Timing variation in an analytically solvable chaotic system

NASA Astrophysics Data System (ADS)

Blakely, J. N.; Milosavljevic, M. S.; Corron, N. J.

2017-02-01

We present analytic solutions for a chaotic dynamical system that do not have the regular timing characteristic of recently reported solvable chaotic systems. The dynamical system can be viewed as a first order filter with binary feedback. The feedback state may be switched only at instants defined by an external clock signal. Generalizing from a period one clock, we show analytic solutions for period two and higher period clocks. We show that even when the clock 'ticks' randomly the chaotic system has an analytic solution. These solutions can be visualized in a stroboscopic map whose complexity increases with the complexity of the clock. We provide both analytic results as well as experimental data from an electronic circuit implementation of the system. Our findings bridge the gap between the irregular timing of well known chaotic systems such as Lorenz and Rossler and the well regulated oscillations of recently reported solvable chaotic systems.

Steering particles by breaking symmetries

NASA Astrophysics Data System (ADS)

Bet, Bram; Samin, Sela; Georgiev, Rumen; Burak Eral, Huseyin; van Roij, René

2018-06-01

We derive general equations of motions for highly-confined particles that perform quasi-two-dimensional motion in Hele-Shaw channels, which we solve analytically, aiming to derive design principles for self-steering particles. Based on symmetry properties of a particle, its equations of motion can be simplified, where we retrieve an earlier-known equation of motion for the orientation of dimer particles consisting of disks (Uspal et al 2013 Nat. Commun. 4), but now in full generality. Subsequently, these solutions are compared with particle trajectories that are obtained numerically. For mirror-symmetric particles, excellent agreement between the analytical and numerical solutions is found. For particles lacking mirror symmetry, the analytic solutions provide means to classify the motion based on particle geometry, while we find that taking the side-wall interactions into account is important to accurately describe the trajectories.

A Semi-Analytical Solution to Time Dependent Groundwater Flow Equation Incorporating Stream-Wetland-Aquifer Interactions

NASA Astrophysics Data System (ADS)

Boyraz, Uǧur; Melek Kazezyılmaz-Alhan, Cevza

2017-04-01

Groundwater is a vital element of hydrologic cycle and the analytical & numerical solutions of different forms of groundwater flow equations play an important role in understanding the hydrological behavior of subsurface water. The interaction between groundwater and surface water bodies can be determined using these solutions. In this study, new hypothetical approaches are implemented to groundwater flow system in order to contribute to the studies on surface water/groundwater interactions. A time dependent problem is considered in a 2-dimensional stream-wetland-aquifer system. The sloped stream boundary is used to represent the interaction between stream and aquifer. The rest of the aquifer boundaries are assumed as no-flux boundary. In addition, a wetland is considered as a surface water body which lies over the whole aquifer. The effect of the interaction between the wetland and the aquifer is taken into account with a source/sink term in the groundwater flow equation and the interaction flow is calculated by using Darcy's approach. A semi-analytical solution is developed for the 2-dimensional groundwater flow equation in 5 steps. First, Laplace and Fourier cosine transforms are employed to obtain the general solution in Fourier and Laplace domain. Then, the initial and boundary conditions are applied to obtain the particular solution. Finally, inverse Fourier transform is carried out analytically and inverse Laplace transform is carried out numerically to obtain the final solution in space and time domain, respectively. In order to verify the semi-analytical solution, an explicit finite difference algorithm is developed and analytical and numerical solutions are compared for synthetic examples. The comparison of the analytical and numerical solutions shows that the analytical solution gives accurate results.

Analytical Studies on the Synchronization of a Network of Linearly-Coupled Simple Chaotic Systems

NASA Astrophysics Data System (ADS)

Sivaganesh, G.; Arulgnanam, A.; Seethalakshmi, A. N.; Selvaraj, S.

2018-05-01

We present explicit generalized analytical solutions for a network of linearly-coupled simple chaotic systems. Analytical solutions are obtained for the normalized state equations of a network of linearly-coupled systems driven by a common chaotic drive system. Two parameter bifurcation diagrams revealing the various hidden synchronization regions, such as complete, phase and phase-lag synchronization are identified using the analytical results. The synchronization dynamics and their stability are studied using phase portraits and the master stability function, respectively. Further, experimental results for linearly-coupled simple chaotic systems are presented to confirm the analytical results. The synchronization dynamics of a network of chaotic systems studied analytically is reported for the first time.

Size separation of analytes using monomeric surfactants

DOEpatents

Yeung, Edward S.; Wei, Wei

2005-04-12

A sieving medium for use in the separation of analytes in a sample containing at least one such analyte comprises a monomeric non-ionic surfactant of the of the general formula, B-A, wherein A is a hydrophilic moiety and B is a hydrophobic moiety, present in a solvent at a concentration forming a self-assembled micelle configuration under selected conditions and having an aggregation number providing an equivalent weight capable of effecting the size separation of the sample solution so as to resolve a target analyte(s) in a solution containing the same, the size separation taking place in a chromatography or electrophoresis separation system.

A GENERALIZED MATHEMATICAL SCHEME TO ANALYTICALLY SOLVE THE ATMOSPHERIC DIFFUSION EQUATION WITH DRY DEPOSITION. (R825689C072)

EPA Science Inventory

Abstract

A generalized mathematical scheme is developed to simulate the turbulent dispersion of pollutants which are adsorbed or deposit to the ground. The scheme is an analytical (exact) solution of the atmospheric diffusion equation with height-dependent wind speed a...

Steady hydromagnetic flows in open magnetic fields. I - A class of analytic solutions. [for stellar winds

NASA Technical Reports Server (NTRS)

Low, B. C.; Tsinganos, K.

1986-01-01

In the case of an establishment of theoretical models of the hydromagnetic solar wind, the inclusion of the effects of the magnetic field in the solar wind makes it extremely dificult to solve the mathematical problem. This paper has the objective to present a set of particular analytic solutions. The general formulation of Tsinganos (1982) is used to identify a class of analytic solutions to the equations of steady hydromagnetic flows in spherical coordinates. Flow in an open magnetic field are studied, taking into account the problem in dimensionless form, the special case of radial flows with alpha = 0, general radial flows, illustrative examples for flows in which alpha is not equal to 0, a parametric study of nonradial flows in which alpha is not equal to zero, variations in the parameter nu, and variations in the initial speed eta.

Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samin, Adib; Lahti, Erik; Zhang, Jinsuo, E-mail: zhang.3558@osu.edu

Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extendedmore » to cases that are more general and may be useful for benchmarking purposes.« less

Analytic solutions for Long's equation and its generalization

NASA Astrophysics Data System (ADS)

Humi, Mayer

2017-12-01

Two-dimensional, steady-state, stratified, isothermal atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular, these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic-type solutions in addition to regular gravity waves. These new analytical solutions provide new insights into the propagation and amplitude of gravity waves over topography.

Anisotropic cosmological solutions in R + R^2 gravity

NASA Astrophysics Data System (ADS)

Müller, Daniel; Ricciardone, Angelo; Starobinsky, Alexei A.; Toporensky, Aleksey

2018-04-01

In this paper we investigate the past evolution of an anisotropic Bianchi I universe in R+R^2 gravity. Using the dynamical system approach we show that there exists a new two-parameter set of solutions that includes both an isotropic "false radiation" solution and an anisotropic generalized Kasner solution, which is stable. We derive the analytic behavior of the shear from a specific property of f( R) gravity and the analytic asymptotic form of the Ricci scalar when approaching the initial singularity. Finally, we numerically check our results.

Analytical solution for the diffusion of a capacitor discharge generated magnetic field pulse in a conductor

NASA Astrophysics Data System (ADS)

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.

Some exact velocity profiles for granular flow in converging hoppers

NASA Astrophysics Data System (ADS)

Cox, Grant M.; Hill, James M.

2005-01-01

Gravity flow of granular materials through hoppers occurs in many industrial processes. For an ideal cohesionless granular material, which satisfies the Coulomb-Mohr yield condition, the number of known analytical solutions is limited. However, for the special case of the angle of internal friction δ equal to ninety degrees, there exist exact parametric solutions for the governing coupled ordinary differential equations for both two-dimensional wedges and three-dimensional cones, both of which involve two arbitrary constants of integration. These solutions are the only known analytical solutions of this generality. Here, we utilize the double-shearing theory of granular materials to determine the velocity field corresponding to these exact parametric solutions for the two problems of gravity flow through converging wedge and conical hoppers. An independent numerical solution for other angles of internal friction is shown to coincide with the analytical solution.

Ascorbic Acid as a Standard for Iodometric Titrations. An Analytical Experiment for General Chemistry

NASA Astrophysics Data System (ADS)

Silva, Cesar R.; Simoni, Jose A.; Collins, Carol H.; Volpe, Pedro L. O.

1999-10-01

Ascorbic acid is suggested as the weighable compound for the standardization of iodine solutions in an analytical experiment in general chemistry. The experiment involves an iodometric titration in which iodine reacts with ascorbic acid, oxidizing it to dehydroascorbic acid. The redox titration endpoint is determined by the first iodine excess that is complexed with starch, giving a deep blue-violet color. The results of the titration of iodine solution using ascorbic acid as a calibration standard were compared with the results acquired by the classic method using a standardized solution of sodium thiosulfate. The standardization of the iodine solution using ascorbic acid was accurate and precise, with the advantages of saving time and avoiding mistakes due to solution preparation. The colorless ascorbic acid solution gives a very clear and sharp titration end point with starch. It was shown by thermogravimetric analysis that ascorbic acid can be dried at 393 K for 2 h without decomposition. This experiment allows general chemistry students to perform an iodometric titration during a single laboratory period, determining with precision the content of vitamin C in pharmaceutical formulations.

A General Solution for Groundwater Flow in Estuarine Leaky Aquifer System with Considering Aquifer Anisotropy

NASA Astrophysics Data System (ADS)

Chen, Po-Chia; Chuang, Mo-Hsiung; Tan, Yih-Chi

2014-05-01

In recent years the urban and industrial developments near the coastal area are rapid and therefore the associated population grows dramatically. More and more water demand for human activities, agriculture irrigation, and aquaculture relies on heavy pumping in coastal area. The decline of groundwater table may result in the problems of seawater intrusion and/or land subsidence. Since the 1950s, numerous studies focused on the effect of tidal fluctuation on the groundwater flow in the coastal area. Many studies concentrated on the developments of one-dimensional (1D) and two-dimensional (2D) analytical solutions describing the tide-induced head fluctuations. For example, Jacob (1950) derived an analytical solution of 1D groundwater flow in a confined aquifer with a boundary condition subject to sinusoidal oscillation. Jiao and Tang (1999) derived a 1D analytical solution of a leaky confined aquifer by considered a constant groundwater head in the overlying unconfined aquifer. Jeng et al. (2002) studied the tidal propagation in a coupled unconfined and confined costal aquifer system. Sun (1997) presented a 2D solution for groundwater response to tidal loading in an estuary. Tang and Jiao (2001) derived a 2D analytical solution in a leaky confined aquifer system near open tidal water. This study aims at developing a general analytical solution describing the head fluctuations in a 2D estuarine aquifer system consisted of an unconfined aquifer, a confined aquifer, and an aquitard between them. Both the confined and unconfined aquifers are considered to be anisotropic. The predicted head fluctuations from this solution will compare with the simulation results from the MODFLOW program. In addition, the solutions mentioned above will be shown to be special cases of the present solution. Some hypothetical cases regarding the head fluctuation in costal aquifers will be made to investigate the dynamic effects of water table fluctuation, hydrogeological conditions, and characteristics of soil on the groundwater level fluctuations in the 2D estuarine leaky aquifer system.

General minimal surface solution for gravitational instantons

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Kalaycı, J.; Nutku, Y.

1997-07-01

We construct the general instanton metric obtained from Weierstrass' general local solution for minimal surfaces using the correspondence between minimal surfaces in three-dimensional Euclidean space and gravitational instantons admitting two Killing vectors. The resulting metric contains one arbitrary analytic function and we show that it can be transformed to the Gibbons-Hawking form of an instanton metric that was reported earlier.

Optimal rendezvous in the neighborhood of a circular orbit

NASA Technical Reports Server (NTRS)

Jones, J. B.

1975-01-01

The minimum velocity change rendezvous solutions, when the motion may be linearized about a circular orbit, fall into two separate regions; the phase-for-free region and the general region. Phase-for-free solutions are derived from the optimum transfer solutions, require the same velocity change expenditure, but may not be unique. Analytic solutions are presented in two of the three subregions. An algorithm is presented for determining the unique solutions in the general region. Various sources of initial conditions are discussed and three examples presented.

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

NASA Technical Reports Server (NTRS)

Lancaster, J. E.

1973-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications.

Providing solid angle formalism for skyshine calculations

PubMed Central

Pahikkala, A. Jussi; Rising, Mary B.; McGinley, Patton H.

2010-01-01

We detail, derive and correct the technical use of the solid angle variable identified in formal guidance that relates skyshine calculations to dose‐equivalent rate. We further recommend it for use with all National Council on Radiation Protection and Measurements (NCRP), Institute of Physics and Engineering in Medicine (IPEM) and similar reports documented. In general, for beams of identical width which have different resulting areas, within ±1.0% maximum deviation the analytical pyramidal solution is 1.27 times greater than a misapplied analytical conical solution through all field sizes up to 40×40 cm2. Therefore, we recommend determining the exact results with the analytical pyramidal solution for square beams and the analytical conical solution for circular beams. PACS number(s): 87.52.‐g, 87.52.Df, 87.52.Tr, 87.53.‐j, 87.53.Bn, 87.53.Dq, 87.66.‐a, 89., 89.60.+x

UNIFORM ESTIMATES FOR SOLUTIONS OF THE \\overline{\\partial}-EQUATION IN PSEUDOCONVEX POLYHEDRA

NASA Astrophysics Data System (ADS)

Sergeev, A. G.; Henkin, G. M.

1981-04-01

It is proved that the nonhomogeneous Cauchy-Riemann equation on an analytic submanifold "in general position" in a Cartesian product of strictly convex domains admits a solution with a uniform estimate. The possibility of weakening the requirement of general position in this result is investigated. Bibliography: 46 titles.

Analytical solutions for sequentially coupled one-dimensional reactive transport problems Part I: Mathematical derivations

NASA Astrophysics Data System (ADS)

Srinivasan, V.; Clement, T. P.

2008-02-01

Multi-species reactive transport equations coupled through sorption and sequential first-order reactions are commonly used to model sites contaminated with radioactive wastes, chlorinated solvents and nitrogenous species. Although researchers have been attempting to solve various forms of these reactive transport equations for over 50 years, a general closed-form analytical solution to this problem is not available in the published literature. In Part I of this two-part article, we derive a closed-form analytical solution to this problem for spatially-varying initial conditions. The proposed solution procedure employs a combination of Laplace and linear transform methods to uncouple and solve the system of partial differential equations. Two distinct solutions are derived for Dirichlet and Cauchy boundary conditions each with Bateman-type source terms. We organize and present the final solutions in a common format that represents the solutions to both boundary conditions. In addition, we provide the mathematical concepts for deriving the solution within a generic framework that can be used for solving similar transport problems.

Mathematical and computational studies of equilibrium capillary free surfaces

NASA Technical Reports Server (NTRS)

Albright, N.; Chen, N. F.; Concus, P.; Finn, R.

1977-01-01

The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated.

Exact Solutions for the Integrable Sixth-Order Drinfeld-Sokolov-Satsuma-Hirota System by the Analytical Methods.

PubMed

Manafian Heris, Jalil; Lakestani, Mehrdad

2014-01-01

We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G'/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.

An algorithm for full parametric solution of problems on the statics of orthotropic plates by the method of boundary states with perturbations

NASA Astrophysics Data System (ADS)

Penkov, V. B.; Ivanychev, D. A.; Novikova, O. S.; Levina, L. V.

2018-03-01

The article substantiates the possibility of building full parametric analytical solutions of mathematical physics problems in arbitrary regions by means of computer systems. The suggested effective means for such solutions is the method of boundary states with perturbations, which aptly incorporates all parameters of an orthotropic medium in a general solution. We performed check calculations of elastic fields of an anisotropic rectangular region (test and calculation problems) for a generalized plane stress state.

Optimal rendezvous in the neighborhood of a circular orbit

NASA Technical Reports Server (NTRS)

Jones, J. B.

1976-01-01

The minimum velocity-change rendezvous solutions, when the motion may be linearized about a circular orbit, fall into two separate regions; the phase-for-free region and the general region. Phase-for-free solutions are derived from the optimum transfer solutions, require the same velocity-change expenditure, but may not be unique. Analytic solutions are presented in two of the three subregions. An algorithm is presented for determining the unique solutions in the general region. Various sources of initial conditions are discussed and three examples are presented.

