil medium with large dispersion coefficients. Previous solutions derived for a transport domain with an unbounded-radial and an infinite thickness of vadose zone boundary conditions give lower concentration predictions compared with the proposed solution at late times. Moreover, the differences between two solutions are amplified when the observation positions are near the groundwater table. In addition, we compare our
International Nuclear Information System (INIS)
Bentonite will be used as a buffer material, according to the TRU waste disposal concept in Japan, to retard radionuclides migration, to restrict seepage of ground water and to filtrate colloids. One of the concern about the buffer material is the long term alteration of bentonite with cementitious material. Long term alteration of bentonite-based materials with alkaline solution has been studied by means of analytical approaches, coupling mass transport and chemical reactions, which suggest changes in various properties of buffer materials. Long term performance assessment of engineered barriers under disposal conditions is important to achieve a reasonable design, eliminating excessive conservatism in the safety assessment. Therefore it is essential for improving the reliance of the performance assessment to verify the analytical results through alteration tests and/or natural analogue. The geochemical analyses indicate that major alteration reactions involve dissolution of portlandite, chalcedony and montmorillonite and formation of C-S-H gel and analcime at the interface between cement and bentonite. However, in the alteration tests assuming interaction between bentonite and cement, secondary minerals due to alteration under the expected condition for geological disposal (equilibrated water with cement at low liquid/solid ratio) had not been observed, though the alteration was observed under accelerated hyper alkaline and high temperatures conditions. The reason is considered that it is difficult to analyze C-S-H gel formed at the interface because of its small quantity. One of examples is the Kunigel V1, a potential buffer material in Japan, which consists of montmorillonite, chalcedony, plagioclase, and calcite. In the XRD analysis of the Kunigel V 1, the locations of the primary peak of the calcite and that of the C-S-H gel overlap, which makes identification of small quantity of C-S-H gel formed as a secondary mineral difficult. Thus development of
International Nuclear Information System (INIS)
The diffusion and distribution coefficients are important parameters in the design of barrier systems used in radioactive repositories. These coefficients can be determined using a two-reservoir configuration, where a saturated porous medium is allocated between two reservoirs filled by stagnant water. One of the reservoirs contains a high concentration of radioisotopes. The goal of this work is to obtain an analytical solution for the concentration of all radioisotopes in the decay chain of a two-reservoir configuration. The analytical solution must be obtained by taking into account the diffusion and sorption processes. Concepts such as overvalued concentration, diffusion and decay factors are employed to this end. It is analytically proven that a factor of the solution is identical for all chains (considering a time scaling factor), if certain parameters do not change. In addition, it is proven that the concentration sensitivity, due to the distribution coefficient variation, depends of the porous medium thickness, which is practically insensitive for small porous medium thicknesses. The analytical solution for the radioisotope concentration is compared with experimental and numerical results available in literature. - Highlights: • Saturated porous media allocated between two reservoirs. • Analytical solution of the isotope transport equation. • Transport considers diffusion, sorption and decay chain
International Nuclear Information System (INIS)
Bubbles in the interstellar medium are produced by astrophysical sources, which continuously or explosively deposit large amounts of energy into the ambient medium. These expanding bubbles can drive shocks in front of them, the dynamics of which is markedly different from the widely used Sedov-von Neumann-Taylor blast wave solution. Here, we present the theory of a bubble-driven shock and show how its properties and evolution are determined by the temporal history of the source energy output, generally referred to as the source luminosity law, L(t). In particular, we find the analytical solutions for a driven shock in two cases: the self-similar scaling law, L∝(t/ts ) p (with p and ts being constants) and the finite activity time case, L∝(1 – t/ts )–p. The latter with p > 0 describes a finite-time-singular behavior, which is relevant to a wide variety of systems with explosive-type energy release. For both luminosity laws, we derived the conditions needed for the driven shock to exist and predict the shock observational signatures. Our results can be relevant to stellar systems with strong winds, merging neutron star/magnetar/black hole systems, and massive stars evolving to supernovae explosions.
Single fermion Green's function in the quantum ordered Fermi-system: Analytic solution
Mukhin, S. I.; Galimzyanov, T. R.
2012-06-01
An exact self-consistent solution for a finite temperature quantum-ordered state of correlated electron system found previously (Mukhin, 2009, 2011) is used to derive the fermionic single-particle Green's function. The quantum order parameter (QOP) found in the form of a periodic (elliptic Jacoby) function of the Matsubara's imaginary time (Mukhin, 2009), plays the role of effective scattering potential seen by electrons. The analytic solution for the Green's function demonstrates the following new features: (1) the pseudo-gap behavior of the single-electron density of states (DOS) near the (shifted) Fermi-level;(2) the side-bands of decreasing intensity away from the Fermi-level; (3) scaling of the quasi-particle energies with the QOP amplitude; (4) fermionic quasi-particles in the QOP state are combined from two confined “odd” and “even” fermions that separately would be unstable. The false-color plot of single-fermion DOS in the limit of a periodic kink-like Matsubara time-dependence of QOP is presented and could be used as prediction for the ARPES experiments. The plot of the DOS transfer between different energies at the “fermi-surface” momentum for a given kink-like QOP is also presented. Some possibly observable consequences of the found finger-prints are discussed.
Analytical quality-by-design approach for sample treatment of BSA-containing solutions
Directory of Open Access Journals (Sweden)
Lien Taevernier
2015-02-01
Full Text Available 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%.
Ferrando, A
2016-01-01
We present a novel procedure to solve the Schr\\"odinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use the scattering modes, which are solutions of the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore permit to solve the problem. To construct the scattering modes one needs to obtain the $F$-polynomials, which play an analogous role than Laguerre polynomials for Laguerre-Gaussian modes. We demonstrate here the recurrence relations needed to determine the $F$-polynomials. To stress the utility and strength of the method we solve first the problem of an initial Gaussian beam with two positive singularities and a negative one embedded in. We show that the solution permits one to obtain analytical expressions. These can used to obtain closed expressions for meaningful q...
Institute of Scientific and Technical Information of China (English)
甄明; 蒋志刚; 宋殿义; 刘飞
2014-01-01
Analytical solutions for the dynamic cylindrical cavity expansion in a com-pressible elastic-plastic cylinder with a finite radius are developed by taking into account of the effect of lateral free boundary, which are different from the traditional cavity expan-sion models for targets with infinite dimensions. The finite cylindrical cavity expansion process begins with an elastic-plastic stage followed by a plastic stage. The elastic-plastic stage ends and the plastic stage starts when the plastic wave front reaches the lateral free boundary. Approximate solutions of radial stress on cavity wall are derived by using the Von-Mise yield criterion and Forrestal’s similarity transformation method. The effects of the lateral free boundary and finite radius on the radial stress on the cavity wall are discussed, and comparisons are also conducted with the finite cylindrical cavity expansion in incompressible elastic-plastic materials. Numerical results show that the lateral free boundary has significant influence on the cavity expansion process and the radial stress on the cavity wall of metal cylinder with a finite radius.
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
Institute of Scientific and Technical Information of China (English)
Fang-fang LI; Jing LIU; Kai YUE
2009-01-01
Analytically solving a three-dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temper-ature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.
International Nuclear Information System (INIS)
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
Ferrando, A.; García-March, M. A.