Approximate bound-state solutions of the Dirac equation for the generalized yukawa potential plus the generalized tensor interaction

NASA Astrophysics Data System (ADS)

Ikot, Akpan N.; Maghsoodi, Elham; Hassanabadi, Hassan; Obu, Joseph A.

2014-05-01

In this paper, we obtain the approximate analytical bound-state solutions of the Dirac particle with the generalized Yukawa potential within the framework of spin and pseudospin symmetries for the arbitrary к state with a generalized tensor interaction. The generalized parametric Nikiforov-Uvarov method is used to obtain the energy eigenvalues and the corresponding wave functions in closed form. We also report some numerical results and present figures to show the effect of the tensor interaction.

A generalized analytical solution for an inclined well in a vertically and horizontally anisotropic confined aquifer and comparisons with MODFLOW

NASA Astrophysics Data System (ADS)

Batu, Vedat

2015-01-01

In this paper, a new generalized three-dimensional complete analytical solution is presented for any well screen shape in a vertically and horizontally anisotropic confined aquifer in x-y-z Cartesian coordinates system for drawdown by taking into account the three principal hydraulic conductivities (Kx, Ky, and Kz) along the x-y-z coordinate directions. The special solution covers a partially-penetrating inclined parallelepiped as well as an inclined line source well. It has been showed that the rectangular parallelepiped screen case solution of Batu (2012) is a special case of this general solution. Like Batu (2012), the horizontal well case is a special case of this solution as well. The solution takes into account both the vertical anisotropy (azx = Kz/Kx) as well as the horizontal anisotropy (ayx = Ky/Kx) and has potential application areas to analyze pumping test drawdown data from partially-penetrating inclined wells by representing them as tiny parallelepiped as well as line sources. Apart from other verifications, the inclined well solution results have also been compared with the results of MODFLOW with very good agreement. The solution has also potential application areas for a partially-penetrating inclined parallelepiped fracture. With this new solution, both the horizontal anisotropy (ayx = Ky/Kx) as well as the vertical anisotropy (azx = Kz/Kx) can also be determined using observed drawdown data.

An analytical solution of groundwater response to tidal fluctuation in a leaky confined aquifer

NASA Astrophysics Data System (ADS)

Jiao, Jiu Jimmy; Tang, Zhonghua

1999-03-01

An analytical solution is derived to investigate the influence of leakage on tidal response in a coastal leaky confined aquifer system. The analytical solution developed here is more general than the traditional solution obtained by Ferris [1951], which can be regarded as a special case of the solution presented in this paper. This solution is based on a conceptual model under the assumption that the groundwater level in the confined aquifer fluctuates in response to sea tide while that of the overlying unconfined aquifer remains constant. This conceptual model is supported by numerous field studies by previous researchers which have demonstrated that the tidal response in an unconfined aquifer may be negligible compared to that in a confined aquifer. The leakage has a significant impact on the tidal behavior of the confined aquifer. Hypothetical studies indicate that both tidal amplitude of groundwater head in the aquifer and the distance over which the aquifer can be disturbed by the sea tide will be considerably reduced because of the existence of leakage. This analytical solution is used to investigate the tidal and piezometer data at the Chek Lap Kok airport, Hong Kong Special Administrative Region, People's Republic of China.

Numerical analysis of the asymptotic two-point boundary value solution for N-body trajectories.

NASA Technical Reports Server (NTRS)

Lancaster, J. E.; Allemann, R. A.

1972-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical boundary value solution applicable to a broad class of trajectory problems. In addition, the earlier first-order solutions have been extended to second-order to determine if improved accuracy is possible. Comparisons between the asymptotic solution and numerical integration for several lunar and interplanetary trajectories show that the asymptotic solution is generally quite accurate. Also, since no iterations are required, a solution to the boundary value problem is obtained in a fraction of the time required for numerically integrated solutions.

Uniform GTD solution for the diffraction by metallic tapes on panelled compact-range reflectors

NASA Technical Reports Server (NTRS)

Somers, G. A.; Pathak, P. H.

1992-01-01

Metallic tape is commonly used to cover the interpanel gaps which occur in paneled compact-range reflectors. It is therefore of interest to study the effect of the scattering by the tape on the field in the target zone of the range. An analytical solution is presented for the target zone fields scattered by 2D metallic tapes. It is formulated by the generalized scattering matrix technique in conjunction with the Wiener-Hopf procedure. An extension to treat 3D tapes can be accomplished using the 2D solution via the equivalent current concept. The analytical solution is compared with a reference moment method solution to confirm the accuracy of the former.

Mechanics of additively manufactured porous biomaterials based on the rhombicuboctahedron unit cell.

PubMed

Hedayati, R; Sadighi, M; Mohammadi-Aghdam, M; Zadpoor, A A

2016-01-01

Thanks to recent developments in additive manufacturing techniques, it is now possible to fabricate porous biomaterials with arbitrarily complex micro-architectures. Micro-architectures of such biomaterials determine their physical and biological properties, meaning that one could potentially improve the performance of such biomaterials through rational design of micro-architecture. The relationship between the micro-architecture of porous biomaterials and their physical and biological properties has therefore received increasing attention recently. In this paper, we studied the mechanical properties of porous biomaterials made from a relatively unexplored unit cell, namely rhombicuboctahedron. We derived analytical relationships that relate the micro-architecture of such porous biomaterials, i.e. the dimensions of the rhombicuboctahedron unit cell, to their elastic modulus, Poisson's ratio, and yield stress. Finite element models were also developed to validate the analytical solutions. Analytical and numerical results were compared with experimental data from one of our recent studies. It was found that analytical solutions and numerical results show a very good agreement particularly for smaller values of apparent density. The elastic moduli predicted by analytical and numerical models were in very good agreement with experimental observations too. While in excellent agreement with each other, analytical and numerical models somewhat over-predicted the yield stress of the porous structures as compared to experimental data. As the ratio of the vertical struts to the inclined struts, α, approaches zero and infinity, the rhombicuboctahedron unit cell respectively approaches the octahedron (or truncated cube) and cube unit cells. For those limits, the analytical solutions presented here were found to approach the analytic solutions obtained for the octahedron, truncated cube, and cube unit cells, meaning that the presented solutions are generalizations of the analytical solutions obtained for several other types of porous biomaterials. Copyright © 2015 Elsevier Ltd. All rights reserved.

Controllable parabolic-cylinder optical rogue wave.

PubMed

Zhong, Wei-Ping; Chen, Lang; Belić, Milivoj; Petrović, Nikola

2014-10-01

We demonstrate controllable parabolic-cylinder optical rogue waves in certain inhomogeneous media. An analytical rogue wave solution of the generalized nonlinear Schrödinger equation with spatially modulated coefficients and an external potential in the form of modulated quadratic potential is obtained by the similarity transformation. Numerical simulations are performed for comparison with the analytical solutions and to confirm the stability of the rogue wave solution obtained. These optical rogue waves are built by the products of parabolic-cylinder functions and the basic rogue wave solution of the standard nonlinear Schrödinger equation. Such rogue waves may appear in different forms, as the hump and paw profiles.

Analytic wave solution with helicon and Trivelpiece-Gould modes in an annular plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carlsson, Johan; Pavarin, Daniele; Walker, Mitchell

2009-11-26

Helicon sources in an annular configuration have applications for plasma thrusters. The theory of Klozenberg et al.[J. P. Klozenberg B. McNamara and P. C. Thonemann, J. Fluid Mech. 21(1965) 545-563] for the propagation and absorption of helicon and Trivelpiece-Gould modes in a cylindrical plasma has been generalized for annular plasmas. Analytic solutions are found also in the annular case, but in the presence of both helicon and Trivelpiece-Gould modes, a heterogeneous linear system of equations must be solved to match the plasma and inner and outer vacuum solutions. The linear system can be ill-conditioned or even exactly singular, leading tomore » a dispersion relation with a discrete set of discontinuities. The coefficients for the analytic solution are calculated by solving the linear system with singular-value decomposition.« less

Generalized analytic solutions and response characteristics of magnetotelluric fields on anisotropic infinite faults

NASA Astrophysics Data System (ADS)

Bing, Xue; Yicai, Ji

2018-06-01

In order to understand directly and analyze accurately the detected magnetotelluric (MT) data on anisotropic infinite faults, two-dimensional partial differential equations of MT fields are used to establish a model of anisotropic infinite faults using the Fourier transform method. A multi-fault model is developed to expand the one-fault model. The transverse electric mode and transverse magnetic mode analytic solutions are derived using two-infinite-fault models. The infinite integral terms of the quasi-analytic solutions are discussed. The dual-fault model is computed using the finite element method to verify the correctness of the solutions. The MT responses of isotropic and anisotropic media are calculated to analyze the response functions by different anisotropic conductivity structures. The thickness and conductivity of the media, influencing MT responses, are discussed. The analytic principles are also given. The analysis results are significant to how MT responses are perceived and to the data interpretation of the complex anisotropic infinite faults.

A transient laboratory method for determining the hydraulic properties of 'tight' rocks-I. Theory

USGS Publications Warehouse

Hsieh, P.A.; Tracy, J.V.; Neuzil, C.E.; Bredehoeft, J.D.; Silliman, Stephen E.

1981-01-01

Transient pulse testing has been employed increasingly in the laboratory to measure the hydraulic properties of rock samples with low permeability. Several investigators have proposed a mathematical model in terms of an initial-boundary value problem to describe fluid flow in a transient pulse test. However, the solution of this problem has not been available. In analyzing data from the transient pulse test, previous investigators have either employed analytical solutions that are derived with the use of additional, restrictive assumptions, or have resorted to numerical methods. In Part I of this paper, a general, analytical solution for the transient pulse test is presented. This solution is graphically illustrated by plots of dimensionless variables for several cases of interest. The solution is shown to contain, as limiting cases, the more restrictive analytical solutions that the previous investigators have derived. A method of computing both the permeability and specific storage of the test sample from experimental data will be presented in Part II. ?? 1981.

A complete analytical solution for the inverse instantaneous kinematics of a spherical-revolute-spherical (7R) redundant manipulator

NASA Technical Reports Server (NTRS)

Podhorodeski, R. P.; Fenton, R. G.; Goldenberg, A. A.

1989-01-01

Using a method based upon resolving joint velocities using reciprocal screw quantities, compact analytical expressions are generated for the inverse solution of the joint rates of a seven revolute (spherical-revolute-spherical) manipulator. The method uses a sequential decomposition of screw coordinates to identify reciprocal screw quantities used in the resolution of a particular joint rate solution, and also to identify a Jacobian null-space basis used for the direct solution of optimal joint rates. The results of the screw decomposition are used to study special configurations of the manipulator, generating expressions for the inverse velocity solution for all non-singular configurations of the manipulator, and identifying singular configurations and their characteristics. Two functions are therefore served: a new general method for the solution of the inverse velocity problem is presented; and complete analytical expressions are derived for the resolution of the joint rates of a seven degree of freedom manipulator useful for telerobotic and industrial robotic application.

Transfer Function of Multi-Stage Active Filters: A Solution Based on Pascal's Triangle and a General Expression

ERIC Educational Resources Information Center

Levesque, Luc

2012-01-01

A method is proposed to simplify analytical computations of the transfer function for electrical circuit filters, which are made from repetitive identical stages. A method based on the construction of Pascal's triangle is introduced and then a general solution from two initial conditions is provided for the repetitive identical stage. The present…

Developing semi-analytical solution for multiple-zone transient storage model with spatially non-uniform storage

NASA Astrophysics Data System (ADS)

Deng, Baoqing; Si, Yinbing; Wang, Jia

2017-12-01

Transient storages may vary along the stream due to stream hydraulic conditions and the characteristics of storage. Analytical solutions of transient storage models in literature didn't cover the spatially non-uniform storage. A novel integral transform strategy is presented that simultaneously performs integral transforms to the concentrations in the stream and in storage zones by using the single set of eigenfunctions derived from the advection-diffusion equation of the stream. The semi-analytical solution of the multiple-zone transient storage model with the spatially non-uniform storage is obtained by applying the generalized integral transform technique to all partial differential equations in the multiple-zone transient storage model. The derived semi-analytical solution is validated against the field data in literature. Good agreement between the computed data and the field data is obtained. Some illustrative examples are formulated to demonstrate the applications of the present solution. It is shown that solute transport can be greatly affected by the variation of mass exchange coefficient and the ratio of cross-sectional areas. When the ratio of cross-sectional areas is big or the mass exchange coefficient is small, more reaches are recommended to calibrate the parameter.

Analytical solution for heat transfer in three-dimensional porous media including variable fluid properties

NASA Technical Reports Server (NTRS)

Siegel, R.; Goldstein, M. E.

1972-01-01

An analytical solution is obtained for flow and heat transfer in a three-dimensional porous medium. Coolant from a reservoir at constant pressure and temperature enters one portion of the boundary of the medium and exits through another portion of the boundary which is at a specified uniform temperature and uniform pressure. The variation with temperature of coolant density and viscosity are both taken into account. A general solution is found that provides the temperature distribution in the medium and the mass and heat fluxes along the portion of the surface through which the coolant is exiting.

Three-dimensional eddy current solution of a polyphase machine test model (abstract)

NASA Astrophysics Data System (ADS)

Pahner, Uwe; Belmans, Ronnie; Ostovic, Vlado

1994-05-01

This abstract describes a three-dimensional (3D) finite element solution of a test model that has been reported in the literature. The model is a basis for calculating the current redistribution effects in the end windings of turbogenerators. The aim of the study is to see whether the analytical results of the test model can be found using a general purpose finite element package, thus indicating that the finite element model is accurate enough to treat real end winding problems. The real end winding problems cannot be solved analytically, as the geometry is far too complicated. The model consists of a polyphase coil set, containing 44 individual coils. This set generates a two pole mmf distribution on a cylindrical surface. The rotating field causes eddy currents to flow in the inner massive and conducting rotor. In the analytical solution a perfect sinusoidal mmf distribution is put forward. The finite element model contains 85824 tetrahedra and 16451 nodes. A complex single scalar potential representation is used in the nonconducting parts. The computation time required was 3 h and 42 min. The flux plots show that the field distribution is acceptable. Furthermore, the induced currents are calculated and compared with the values found from the analytical solution. The distribution of the eddy currents is very close to the distribution of the analytical solution. The most important results are the losses, both local and global. The value of the overall losses is less than 2% away from those of the analytical solution. Also the local distribution of the losses is at any given point less than 7% away from the analytical solution. The deviations of the results are acceptable and are partially due to the fact that the sinusoidal mmf distribution was not modeled perfectly in the finite element method.

Calibration-free concentration analysis for an analyte prone to self-association.

PubMed

Imamura, Hiroshi; Honda, Shinya

2017-01-01

Calibration-free concentration analysis (CFCA) based on surface plasmon resonance uses the diffusion coefficient of an analyte to determine the concentration of that analyte in a bulk solution. In general, CFCA is avoided when investigating analytes prone to self-association, as the heterogeneous diffusion coefficient results in a loss of precision. The derivation for self-association of the analyte was presented here. By using the diffusion coefficient for the monomeric state, CFCA provides the lowest possible concentration even though the analyte is self-associated. Copyright © 2016 Elsevier Inc. All rights reserved.

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 2: Derivations of second-order asymptotic boundary value solutions

NASA Technical Reports Server (NTRS)

Lancaster, J. E.

1973-01-01

Previously published asymptotic solutions for lunar and interplanetery trajectories have been modified and combined to formulate a general analytical solution to the problem of N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The complete derivation of the second-order solution, including the application of a regorous matching principle, is given. It is shown that the outer and inner expansions can be matched in a region of order mu to the alpha power, where 2/5 alpha 1/2, and mu (the moon/earth or planet/sun mass ratio) is much less than one. The second-order asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-Earth, and interplanetary solutions. Each is presented as an explicit analytical solution which does not require iterative steps to satisfy the boundary conditions. The complete derivation of each solution is shown, as well as instructions for numerical evaluation. For Vol. 1, see N73-27738.

Local fields and effective conductivity tensor of ellipsoidal particle composite with anisotropic constituents

NASA Astrophysics Data System (ADS)

Kushch, Volodymyr I.; Sevostianov, Igor; Giraud, Albert

2017-11-01

An accurate semi-analytical solution of the conductivity problem for a composite with anisotropic matrix and arbitrarily oriented anisotropic ellipsoidal inhomogeneities has been obtained. The developed approach combines the superposition principle with the multipole expansion of perturbation fields of inhomogeneities in terms of ellipsoidal harmonics and reduces the boundary value problem to an infinite system of linear algebraic equations for the induced multipole moments of inhomogeneities. A complete full-field solution is obtained for the multi-particle models comprising inhomogeneities of diverse shape, size, orientation and properties which enables an adequate account for the microstructure parameters. The solution is valid for the general-type anisotropy of constituents and arbitrary orientation of the orthotropy axes. The effective conductivity tensor of the particulate composite with anisotropic constituents is evaluated in the framework of the generalized Maxwell homogenization scheme. Application of the developed method to composites with imperfect ellipsoidal interfaces is straightforward. Their incorporation yields probably the most general model of a composite that may be considered in the framework of analytical approach.

Quantifying risks with exact analytical solutions of derivative pricing distribution

NASA Astrophysics Data System (ADS)

Zhang, Kun; Liu, Jing; Wang, Erkang; Wang, Jin

2017-04-01

Derivative (i.e. option) pricing is essential for modern financial instrumentations. Despite of the previous efforts, the exact analytical forms of the derivative pricing distributions are still challenging to obtain. In this study, we established a quantitative framework using path integrals to obtain the exact analytical solutions of the statistical distribution for bond and bond option pricing for the Vasicek model. We discuss the importance of statistical fluctuations away from the expected option pricing characterized by the distribution tail and their associations to value at risk (VaR). The framework established here is general and can be applied to other financial derivatives for quantifying the underlying statistical distributions.

Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)

NASA Technical Reports Server (NTRS)

Syed, H. H.; Volakis, John L.

1991-01-01

Rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristics to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

Higher-n triangular dilatonic black holes

NASA Astrophysics Data System (ADS)

Zadora, Anton; Gal'tsov, Dmitri V.; Chen, Chiang-Mei

2018-04-01

Dilaton gravity with the form fields is known to possess dyon solutions with two horizons for the discrete "triangular" values of the dilaton coupling constant a =√{ n (n + 1) / 2 }. This sequence first obtained numerically and then explained analytically as consequence of the regularity of the dilaton, should have some higher-dimensional and/or group theoretical origin. Meanwhile, this origin was explained earlier only for n = 1 , 2 in which cases the solutions were known analytically. We extend this explanation to n = 3 , 5 presenting analytical triangular solutions for the theory with different dilaton couplings a , b in electric and magnetic sectors in which case the quantization condition reads ab = n (n + 1) / 2. The solutions are derived via the Toda chains for B2 and G2 Lie algebras. They are found in the closed form in general D space-time dimensions. Solutions satisfy the entropy product rules indicating on the microscopic origin of their entropy and have negative binding energy in the extremal case.

On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid

NASA Astrophysics Data System (ADS)

Khan, M.; Anjum, Asia; Qi, Haitao; Fetecau, C.

2010-02-01

This paper deals with exact solutions for some oscillating motions of a generalized Oldroyd-B fluid. The fractional calculus approach is used in the constitutive relationship of fluid model. Analytical expressions for the velocity field and the corresponding shear stress for flows due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient are determined using Fourier sine and Laplace transforms. The obtained solutions are presented under integral and series forms in terms of the Mittag-Leffler functions. For α = β = 1, our solutions tend to the similar solutions for ordinary Oldroyd-B fluid. A comparison between generalized and ordinary Oldroyd-B fluids is shown by means of graphical illustrations.

An efficient approach for treating composition-dependent diffusion within organic particles

DOE PAGES

O'Meara, Simon; Topping, David O.; Zaveri, Rahul A.; ...

2017-09-07

Mounting evidence demonstrates that under certain conditions the rate of component partitioning between the gas and particle phase in atmospheric organic aerosol is limited by particle-phase diffusion. To date, however, particle-phase diffusion has not been incorporated into regional atmospheric models. An analytical rather than numerical solution to diffusion through organic particulate matter is desirable because of its comparatively small computational expense in regional models. Current analytical models assume diffusion to be independent of composition and therefore use a constant diffusion coefficient. To realistically model diffusion, however, it should be composition-dependent (e.g. due to the partitioning of components that plasticise, vitrifymore » or solidify). This study assesses the modelling capability of an analytical solution to diffusion corrected to account for composition dependence against a numerical solution. Results show reasonable agreement when the gas-phase saturation ratio of a partitioning component is constant and particle-phase diffusion limits partitioning rate (<10% discrepancy in estimated radius change). However, when the saturation ratio of the partitioning component varies, a generally applicable correction cannot be found, indicating that existing methodologies are incapable of deriving a general solution. Until such time as a general solution is found, caution should be given to sensitivity studies that assume constant diffusivity. Furthermore, the correction was implemented in the polydisperse, multi-process Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) and is used to illustrate how the evolution of number size distribution may be accelerated by condensation of a plasticising component onto viscous organic particles.« less

An efficient approach for treating composition-dependent diffusion within organic particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Meara, Simon; Topping, David O.; Zaveri, Rahul A.

Mounting evidence demonstrates that under certain conditions the rate of component partitioning between the gas and particle phase in atmospheric organic aerosol is limited by particle-phase diffusion. To date, however, particle-phase diffusion has not been incorporated into regional atmospheric models. An analytical rather than numerical solution to diffusion through organic particulate matter is desirable because of its comparatively small computational expense in regional models. Current analytical models assume diffusion to be independent of composition and therefore use a constant diffusion coefficient. To realistically model diffusion, however, it should be composition-dependent (e.g. due to the partitioning of components that plasticise, vitrifymore » or solidify). This study assesses the modelling capability of an analytical solution to diffusion corrected to account for composition dependence against a numerical solution. Results show reasonable agreement when the gas-phase saturation ratio of a partitioning component is constant and particle-phase diffusion limits partitioning rate (<10% discrepancy in estimated radius change). However, when the saturation ratio of the partitioning component varies, a generally applicable correction cannot be found, indicating that existing methodologies are incapable of deriving a general solution. Until such time as a general solution is found, caution should be given to sensitivity studies that assume constant diffusivity. Furthermore, the correction was implemented in the polydisperse, multi-process Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) and is used to illustrate how the evolution of number size distribution may be accelerated by condensation of a plasticising component onto viscous organic particles.« less

Modeling of Compressible Flow with Friction and Heat Transfer Using the Generalized Fluid System Simulation Program (GFSSP)

NASA Technical Reports Server (NTRS)

Bandyopadhyay, Alak; Majumdar, Alok

2007-01-01

The present paper describes the verification and validation of a quasi one-dimensional pressure based finite volume algorithm, implemented in Generalized Fluid System Simulation Program (GFSSP), for predicting compressible flow with friction, heat transfer and area change. The numerical predictions were compared with two classical solutions of compressible flow, i.e. Fanno and Rayleigh flow. Fanno flow provides an analytical solution of compressible flow in a long slender pipe where incoming subsonic flow can be choked due to friction. On the other hand, Raleigh flow provides analytical solution of frictionless compressible flow with heat transfer where incoming subsonic flow can be choked at the outlet boundary with heat addition to the control volume. Nonuniform grid distribution improves the accuracy of numerical prediction. A benchmark numerical solution of compressible flow in a converging-diverging nozzle with friction and heat transfer has been developed to verify GFSSP's numerical predictions. The numerical predictions compare favorably in all cases.

Analytical general solutions for static wormholes in f(R,T) gravity

NASA Astrophysics Data System (ADS)

Moraes, P. H. R. S.; Correa, R. A. C.; Lobato, R. V.

2017-07-01

Originally proposed as a tool for teaching the general theory of relativity, wormholes are today approached in many different ways and are seeing as an efficient alternative for interstellar and time travel. Attempts to achieve observational signatures of wormholes have been growing as the subject has become more and more popular. In this article we investigate some f(R,T) theoretical predictions for static wormholes, i.e., wormholes whose throat radius can be considered a constant. Since the T-dependence in f(R,T) gravity is due to the consideration of quantum effects, a further investigation of wormholes in such a theory is well motivated. We obtain the energy conditions of static wormholes in f(R,T) gravity and apply an analytical approach to find their physical and geometrical solutions. We highlight that our results are in agreement with previous solutions and assumptions presented in the literature.

Analytical general solutions for static wormholes in f ( R , T ) gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moraes, P.H.R.S.; Correa, R.A.C.; Lobato, R.V., E-mail: moraes.phrs@gmail.com, E-mail: fis04132@gmail.com, E-mail: ronaldo.lobato@icranet.org

Originally proposed as a tool for teaching the general theory of relativity, wormholes are today approached in many different ways and are seeing as an efficient alternative for interstellar and time travel. Attempts to achieve observational signatures of wormholes have been growing as the subject has become more and more popular. In this article we investigate some f ( R , T ) theoretical predictions for static wormholes, i.e., wormholes whose throat radius can be considered a constant. Since the T -dependence in f ( R , T ) gravity is due to the consideration of quantum effects, a furthermore » investigation of wormholes in such a theory is well motivated. We obtain the energy conditions of static wormholes in f ( R , T ) gravity and apply an analytical approach to find their physical and geometrical solutions. We highlight that our results are in agreement with previous solutions and assumptions presented in the literature.« less

Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

NASA Astrophysics Data System (ADS)

Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

2016-09-01

A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

Analytical Solution of Displacements Around Circular Openings in Generalized Hoek-Brown Rocks

NASA Astrophysics Data System (ADS)

Huang, Houxu; Li, Jie; Wei, Jiuqi

2017-09-01

The rock in plastic region is divided into numbers of elements by the slip lines, resulted from shear localization. During the deformation process, the elements will slip along the slip lines and the displacement field is discontinuous. Slip lines around circular opening in isotropic rock, subjected to hydrostatic stress are described by the logarithmic spirals. Deformation of the plastic region is mainly attributed to the slippage. Relationship between the shear stresses and slippage on slip lines is presented, based on the study of Revuzhenko and Shemyakin. Relations between slippage and rock failure are described, based on the elastic-brittle-plastic model. An analytical solution is presented for the plane strain analysis of displacements around circular openings in the Generalized Hoek-Brown rock. With properly choosing of slippage parameters, results obtained by using the proposed solution agree well with those presented in published sources.

Latent structure of the Wisconsin Card Sorting Test: a confirmatory factor analytic study.

PubMed

Greve, Kevin W; Stickle, Timothy R; Love, Jeffrey M; Bianchini, Kevin J; Stanford, Matthew S

2005-05-01

The present study represents the first large scale confirmatory factor analysis of the Wisconsin Card Sorting Test (WCST). The results generally support the three factor solutions reported in the exploratory factor analysis literature. However, only the first factor, which reflects general executive functioning, is statistically sound. The secondary factors, while likely reflecting meaningful cognitive abilities, are less stable except when all subjects complete all 128 cards. It is likely that having two discontinuation rules for the WCST has contributed to the varied factor analytic solutions reported in the literature and early discontinuation may result in some loss of useful information. Continued multivariate research will be necessary to better clarify the processes underlying WCST performance and their relationships to one another.

Non-Schwarzschild black-hole metric in four dimensional higher derivative gravity: Analytical approximation

NASA Astrophysics Data System (ADS)

Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.

2017-09-01

Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. Lü, A. Perkins, C. Pope, and K. Stelle [Phys. Rev. Lett. 114, 171601 (2015), 10.1103/PhysRevLett.114.171601] found a numerical solution describing a spherically symmetric non-Schwarzschild asymptotically flat black hole in Einstein gravity with added higher derivative terms. Using the general and quickly convergent parametrization in terms of the continued fractions, we represent this numerical solution in the analytical form, which is accurate not only near the event horizon or far from the black hole, but in the whole space. Thereby, the obtained analytical form of the metric allows one to study easily all the further properties of the black hole, such as thermodynamics, Hawking radiation, particle motion, accretion, perturbations, stability, quasinormal spectrum, etc. Thus, the found analytical approximate representation can serve in the same way as an exact solution.

Tidally induced residual current over the Malin Sea continental slope

NASA Astrophysics Data System (ADS)

Stashchuk, Nataliya; Vlasenko, Vasiliy; Hosegood, Phil; Nimmo-Smith, W. Alex M.

2017-05-01

Tidally induced residual currents generated over shelf-slope topography are investigated analytically and numerically using the Massachusetts Institute of Technology general circulation model. Observational support for the presence of such a slope current was recorded over the Malin Sea continental slope during the 88-th cruise of the RRS ;James Cook; in July 2013. A simple analytical formula developed here in the framework of time-averaged shallow water equations has been validated against a fully nonlinear nonhydrostatic numerical solution. A good agreement between analytical and numerical solutions is found for a wide range of input parameters of the tidal flow and bottom topography. In application to the Malin Shelf area both the numerical model and analytical solution predicted a northward moving current confined to the slope with its core located above the 400 m isobath and with vertically averaged maximum velocities up to 8 cm s-1, which is consistent with the in-situ data recorded at three moorings and along cross-slope transects.

Multiexponential models of (1+1)-dimensional dilaton gravity and Toda-Liouville integrable models

NASA Astrophysics Data System (ADS)

de Alfaro, V.; Filippov, A. T.

2010-01-01

We study general properties of a class of two-dimensional dilaton gravity (DG) theories with potentials containing several exponential terms. We isolate and thoroughly study a subclass of such theories in which the equations of motion reduce to Toda and Liouville equations. We show that the equation parameters must satisfy a certain constraint, which we find and solve for the most general multiexponential model. It follows from the constraint that integrable Toda equations in DG theories generally cannot appear without accompanying Liouville equations. The most difficult problem in the two-dimensional Toda-Liouville (TL) DG is to solve the energy and momentum constraints. We discuss this problem using the simplest examples and identify the main obstacles to solving it analytically. We then consider a subclass of integrable two-dimensional theories where scalar matter fields satisfy the Toda equations and the two-dimensional metric is trivial. We consider the simplest case in some detail. In this example, we show how to obtain the general solution. We also show how to simply derive wavelike solutions of general TL systems. In the DG theory, these solutions describe nonlinear waves coupled to gravity and also static states and cosmologies. For static states and cosmologies, we propose and study a more general one-dimensional TL model typically emerging in one-dimensional reductions of higher-dimensional gravity and supergravity theories. We especially attend to making the analytic structure of the solutions of the Toda equations as simple and transparent as possible.

Siewert solutions of transcendental equations, generalized Lambert functions and physical applications

NASA Astrophysics Data System (ADS)

Barsan, Victor

2018-05-01

Several classes of transcendental equations, mainly eigenvalue equations associated to non-relativistic quantum mechanical problems, are analyzed. Siewert's systematic approach of such equations is discussed from the perspective of the new results recently obtained in the theory of generalized Lambert functions and of algebraic approximations of various special or elementary functions. Combining exact and approximate analytical methods, quite precise analytical outputs are obtained for apparently untractable problems. The results can be applied in quantum and classical mechanics, magnetism, elasticity, solar energy conversion, etc.

Lie symmetry analysis, conservation laws and exact solutions of the time-fractional generalized Hirota-Satsuma coupled KdV system

NASA Astrophysics Data System (ADS)

Saberi, Elaheh; Reza Hejazi, S.

2018-02-01

In the present paper, Lie point symmetries of the time-fractional generalized Hirota-Satsuma coupled KdV (HS-cKdV) system based on the Riemann-Liouville derivative are obtained. Using the derived Lie point symmetries, we obtain similarity reductions and conservation laws of the considered system. Finally, some analytic solutions are furnished by means of the invariant subspace method in the Caputo sense.

Magnetically-driven medical robots: An analytical magnetic model for endoscopic capsules design

NASA Astrophysics Data System (ADS)

Li, Jing; Barjuei, Erfan Shojaei; Ciuti, Gastone; Hao, Yang; Zhang, Peisen; Menciassi, Arianna; Huang, Qiang; Dario, Paolo

2018-04-01

Magnetic-based approaches are highly promising to provide innovative solutions for the design of medical devices for diagnostic and therapeutic procedures, such as in the endoluminal districts. Due to the intrinsic magnetic properties (no current needed) and the high strength-to-size ratio compared with electromagnetic solutions, permanent magnets are usually embedded in medical devices. In this paper, a set of analytical formulas have been derived to model the magnetic forces and torques which are exerted by an arbitrary external magnetic field on a permanent magnetic source embedded in a medical robot. In particular, the authors modelled cylindrical permanent magnets as general solution often used and embedded in magnetically-driven medical devices. The analytical model can be applied to axially and diametrically magnetized, solid and annular cylindrical permanent magnets in the absence of the severe calculation complexity. Using a cylindrical permanent magnet as a selected solution, the model has been applied to a robotic endoscopic capsule as a pilot study in the design of magnetically-driven robots.

Analytical solutions for the profile of two-dimensional droplets with finite-length precursor films

NASA Astrophysics Data System (ADS)

Perazzo, Carlos Alberto; Mac Intyre, J. R.; Gomba, J. M.