2016-06-01
We present a novel procedure for solving the Schrödinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use scattering modes, which are solutions to the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore allow the problem to be solved. To construct the scattering modes one needs to obtain a particular set of polynomials, which play an analogous role to Laguerre polynomials for Laguerre–Gaussian modes. We demonstrate here the recurrence relations needed to determine these polynomials. To stress the utility and strength of the method we solve first the problem of an initial Gaussian beam with two positive singularities and a negative one embedded in it. We show that the solution permits one to obtain analytical expressions. These can used to obtain mathematical expressions for meaningful quantities, such as the distance at which the positive and negative singularities merge, closing the loop of a vortex line. Furthermore, we present an example of the calculation of an specific discrete-Gauss state, which is the solution of the diffraction of a Laguerre–Gauss state showing definite angular momentum (that is, a highly charged vortex) by a thin diffractive element showing certain discrete symmetry. We show that this problem is therefore solved in a much simpler way than by using the previous procedure based on the integral Fresnel diffraction method.
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.
International Nuclear Information System (INIS)
A new analytical, one dimensional method to obtain the induced current shapes and simulation of chasrge shapes for p+ -n-n+ silicon detectors in the case of minimum ionization particle has been developed here. jExact solutions have been found for both electron and hole current shapes. Simulations of induced charge shapes of detectors have also been given. The results of this work are consistent with the earlier work where a semi-analytical method had been used
Sameer M. Ikhdair; Sever, Ramazan
2009-01-01
We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. In the framework of the spin and pseudospin symmetry concept, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of the two Dirac particles are obtained, in closed form, by means of the Nikiforov-Uvarov method which is based on solving the second-order linear differential equation by re...
Grossman, P D; Colburn, J C; Lauer, H H; Nielsen, R G; Riggin, R M; Sittampalam, G S; Rickard, E C
1989-06-01
The application of free solution capillary electrophoresis (FSCE) to the separation of protein and peptide mixtures is presented. Both qualitative and quantitative aspects of FSCE separations are considered. In addition, a brief introduction describing the separation principle behind FSCE separations and a discussion of electrophoretic mobility are included. The applications were chosen in order to highlight the selectivity of FSCE separations and to demonstrate applications of potential practical interest to the bioanalytical chemist. Comparison of FSCE relative to traditional analytical separation alternatives is stressed throughout. The examples are presented in three broad categories: protein separations, peptide separations, and the application of both to the analysis of recombinant protein products. In the first section, FSCE separations of peptide mixtures are presented which demonstrate the suitability of FSCE for the analysis of the purity of peptide samples, the homogeneity of peptide samples prior to sequencing, the identity of peptides by using electrophoretic mobility values, and the reduction of an intrachain disulfide bridge. In the second section, protein separations are presented that show the resolution of glycoproteins having the same primary structure and the separation of immune complexes from free unreacted antibody and antigen. In the final section, highly purified and well-characterized samples of biosynthetic human insulin (BHI), biosynthetic human growth hormone (hGH), and their derivatives were used to evaluate FSCE as a complement and/or alternative to conventional analytical separation techniques for the determination of purity and identity of biosynthetic human proteins. In addition, the quantitative aspects of FSCE analysis such as linearity of response, precision, and limit of detection were examined. PMID:2757205
Koonprasert, Sanoe; Sangsawang, Rilrada
2008-09-01
This paper presents the analytical solutions and symbolic computations for the temperature distribution of the annular fin under fully-wet surface condition. During the process of dehumidification, the annular fin is separated into two regions. The mathematical models for each region are based on the conservation of energy principle. An assumption used in this paper is the humidity ratio of the saturated air on the wet surface varies linearly with the local fin temperature. The mathematical models are solved by the Cauchy-Euler Equation and modified Bessel Equation to form analytical solutions. Besides, the symbolic computations are shown by the Maple software to visualize the temperature distribution along the fin.
Iasiello, Marcello; Vafai, Kambiz; Andreozzi, Assunta; Bianco, Nicola
2016-01-25
An analytical solution for Low-Density Lipoprotein transport through an arterial wall under hyperthermia conditions is established in this work. A four-layer model is used to characterize the arterial wall. Transport governing equations are obtained as a combination between Staverman-Kedem-Katchalsky membrane equations and volume-averaged porous media equations. Temperature and solute transport fields are coupled by means of Ludwig-Soret effect. Results are in excellent agreement with numerical and analytical literature data under isothermal conditions, and with numerical literature data for the hyperthermia case. Effects of hypertension combined with hyperthermia, are also analyzed in this work. PMID:26806687
A Three-Dimensional Analytical Solution for the Study of Air Pollutant Dispersion in a Finite Layer
Marie, Ema'a. Ema'a. Jean; Hubert, Ben-Bolie Germain; Patrice, Ele Abiama; Zarma, Ali; Pierre, Owono Ateba
2015-05-01
We present a closed-form analytical solution for the advection-diffusion equation, where the planetary boundary layer is divided into subdomains, where in each subdomain averaged values of eddy diffusivity and wind speed are assumed. The solution procedure combines an appropriate auxiliary eigenvalue problem with mathematical induction. A transcendental equation giving the eigenvalues for any numbers of subdomains is also developed. Convergence of the solution is numerically verified. The solution is used to evaluate the model against the Copenhagen experiment and computed results are in agreement with experimental ones.
International Nuclear Information System (INIS)
An analytical model for solute advection and dispersion in a two-layered liner consisting of a geosynthetic clay liner (GCL) and a soil liner (SL) considering the effect of biodegradation was proposed. The analytical solution was derived by Laplace transformation and was validated over a range of parameters using the finite-layer method based software Pollute v7.0. Results show that if the half-life of the solute in GCL is larger than 1 year, the degradation in GCL can be neglected for solute transport in GCL/SL. When the half-life of GCL is less than 1 year, neglecting the effect of degradation in GCL on solute migration will result in a large difference of relative base concentration of GCL/SL (e.g., 32% for the case with half-life of 0.01 year). The 100-year solute base concentration can be reduced by a factor of 2.2 when the hydraulic conductivity of the SL was reduced by an order of magnitude. The 100-year base concentration was reduced by a factor of 155 when the half life of the contaminant in the SL was reduced by an order of magnitude. The effect of degradation is more important in approving the groundwater protection level than the hydraulic conductivity. The analytical solution can be used for experimental data fitting, verification of complicated numerical models and preliminary design of landfill liner systems. - Highlights: •Degradation of contaminants was considered in modeling solute transport in GCL/SL. •Analytical solutions were derived for assessment of GCL/SL with degradation. •Degradation in GCL can be ignored as half-life is larger than 1 year. •Base concentration is more sensitive to half-life of SL than to permeability of SL
Indian Academy of Sciences (India)
Atul Kumar; Dilip Kumar Jaiswal; Naveen Kumar
2009-10-01
Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal ﬁnite initially solute free domain,for two dispersion problems.In the ﬁrst one,temporally dependent solute dispersion along uniform ﬂow in homogeneous domain is studied.In the second problem the velocity is considered spatially dependent due to the inhomogeneity of the domain and the dispersion is considered proportional to the square of the velocity. The velocity is linearly interpolated to represent small increase in it along the ﬁnite domain.This analytical solution is compared with the numerical solution in case the dispersion is proportional to the same linearly interpolated velocity.The input condition is considered continuous of uniform and of increasing nature both.The analytical solutions are obtained by using Laplace transformation technique.In that process new independent space and time variables have been introduced. The effects of the dependency of dispersion with time and the inhomogeneity of the domain on the solute transport are studied separately with the help of graphs.
International Nuclear Information System (INIS)
In this work, we report a genuine general analytical solution for the linearized SN radiative-conductive transfer problem in a heterogeneous plane parallel atmosphere with the albedo coefficient depending continuously on the spatial variable. By general solution, we mean that the solution is valid for an arbitrary albedo coefficient continuous functions of the spatial variable having the property of fulfill the requirements of existence and uniqueness. The key feature of this novel approach embodies the steps: following the idea of the Decomposition method, we transform the original problem into a set of recursive problems with constant albedo coefficients, having the main feature that the sources terms takes the information of the spatial dependency of the albedo coefficient into account. This procedure allows us to solve, analytically, the resulting recursive system by the LTSN method developed for a constant albedo coefficient. Finally, we present the error control analysis of the solution and numerical comparisons against the literature results.
Energy Technology Data Exchange (ETDEWEB)
Babakhani, D. [Department of Chemical Engineering, Faculty of Engineering, University of Isfahan (Iran, Islamic Republic of)
2009-12-15
An analytical solution of simultaneous heat and mass transfer processes in a packed bed liquid desiccant dehumidifier/regenerator is developed. Various dimensionless parameters and reliable assumptions are used in order to develop this solution. The outlet parameters predicted with the analytical solution show very good agreement with the experimental data available in the literature. The results show that using a Lewis number value of Le=1.1 instead of Le=1 gives a better prediction of the performance of the dehumidifier. In addition, the use of Le=0.9 instead of Le=1 can give a better prediction of the outlet parameters of the regenerator. The benefits of the present solution are its simplicity and easy application for the simulation of air dehumidification and liquid desiccant regeneration processes. (Abstract Copyright [2009], Wiley Periodicals, Inc.)
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.
An analytical solution to time-dependent fission-product diffusion in an HTGR core
International Nuclear Information System (INIS)
An analytical time-dependent fission-product diffusion model is solved for the fuel-moderator regions of a high temperature gas-cooled reactor (HTGR) during a hypothetical loss of forced circulation (LOFC) accident. A conservative approximate 1-D model is developed for the fuel and moderator regions, represented in cylindrical and slab geometries, from consideration of the hexagonal fuel-element symmetry. Transport is assumed along the shortest diffusion path and the concentration change across the fuel-moderator interface is approximated by a jump condition. The model is solved by construction of the Green's functions for the Laplace-transformed equations and identification of the pole structure. The concentration and current inverse Laplace transforms are obtained by the Cauchy residue theorem in each region for cubic piecewise polynomial initial conditions. A computer program was developed and validated to evaluate the solution, serve as a benchmark for more sophisticated numerical models and to investigate 90Sr diffusion during a hypothetical LOFC. (author)
International Nuclear Information System (INIS)
The electromagnetic concentrative coils are indispensable in the functional magnetic stimulation and have potential applications in nondestructive testing. In this paper, we propose a figure-8-shaped coil being composed of two arbitrary oblique elliptical coils, which can change the electromagnetic concentrative region and the magnitude of eddy current density by changing the elliptical shape and/or spread angle between two elliptical coils. Pulsed current is usually the excitation source in the functional magnetic stimulation, so in this paper we derive the analytical solutions of transient pulsed eddy current field in the time domain due to the elliptical concentrative coil placed in an arbitrary position over a half-infinite plane conductor by making use of the scale-transformation, the Laplace transform and the Fourier transform are used in our derivation. Calculation results of field distributions produced by the figure-8-shaped elliptical coil show some behaviours as follows: 1) the eddy currents are focused on the conductor under the geometric symmetric centre of figure-8-shaped coil; 2) the greater the scale factor of ellipse is, the higher the eddy current density is and the wider the concentrative area of eddy current along y axis is; 3) the maximum magnitude of eddy current density increases with the increase of spread angle. When spread angle is 180°, there are two additional reverse concentrative areas on both sides of x axis. (general)
Analytical and numerical solution along with PC spreadsheets modeling for a composite fin
Mokheimer, E. M. A.; Antar, M. A.; Farooqi, J.; Zubair, S. M.
Heat transfer through composite fins is investigated by both analytical and numerical methods. In this regard, governing differential equations of the two dimensional fin and one dimensional cladding are studied to examine the effect of Biot number and ratio of thermal conductivities of the fin material to the cladding, on the dimensionless temperature profiles. The results show that one dimensional analysis, traditionally used in fin analysis, is not applicable for composite fins, particularly when the conductivity ratio of the composite fin materials is low. In addition, the use of spreadsheet programs in solving the fin problem is investigated in somewhat more detail with regard to the solution as well as presentation of the graphical results. Zusammenfassung Die Wärmeabfuhr durch Kompositrippen wird sowohl analytisch, als auch numerisch untersucht, wobei die Rippe selbst als zweidimensionales, die Umhüllung als eindimensionales Gebiet den Differentialgleichungen der Wärmeleitung zugrunde gelegt werden. Dem Einfluß der Biot-Zahl und des Verhältnisses der Wärmeleitfähigkeiten von Rippen- und Umhüllungsmaterial auf die dimensionslosen Temperaturprofile gilt besonderes Interesse. Die Ergebnisse zeigen, daß die übliche eindimensionale Rippentheorie bei Kompositrippen nicht hinreicht, besonders wenn das Verhältnis der Leitfähigkeiten beider Materialien niedrig ist. Die Methode der Tabellenberechnung wird besonders eingehend behandelt und zwar sowohl mit Blick auf die Lösung, wie auch die graphische Darstellung der Ergebnisse.
An analytic solution to LO coupled DGLAP evolution equations: a new pQCD tool
Block, Martin M; Ha, Phuoc; McKay, Douglas W
2010-01-01
We have analytically solved the LO pQCD singlet DGLAP equations using Laplace transform techniques. Newly-developed highly accurate numerical inverse Laplace transform algorithms allow us to write fully decoupled solutions for the singlet structure function F_s(x,Q^2)and G(x,Q^2) as F_s(x,Q^2)={\\cal F}_s(F_{s0}(x), G_0(x)) and G(x,Q^2)={\\cal G}(F_{s0}(x), G_0(x)). Here {\\cal F}_s and \\cal G are known functions of the initial boundary conditions F_{s0}(x) = F_s(x,Q_0^2) and G_{0}(x) = G(x,Q_0^2), i.e., the chosen starting functions at the virtuality Q_0^2. For both G and F_s, we are able to either devolve or evolve each separately and rapidly, with very high numerical accuracy, a computational fractional precision of O(10^{-9}). Armed with this powerful new tool in the pQCD arsenal, we compare our numerical results from the above equations with the published MSTW2008 and CTEQ6L LO gluon and singlet F_s distributions, starting from their initial values at Q_0^2=1 GeV^2 and 1.69 GeV^2, respectively, using their ...
Dodin, Amro; Brumer, Paul
2015-01-01
We present closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter $\\zeta=\\frac{1}{2}(\\gamma_1+\\gamma_2)/\\Delta_p$, where $\\gamma_i$ are the radiative decay rates of the excited levels $i=1,2$, and $\\Delta_p=\\sqrt{\\Delta^2 + (1-p^2)\\gamma_1\\gamma_2}$ depends on the excited-state level splitting $\\Delta>0$ and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit ($\\zeta\\gg1$), approach a long-lived quasi-steady state in the overdamped limit ($\\zeta\\ll 1$), and display an intermediate behavior at critical damping ($\\zeta= 1$). The sudden incoherent turn-on generat...