2017-12-01

By means of the lubrication approximation we obtain the full family of static bidimensional profiles of a liquid resting on a substrate under partial-wetting conditions imposed by a disjoining-conjoining pressure. We show that for a set of quite general disjoining-conjoining pressure potentials, the free surface can adopt only five nontrivial static patterns; in particular, we find solutions when the height goes to zero which describe satisfactorily the complete free surface for a finite amount of fluid deposited on a substrate. To test the extension of the applicability of our solutions, we compare them with those obtained when the lubrication approximations are not employed and under conditions where the lubrication hypothesis are not strictly valid, and also with axisymmetric solutions. For a given disjoining-conjoining potential, we report a new analytical solution that accounts for all the five possible solutions.

Construction Method of Analytical Solutions to the Mathematical Physics Boundary Problems for Non-Canonical Domains

NASA Astrophysics Data System (ADS)

Mobarakeh, Pouyan Shakeri; Grinchenko, Victor T.

2015-06-01

The majority of practical cases of acoustics problems requires solving the boundary problems in non-canonical domains. Therefore construction of analytical solutions of mathematical physics boundary problems for non-canonical domains is both lucrative from the academic viewpoint, and very instrumental for elaboration of efficient algorithms of quantitative estimation of the field characteristics under study. One of the main solving ideologies for such problems is based on the superposition method that allows one to analyze a wide class of specific problems with domains which can be constructed as the union of canonically-shaped subdomains. It is also assumed that an analytical solution (or quasi-solution) can be constructed for each subdomain in one form or another. However, this case implies some difficulties in the construction of calculation algorithms, insofar as the boundary conditions are incompletely defined in the intervals, where the functions appearing in the general solution are orthogonal to each other. We discuss several typical examples of problems with such difficulties, we study their nature and identify the optimal methods to overcome them.

The role of light microscopy in aerospace analytical laboratories

NASA Technical Reports Server (NTRS)

Crutcher, E. R.

1977-01-01

Light microscopy has greatly reduced analytical flow time and added new dimensions to laboratory capability. Aerospace analytical laboratories are often confronted with problems involving contamination, wear, or material inhomogeneity. The detection of potential problems and the solution of those that develop necessitate the most sensitive and selective applications of sophisticated analytical techniques and instrumentation. This inevitably involves light microscopy. The microscope can characterize and often identify the cause of a problem in 5-15 minutes with confirmatory tests generally less than one hour. Light microscopy has and will make a very significant contribution to the analytical capabilities of aerospace laboratories.

Baecklund transformation, Lax pair, and solutions for the Caudrey-Dodd-Gibbon equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qu Qixing; Sun Kun; Jiang Yan

2011-01-15

By using Bell polynomials and symbolic computation, we investigate the Caudrey-Dodd-Gibbon equation analytically. Through a generalization of Bells polynomials, its bilinear form is derived, based on which, the periodic wave solution and soliton solutions are presented. And the soliton solutions with graphic analysis are also given. Furthermore, Baecklund transformation and Lax pair are derived via the Bells exponential polynomials. Finally, the Ablowitz-Kaup-Newell-Segur system is constructed.

Gravity discharge vessel revisited: An explicit Lambert W function solution

NASA Astrophysics Data System (ADS)

Digilov, Rafael M.

2017-07-01

Based on the generalized Poiseuille equation modified by a kinetic energy correction, an explicit solution for the time evolution of a liquid column draining under gravity through an exit capillary tube is derived in terms of the Lambert W function. In contrast to the conventional exponential behavior, as implied by the Poiseuille law, a new analytical solution gives a full account for the volumetric flow rate of a fluid through a capillary of any length and improves the precision of viscosity determination. The theoretical consideration may be of interest to students as an example of how implicit equations in the field of physics can be solved analytically using the Lambert function.

Analytic theory of orbit contraction

NASA Technical Reports Server (NTRS)

Vinh, N. X.; Longuski, J. M.; Busemann, A.; Culp, R. D.

1977-01-01

The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory.

A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2016-01-01

This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

A new approach to exact optical soliton solutions for the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Gómez-Aguilar, J. F.; Baleanu, Dumitru

2018-05-01

By using the modified homotopy analysis transform method, we construct the analytical solutions of the space-time generalized nonlinear Schrödinger equation involving a new fractional conformable derivative in the Liouville-Caputo sense and the fractional-order derivative with the Mittag-Leffler law. Employing theoretical parameters, we present some numerical simulations and compare the solutions obtained.

A stochastic method for Brownian-like optical transport calculations in anisotropic biosuspensions and blood

NASA Astrophysics Data System (ADS)

Miller, Steven

1998-03-01

A generic stochastic method is presented that rapidly evaluates numerical bulk flux solutions to the one-dimensional integrodifferential radiative transport equation, for coherent irradiance of optically anisotropic suspensions of nonspheroidal bioparticles, such as blood. As Fermat rays or geodesics enter the suspension, they evolve into a bundle of random paths or trajectories due to scattering by the suspended bioparticles. Overall, this can be interpreted as a bundle of Markov trajectories traced out by a "gas" of Brownian-like point photons being scattered and absorbed by the homogeneous distribution of uncorrelated cells in suspension. By considering the cumulative vectorial intersections of a statistical bundle of random trajectories through sets of interior data planes in the space containing the medium, the effective equivalent information content and behavior of the (generally unknown) analytical flux solutions of the radiative transfer equation rapidly emerges. The fluxes match the analytical diffuse flux solutions in the diffusion limit, which verifies the accuracy of the algorithm. The method is not constrained by the diffusion limit and gives correct solutions for conditions where diffuse solutions are not viable. Unlike conventional Monte Carlo and numerical techniques adapted from neutron transport or nuclear reactor problems that compute scalar quantities, this vectorial technique is fast, easily implemented, adaptable, and viable for a wide class of biophotonic scenarios. By comparison, other analytical or numerical techniques generally become unwieldy, lack viability, or are more difficult to utilize and adapt. Illustrative calculations are presented for blood medias at monochromatic wavelengths in the visible spectrum.

Application of geometric approximation to the CPMG experiment: Two- and three-site exchange.

PubMed

Chao, Fa-An; Byrd, R Andrew

2017-04-01

The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C α , H α , etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain. Published by Elsevier Inc.

Soliton and periodic solutions for time-dependent coefficient non-linear equation

NASA Astrophysics Data System (ADS)

Guner, Ozkan

2016-01-01

In this article, we establish exact solutions for the generalized (3+1)-dimensional variable coefficient Kadomtsev-Petviashvili (GVCKP) equation. Using solitary wave ansatz in terms of ? functions and the modified sine-cosine method, we find exact analytical bright soliton solutions and exact periodic solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The effectiveness and reliability of the method are shown by its application to the GVCKP equation.

A series solution for horizontal infiltration in an initially dry aquifer

NASA Astrophysics Data System (ADS)

Furtak-Cole, Eden; Telyakovskiy, Aleksey S.; Cooper, Clay A.

2018-06-01

The porous medium equation (PME) is a generalization of the traditional Boussinesq equation for hydraulic conductivity as a power law function of height. We analyze the horizontal recharge of an initially dry unconfined aquifer of semi-infinite extent, as would be found in an aquifer adjacent a rising river. If the water level can be modeled as a power law function of time, similarity variables can be introduced and the original problem can be reduced to a boundary value problem for a nonlinear ordinary differential equation. The position of the advancing front is not known ahead of time and must be found in the process of solution. We present an analytical solution in the form of a power series, with the coefficients of the series given by a recurrence relation. The analytical solution compares favorably with a highly accurate numerical solution, and only a small number of terms of the series are needed to achieve high accuracy in the scenarios considered here. We also conduct a series of physical experiments in an initially dry wedged Hele-Shaw cell, where flow is modeled by a special form of the PME. Our analytical solution closely matches the hydraulic head profiles in the Hele-Shaw cell experiment.

Analytical Results from Salt Solution Feed Tank (SSFT) Samples HTF-16-6 and HTF-16-40

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peters, T.

Two samples from the Salt Solution Feed Tank (SSFT) were analyzed by SRNL, HTF-16-6 and HTF-16-40. Multiple analyses of these samples indicate a general composition almost identical to that of the Salt Batch 8-B feed and the Tank 21H sample results.

STEADY GENERAL RELATIVISTIC MAGNETOHYDRODYNAMIC INFLOW/OUTFLOW SOLUTION ALONG LARGE-SCALE MAGNETIC FIELDS THAT THREAD A ROTATING BLACK HOLE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pu, Hung-Yi; Nakamura, Masanori; Hirotani, Kouichi

2015-03-01

General relativistic magnetohydrodynamic (GRMHD) flows along magnetic fields threading a black hole can be divided into inflow and outflow parts, according to the result of the competition between the black hole gravity and magneto-centrifugal forces along the field line. Here we present the first self-consistent, semi-analytical solution for a cold, Poynting flux–dominated (PFD) GRMHD flow, which passes all four critical (inner and outer, Alfvén, and fast magnetosonic) points along a parabolic streamline. By assuming that the dominating (electromagnetic) component of the energy flux per flux tube is conserved at the surface where the inflow and outflow are separated, the outflowmore » part of the solution can be constrained by the inflow part. The semi-analytical method can provide fiducial and complementary solutions for GRMHD simulations around the rotating black hole, given that the black hole spin, global streamline, and magnetizaion (i.e., a mass loading at the inflow/outflow separation) are prescribed. For reference, we demonstrate a self-consistent result with the work by McKinney in a quantitative level.« less

Ultimate Lateral Capacity of Rigid Pile in c- φ Soil

NASA Astrophysics Data System (ADS)

Zhang, Wei-min

2018-03-01

To date no analytical solution of the pile ultimate lateral capacity for the general c- φ soil has been obtained. In the present study, a new dimensionless embedded ratio was proposed and the analytical solutions of ultimate lateral capacity and rotation center of rigid pile in c- φ soils were obtained. The results showed that both the dimensionless ultimate lateral capacity and dimensionless rotation center were the univariate functions of the embedded ratio. Also, the ultimate lateral capacity in the c- φ soil was the combination of the ultimate lateral capacity ( f c ) in the clay, and the ultimate lateral capacity ( f φ ) in the sand. Therefore, the Broms chart for clay, solution for clay ( φ=0) put forward by Poulos and Davis, solution for sand ( c=0) obtained by Petrasovits and Awad, and Kondner's ultimate bending moment were all proven to be the special cases of the general solution in the present study. A comparison of the field and laboratory tests in 93 cases showed that the average ratios of the theoretical values to the experimental value ranged from 0.85 to 1.15. Also, the theoretical values displayed a good agreement with the test values.

Analytical Solutions of the Gravitational Field Equations in de Sitter and Anti-de Sitter Spacetimes

NASA Astrophysics Data System (ADS)

Da Rocha, R.; Capelas Oliveira, E.

2009-01-01

The generalized Laplace partial differential equation, describing gravitational fields, is investigated in de Sitter spacetime from several metric approaches—such as the Riemann, Beltrami, Börner-Dürr, and Prasad metrics—and analytical solutions of the derived Riccati radial differential equations are explicitly obtained. All angular differential equations trivially have solutions given by the spherical harmonics and all radial differential equations can be written as Riccati ordinary differential equations, which analytical solutions involve hypergeometric and Bessel functions. In particular, the radial differential equations predict the behavior of the gravitational field in de Sitter and anti-de Sitter spacetimes, and can shed new light on the investigations of quasinormal modes of perturbations of electromagnetic and gravitational fields in black hole neighborhood. The discussion concerning the geometry of de Sitter and anti-de Sitter spacetimes is not complete without mentioning how the wave equation behaves on such a background. It will prove convenient to begin with a discussion of the Laplace equation on hyperbolic space, partly since this is of interest in itself and also because the wave equation can be investigated by means of an analytic continuation from the hyperbolic space. We also solve the Laplace equation associated to the Prasad metric. After introducing the so called internal and external spaces—corresponding to the symmetry groups SO(3,2) and SO(4,1) respectively—we show that both radial differential equations can be led to Riccati ordinary differential equations, which solutions are given in terms of associated Legendre functions. For the Prasad metric with the radius of the universe independent of the parametrization, the internal and external metrics are shown to be of AdS-Schwarzschild-like type, and also the radial field equations arising are shown to be equivalent to Riccati equations whose solutions can be written in terms of generalized Laguerre polynomials and hypergeometric confluent functions.

The general solution to the classical problem of finite Euler Bernoulli beam

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Amba-Rao, C. L.

1977-01-01

An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.

A Generalized Wall Function

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Povinelli, Louis A.; Liu, Nan-Suey; Potapczuk, Mark G.; Lumley, J. L.

1999-01-01

The asymptotic solutions, described by Tennekes and Lumley (1972), for surface flows in a channel, pipe or boundary layer at large Reynolds numbers are revisited. These solutions can be extended to more complex flows such as the flows with various pressure gradients, zero wall stress and rough surfaces, etc. In computational fluid dynamics (CFD), these solutions can be used as the boundary conditions to bridge the near-wall region of turbulent flows so that there is no need to have the fine grids near the wall unless the near-wall flow structures are required to resolve. These solutions are referred to as the wall functions. Furthermore, a generalized and unified law of the wall which is valid for whole surface layer (including viscous sublayer, buffer layer and inertial sublayer) is analytically constructed. The generalized law of the wall shows that the effect of both adverse and favorable pressure gradients on the surface flow is very significant. Such as unified wall function will be useful not only in deriving analytic expressions for surface flow properties but also bringing a great convenience for CFD methods to place accurate boundary conditions at any location away from the wall. The extended wall functions introduced in this paper can be used for complex flows with acceleration, deceleration, separation, recirculation and rough surfaces.

Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Onate, C.A., E-mail: oaclems14@physicist.net; Onyeaju, M.C.; Ikot, A.N.

2016-12-15

The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

NASA Astrophysics Data System (ADS)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

Stress fields around two pores in an elastic body: exact quadrature domain solutions.

PubMed

Crowdy, Darren

2015-08-08

Analytical solutions are given for the stress fields, in both compression and far-field shear, in a two-dimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the Schottky-Klein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores.

General Analytical Procedure for Determination of Acidity Parameters of Weak Acids and Bases

PubMed Central

Pilarski, Bogusław; Kaliszan, Roman; Wyrzykowski, Dariusz; Młodzianowski, Janusz; Balińska, Agata

2015-01-01

The paper presents a new convenient, inexpensive, and reagent-saving general methodology for the determination of pK a values for components of the mixture of diverse chemical classes weak organic acids and bases in water solution, without the need to separate individual analytes. The data obtained from simple pH-metric microtitrations are numerically processed into reliable pK a values for each component of the mixture. Excellent agreement has been obtained between the determined pK a values and the reference literature data for compounds studied. PMID:25692072

General analytical procedure for determination of acidity parameters of weak acids and bases.

PubMed

Pilarski, Bogusław; Kaliszan, Roman; Wyrzykowski, Dariusz; Młodzianowski, Janusz; Balińska, Agata

2015-01-01

The paper presents a new convenient, inexpensive, and reagent-saving general methodology for the determination of pK a values for components of the mixture of diverse chemical classes weak organic acids and bases in water solution, without the need to separate individual analytes. The data obtained from simple pH-metric microtitrations are numerically processed into reliable pK a values for each component of the mixture. Excellent agreement has been obtained between the determined pK a values and the reference literature data for compounds studied.

Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Bertola, Marco; El, Gennady A.; Tovbis, Alexander

2016-10-01

Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrödinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration of multiphase, or finite-band, fNLS solutions of whom the standard SFBs and the structures forming due to their collisions represent particular, degenerate, cases. A generalized rogue wave notion then naturally enters as a large-amplitude localized coherent structure occurring within a finite-band fNLS solution. In this paper, we use the winding of real tori to show the mechanism of the appearance of such generalized rogue waves and derive an analytical criterion distinguishing finite-band potentials of the fNLS equation that exhibit generalized rogue waves.

General solution of the Dirac equation for quasi-two-dimensional electrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eremko, Alexander, E-mail: eremko@bitp.kiev.ua; Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua; Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua

2016-06-15

The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that themore » general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.« less

Generalized analytical solutions to multispecies transport equations with scale-dependent dispersion coefficients subject to time-dependent boundary conditions

NASA Astrophysics Data System (ADS)

Chen, J. S.; Chiang, S. Y.; Liang, C. P.

2017-12-01

It is essential to develop multispecies transport analytical models based on a set of advection-dispersion equations (ADEs) coupled with sequential first-order decay reactions for the synchronous prediction of plume migrations of both parent and its daughter species of decaying contaminants such as radionuclides, dissolved chlorinated organic compounds, pesticides and nitrogen. Although several analytical models for multispecies transport have already been reported, those currently available in the literature have primarily been derived based on ADEs with constant dispersion coefficients. However, there have been a number of studies demonstrating that the dispersion coefficients increase with the solute travel distance as a consequence of variation in the hydraulic properties of the porous media. This study presents novel analytical models for multispecies transport with distance-dependent dispersion coefficients. The correctness of the derived analytical models is confirmed by comparing them against the numerical models. Results show perfect agreement between the analytical and numerical models. Comparison of our new analytical model for multispecies transport with scale-dependent dispersion to an analytical model with constant dispersion is made to illustrate the effects of the dispersion coefficients on the multispecies transport of decaying contaminants.

On the existence of topological dyons and dyonic black holes in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups

NASA Astrophysics Data System (ADS)

Baxter, J. Erik

2018-05-01

Here we study the global existence of "hairy" dyonic black hole and dyon solutions to four-dimensional, anti-de Sitter Einstein-Yang-Mills theories for a general simply connected and semisimple gauge group G, for the so-called topologically symmetric systems, concentrating here on the regular case. We generalise here cases in the literature which considered purely magnetic spherically symmetric solutions for a general gauge group and topological dyonic solutions for s u (N ) . We are able to establish the global existence of non-trivial solutions to all such systems, both near existing embedded solutions and as |Λ| → ∞. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the s u (N ) case proved important to stability. We believe that these are the most general analytically proven solutions in 4D anti-de Sitter Einstein-Yang-Mills systems to date.

Approximate analytical solutions in the analysis of thin elastic plates

NASA Astrophysics Data System (ADS)

Goloskokov, Dmitriy P.; Matrosov, Alexander V.

2018-05-01

Two approaches to the construction of approximate analytical solutions for bending of a rectangular thin plate are presented: the superposition method based on the method of initial functions (MIF) and the one built using the Green's function in the form of orthogonal series. Comparison of two approaches is carried out by analyzing a square plate clamped along its contour. Behavior of the moment and the shear force in the neighborhood of the corner points is discussed. It is shown that both solutions give identical results at all points of the plate except for the neighborhoods of the corner points. There are differences in the values of bending moments and generalized shearing forces in the neighborhoods of the corner points.

Analytical Solutions, Moments, and Their Asymptotic Behaviors for the Time-Space Fractional Cable Equation

NASA Astrophysics Data System (ADS)

Li, Can; Deng, Wei-Hua

2014-07-01

Following the fractional cable equation established in the letter [B.I. Henry, T.A.M. Langlands, and S.L. Wearne, Phys. Rev. Lett. 100 (2008) 128103], we present the time-space fractional cable equation which describes the anomalous transport of electrodiffusion in nerve cells. The derivation is based on the generalized fractional Ohm's law; and the temporal memory effects and spatial-nonlocality are involved in the time-space fractional model. With the help of integral transform method we derive the analytical solutions expressed by the Green's function; the corresponding fractional moments are calculated; and their asymptotic behaviors are discussed. In addition, the explicit solutions of the considered model with two different external current injections are also presented.

21 CFR 177.1960 - Vinyl chloride-hexene-1 copolymers.

Code of Federal Regulations, 2014 CFR

2014-04-01

... determined by any suitable analytical procedure of generally accepted applicability. (ii) Inherent viscosity... D1243-79, “Standard Test Method for Dilute Solution Viscosity of Vinyl Chloride Polymers,” which is...

Direct Linearization and Adjoint Approaches to Evaluation of Atmospheric Weighting Functions and Surface Partial Derivatives: General Principles, Synergy and Areas of Application

NASA Technical Reports Server (NTRS)

Ustino, Eugene A.

2006-01-01

This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches

Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. III: nonspherical Schwarzschild waves and singularities at null infinity

NASA Astrophysics Data System (ADS)

Frauendiener, Jörg; Hennig, Jörg

2018-03-01

We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Frauendiener and Hennig (2017 Class. Quantum Grav. 34 045005), to the case of general, nonsymmetric solutions. A key element of our approach is the modern standard representation of spacelike infinity as a cylinder. With a decomposition into spherical harmonics, we reduce the four-dimensional wave equation to a family of two-dimensional equations. These equations can be used to study the behaviour at the cylinder, where the solutions turn out to have, in general, logarithmic singularities at infinitely many orders. We derive regularity conditions that may be imposed on the initial data, in order to avoid the first singular terms. We then demonstrate that the fully pseudospectral time evolution scheme can be applied to this problem leading to a highly accurate numerical reconstruction of the nonsymmetric solutions. We are particularly interested in the behaviour of the solutions at future null infinity, and we numerically show that the singularities spread to null infinity from the critical set, where the cylinder approaches null infinity. The observed numerical behaviour is consistent with similar logarithmic singularities found analytically on the critical set. Finally, we demonstrate that even solutions with singularities at low orders can be obtained with high accuracy by virtue of a coordinate transformation that converts solutions with logarithmic singularities into smooth solutions.

Artificial Intelligence Methods in Pursuit Evasion Differential Games

DTIC Science & Technology

1990-07-30

objectives, sometimes with fuzzy ones. Classical optimization, control or game theoretic methods are insufficient for their resolution. I Solution...OVERALL SATISFACTION WITH SCHOOL 120 FIGURE 5.13 EXAMPLE AHP HIERARCHY FOR CHOOSING MOST APPROPRIATE DIFFERENTIAL GAME AND PARAMETRIZATION 125 FIGURE 5.14...the Analytical Hierarchy Process originated by T.L. Saaty of the Wharton School. The Analytic Hierarchy Process ( AHP ) is a general theory of

On parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems

NASA Astrophysics Data System (ADS)

Lastra, A.; Malek, S.

2015-11-01

We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter ɛ with vanishing initial data at complex time t = 0 and whose coefficients depend analytically on (ɛ, t) near the origin in C2 and are bounded holomorphic on some horizontal strip in C w.r.t. the space variable. This problem is assumed to be non-Kowalevskian in time t, therefore analytic solutions at t = 0 cannot be expected in general. Nevertheless, we are able to construct a family of actual holomorphic solutions defined on a common bounded open sector with vertex at 0 in time and on the given strip above in space, when the complex parameter ɛ belongs to a suitably chosen set of open bounded sectors whose union form a covering of some neighborhood Ω of 0 in C*. These solutions are achieved by means of Laplace and Fourier inverse transforms of some common ɛ-depending function on C × R, analytic near the origin and with exponential growth on some unbounded sectors with appropriate bisecting directions in the first variable and exponential decay in the second, when the perturbation parameter belongs to Ω. Moreover, these solutions satisfy the remarkable property that the difference between any two of them is exponentially flat for some integer order w.r.t. ɛ. With the help of the classical Ramis-Sibuya theorem, we obtain the existence of a formal series (generally divergent) in ɛ which is the common Gevrey asymptotic expansion of the built up actual solutions considered above.

(Compactified) black branes in four dimensional f(R)-gravity

NASA Astrophysics Data System (ADS)

Dimakis, N.; Giacomini, Alex; Paliathanasis, Andronikos

2018-02-01

A new family of analytical solutions in a four dimensional static spacetime is presented for f (R) -gravity. In contrast to General Relativity, we find that a non trivial black brane/string solution is supported in vacuum power law f (R) -gravity for appropriate values of the parameters characterizing the model and when axisymmetry is introduced in the line element. For the aforementioned solution, we perform a brief investigation over its basic thermodynamic quantities.

Exact solutions for laminated composite cylindrical shells in cylindrical bending

NASA Technical Reports Server (NTRS)

Yuan, F. G.

1992-01-01

Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.

The Green's functions for peridynamic non-local diffusion.

PubMed

Wang, L J; Xu, J F; Wang, J X

2016-09-01

In this work, we develop the Green's function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green's functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green's functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems.

Generalized bipartite quantum state discrimination problems with sequential measurements

NASA Astrophysics Data System (ADS)

Nakahira, Kenji; Kato, Kentaro; Usuda, Tsuyoshi Sasaki

2018-02-01

We investigate an optimization problem of finding quantum sequential measurements, which forms a wide class of state discrimination problems with the restriction that only local operations and one-way classical communication are allowed. Sequential measurements from Alice to Bob on a bipartite system are considered. Using the fact that the optimization problem can be formulated as a problem with only Alice's measurement and is convex programming, we derive its dual problem and necessary and sufficient conditions for an optimal solution. Our results are applicable to various practical optimization criteria, including the Bayes criterion, the Neyman-Pearson criterion, and the minimax criterion. In the setting of the problem of finding an optimal global measurement, its dual problem and necessary and sufficient conditions for an optimal solution have been widely used to obtain analytical and numerical expressions for optimal solutions. Similarly, our results are useful to obtain analytical and numerical expressions for optimal sequential measurements. Examples in which our results can be used to obtain an analytical expression for an optimal sequential measurement are provided.

Fock space, symbolic algebra, and analytical solutions for small stochastic systems.

PubMed

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.

Satellite attitude motion models for capture and retrieval investigations

NASA Technical Reports Server (NTRS)

Cochran, John E., Jr.; Lahr, Brian S.

1986-01-01

The primary purpose of this research is to provide mathematical models which may be used in the investigation of various aspects of the remote capture and retrieval of uncontrolled satellites. Emphasis has been placed on analytical models; however, to verify analytical solutions, numerical integration must be used. Also, for satellites of certain types, numerical integration may be the only practical or perhaps the only possible method of solution. First, to provide a basis for analytical and numerical work, uncontrolled satellites were categorized using criteria based on: (1) orbital motions, (2) external angular momenta, (3) internal angular momenta, (4) physical characteristics, and (5) the stability of their equilibrium states. Several analytical solutions for the attitude motions of satellite models were compiled, checked, corrected in some minor respects and their short-term prediction capabilities were investigated. Single-rigid-body, dual-spin and multi-rotor configurations are treated. To verify the analytical models and to see how the true motion of a satellite which is acted upon by environmental torques differs from its corresponding torque-free motion, a numerical simulation code was developed. This code contains a relatively general satellite model and models for gravity-gradient and aerodynamic torques. The spacecraft physical model for the code and the equations of motion are given. The two environmental torque models are described.

Modeling of the Temperature Field Recovery in the Oil Pool

NASA Astrophysics Data System (ADS)

Khabibullin, I. L.; Davtetbaev, A. Ya.; Mar'in, D. F.; Khisamov, A. A.

2018-05-01

This paper considers the problem on mathematical modeling of the temperature field recovery in the oil pool upon termination of injection of water into the pool. The problem is broken down into two stages: injection of water and temperature and pressure recovery upon termination of injection. A review of the existing mathematical models is presented, analytical solutions for a number of cases have been constructed, and a comparison of the analytical solutions of different models has been made. In the general form, the expression has been obtained that permits determining the temperature change in the oil pool upon termination of injection of water (recovery of the temperature field).

Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application

NASA Astrophysics Data System (ADS)

Kundu, Anjan

2016-08-01

Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any analytic function, was made long ago by Belavin and Polyakov (BP). We propose an innovative generalization of the BP solution for an anisotropic ferromagnet, based on a physically motivated geometric (in-)equality, which takes the exact Skyrmion to a new class of functions beyond analyticity. The possibility of stabilizing such metastable states in helimagnets is discussed with the construction of individual Skyrmion, Skyrmion crystal and lattice with asymmetry, likely to be detected in precision experiments.

Spin dephasing in a magnetic dipole field.

PubMed

Ziener, C H; Kampf, T; Reents, G; Schlemmer, H-P; Bauer, W R

2012-05-01

Transverse relaxation by dephasing in an inhomogeneous field is a general mechanism in physics, for example, in semiconductor physics, muon spectroscopy, or nuclear magnetic resonance. In magnetic resonance imaging the transverse relaxation provides information on the properties of several biological tissues. Since the dipole field is the most important part of the multipole expansion of the local inhomogeneous field, dephasing in a dipole field is highly important in relaxation theory. However, there have been no analytical solutions which describe the dephasing in a magnetic dipole field. In this work we give a complete analytical solution for the dephasing in a magnetic dipole field which is valid over the whole dynamic range.

Helmholtz dark solitons.

PubMed

Chamorro-Posada, P; McDonald, G S

2003-05-15

A general dark-soliton solution of the Helmholtz equation (with defocusing Kerr nonlinearity) that has on- and off-axis, gray and black, paraxial and Helmholtz solitons as particular solutions, is reported. Modifications to soliton transverse velocity, width, phase period, and existence conditions are derived and explained in geometrical terms. Simulations verify analytical predictions and also demonstrate spontaneous formation of Helmholtz solitons and transparency of their interactions.

Numerical Tests and Properties of Waves in Radiating Fluids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, B M; Klein, R I

2009-09-03

We discuss the properties of an analytical solution for waves in radiating fluids, with a view towards its implementation as a quantitative test of radiation hydrodynamics codes. A homogeneous radiating fluid in local thermodynamic equilibrium is periodically driven at the boundary of a one-dimensional domain, and the solution describes the propagation of the waves thus excited. Two modes are excited for a given driving frequency, generally referred to as a radiative acoustic wave and a radiative diffusion wave. While the analytical solution is well known, several features are highlighted here that require care during its numerical implementation. We compare themore » solution in a wide range of parameter space to a numerical integration with a Lagrangian radiation hydrodynamics code. Our most significant observation is that flux-limited diffusion does not preserve causality for waves on a homogeneous background.« less

A semi-analytical solution for elastic analysis of rotating thick cylindrical shells with variable thickness using disk form multilayers.

PubMed

Zamani Nejad, Mohammad; Jabbari, Mehdi; Ghannad, Mehdi

2014-01-01

Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found.

A Semi-Analytical Solution for Elastic Analysis of Rotating Thick Cylindrical Shells with Variable Thickness Using Disk Form Multilayers

PubMed Central

Zamani Nejad, Mohammad; Jabbari, Mehdi; Ghannad, Mehdi

2014-01-01

Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found. PMID:24719582

Relativistic self-similar dynamic gravitational collapses of a quasi-spherical general polytropic magnetofluid

NASA Astrophysics Data System (ADS)

Lou, Yu-Qing; Xia, Yu-Kai

2017-05-01

We study magnetohydrodynamic (MHD) self-similar collapses and void evolution, with or without shocks, of a general polytropic quasi-spherical magnetofluid permeated by random transverse magnetic fields under the Paczynski-Wiita gravity that captures essential general relativistic effects of a Schwarzschild black hole (BH) with a growing mass. Based on the derived set of non-linear MHD ordinary differential equations, we obtain various asymptotic MHD solutions, the geometric and analytical properties of the magnetosonic critical curve (MSCC) and MHD shock jump conditions. Novel asymptotic MHD solution behaviours near the rim of central expanding voids are derived analytically. By exploring numerical global MHD solutions, we identify allowable boundary conditions at large radii that accommodate a smooth solution and show that a reasonable amount of magnetization significantly increases the mass accretion rate in the expansion-wave-collapse solution scenario. We also construct the counterparts of envelope-expansion-core-collapse solutions that cross the MSCC twice, which are found to be closely paired with a sequence of global smooth solutions satisfying a novel type of central MHD behaviours. MHD shocks with static outer and various inner flow profiles are also examined. Astrophysical applications include dynamic core collapses of magnetized massive stars and compact objects as well as formation of supermassive, hypermassive, dark matter and mixed matter BHs in the Universe, including the early Universe. Such gigantic BHs can be detected in X-ray/gamma-ray sources, quasars, ultraluminous infrared galaxies or extremely luminous infrared galaxies and dark matter overwhelmingly dominated elliptical galaxies as well as massive dark matter halos, etc. Gravitational waves and electromagnetic wave emissions in broad band (including e.g., gamma-ray bursts and fast radio bursts) can result from this type of dynamic collapses of forming BHs involving magnetized media.

A new method for constructing analytic elements for groundwater flow.

NASA Astrophysics Data System (ADS)

Strack, O. D.

2007-12-01

The analytic element method is based upon the superposition of analytic functions that are defined throughout the infinite domain, and can be used to meet a variety of boundary conditions. Analytic elements have been use successfully for a number of problems, mainly dealing with the Poisson equation (see, e.g., Theory and Applications of the Analytic Element Method, Reviews of Geophysics, 41,2/1005 2003 by O.D.L. Strack). The majority of these analytic elements consists of functions that exhibit jumps along lines or curves. Such linear analytic elements have been developed also for other partial differential equations, e.g., the modified Helmholz equation and the heat equation, and were constructed by integrating elementary solutions, the point sink and the point doublet, along a line. This approach is limiting for two reasons. First, the existence is required of the elementary solutions, and, second, the integration tends to limit the range of solutions that can be obtained. We present a procedure for generating analytic elements that requires merely the existence of a harmonic function with the desired properties; such functions exist in abundance. The procedure to be presented is used to generalize this harmonic function in such a way that the resulting expression satisfies the applicable differential equation. The approach will be applied, along with numerical examples, for the modified Helmholz equation and for the heat equation, while it is noted that the method is in no way restricted to these equations. The procedure is carried out entirely in terms of complex variables, using Wirtinger calculus.