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. PMID:24815259
Institute of Scientific and Technical Information of China (English)
ZHAO Cun-bao; ZHANG Jia-zhong; XING Hai-yan; HUANG Wen-hu
2007-01-01
Based on the dynamic theories of water waves and Mindlin plates,the analytic solution of interaction between surface waves and two-dimensional floating elastic plates with edge-restraint is constructed by use of the Wiener-Hopf technique.Firstly,without regard for elastic edge restraint,the wave-induced responses of elastic floating plate analyzed by the present method are in good agreement with the results from literature and experimental results.Therefore,it can be shown that the present method is valid.Secondly,three end-restraint cases (i.e.,the left-end elastic restraints,the both-end elastic restraints,and the right-end elastic restraints) are proposed to reduce the vibration of floating plates,in which the spring is used to connect the sea bottom and the floating plate's left (or right) edge.The relations between the spring stiffness and the parameters of wave-induced responses of floating plates are discussed.Moreover,the effective method to reduce the vibration of floating elastic plates can be obtained through comparison.
Xu, C.; Mudunuru, M. K.; Nakshatrala, K. B.
2016-06-01
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 solution for the lubrication force between two spheres in a bi-viscous fluid
Vázquez-Quesada, A.; Ellero, M.
2016-07-01
An analytical solution for the calculation of the normal lubrication force acting between two moving spheres embedded in a shear-thinning fluid represented by a bi-viscous model is provided. The resulting force between the suspended spheres exhibits a consistent transition between the Newtonian constant-viscosity limits and it reduces to the well-known standard Newtonian lubrication theory for viscosity-ratio approaching one. Effects of several physical parameters of the theory are analyzed under relevant physical conditions, i.e., for a prototypical case of two non-colloidal spheres immersed in a non-Newtonian fluid with rheology parameterized by a bi-viscosity model. Topological results for high/low-viscosity regions in the gap between spheres are also analyzed in detail showing a rich phenomenology. The presented model enables the extension of lubrication dynamics for suspensions interacting with non-Newtonian matrices and provides a clean theoretical framework for new numerical computations of flow of dense complex particulate systems.
An analytical solution of the gyrokinetic equation for the calculation of neoclassical effects
Casolari, Andrea
2016-01-01
The purpose of this document is to find an analytical solution for the gyrokinetic equation under specific, simplificative hypotheses. The case I am considering is that of a collisional plasma in the presence of a chain of magnetic islands. The presence of the magnetic islands causes the onset of perturbative fields, in particular an electrostatic field, with a gradient length-scale comparable with the island's width. When the island's width w becomes comparable with the ion Larmor radius rho_i , the drift-kinetic equation is inadequate to treat the transport and the calculation of the neoclassical effects. Nevertheless, I'm going to solve the equation with the methods described by S. P. Hirshman and D. J. Sigmar in the review paper "Neoclassical transport of impurities in tokamak plasmas", which was developed to solve the drift-kinetic equation in different regimes of collisionality. I'm going to remind first the drift-kinetic theory, which was largely used to study classical and neoclassical transport in ma...
Marcello Romano
2012-01-01
New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial ...
The Ray Tracing Analytical Solution within the RAMOD framework. The case of a Gaia-like observer
Crosta, Mariateresa; Vecchiato, Alberto; Felice, Fernando; Lattanzi, Mario Gilberto
2015-01-01
This paper presents the analytical solution of the inverse ray tracing problem for photons emitted by a star and collected by an observer located in the gravitational field of the Solar System. This solution has been conceived to suit the accuracy achievable by the ESA Gaia satellite (launched on December 19, 2013) consistently with the measurement protocol in General relativity adopted within the RAMOD framework. Aim of this study is to provide a general relativistic tool for the science exp...
Hu, Huayu
2015-01-01
Nonperturbative calculation of QED processes participated by a strong electromagnetic field, especially provided by strong laser facilities at present and in the near future, generally resorts to the Furry picture with the usage of analytical solutions of the particle dynamical equation, such as the Klein-Gordon equation and Dirac equation. However only for limited field configurations such as a plane-wave field could the equations be solved analytically. Studies have shown significant interests in QED processes in a strong field composed of two counter-propagating laser waves, but the exact solutions in such a field is out of reach. In this paper, inspired by the observation of the structure of the solutions in a plane-wave field, we develop a new method and obtain the analytical solution for the Klein-Gordon equation and equivalently the action function of the solution for the Dirac equation in this field, under a largest dynamical parameter condition that there exists an inertial frame in which the particl...
Time-domain analytic solutions of two-wire transmission line excited by a plane-wave field
International Nuclear Information System (INIS)
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)
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 ove
Directory of Open Access Journals (Sweden)
I. S. Kulikov
2014-11-01
Full Text Available The paper considers specific features of a stress-strain state of structure elements which have cylindrical form and which are subjected to the high temperature field, neutron irradiation. An analytical solution concerning displacement and stress dependences on a cylinder radius has been obtained and curve dependences have been constructed in the paper..
Analytical Solutions of the Fokker-Planck Equation for Generalized Morse and Hulthén Potentials
Anjos, R. C.; Freitas, G. B.; Coimbra-Araújo, C. H.
2016-01-01
In the present contribution we analytically calculate solutions of the transition probability of the Fokker-Planck equation (FPE) for both the generalized Morse potential and the Hulthén potential. The method is based on the formal analogy of the FPE with the Schrödinger equation using techniques from supersymmetric quantum mechanics.
Institute of Scientific and Technical Information of China (English)
XING Yong-Zhong
2009-01-01
The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.
Sakamoto, Noboru; Schaft, Arjan J. van der
2007-01-01
In this paper, an analytical approximation approach for the stabilizing solution of the Hamilton-Jacobi equation using stable manifold theory is proposed. The proposed method gives approximated flows on the stable manifold of the associated Hamiltonian system and provides approximations of the stabl
Energy Technology Data Exchange (ETDEWEB)
Cui Yi; Huo Yongzhong [Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433 (China); Ding Shurong, E-mail: dsr1971@163.com [Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433 (China) and Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institution of China, Chengdu 610041, Sichuan (China); Zhang Lin; Li Yuanming [Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institution of China, Chengdu 610041, Sichuan (China)
2012-05-15
An analytical solution of gas concentration for the equivalent spherical grain is obtained first in Laplace space, then the inverse-Laplace transformed solution is further developed. The corresponding analytical expressions for the grain boundary gaseous swelling and the fission gas release in UO{sub 2} nuclear fuels are developed in the absence of grain growth. The following phenomena and assumptions are taken into account in our model, including the gas atom diffusion, saturation and the time-varying piece-wise inter-granular resolution. The explicit expression for saturation time of the grain boundary gas atoms is also obtained. Our approximated analytical solutions for the fission gas behaviors are validated through comparison with those solved by finite difference method. Good agreement has been achieved for the cases with different input parameters. Based on the developed analytical solutions, the effects of the grain sizes and the external pressure on the fission gas behaviors are investigated. This study lays a foundation for the multi-scale simulation of the thermo-mechanical behaviors in nuclear fuel elements.
International Nuclear Information System (INIS)
An analytical solution of gas concentration for the equivalent spherical grain is obtained first in Laplace space, then the inverse-Laplace transformed solution is further developed. The corresponding analytical expressions for the grain boundary gaseous swelling and the fission gas release in UO2 nuclear fuels are developed in the absence of grain growth. The following phenomena and assumptions are taken into account in our model, including the gas atom diffusion, saturation and the time-varying piece-wise inter-granular resolution. The explicit expression for saturation time of the grain boundary gas atoms is also obtained. Our approximated analytical solutions for the fission gas behaviors are validated through comparison with those solved by finite difference method. Good agreement has been achieved for the cases with different input parameters. Based on the developed analytical solutions, the effects of the grain sizes and the external pressure on the fission gas behaviors are investigated. This study lays a foundation for the multi-scale simulation of the thermo-mechanical behaviors in nuclear fuel elements.