General relativistic razor-thin disks with magnetically polarized matter

NASA Astrophysics Data System (ADS)

Navarro-Noguera, Anamaría; Lora-Clavijo, F. D.; González, Guillermo A.

2018-06-01

The origin of magnetic fields in the universe still remains unknown and constitutes one of the most intriguing questions in astronomy and astrophysics. Their significance is enormous since they have a strong influence on many astrophysical phenomena. In regards of this motivation, theoretical models of galactic disks with sources of magnetic field may contribute to understand the physics behind them. Inspired by this, we present a new family of analytical models for thin disks composed by magnetized material. The solutions are axially symmetric, conformastatic and are obtained by solving the Einstein-Maxwell Field Equations for continuum media without the test field approximation, and assuming that the sources are razor-thin disk of magnetically polarized matter. We find analytical expressions for the surface energy density, the pressure, the polarization vector, the electromagnetic fields, the mass and the rotational velocity for circular orbits, for two particular solutions. In each case, the energy-momentum tensor agrees with the energy conditions and also the convergence of the mass for all the solutions is proved. Since the solutions are well-behaved, they may be used to model astrophysical thin disks, and also may contribute as initial data in numerical simulations. In addition, the process to obtain the solutions is described in detail, which may be used as a guide to find solutions with magnetized material in General Relativity.

An Improved Correlation between Impression and Uniaxial Creep

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hsueh, Chun-Hway; Miranda, Pedro; Becher, Paul F

2006-01-01

A semiempirical correlation between impression and uniaxial creep has been established by Hyde et al. [Int. J. Mech. Sci. 35, 451 (1993) ] using finite element results for materials exhibiting general power-law creep with the stress exponent n in the range 2 {<=} n {<=} 15. Here, we derive the closed-form solution for a special case of viscoelastic materials, i.e., n = 1, subjected to impression creep and obtain the exact correlation between impression and uniaxial creep. This analytical solution serves as a checkpoint for the finite element results. We then perform finite element analyses for the general case tomore » derive a semiempirical correlation, which agrees well with both analytical viscoelastic results and the existing experimental data. Our improved correlation agrees with the correlation of Hyde et al. for n {>=} 4, and the difference increases with decreasing n for n<4.« less

On the solution of integral equations with a generalized Cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

Analytical solution of the optimal three dimensional reentry problem using Chapman's exact equations

NASA Technical Reports Server (NTRS)

Vinh, N. X.; Busemann, A.; Culp, R. D.

1974-01-01

This paper presents the general solution for the optimal three dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere. A set of dimensionless variables is introduced, and the resulting exact equations of motion have the distinctive advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a general lift-drag polar is used to define the aerodynamic control. Hence, the results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary polar and entering any planetary atmosphere.

Parsec-Scale Obscuring Accretion Disk with Large-Scale Magnetic Field in AGNs

NASA Technical Reports Server (NTRS)

Dorodnitsyn, A.; Kallman, T.

2017-01-01

A magnetic field dragged from the galactic disk, along with inflowing gas, can provide vertical support to the geometrically and optically thick pc (parsec) -scale torus in AGNs (Active Galactic Nuclei). Using the Soloviev solution initially developed for Tokamaks, we derive an analytical model for a rotating torus that is supported and confined by a magnetic field. We further perform three-dimensional magneto-hydrodynamic simulations of X-ray irradiated, pc-scale, magnetized tori. We follow the time evolution and compare models that adopt initial conditions derived from our analytic model with simulations in which the initial magnetic flux is entirely contained within the gas torus. Numerical simulations demonstrate that the initial conditions based on the analytic solution produce a longer-lived torus that produces obscuration that is generally consistent with observed constraints.

Parsec-scale Obscuring Accretion Disk with Large-scale Magnetic Field in AGNs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dorodnitsyn, A.; Kallman, T.

A magnetic field dragged from the galactic disk, along with inflowing gas, can provide vertical support to the geometrically and optically thick pc-scale torus in AGNs. Using the Soloviev solution initially developed for Tokamaks, we derive an analytical model for a rotating torus that is supported and confined by a magnetic field. We further perform three-dimensional magneto-hydrodynamic simulations of X-ray irradiated, pc-scale, magnetized tori. We follow the time evolution and compare models that adopt initial conditions derived from our analytic model with simulations in which the initial magnetic flux is entirely contained within the gas torus. Numerical simulations demonstrate thatmore » the initial conditions based on the analytic solution produce a longer-lived torus that produces obscuration that is generally consistent with observed constraints.« less

Diffusion in the special theory of relativity.

PubMed

Herrmann, Joachim

2009-11-01

The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

The Generalized Uncertainty Principle and Harmonic Interaction in Three Spatial Dimensions

NASA Astrophysics Data System (ADS)

Hassanabadi, H.; Hooshmand, P.; Zarrinkamar, S.

2015-01-01

In three spatial dimensions, the generalized uncertainty principle is considered under an isotropic harmonic oscillator interaction in both non-relativistic and relativistic regions. By using novel transformations and separations of variables, the exact analytical solution of energy eigenvalues as well as the wave functions is obtained. Time evolution of the non-relativistic region is also reported.

The application of the principles of invariance to the radiative transfer equation in plant canopies

NASA Technical Reports Server (NTRS)

Ganapol, B. D.; Myneni, R. B.

1992-01-01

Solutions of the radiative transfer equation describing photon interactions with vegetation canopies are important in remote sensing since they provide the canopy reflectance distribution required in the interpretation of satellite acquired information. The general one-dimensional two-angle transport problem for a finite copy of arbitrary leaf angle distribution is considered. Analytical solutions are obtained in terms of generalized Chandrasekhar's X- and Y-functions by invoking the principles of invariance. A critical step in the formulation involves the decomposition of the integral of the scattering phase function into a product of known functions of the incident and scattered photon directions. Several simplified cases previously considered in the literature are derived from the generalized solution. Various symmetries obeyed by the scattering operator and reciprocity relations are formally proved.

A solution to Schroder's equation in several variables

DOE PAGES

Bridges, Robert A.

2016-03-04

For this paper, let φ be an analytic self-map of the n -ball, having 0 as the attracting fixed point and having full-rank near 0. We consider the generalized Schroder's equation, F °φ=φ'(0) kF with ka positive integer and prove there is always a solution F with linearly independent component functions, but that such an F cannot have full rank except possibly when k=1. Furthermore, when k=1 (Schroder's equation), necessary and sufficient conditions on φ are given to ensure F has full rank near 0 without the added assumption of diagonalizability as needed in the 2003 Cowen/MacCluer paper. In responsemore » to Enoch's 2007 paper, it is proven that any formal power series solution indeed represents an analytic function on the whole unit ball. Finally, how exactly resonance can lead to an obstruction of a full rank solution is discussed as well as some consequences of having solutions to Schroder's equation.« less

Laboratory longitudinal diffusion tests: 1. Dimensionless formulations and validity of simplified solutions

NASA Astrophysics Data System (ADS)

Takeda, M.; Nakajima, H.; Zhang, M.; Hiratsuka, T.

2008-04-01

To obtain reliable diffusion parameters for diffusion testing, multiple experiments should not only be cross-checked but the internal consistency of each experiment should also be verified. In the through- and in-diffusion tests with solution reservoirs, test interpretation of different phases often makes use of simplified analytical solutions. This study explores the feasibility of steady, quasi-steady, equilibrium and transient-state analyses using simplified analytical solutions with respect to (i) valid conditions for each analytical solution, (ii) potential error, and (iii) experimental time. For increased generality, a series of numerical analyses are performed using unified dimensionless parameters and the results are all related to dimensionless reservoir volume (DRV) which includes only the sorptive parameter as an unknown. This means the above factors can be investigated on the basis of the sorption properties of the testing material and/or tracer. The main findings are that steady, quasi-steady and equilibrium-state analyses are applicable when the tracer is not highly sorptive. However, quasi-steady and equilibrium-state analyses become inefficient or impractical compared to steady state analysis when the tracer is non-sorbing and material porosity is significantly low. Systematic and comprehensive reformulation of analytical models enables the comparison of experimental times between different test methods. The applicability and potential error of each test interpretation can also be studied. These can be applied in designing, performing, and interpreting diffusion experiments by deducing DRV from the available information for the target material and tracer, combined with the results of this study.

Analytical steady-state solutions for water-limited cropping systems using saline irrigation water

NASA Astrophysics Data System (ADS)

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.

Forward and back diffusion through argillaceous formations

NASA Astrophysics Data System (ADS)

Yang, Minjune; Annable, Michael D.; Jawitz, James W.

2017-05-01

The exchange of solutes between aquifers and lower-permeability argillaceous formations is of considerable interest for solute and contaminant fate and transport. We present a synthesis of analytical solutions for solute diffusion between aquifers and single aquitard systems, validated in well-controlled experiments, and applied to several data sets from laboratory and field-scale problems with diffusion time and length scales ranging from 10-2 to 108 years and 10-2 to 102 m. One-dimensional diffusion models were applied using the method of images to consider the general cases of a finite aquitard bounded by two aquifers at the top and bottom, or a semiinfinite aquitard bounded by an aquifer. The simpler semiinfinite equations are appropriate for all domains with dimensionless relative diffusion length, ZD < 0.7. At dimensionless length scales above this threshold, application of semiinfinite equations to aquitards of finite thickness leads to increasing errors and solutions based on the method of images are required. Measured resident solute concentration profiles in aquitards and flux-averaged solute concentrations in surrounding aquifers were accurately modeled by appropriately accounting for generalized dynamic aquifer-aquitard boundary conditions, including concentration gradient reversals. Dimensionless diffusion length scales were used to illustrate the transferability of these relatively simple models to physical systems with dimensions that spanned 10 orders of magnitude. The results of this study offer guidance on the application of a simplified analytical approach to environmentally important layered problems with one or two diffusion interfaces.

Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra

NASA Astrophysics Data System (ADS)

Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.

2016-05-01

Three loop ladder and V-topology diagrams contributing to the massive operator matrix element AQg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.

Application of artificial intelligence to impulsive orbital transfers

NASA Technical Reports Server (NTRS)

Burns, Rowland E.

1987-01-01

A generalized technique for the numerical solution of any given class of problems is presented. The technique requires the analytic (or numerical) solution of every applicable equation for all variables that appear in the problem. Conditional blocks are employed to rapidly expand the set of known variables from a minimum of input. The method is illustrated via the use of the Hohmann transfer problem from orbital mechanics.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-10-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ω_i while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-09-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev

2017-11-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter

NASA Astrophysics Data System (ADS)

Bisnovatyi-Kogan, G. S.; Glushikhina, M. V.

2018-04-01

The solution of Boltzmann equation for plasma in magnetic field with arbitrarily degenerate electrons and nondegenerate nuclei is obtained by Chapman-Enskog method. Functions generalizing Sonine polynomials are used for obtaining an approximate solution. Fully ionized plasma is considered. The tensor of the heat conductivity coefficients in nonquantized magnetic field is calculated. For nondegenerate and strongly degenerate plasma the asymptotic analytic formulas are obtained and compared with results of previous authors. The Lorentz approximation with neglecting of electron-electron encounters is asymptotically exact for strongly degenerate plasma. For the first time, analytical expressions for the heat conductivity tensor for nondegenerate electrons in the presence of a magnetic field are obtained in the three-polynomial approximation with account of electron-electron collisions. Account of the third polynomial improved substantially the precision of results. In the two-polynomial approximation, the obtained solution coincides with the published results. For strongly degenerate electrons, an asymptotically exact analytical solution for the heat conductivity tensor in the presence of a magnetic field is obtained for the first time. This solution has a considerably more complicated dependence on the magnetic field than those in previous publications and gives a several times smaller relative value of the thermal conductivity across the magnetic field at ωτ * 0.8.

A study of methods to predict and measure the transmission of sound through the walls of light aircraft. Integration of certain singular boundary element integrals for applications in linear acoustics

NASA Technical Reports Server (NTRS)

Zimmerle, D.; Bernhard, R. J.

1985-01-01

An alternative method for performing singular boundary element integrals for applications in linear acoustics is discussed. The method separates the integral of the characteristic solution into a singular and nonsingular part. The singular portion is integrated with a combination of analytic and numerical techniques while the nonsingular portion is integrated with standard Gaussian quadrature. The method may be generalized to many types of subparametric elements. The integrals over elements containing the root node are considered, and the characteristic solution for linear acoustic problems are examined. The method may be generalized to most characteristic solutions.

Optimum three-dimensional atmospheric entry from the analytical solution of Chapman's exact equations

NASA Technical Reports Server (NTRS)

Busemann, A.; Vinh, N. X.; Culp, R. D.

1974-01-01

The general solution for the optimum three-dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere is developed. A set of dimensionless variables, modified Chapman variables, is introduced. The resulting exact equations of motion, referred to as Chapman's exact equations, have the advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a completely general lift-drag relationship is used in the derivation. The results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary drag polar, and entering any planetary atmosphere. The aerodynamic controls chosen are the lift coefficient and the bank angle. General optimum control laws for these controls are developed. Several earlier particular solutions are shown to be special cases of this general result. Results are valid for both free and constrained terminal position.

General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Elhanbaly, A.; Schlickeiser, Reinhard

2018-06-01

Anomalous diffusion models of energetic particles in space plasmas are developed by introducing the fractional Parker diffusion-convection equation. Analytical solution of the space-time fractional equation is obtained by use of the Caputo and Riesz-Feller fractional derivatives with the Laplace-Fourier transforms. The solution is given in terms of the Fox H-function. Profiles of particle densities are illustrated for different values of the space fractional order and the so-called skewness parameter.

Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: Phase-plane, multi-infinite series and variational approaches

NASA Astrophysics Data System (ADS)

Gambino, G.; Tanriver, U.; Guha, P.; Choudhury, A. Ghose; Choudhury, S. Roy

2015-02-01

In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddle equilibrium points of the corresponding traveling-wave equations, as well as ensure simultaneous convergence and continuity of the multi-infinite series solutions for the homoclinic/heteroclinic orbits anchored by these saddle points. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. And finally, variational methods are employed to generate families of both regular and embedded solitary wave solutions for the SPE PDE. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and it is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in analytical form (within the assumed ansatz for the trial functions). Thus, a direct error analysis is performed, showing the accuracy of the resulting solitary waves. Given the importance of solitary wave solutions in wave dynamics and information propagation in nonlinear PDEs, as well as the fact that not much is known about solutions of the family of generalized SPE equations considered here, the results obtained are both new and timely.

An advanced analytical solution for pressure build-up during CO2 injection into infinite saline aquifers: The role of compressibility

NASA Astrophysics Data System (ADS)

Wu, Haiqing; Bai, Bing; Li, Xiaochun

2018-02-01

Existing analytical or approximate solutions that are appropriate for describing the migration mechanics of CO2 and the evolution of fluid pressure in reservoirs do not consider the high compressibility of CO2, which reduces their calculation accuracy and application value. Therefore, this work first derives a new governing equation that represents the movement of complex fluids in reservoirs, based on the equation of continuity and the generalized Darcy's law. A more rigorous definition of the coefficient of compressibility of fluid is then presented, and a power function model (PFM) that characterizes the relationship between the physical properties of CO2 and the pressure is derived. Meanwhile, to avoid the difficulty of determining the saturation of fluids, a method that directly assumes the average relative permeability of each fluid phase in different fluid domains is proposed, based on the theory of gradual change. An advanced analytical solution is obtained that includes both the partial miscibility and the compressibility of CO2 and brine in evaluating the evolution of fluid pressure by integrating within different regions. Finally, two typical sample analyses are used to verify the reliability, improved nature and universality of this new analytical solution. Based on the physical characteristics and the results calculated for the examples, this work elaborates the concept and basis of partitioning for use in further work.

Laser backscattering analytical model of Doppler power spectra about rotating convex quadric bodies of revolution

NASA Astrophysics Data System (ADS)

Gong, YanJun; Wu, ZhenSen; Wang, MingJun; Cao, YunHua

2010-01-01

We propose an analytical model of Doppler power spectra in backscatter from arbitrary rough convex quadric bodies of revolution (whose lateral surface is a quadric) rotating around axes. In the global Cartesian coordinate system, the analytical model deduced is suitable for general convex quadric body of revolution. Based on this analytical model, the Doppler power spectra of cones, cylinders, paraboloids of revolution, and sphere-cones combination are proposed. We analyze numerically the influence of geometric parameters, aspect angle, wavelength and reflectance of rough surface of the objects on the broadened spectra because of the Doppler effect. This analytical solution may contribute to laser Doppler velocimetry, and remote sensing of ballistic missile that spin.