International Nuclear Information System (INIS)
This report describes the practical methods for analyzing of Tellurium content in Na131I solution produced at the Dalat Nuclear Research Institute. We studied analytical methods to control Tellurium content in final Na131I solution product used in medical purposes by three methods such as: spot test, gamma spectrometric and spectrophotometric methods. These investigation results are shown that the spot test method is suitable for controlling Tellurium trace in the final product. This spot test can be determinate Tellurium trace less than 10 ppm and are used to quality control of Na131I solution using in medical application. (author)
International Nuclear Information System (INIS)
We construct explicit multisoliton complex solutions for multicomponent Bose–Einstein condensate systems with time- and spatial-coordinate-dependent atomic potentials and interactions. The exact solutions are used to analyze the important solitary matter wave properties such as the profiles of temporal and spatial multimode beams as well as focusing effects. Results demonstrate that soliton complexes can be controlled nonlinearly during the interaction by modulating the external potentials and nonlinearities. - Highlights: • An algebraic approach is proposed for the dynamics of multicomponent BECs. • External potentials and nonlinearities are time and space-dependent. • Analytical solutions are constructed. • Multisoliton complexes are predicted
Energy Technology Data Exchange (ETDEWEB)
Chen, Jun, E-mail: chenjun.sun@gmail.com; Liu, Yun-xian, E-mail: liuyx@cjlu.edu.cn
2014-09-05
We construct explicit multisoliton complex solutions for multicomponent Bose–Einstein condensate systems with time- and spatial-coordinate-dependent atomic potentials and interactions. The exact solutions are used to analyze the important solitary matter wave properties such as the profiles of temporal and spatial multimode beams as well as focusing effects. Results demonstrate that soliton complexes can be controlled nonlinearly during the interaction by modulating the external potentials and nonlinearities. - Highlights: • An algebraic approach is proposed for the dynamics of multicomponent BECs. • External potentials and nonlinearities are time and space-dependent. • Analytical solutions are constructed. • Multisoliton complexes are predicted.
Analytic Solution to the Problem of Aircraft Electric Field Mill Calibration
Koshak, William
2003-01-01
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 M(sub ix), E(sub x), is the contribution of the E(sub x) field to the i(th) mill output. Similarly, net aircraft charge (described by a "charge field component" E(sub q)) contributes an amount M(sub iq)E(sub q) to the output of the i(th) sensor. The central difficulty in obtaining M stems from the fact that the impressed field (E(sub x), E(sub y), E(sub z), E(sub q) 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. Unfortunately, none of the iterative methods guarantee absolute convergence to correct values (i.e., absolute convergence to correct values has not been rigorously proven). 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 possible to solve for a single 2m
Energy Technology Data Exchange (ETDEWEB)
Gunes, Hasan [Department of Mechanical Engineering, Istanbul Technical University, Gumussuyu (Turkey)
2003-12-01
In this study, we derive analytical expressions describing the variation of field variables in steady, 2-D and 3-D natural convection in a vertical channel with discrete in-space, flush-mounted heat sources. The expressions are valid for sufficiently small Grasof numbers. The solution are governed by the following dimensionless parameters: aspect ratios defining the geometry of the problem, Prandtl number, Grashof number and dimensionless channel reference temperature. Test case solutions are obtained numerically to assess the accuracy of the derived expressions. For small values Gr, the derived expressions are in excellent agreement with the numerical solutions in the entire computational domain. Analytical expressions for the net volume flow rate through the channel and Nusselt number variation are also given. (orig.)
Bulusu, Jayashree; Sinha, A. K.; Vichare, Geeta
2016-06-01
An analytic solution has been formulated to study the role of ionospheric conductivity on toroidal field line oscillations in the Earth's magnetosphere. The effect of ionospheric conductivity is addressed in two limits, viz, (a) when conductance of Alfvén wave is much different from ionospheric Pedersen conductance and (b) when conductance of Alfvén wave is close to the ionospheric Pedersen conductance. In the former case, the damping is not significant and standing wave structures are formed. However, in the latter case, the damping is significant leading to mode translation. Conventionally, "rigid-end" and "free-end" cases refer to eigenstructures for infinitely large and vanishingly small limit of ionospheric conductivity, respectively. The present work shows that when the Pedersen conductance overshoots (undershoots) the Alfvén wave conductance, a free-end (rigid-end) mode gets transformed to rigid-end (free-end) mode with an increase (decrease) in harmonic number. This transformation takes place within a small interval of ionospheric Pedersen conductance around Alfvén wave conductance, beyond which the effect of conductivity on eigenstructures of field line oscillations is small. This regime of conductivity limit (the difference between upper and lower limits of the interval) decreases with increase in harmonic number. Present paper evaluates the damping effect for density index other than the standard density index m = 6, using perturbation technique. It is found that for a small departure from m = 6, both mode frequency and damping rate become a function of Pedersen conductivity.
International Nuclear Information System (INIS)
Several numerical and analytical solutions of the radiative transfer equation (RTE) were compared for plane albedo in a problem of solar light reflection by sea water. The study incorporated the simplest case-a semi-infinite one-dimensional plane-parallel absorbing and scattering homogeneous layer illuminated by a monodirectional light beam. Inelastic processes (such as Raman scattering and fluorescence), polarization and air-water surface refraction-reflection effects, were not considered. Algorithms were based on the invariant imbedding method and two different variants of the discrete ordinate method (DOM). Calculations were performed using parameters across all possible ranges (single-scattering albedo ω0 and refracted solar zenith angle θ1), but with a special emphasis on natural waters. All computations were made for two scattering phase functions, which included an almost isotropic Rayleigh phase function and strongly anisotropic double-peaked Fournier-Forand-Mobley phase function. Models were validated using quasi-single-scattering (QSSA) and exponential approximations, which represent the extreme cases of ω0→0 and ω0→1, respectively. All methods yielded relative differences within 1.8% for modeled natural waters. An analysis of plane albedo behavior resulted in the development of a new extended QSSA approximation, which when applied in conjunction with the extended Hapke approximation developed earlier, resulted in a maximum relative error of 2.7%. The study results demonstrated that for practical applications, the estimation of inherent optical properties from observed reflectance can best be achieved using an extended Hapke approximation.
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 new 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 clear advantages over available alternatives, including: (i) the new solutions were derived from a complete physical-mathematical description of the system, rather than based on an ad hoc formulation; (ii) the new 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.
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.
Abundant soliton solutions for the coupled Schrödinger-Boussinesq system via an analytical method
Manafian, Jalil; Aghdaei, Mehdi Fazli
2016-04-01
In this paper, the improved tan(Φ(ξ)/2)-expansion method is proposed to find the exact soliton solutions of the coupled Schrödinger-Boussinesq (SB) system. The exact particular solutions are of five types: hyperbolic function solution (exact soliton wave solution), trigonometric function solution (exact periodic wave solution), rational exponential solution (exact singular kink-type wave solution), logarithmic solution and rational solution (exact singular cupson wave solution). We obtained the further solutions comparing with other methods. The results demonstrate that the new tan(Φ(ξ)/2)-expansion method is more efficient than the Ansatz method applied by Bilige et al. (2013). Recently this method was developed for searching the exact travelling-wave solutions of nonlinear partial differential equations. Abundant exact travelling-wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play an important role in Laser and plasma. It is shown that this method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving the nonlinear problems.
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.
Romano, Marcello
2008-08-01
New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes’ theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a “virtual” spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this “virtual” body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.
Dodin, Amro; Tscherbul, Timur V; Brumer, Paul
2016-06-28
Closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath, relevant to light harvesting processes, are obtained and discussed. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter ζ=12(γ1+γ2)/Δp, where γi are the radiative decay rates of the excited levels i = 1, 2, and Δp=Δ(2)+(1-p(2))γ1γ2 depends on the excited-state level splitting Δ > 0 and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit (ζ ≫ 1), approach a long-lived quasi-steady state in the overdamped limit (ζ ≪ 1), and display an intermediate behavior at critical damping (ζ = 1). The sudden incoherent turn-on is shown to generate a mixture of excited eigenstates |e1〉 and |e2〉 and their in-phase coherent superposition |ϕ+〉=1r1+r2(r1|e1〉+r2|e2〉), which is remarkably long-lived in the overdamped limit (where r1 and r2 are the incoherent pumping rates). Formation of this coherent superposition enhances the decay rate from the excited states to the ground state. In the strongly asymmetric V-system where the coupling strengths between the ground state and the excited states differ significantly, additional asymptotic quasistationary coherences are identified, which arise due to slow equilibration of one of the excited states. Finally, we demonstrate that noise-induced Fano coherences are maximized with respect to populations when r1 = r2 and the transition dipole moments are fully aligned. PMID:27369498
Dodin, Amro; Tscherbul, Timur V.; Brumer, Paul
2016-06-01
Closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath, relevant to light harvesting processes, are obtained and discussed. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter ζ = /1 2 ( γ 1 + γ 2) / Δ p , where γi are the radiative decay rates of the excited levels i = 1, 2, and Δ p = √{ Δ 2 + ( 1 - p 2) γ 1 γ 2 } depends on the excited-state level splitting Δ > 0 and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit (ζ ≫ 1), approach a long-lived quasi-steady state in the overdamped limit (ζ ≪ 1), and display an intermediate behavior at critical damping (ζ = 1). The sudden incoherent turn-on is shown to generate a mixture of excited eigenstates |e1> and |e2> and their in-phase coherent superposition | ϕ + > = /1 √{ r 1 + r 2 } ( √{ r 1 } | e 1 > + √{ r 2 } | e 2 >) , which is remarkably long-lived in the overdamped limit (where r1 and r2 are the incoherent pumping rates). Formation of this coherent superposition enhances the decay rate from the excited states to the ground state. In the strongly asymmetric V-system where the coupling strengths between the ground state and the excited states differ significantly, additional asymptotic quasistationary coherences are identified, which arise due to slow equilibration of one of the excited states. Finally, we demonstrate that noise-induced Fano coherences are maximized with respect to populations when r1 = r2 and the transition dipole moments are fully aligned.
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...
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R. K.
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 tec......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...... 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...
Analytic solutions for thermal conduction from heat producing cylinders and spheres
International Nuclear Information System (INIS)
Solution methods are developed to determine the temperature fields surrounding time dependent, cylindrical or spherical heat sources located in an infinite or semi-infinite medium. The method of superposition is employed to extend the single source solutions to the case of multiple heat sources. Numerical procedures are developed to efficiently evaluate the integral heat source solutions. Two computer programs based on the solution procedure are described. Complete user instructions and example problems for these programs are presented
Chen, Yunmin; Xie, Haijian; Ke, Han; Chen, Renpeng
2009-09-01
An analytical solution for one-dimensional contaminant diffusion through multi-layered media is derived regarding the change of the concentration of contaminants at the top boundary with time. The model accounts for the arbitrary initial conditions and the conditions of zero concentration and zero mass flux on the bottom boundary. The average degree of diffusion of the layered system is introduced on the basis of the solution. The results obtained by the presented analytical solutions agree well with those obtained by the numerical methods presented in the literature papers. The application of the analytical solution to the problem of landfill liner design is illustrated by considering a composite liner consisting of geomembrane and compacted clay liner. The results show that the 100-year mass flux of benzene at the bottom of the composite liner is 45 times higher than that of acetone for the same composite liner. The half-life of the contaminant has a great influence on the solute flux of benzene diffused into the underlying aquifer. Results also indicates that an additional 2.9-5.0 m of the conventional (untreated) compacted clay liner under the geomembrane is required to achieve the same level of protection as provided by 0.60 m of the Hexadecyltrimethylammonium (HDTMA)-treated compacted clay liners in conjunction with the geomembrane. Applications of the solution are also presented in the context of a contaminated two-layered media to demonstrate that different boundary and initial conditions can greatly affect the decontamination rate of the problem. The method is relatively simple to apply and can be used for performing equivalency analysis of landfill liners, preliminary design of groundwater remediation system, evaluating experimental results, and verifying more complex numerical models.
International Nuclear Information System (INIS)
A non-dissipative drift kinetic simulation scheme, which rigorously satisfies the time-reversibility, is applied to the three-mode coupling problem of the ion temperature gradient (ITG) instability. It is found from the simulation that the three-mode ITG system repeats growth and decay with a period which shows a logarithmic divergence for infinitesimal initial perturbations. Accordingly, time average of the mode amplitude vanishes, as the initial amplitude approaches to zero. An exact solution is analytically given for a class of initial conditions. An excellent agreement is confirmed between the analytical solution and numerical results. The results obtained here provide a useful reference for basic benchmarking of theories and simulation of the ITG modes. (author)
International Nuclear Information System (INIS)
Analytical solution of transverse shear strain vibration of a tube caused by internal gaseous detonation near the second critical speed (shear group velocity) is not reported in the literature. It is performed based on a steady state model and first order shear deformation theories (model I and II) in this paper, and the results are verified through comparison with the finite element results reported in the literature. There are no known experimental ways of directly measuring dynamic transverse shear strain and only theoretical results and numerical data are available. The finite element method is very time consuming compared with the analytical solution. It is shown in this paper that the resonance phenomenon of the transverse shear strain vibration near the second critical speed can be predicted by steady state model and first order shear deformation theories. The first order shear deformation theory (model II) has a good agreement with finite element results in prediction of dynamic amplification factors and critical speeds.
Yovanovich, M. M.; Culham, J. R.; Lemczyk, T. F.
1986-01-01
One and two-dimensional solutions are obtained for annular fins of constant cross-section having uniform base, end and side conductances. The solutions are dependent upon one geometric parameter and three fin parameters which relate the internal conductive resistance to the three boundary resistances. The two and one-dimensional solutions are compared by means of the heat flow rate or fin efficiency ratios. Simple polynomials are developed for fast, accurate numerical computation of the modified Bessel functions which appear in the solutions. For annular fins used in typical microelectronic applications the analytical expressions are also reduced to alternate expressions which are shown to be expressible by means of simple polynomials which converge to unity for large values of the arguments. Numerical computations were performed on an IBM-PC and some typical results are reported in graphical form. These plots give the heat loss ratio as a function of the dimensionless geometric and fin parameters.
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. PMID:26284787
Directory of Open Access Journals (Sweden)
Ashlee N Ford Versypt
Full Text Available 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.