Optimum design of structures subject to general periodic loads

NASA Technical Reports Server (NTRS)

Reiss, Robert; Qian, B.

1989-01-01

A simplified version of Icerman's problem regarding the design of structures subject to a single harmonic load is discussed. The nature of the restrictive conditions that must be placed on the design space in order to ensure an analytic optimum are discussed in detail. Icerman's problem is then extended to include multiple forcing functions with different driving frequencies. And the conditions that now must be placed upon the design space to ensure an analytic optimum are again discussed. An important finding is that all solutions to the optimality condition (analytic stationary design) are local optima, but the global optimum may well be non-analytic. The more general problem of distributing the fixed mass of a linear elastic structure subject to general periodic loads in order to minimize some measure of the steady state deflection is also considered. This response is explicitly expressed in terms of Green's functional and the abstract operators defining the structure. The optimality criterion is derived by differentiating the response with respect to the design parameters. The theory is applicable to finite element as well as distributed parameter models.

A coupled analytical model for hydrostatic response of 1-3 piezocomposites.

PubMed

Rajapakse, Nimal; Chen, Yue

2008-08-01

This study presents a fully coupled analysis of a unit cell of a 1-3 piezocomposite under hydrostatic loading. The governing equations for coupled axisymmetric electroelastic field of a transversely isotropic piezoelectric medium and a transversely isotropic elastic medium are used. A reduced form of the analytical general solutions expressed in terms of series of modified Bessel functions of the first and second kind are used. The solution of the boundary-value problem corresponding to a unit cell is presented. The effective properties of a 1-3 piezocomposite are obtained for different fiber volume fractions, polymer and piezoceramic properties, and fiber aspect ratios. Comparisons with previously reported simplified and uncoupled models are made.

Modeling and Analysis of Large Amplitude Flight Maneuvers

NASA Technical Reports Server (NTRS)

Anderson, Mark R.

2004-01-01

Analytical methods for stability analysis of large amplitude aircraft motion have been slow to develop because many nonlinear system stability assessment methods are restricted to a state-space dimension of less than three. The proffered approach is to create regional cell-to-cell maps for strategically located two-dimensional subspaces within the higher-dimensional model statespace. These regional solutions capture nonlinear behavior better than linearized point solutions. They also avoid the computational difficulties that emerge when attempting to create a cell map for the entire state-space. Example stability results are presented for a general aviation aircraft and a micro-aerial vehicle configuration. The analytical results are consistent with characteristics that were discovered during previous flight-testing.

Diffraction in volume reflection gratings with variable fringe contrast.

PubMed

Brotherton-Ratcliffe, David; Bjelkhagen, Hans; Osanlou, Ardeshir; Excell, Peter

2015-06-01

The PSM model is used to analyze the process of diffraction occurring in volume reflection gratings in which fringe contrast is an arbitrary function of distance within the grating. General analytic expressions for diffraction efficiency at Bragg resonance are obtained for unslanted panchromatic lossless reflection gratings at oblique incidence. These formulas are then checked for several diverse fringe contrast profiles with numerical solutions of the Helmholtz equation, where exceptionally good agreement is observed. Away from Bragg resonance, the case of the hyperbolically decaying fringe contrast profile is shown to lead to an analytic expression for the diffraction efficiency and this is again compared successfully with numerical solutions of the Helmholtz equation.

Exact and approximate solutions for transient squeezing flow

NASA Astrophysics Data System (ADS)

Lang, Ji; Santhanam, Sridhar; Wu, Qianhong

2017-10-01

In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity of the analytical approaches. The study presented herein fills the gap in the literature and will have a broad impact on industrial and biomedical applications.

Fundamental Solution For The Self-healing Fracture Pulse

NASA Astrophysics Data System (ADS)

Nielsen, S.; Madariaga, R.

We find the analytical solution for a fundamental fracture mode in the form of a self- similar, self-healing pulse. The existence of such a fracture mode was strongly sug- gested by recent numerical findings but, to our knwledge, no formal proof had been proposed up to date. We present a two dimensional, anti-plane solution for fixed rup- ture and healing velocities, that satisfies both wave equation and stress conditions; we argue that such a solution is plausible even in the absence of rate-weakening in the friction, as an alternative to the classic crack solution. In practice, the impulsive mode rather than the expanding crack mode is selected depending on details of fracture initiation, and is therafter self-maintained. We discuss stress concentration, fracture energy, rupture velocity and compare them to the case of a crack. The analytical study is complemented by various numerical examples and comparisons. On more general grounds, we argue that an infinity of marginally stable fracture modes may exist other than the crack solution or the impulseive fracture described here.

The Green’s functions for peridynamic non-local diffusion

PubMed Central

Wang, L. J.; Xu, J. F.

2016-01-01

In this work, we develop the Green’s function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green’s functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green’s functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems. PMID:27713658

Approximate Solutions for Ideal Dam-Break Sediment-Laden Flows on Uniform Slopes

NASA Astrophysics Data System (ADS)

Ni, Yufang; Cao, Zhixian; Borthwick, Alistair; Liu, Qingquan

2018-04-01

Shallow water hydro-sediment-morphodynamic (SHSM) models have been applied increasingly widely in hydraulic engineering and geomorphological studies over the past few decades. Analytical and approximate solutions are usually sought to verify such models and therefore confirm their credibility. Dam-break flows are often evoked because such flows normally feature shock waves and contact discontinuities that warrant refined numerical schemes to solve. While analytical and approximate solutions to clear-water dam-break flows have been available for some time, such solutions are rare for sediment transport in dam-break flows. Here we aim to derive approximate solutions for ideal dam-break sediment-laden flows resulting from the sudden release of a finite volume of frictionless, incompressible water-sediment mixture on a uniform slope. The approximate solutions are presented for three typical sediment transport scenarios, i.e., pure advection, pure sedimentation, and concurrent entrainment and deposition. Although the cases considered in this paper are not real, the approximate solutions derived facilitate suitable benchmark tests for evaluating SHSM models, especially presently when shock waves can be numerically resolved accurately with a suite of finite volume methods, while the accuracy of the numerical solutions of contact discontinuities in sediment transport remains generally poorer.

A generalized analytical model for radiative transfer in vacuum thermal insulation of space vehicles

NASA Astrophysics Data System (ADS)

Krainova, Irina V.; Dombrovsky, Leonid A.; Nenarokomov, Aleksey V.; Budnik, Sergey A.; Titov, Dmitry M.; Alifanov, Oleg M.

2017-08-01

The previously developed spectral model for radiative transfer in vacuum thermal insulation of space vehicles is generalized to take into account possible thermal contact between a fibrous spacer and one of the neighboring aluminum foil layers. An approximate analytical solution based on slightly modified two-flux approximation for radiative transfer in a semi-transparent fibrous spacer is derived. It was shown that thermal contact between the spacer and adjacent foil may decrease significantly the quality of thermal insulation because of an increase in radiative flux to/from the opposite aluminum foil. Theoretical predictions are confirmed by comparison with new results of laboratory experiments.

Analytical Solutions to Backreaction on Cosmic Strings

NASA Astrophysics Data System (ADS)

Wachter, Jeremy M.

2017-08-01

We present analytical studies of gravitational and electromagnetic backreaction on cosmic strings. For oscillating loops of cosmic string, we present a general argument for how kinks must change; additionally, we apply this general argument to the geometrically simple case of the Garfinkle-Vachaspati loop. Our results suggest that the formation of cusps on loops is delayed, and so we should expect fewer cuspy signatures to be seen in gravitational wave observations. Electromagnetic backreaction we show to reduce currents on a string at least as rapidly as necessary to avoid a paradox, and currents induced on a superconducting straight string will be asymptotically reduced to zero.

Transient well flow in layered aquifer systems: the uniform well-face drawdown solution

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1999-11-01

Previously a hybrid analytical-numerical solution for the general problem of computing transient well flow in vertically heterogeneous aquifers was proposed by the author. The radial component of flow was treated analytically, while the finite-difference technique was used for the vertical flow component only. In the present work the hybrid solution has been modified by replacing the previously assumed uniform well-face gradient (UWG) boundary condition in such a way that the drawdown remains uniform along the well screen. The resulting uniform well-face drawdown (UWD) solution also includes the effects of a finite diameter well, wellbore storage and a thin skin, while partial penetration and vertical heterogeneity are accommodated by the one-dimensional discretization. Solutions are proposed for well flow caused by constant, variable and slug discharges. The model was verified by comparing wellbore drawdowns and well-face flux distributions with published numerical solutions. Differences between UWG and UWD well flow will occur in all situations with vertical flow components near the well, which is demonstrated by considering: (1) partially penetrating wells in confined aquifers, (2) fully penetrating wells in unconfined aquifers with delayed response and (3) layered aquifers and leaky multiaquifer systems. The presented solution can be a powerful tool for solving many well-hydraulic problems, including well tests, flowmeter tests, slug tests and pumping tests. A computer program for the analysis of pumping tests, based on the hybrid analytical-numerical technique and UWG or UWD conditions, is available from the author.

On application of asymmetric Kan-like exact equilibria to the Earth magnetotail modeling

NASA Astrophysics Data System (ADS)

Korovinskiy, Daniil B.; Kubyshkina, Darya I.; Semenov, Vladimir S.; Kubyshkina, Marina V.; Erkaev, Nikolai V.; Kiehas, Stefan A.

2018-04-01

A specific class of solutions of the Vlasov-Maxwell equations, developed by means of generalization of the well-known Harris-Fadeev-Kan-Manankova family of exact two-dimensional equilibria, is studied. The examined model reproduces the current sheet bending and shifting in the vertical plane, arising from the Earth dipole tilting and the solar wind nonradial propagation. The generalized model allows magnetic configurations with equatorial magnetic fields decreasing in a tailward direction as slow as 1/x, contrary to the original Kan model (1/x3); magnetic configurations with a single X point are also available. The analytical solution is compared with the empirical T96 model in terms of the magnetic flux tube volume. It is found that parameters of the analytical model may be adjusted to fit a wide range of averaged magnetotail configurations. The best agreement between analytical and empirical models is obtained for the midtail at distances beyond 10-15 RE at high levels of magnetospheric activity. The essential model parameters (current sheet scale, current density) are compared to Cluster data of magnetotail crossings. The best match of parameters is found for single-peaked current sheets with medium values of number density, proton temperature and drift velocity.

Analytical model for investigation of interior noise characteristics in aircraft with multiple propellers including synchrophasing

NASA Technical Reports Server (NTRS)

Fuller, C. R.

1986-01-01

A simplified analytical model of transmission of noise into the interior of propeller-driven aircraft has been developed. The analysis includes directivity and relative phase effects of the propeller noise sources, and leads to a closed form solution for the coupled motion between the interior and exterior fields via the shell (fuselage) vibrational response. Various situations commonly encountered in considering sound transmission into aircraft fuselages are investigated analytically and the results obtained are compared to measurements in real aircraft. In general the model has proved successful in identifying basic mechanisms behind noise transmission phenomena.

An analytical theory of a scattering of radio waves on meteoric ionization - II. Solution of the integro-differential equation in case of backscatter

NASA Astrophysics Data System (ADS)

Pecina, P.

2016-12-01

The integro-differential equation for the polarization vector P inside the meteor trail, representing the analytical solution of the set of Maxwell equations, is solved for the case of backscattering of radio waves on meteoric ionization. The transversal and longitudinal dimensions of a typical meteor trail are small in comparison to the distances to both transmitter and receiver and so the phase factor appearing in the kernel of the integral equation is large and rapidly changing. This allows us to use the method of stationary phase to obtain an approximate solution of the integral equation for the scattered field and for the corresponding generalized radar equation. The final solution is obtained by expanding it into the complete set of Bessel functions, which results in solving a system of linear algebraic equations for the coefficients of the expansion. The time behaviour of the meteor echoes is then obtained using the generalized radar equation. Examples are given for values of the electron density spanning a range from underdense meteor echoes to overdense meteor echoes. We show that the time behaviour of overdense meteor echoes using this method is very different from the one obtained using purely numerical solutions of the Maxwell equations. Our results are in much better agreement with the observations performed e.g. by the Ondřejov radar.

General analytical solutions for DC/AC circuit-network analysis

NASA Astrophysics Data System (ADS)

Rubido, Nicolás; Grebogi, Celso; Baptista, Murilo S.

2017-06-01

In this work, we present novel general analytical solutions for the currents that are developed in the edges of network-like circuits when some nodes of the network act as sources/sinks of DC or AC current. We assume that Ohm's law is valid at every edge and that charge at every node is conserved (with the exception of the source/sink nodes). The resistive, capacitive, and/or inductive properties of the lines in the circuit define a complex network structure with given impedances for each edge. Our solution for the currents at each edge is derived in terms of the eigenvalues and eigenvectors of the Laplacian matrix of the network defined from the impedances. This derivation also allows us to compute the equivalent impedance between any two nodes of the circuit and relate it to currents in a closed circuit which has a single voltage generator instead of many input/output source/sink nodes. This simplifies the treatment that could be done via Thévenin's theorem. Contrary to solving Kirchhoff's equations, our derivation allows to easily calculate the redistribution of currents that occurs when the location of sources and sinks changes within the network. Finally, we show that our solutions are identical to the ones found from Circuit Theory nodal analysis.

Theoretical performance of cross-wind axis turbines with results for a catenary vertical axis configuration

NASA Technical Reports Server (NTRS)

Muraca, R. J.; Stephens, M. V.; Dagenhart, J. R.

1975-01-01

A general analysis capable of predicting performance characteristics of cross-wind axis turbines was developed, including the effects of airfoil geometry, support struts, blade aspect ratio, windmill solidity, blade interference and curved flow. The results were compared with available wind tunnel results for a catenary blade shape. A theoretical performance curve for an aerodynamically efficient straight blade configuration was also presented. In addition, a linearized analytical solution applicable for straight configurations was developed. A listing of the computer program developed for numerical solutions of the general performance equations is included in the appendix.

Purely numerical approach for analyzing flow to a well intercepting a vertical fracture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Narasimhan, T.N.; Palen, W.A.

1979-03-01

A numerical method, based on an Integral Finite Difference approach, is presented to investigate wells intercepting fractures in general and vertical fractures in particular. Such features as finite conductivity, wellbore storage, damage, and fracture deformability and its influence as permeability are easily handled. The advantage of the numerical approach is that it is based on fewer assumptions than analytic solutions and hence has greater generality. Illustrative examples are given to validate the method against known solutions. New results are presenteed to demonstrate the applicability of the method to problems not apparently considered in the literature so far.

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

NASA Astrophysics Data System (ADS)

Zheng, R.-F.; Wu, T.-H.; Li, X.-Y.; Chen, W.-Q.

2018-06-01

The problem of a penny-shaped crack embedded in an infinite space of transversely isotropic multi-ferroic composite medium is investigated. The crack is assumed to be subjected to uniformly distributed mechanical, electric and magnetic loads applied symmetrically on the upper and lower crack surfaces. The semi-permeable (limited-permeable) electro-magnetic boundary condition is adopted. By virtue of the generalized method of potential theory and the general solutions, the boundary integro-differential equations governing the mode I crack problem, which are of nonlinear nature, are established and solved analytically. Exact and complete coupling magneto-electro-elastic field is obtained in terms of elementary functions. Important parameters in fracture mechanics on the crack plane, e.g., the generalized crack surface displacements, the distributions of generalized stresses at the crack tip, the generalized stress intensity factors and the energy release rate, are explicitly presented. To validate the present solutions, a numerical code by virtue of finite element method is established for 3D crack problems in the framework of magneto-electro-elasticity. To evaluate conveniently the effect of the medium inside the crack, several empirical formulae are developed, based on the numerical results.

VERTPAK1. Code Verification Analytic Solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golis, M.J.