DEFF Research Database (Denmark)
Andriollo, Tito; Thorborg, Jesper; Hattel, Jesper Henri
2016-01-01
In the present paper, for the first time in literature an exact analytical solution to Lemaitre's isotropic damage model is developed for the special case of uniaxial tensile testing. This is achieved by taking advantage of a convenient formulation of the isotropic hardening function, which allows...... optimization, as all issues associated with classical numerical solution procedures of the constitutive equations are eliminated. In addition, an implicit implementation of the plane stress projected version of Lemaitre's model is discussed, showing that the resulting algebraic system can be reduced to a...
Directory of Open Access Journals (Sweden)
K. S. Adegbie
2007-01-01
Full Text Available We examine steady incompressible flow of viscous liquids between parallel heated walls of plane Couette device. The temperature of the upper and lower walls of the device are maintained at T = Tb and T = T0 respectively. Of a particular interest are exact analytical solutions of the coupled non-linear differential equations resulting from plane Couette flow obtained for the temperature and velocity distributions respectively. The criterion for which the solutions are valid was determined by the temperature difference, Î±, between the upper and lower walls. The analysis reveals that the shear stress obtained at the walls exists when the temperature difference α> 0.
He, Xiaolong; de la Llave, Rafael
2016-08-01
We construct analytic quasi-periodic solutions of a state-dependent delay differential equation with quasi-periodically forcing. We show that if we consider a family of problems that depends on one dimensional parameters (with some non-degeneracy conditions), there is a positive measure set Π of parameters for which the system admits analytic quasi-periodic solutions. The main difficulty to be overcome is the appearance of small divisors and this is the reason why we need to exclude parameters. Our main result is proved by a Nash-Moser fast convergent method and is formulated in the a-posteriori format of numerical analysis. That is, given an approximate solution of a functional equation which satisfies some non-degeneracy conditions, we can find a true solution close to it. This is in sharp contrast with the finite regularity theory developed in [18]. We conjecture that the exclusion of parameters is a real phenomenon and not a technical difficulty. More precisely, for generic families of perturbations, the quasi-periodic solutions are only finitely differentiable in open sets in the complement of parameters set Π.
International Nuclear Information System (INIS)
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
Mignard, Laurence; Denoual, Matthieu; Lavastre, Olivier; Floner, Didier; Geneste, Florence
2013-01-01
Polarography with dropping mercury electrode has been widely used in electroanalysis. However, the method is less and less employed due to the toxicity of mercury. In this work, we have shown that it is possible to replace the dropping electrode by a working electrode array, allowing the renewal of the electrode surface and of the analytical solution during the analysis. This new concept has been demonstrated on copper analysis. Sampled current voltammetry has been carried out on an electrode...
Sunday O. Edeki; Olabisi O. Ugbebor; Owoloko, Enahoro A.
2015-01-01
In this paper, a proposed computational method referred to as Projected Differential Transformation Method (PDTM) resulting from the modification of the classical Differential Transformation Method (DTM) is applied, for the first time, to the Black–Scholes Equation for European Option Valuation. The results obtained converge faster to their associated exact solution form; these easily computed results represent the analytical values of the associated European call options, and the same algor...
International Nuclear Information System (INIS)
The analytical solution of the Schroedinger equation for the Manning–Rosen potential plus a ring-shaped-like potential is obtained by applying the Nikiforov–Uvarov method by using the improved approximation scheme to the centrifugal potential for arbitrary l states. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary l states. (author)
Institute of Scientific and Technical Information of China (English)
CAI Liang; ZHANG Ping; YANG Tao; PAN Xiao-Yin
2011-01-01
By using the path integral approach, we investigate the problem of Hooke's atom (two electrons interacting with Coulomb potential in an external harmonic-oscillator potential) in an arbitrary time-dependent electric field. For a certain infinite set of discrete oscillator frequencies, we obtain the analytical solutions. The ground state polarization of the atom is then calculated. The same result is also obtained through linear response theory.
Sun, Tao; Morgan, Hywel; Green, Nicolas G
2007-01-01
Analysis of the movement of particles in a nonuniform field requires accurate knowledge of the electric field distribution in the system. This paper describes a method for analytically solving the electric field distribution above interdigitated electrode arrays used for dielectrophoresis (DEP) and traveling wave dielectrophoresis (twDEP), using the Schwarz-Christoffel mapping method. The electric field solutions are used to calculate the dielectrophoretic force in both cases, and the traveli...
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
Carleton, O.
1972-01-01
Consideration is given specifically to sixth order elliptic partial differential equations in two independent real variables x, y such that the coefficients of the highest order terms are real constants. It is assumed that the differential operator has distinct characteristics and that it can be factored as a product of second order operators. By analytically continuing into the complex domain and using the complex characteristic coordinates of the differential equation, it is shown that its solutions, u, may be reflected across analytic arcs on which u satisfies certain analytic boundary conditions. Moreover, a method is given whereby one can determine a region into which the solution is extensible. It is seen that this region of reflection is dependent on the original domain of difinition of the solution, the arc and the coefficients of the highest order terms of the equation and not on any sufficiently small quantities; i.e., the reflection is global in nature. The method employed may be applied to similar differential equations of order 2n.
Analytical and Numerical Solutions of Vapor Flow in a Flat Plate Heat Pipe
Directory of Open Access Journals (Sweden)
Mohsen GOODARZI
2012-03-01
Full Text Available In this paper, the optimal homotopy analysis method (OHAM and differential transform method (DTM were applied to solve the problem of 2D vapor flow in flat plate heat pipes. The governing partial differential equations for this problem were reduced to a non-linear ordinary differential equation, and then non-dimensional velocity profiles and axial pressure distributions along the entire length of the heat pipe were obtained using homotopy analysis, differential transform, and numerical fourth-order Runge-Kutta methods. The reliability of the two analytical methods was examined by comparing the analytical results with numerical ones. A brief discussion about the advantages of the two applied analytical methods relative to each other is presented. Furthermore, the effects of the Reynolds number and the ratio of condenser to evaporator lengths on the flow variables were discussed.Graphical abstract
Zech, Alraune; Attinger, Sabine
2016-05-01
A new method is presented which allows interpreting steady-state pumping tests in heterogeneous isotropic transmissivity fields. In contrast to mean uniform flow, pumping test drawdowns in heterogeneous media cannot be described by a single effective or equivalent value of hydraulic transmissivity. An effective description of transmissivity is required, being a function of the radial distance to the well and including the parameters of log-transmissivity: mean, variance, and correlation length. Such a model is provided by the upscaling procedure radial coarse graining, which describes the transition of near-well to far-field transmissivity effectively. Based on this approach, an analytical solution for a steady-state pumping test drawdown is deduced. The so-called effective well flow solution is derived for two cases: the ensemble mean of pumping tests and the drawdown within an individual heterogeneous transmissivity field. The analytical form of the solution allows inversely estimating the parameters of aquifer heterogeneity. For comparison with the effective well flow solution, virtual pumping tests are performed and analysed for both cases, the ensemble mean drawdown and pumping tests at individual transmissivity fields. Interpretation of ensemble mean drawdowns showed proof of the upscaling method. The effective well flow solution reproduces the drawdown for two-dimensional pumping tests in heterogeneous media in contrast to Thiem's solution for homogeneous media. Multiple pumping tests conducted at different locations within an individual transmissivity field are analysed, making use of the effective well flow solution to show that all statistical parameters of aquifer heterogeneity can be inferred under field conditions. Thus, the presented method is a promising tool with which to estimate parameters of aquifer heterogeneity, in particular variance and horizontal correlation length of log-transmissivity fields from steady-state pumping test measurements.
New analytical solution to calculate linear absorption coefficients of beta radiations
International Nuclear Information System (INIS)
The paper deals with an alternative model of beta radiation transmissions through attenuation layers and brings another analytical description of this phenomenon. The model is validated with a reliable data set and brings a possibility to calculate characteristic material parameters with low uncertainties. Using no correction factors, these calculations can be considered fundamental and inspiring for further research in the field. - Highlights: • New analytical model of beta radiation transmission curve in 2π geometry has been proposed. • Linear absorption coefficients in aluminum and Mylar were calculated for 19 radionuclides. • An empirical relationship between the calculated range parameter and average energy of beta radiation emitted by radionuclides was established
Sakalli, I.
2016-01-01
Hawking radiation of charged massive spin-0 particles are studied in the gravitational, electromagnetic, dilaton, and axion fields of rotating linear dilaton black holes. In this geometry, we separate the covariant Klein--Gordon equation into radial and angular parts and obtain the exact solutions of both the equations in terms of the confluent Heun functions. Using the radial solution, we analyze the behavior of the wave solutions near the event horizon of the rotating linear dilaton black h...
An analytical solution of Shallow Water system coupled to Exner equation
Berthon, Christophe; Le, Minh H; Delestre, Olivier
2011-01-01
In this paper, an exact smooth solution for the equations modeling the bedload transport of sediment in Shallow Water is presented. This solution is valid for a large family of sedimentation laws which are widely used in erosion modeling such as the Grass model or those of Meyer-Peter & Muller. One of the main interest of this solution is the derivation of numerical benchmarks to valid the approximation methods.
Zeldovich flow on cosmic vacuum background: new exact nonlinear analytical solution
Chernin, Arthur D.; Nagirner, Dmitrij I.; Starikova, Svetlana V.
2001-01-01
A new exact nonlinear Newtonian solution for a plane matter flow superimposed on the isotropic Hubble expansion is reported. The dynamical effect of cosmic vacuum is taken into account. The solution describes the evolution of nonlinear perturbations via gravitational instability of matter and the termination of the perturbation growth by anti-gravity of vacuum at the epoch of transition from matter domination to vacuum domination. On this basis, an `approximate' 3D solution is suggested as an...
Kurylyk, Barret L.; McKenzie, Jeffrey M; MacQuarrie, Kerry T. B.; Voss, Clifford I.
2014-01-01
Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.
International Nuclear Information System (INIS)
In this work, we report an analytical solution for the set of SN equations for the angular flux, in a rectangle, using the double Laplace transform technique. Its main idea comprehends the steps: application of the Laplace transform in one space variable, solution of the resulting equation by the LTSN method and reconstruction of the double Laplace transformed angular flux using the inversion theorem of the Laplace transform. We must emphasize that we perform the Laplace inversion by the LTSN method in the x direction, meanwhile we evaluate the inversion in the y direction performing the calculation of the corresponding line integral solution by the Stefest method. We have also to figure out that the application of Laplace transform to this type of boundary value problem introduces additional unknown functions associated to the partial derivatives of the angular flux at boundary. Based on the good results attained by the nodal LTSN method, we assume that the angular flux at boundary is also approximated by an exponential function. By analytical we mean that no approximation is done along the solution derivation except for the exponential hypothesis for the exiting angular flux at boundary. For sake of completeness, we report numerical comparisons of the obtained results against the ones of the literature. (author)
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
New analytical solution to calculate linear absorption coefficients of beta radiations.
Švec, Anton
2015-08-01
The paper deals with an alternative model of beta radiation transmissions through attenuation layers and brings another analytical description of this phenomenon. The model is validated with a reliable data set and brings a possibility to calculate characteristic material parameters with low uncertainties. Using no correction factors, these calculations can be considered fundamental and inspiring for further research in the field. PMID:25989183
Exact analytic self-similar solution of a wave attractor field
Maas, L.
2009-01-01
Stratified and rotating fluids support obliquely propagating internal waves. A symmetry-breaking shape of the fluid domain focuses them on a wave attractor. For a trapezoidal basin, it is here shown how to determine the internal wave field analytically. This requires solving the wave equation on a c
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
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 are...
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
An Analytic Solution of Hydrodynamic Equations with Source Terms in Heavy Ion Collisions
Zhuang, Pengfei; Yang, Zhenwei
2000-01-01
The energy and baryon densities in heavy ion collisions are estimated by analytically solving a 1+1 dimensional hydrodynamical model with source terms. Particularly, a competition between the energy and baryon sources and the expansion of the system is discussed in detail.
Microchannel electrokinetics of charged analytes in buffered solutions near floating electrodes
DEFF Research Database (Denmark)
Andersen, Mathias Bækbo; Wolfcale, Trevor; Gregersen, Misha Marie; Pennathur, Sumita; Bruus, Henrik
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 as...
Analytical Solution of the Space-Time Fractional Nonlinear Schrödinger Equation
Abdel-Salam, Emad A.-B.; Yousif, Eltayeb A.; El-Aasser, Mostafa A.
2016-02-01
The space-time fractional nonlinear Schrödinger equation is solved by mean of on the fractional Riccati expansion method. These solutions include generalized trigonometric and hyperbolic functions which could be useful for further understanding of mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time.
Analytical properties and exact solutions of the Lotka-Volterra competition system
International Nuclear Information System (INIS)
The system of nonlinear differential equations describing the Lotka-Volterra competition model with diffusion has been considered. The Painleve property of this reaction-diffusion system has been studied. Exact traveling wave solutions of the Lotka-Volterra competition system have been found. Periodic solutions expressed in terms of the Weierstrass elliptic function have also been determined
An Analytical Solution for One-Dimensional Water Infiltration and Redistribution in Unsaturated Soil
Institute of Scientific and Technical Information of China (English)
WANG Quan-Jiu; R. HORTON; FAN Jun
2009-01-01
Soil infiltration and redistribution are important processes in field water cycle, and it is necessary to develop a simple model to describe the processes. In this study, an algebraic solution for one-dimensional water infiltration and redistribution without evaporation in unsaturated soil was developed based on Richards equation. The algebraic solution had three parameters, namely, the saturated water conductivity, the comprehensive shape coefficient of the soil water content distribution, and the soil suction allocation coefficient. To analyze the physical features of these parameters, a relationship between the Green-Ampt model and the algebraic solution was established. The three parameters were estimated based on experimental observations, whereas the soil water content and the water infiltration duration were calculated using the algebraic solution. The calculated soil water content and infiltration duration were compared with the experimental observations, and the results indicated that the algebraic solution accurately described the unsaturated soil water flow processes.
Rehbinder, G.
2010-03-01
The generalized radial flow model describes mathematically nonsteady flow of arbitrary dimensionality from a source in a porous medium. Closed solutions of the corresponding equation have hitherto been considered as impractical except for one simple special case. Two closed solutions of the generalized radial flow equation, corresponding to given head in or given discharge from the source have been derived. The noninteger dimensionality is the only parameter in the problem. The solutions become not valid if the time tends to infinity, such as for 1-D and 2-D flows. The influence of a possible noninteger dimensionality has attracted interest in connection with the flow of groundwater in fractured rock, particularly around a repository for nuclear waste or in connection with grouting. In contrast to numerical solutions, the closed solutions offer simple means for evaluation of field tests.