1983-04-01

VERTPAK1 is a package of analytical solutions used in verification of numerical codes that simulate fluid flow, rock deformation, and solute transport in fractured and unfractured porous media. VERTPAK1 contains the following: BAREN, an analytical solution developed by Barenblatt, Zhelton and Kochina (1960) for describing transient flow to a well penetrating a (double porosity) confined aquifer; GIBMAC, an analytical solution developed by McNamee and Gibson (1960) for describing consolidation of a semi-infinite soil medium subject to a strip (plane strain) or cylindrical (axisymmetric) loading; GRINRH, an analytical solution developed by Gringarten (1971) for describing transient flow to a partially penetratingmore » well in a confined aquifer containing a single horizontal fracture; GRINRV, an analytical solution developed by Gringarten, Ramey, and Raghavan (1974) for describing transient flow to a fully penetrating well in a confined aquifer containing a single vertical fracture; HART, an analytical solution given by Nowacki (1962) and implemented by HART (1981) for describing the elastic behavior of an infinite solid subject to a line heat source; LESTER, an analytical solution presented by Lester, Jansen, and Burkholder (1975) for describing one-dimensional transport of radionuclide chains through an adsorbing medium; STRELT, an analytical solution presented by Streltsova-Adams (1978) for describing transient flow to a fully penetrating well in a (double porosity) confined aquifer; and TANG, an analytical solution developed by Tang, Frind, and Sudicky (1981) for describing solute transport in a porous medium containing a single fracture.« less

Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation

NASA Astrophysics Data System (ADS)

Gao, Hui; Cheng, Wenguang; Xu, Tianzhou; Wang, Gangwei

2018-03-01

The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalousmore » diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.« less

Analytic solutions in nonlinear massive gravity.

PubMed

Koyama, Kazuya; Niz, Gustavo; Tasinato, Gianmassimo

2011-09-23

We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free nonlinear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism, recovering general relativity below a Vainshtein radius given by (r(g)m(2))(1/3), where m is the graviton mass and r(g) is the Schwarzschild radius of a matter source. Another branch of exact solutions exists, corresponding to de Sitter-Schwarzschild spacetimes where the curvature scale of de Sitter space is proportional to the mass squared of the graviton.

Analytical Solution for Optimum Design of Furrow Irrigation Systems

NASA Astrophysics Data System (ADS)

Kiwan, M. E.

1996-05-01

An analytical solution for the optimum design of furrow irrigation systems is derived. The non-linear calculus optimization method is used to formulate a general form for designing the optimum system elements under circumstances of maximizing the water application efficiency of the system during irrigation. Different system bases and constraints are considered in the solution. A full irrigation water depth is considered to be achieved at the tail of the furrow line. The solution is based on neglecting the recession and depletion times after off-irrigation. This assumption is valid in the case of open-end (free gradient) furrow systems rather than closed-end (closed dike) systems. Illustrative examples for different systems are presented and the results are compared with the output obtained using an iterative numerical solution method. The final derived solution is expressed as a function of the furrow length ratio (the furrow length to the water travelling distance). The function of water travelling developed by Reddy et al. is considered for reaching the optimum solution. As practical results from the study, the optimum furrow elements for free gradient systems can be estimated to achieve the maximum application efficiency, i.e. furrow length, water inflow rate and cutoff irrigation time.

Hydrodynamics beyond Navier-Stokes: the slip flow model.

PubMed

Yudistiawan, Wahyu P; Ansumali, Santosh; Karlin, Iliya V

2008-07-01

Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali, Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation-the nine-bit model in two dimensions--in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.

Analytical volcano deformation modelling: A new and fast generalized point-source approach with application to the 2015 Calbuco eruption

NASA Astrophysics Data System (ADS)

Nikkhoo, M.; Walter, T. R.; Lundgren, P.; Prats-Iraola, P.

2015-12-01

Ground deformation at active volcanoes is one of the key precursors of volcanic unrest, monitored by InSAR and GPS techniques at high spatial and temporal resolution, respectively. Modelling of the observed displacements establishes the link between them and the underlying subsurface processes and volume change. The so-called Mogi model and the rectangular dislocation are two commonly applied analytical solutions that allow for quick interpretations based on the location, depth and volume change of pressurized spherical cavities and planar intrusions, respectively. Geological observations worldwide, however, suggest elongated, tabular or other non-equidimensional geometries for the magma chambers. How can these be modelled? Generalized models such as the Davis's point ellipsoidal cavity or the rectangular dislocation solutions, are geometrically limited and could barely improve the interpretation of data. We develop a new analytical artefact-free solution for a rectangular dislocation, which also possesses full rotational degrees of freedom. We construct a kinematic model in terms of three pairwise-perpendicular rectangular dislocations with a prescribed opening only. This model represents a generalized point source in the far field, and also performs as a finite dislocation model for planar intrusions in the near field. We show that through calculating the Eshelby's shape tensor the far-field displacements and stresses of any arbitrary triaxial ellipsoidal cavity can be reproduced by using this model. Regardless of its aspect ratios, the volume change of this model is simply the sum of the volume change of the individual dislocations. Our model can be integrated in any inversion scheme as simply as the Mogi model, profiting at the same time from the advantages of a generalized point source. After evaluating our model by using a boundary element method code, we apply it to ground displacements of the 2015 Calbuco eruption, Chile, observed by the Sentinel-1 satellite. We infer the parameters of a deflating elongated source located beneath Calbuco, and find significant differences to Mogi type solutions. The results imply that interpretations based on our model may help us better understand source characteristics, and in the case of Calubuco volcano infer a volcano-tectonic coupling mechanism.

New Exact Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Fireballs

NASA Astrophysics Data System (ADS)

Csörgő, Tamás; Kasza, Gábor; Csanád, Máté; Jiang, Zefang

2018-06-01

We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables like the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton-proton and heavy ion collision data at RHIC and LHC. In the longitudinally boost-invariant limit, these new solutions approach the Hwa-Bjorken solution and the corresponding rapidity distributions approach a rapidity plateaux.

Four-center bubbled BPS solutions with a Gibbons-Hawking base

NASA Astrophysics Data System (ADS)

Heidmann, Pierre

2017-10-01

We construct four-center bubbled BPS solutions with a Gibbons-Hawking base space. We give a systematic procedure to build scaling solutions: starting from three-supertube configurations and using generalized spectral flows and gauge transformations to extend to solutions with four Gibbons-Hawking centers. This allows us to construct very large families of smooth horizonless solutions that have the same charges and angular momentum as supersymmetric black holes with a macroscopically large horizon area. Our construction reveals that all scaling solutions with four Gibbons Hawking centers have an angular momentum at around 99% of the cosmic censorship bound. We give both an analytical and a numerical explanation for this unexpected feature.

An Analytical Study of Prostate-Specific Antigen Dynamics.

PubMed

Esteban, Ernesto P; Deliz, Giovanni; Rivera-Rodriguez, Jaileen; Laureano, Stephanie M

2016-01-01

The purpose of this research is to carry out a quantitative study of prostate-specific antigen dynamics for patients with prostatic diseases, such as benign prostatic hyperplasia (BPH) and localized prostate cancer (LPC). The proposed PSA mathematical model was implemented using clinical data of 218 Japanese patients with histological proven BPH and 147 Japanese patients with LPC (stages T2a and T2b). For prostatic diseases (BPH and LPC) a nonlinear equation was obtained and solved in a close form to predict PSA progression with patients' age. The general solution describes PSA dynamics for patients with both diseases LPC and BPH. Particular solutions allow studying PSA dynamics for patients with BPH or LPC. Analytical solutions have been obtained and solved in a close form to develop nomograms for a better understanding of PSA dynamics in patients with BPH and LPC. This study may be useful to improve the diagnostic and prognosis of prostatic diseases.

An analytical study on groundwater flow in drainage basins with horizontal wells

NASA Astrophysics Data System (ADS)

Wang, Jun-Zhi; Jiang, Xiao-Wei; Wan, Li; Wang, Xu-Sheng; Li, Hailong

2014-06-01

Analytical studies on release/capture zones are often limited to a uniform background groundwater flow. In fact, for basin-scale problems, the undulating water table would lead to the development of hierarchically nested flow systems, which are more complex than a uniform flow. Under the premise that the water table is a replica of undulating topography and hardly influenced by wells, an analytical solution of hydraulic head is derived for a two-dimensional cross section of a drainage basin with horizontal injection/pumping wells. Based on the analytical solution, distributions of hydraulic head, stagnation points and flow systems (including release/capture zones) are explored. The superposition of injection/pumping wells onto the background flow field leads to the development of new internal stagnation points and new flow systems (including release/capture zones). Generally speaking, the existence of n injection/pumping wells would result in up to n new internal stagnation points and up to 2n new flow systems (including release/capture zones). The analytical study presented, which integrates traditional well hydraulics with the theory of regional groundwater flow, is useful in understanding basin-scale groundwater flow influenced by human activities.

A Mathematica program for the approximate analytical solution to a nonlinear undamped Duffing equation by a new approximate approach

NASA Astrophysics Data System (ADS)

Wu, Dongmei; Wang, Zhongcheng

2006-03-01

According to Mickens [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563], the general HB (harmonic balance) method is an approximation to the convergent Fourier series representation of the periodic solution of a nonlinear oscillator and not an approximation to an expansion in terms of a small parameter. Consequently, for a nonlinear undamped Duffing equation with a driving force Bcos(ωx), to find a periodic solution when the fundamental frequency is identical to ω, the corresponding Fourier series can be written as y˜(x)=∑n=1m acos[(2n-1)ωx]. How to calculate the coefficients of the Fourier series efficiently with a computer program is still an open problem. For HB method, by substituting approximation y˜(x) into force equation, expanding the resulting expression into a trigonometric series, then letting the coefficients of the resulting lowest-order harmonic be zero, one can obtain approximate coefficients of approximation y˜(x) [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563]. But for nonlinear differential equations such as Duffing equation, it is very difficult to construct higher-order analytical approximations, because the HB method requires solving a set of algebraic equations for a large number of unknowns with very complex nonlinearities. To overcome the difficulty, forty years ago, Urabe derived a computational method for Duffing equation based on Galerkin procedure [M. Urabe, A. Reiter, Numerical computation of nonlinear forced oscillations by Galerkin's procedure, J. Math. Anal. Appl. 14 (1966) 107-140]. Dooren obtained an approximate solution of the Duffing oscillator with a special set of parameters by using Urabe's method [R. van Dooren, Stabilization of Cowell's classic finite difference method for numerical integration, J. Comput. Phys. 16 (1974) 186-192]. In this paper, in the frame of the general HB method, we present a new iteration algorithm to calculate the coefficients of the Fourier series. By using this new method, the iteration procedure starts with a(x)cos(ωx)+b(x)sin(ωx), and the accuracy may be improved gradually by determining new coefficients a,a,… will be produced automatically in an one-by-one manner. In all the stage of calculation, we need only to solve a cubic equation. Using this new algorithm, we develop a Mathematica program, which demonstrates following main advantages over the previous HB method: (1) it avoids solving a set of associate nonlinear equations; (2) it is easier to be implemented into a computer program, and produces a highly accurate solution with analytical expression efficiently. It is interesting to find that, generally, for a given set of parameters, a nonlinear Duffing equation can have three independent oscillation modes. For some sets of the parameters, it can have two modes with complex displacement and one with real displacement. But in some cases, it can have three modes, all of them having real displacement. Therefore, we can divide the parameters into two classes, according to the solution property: there is only one mode with real displacement and there are three modes with real displacement. This program should be useful to study the dynamically periodic behavior of a Duffing oscillator and can provide an approximate analytical solution with high-accuracy for testing the error behavior of newly developed numerical methods with a wide range of parameters. Program summaryTitle of program:AnalyDuffing.nb Catalogue identifier:ADWR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWR_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Computer for which the program is designed and others on which it has been tested:the program has been designed for a microcomputer and been tested on the microcomputer. Computers:IBM PC Installations:the address(es) of your computer(s) Operating systems under which the program has been tested:Windows XP Programming language used:Software Mathematica 4.2, 5.0 and 5.1 No. of lines in distributed program, including test data, etc.:23 663 No. of bytes in distributed program, including test data, etc.:152 321 Distribution format:tar.gz Memory required to execute with typical data:51 712 Bytes No. of bits in a word: No. of processors used:1 Has the code been vectorized?:no Peripherals used:no Program Library subprograms used:no Nature of physical problem:To find an approximate solution with analytical expressions for the undamped nonlinear Duffing equation with periodic driving force when the fundamental frequency is identical to the driving force. Method of solution:In the frame of the general HB method, by using a new iteration algorithm to calculate the coefficients of the Fourier series, we can obtain an approximate analytical solution with high-accuracy efficiently. Restrictions on the complexity of the problem:For problems, which have a large driving frequency, the convergence may be a little slow, because more iterative times are needed. Typical running time:several seconds Unusual features of the program:For an undamped Duffing equation, it can provide all the solutions or the oscillation modes with real displacement for any interesting parameters, for the required accuracy, efficiently. The program can be used to study the dynamically periodic behavior of a nonlinear oscillator, and can provide a high-accurate approximate analytical solution for developing high-accurate numerical method.

Magnetoacoustic Waves and the Kelvin-Helmholtz Instability in a Steady Asymmetric Slab. I: The Effects of Varying Density Ratios

NASA Astrophysics Data System (ADS)

Barbulescu, M.; Erdélyi, R.

2018-06-01

Recent observations have shown that bulk flow motions in structured solar plasmas, most evidently in coronal mass ejections (CMEs), may lead to the formation of Kelvin-Helmholtz instabilities (KHIs). Analytical models are thus essential in understanding both how the flows affect the propagation of magnetohydrodynamic (MHD) waves, and what the critical flow speed is for the formation of the KHI. We investigate both these aspects in a novel way: in a steady magnetic slab embedded in an asymmetric environment. The exterior of the slab is defined as having different equilibrium values of the background density, pressure, and temperature on either side. A steady flow and constant magnetic field are present in the slab interior. Approximate solutions to the dispersion relation are obtained analytically and classified with respect to mode and speed. General solutions and the KHI thresholds are obtained numerically. It is shown that, generally, both the KHI critical value and the cut-off speeds for magnetoacoustic waves are lowered by the external asymmetry.

Few-cycle optical rogue waves: complex modified Korteweg-de Vries equation.

PubMed

He, Jingsong; Wang, Lihong; Li, Linjing; Porsezian, K; Erdélyi, R

2014-06-01

In this paper, we consider the complex modified Korteweg-de Vries (mKdV) equation as a model of few-cycle optical pulses. Using the Lax pair, we construct a generalized Darboux transformation and systematically generate the first-, second-, and third-order rogue wave solutions and analyze the nature of evolution of higher-order rogue waves in detail. Based on detailed numerical and analytical investigations, we classify the higher-order rogue waves with respect to their intrinsic structure, namely, fundamental pattern, triangular pattern, and ring pattern. We also present several new patterns of the rogue wave according to the standard and nonstandard decomposition. The results of this paper explain the generalization of higher-order rogue waves in terms of rational solutions. We apply the contour line method to obtain the analytical formulas of the length and width of the first-order rogue wave of the complex mKdV and the nonlinear Schrödinger equations. In nonlinear optics, the higher-order rogue wave solutions found here will be very useful to generate high-power few-cycle optical pulses which will be applicable in the area of ultrashort pulse technology.

Odor Recognition vs. Classification in Artificial Olfaction

NASA Astrophysics Data System (ADS)

Raman, Baranidharan; Hertz, Joshua; Benkstein, Kurt; Semancik, Steve

2011-09-01

Most studies in chemical sensing have focused on the problem of precise identification of chemical species that were exposed during the training phase (the recognition problem). However, generalization of training to predict the chemical composition of untrained gases based on their similarity with analytes in the training set (the classification problem) has received very limited attention. These two analytical tasks pose conflicting constraints on the system. While correct recognition requires detection of molecular features that are unique to an analyte, generalization to untrained chemicals requires detection of features that are common across a desired class of analytes. A simple solution that addresses both issues simultaneously can be obtained from biological olfaction, where the odor class and identity information are decoupled and extracted individually over time. Mimicking this approach, we proposed a hierarchical scheme that allowed initial discrimination between broad chemical classes (e.g. contains oxygen) followed by finer refinements using additional data into sub-classes (e.g. ketones vs. alcohols) and, eventually, specific compositions (e.g. ethanol vs. methanol) [1]. We validated this approach using an array of temperature-controlled chemiresistors. We demonstrated that a small set of training analytes is sufficient to allow generalization to novel chemicals and that the scheme provides robust categorization despite aging. Here, we provide further characterization of this approach.

Interplay between gravity and quintessence: a set of new GR solutions

NASA Astrophysics Data System (ADS)

Chernin, Arthur D.; Santiago, David I.; Silbergleit, Alexander S.

2002-02-01

A set of new exact analytical general relativity (GR) solutions with time-dependent and spatially inhomogeneous quintessence demonstrate (1) a static non-empty space-time with a horizon-type singular surface; (2) time-dependent spatially homogeneous `spheres' which are completely different in geometry from the Friedmann isotropic models; (3) infinitely strong anti-gravity at a `true' singularity where the density is infinitely large. It is also found that (4) the GR solutions allow for an extreme `density-free' form of energy that can generate regular space-time geometries.

Inverted glass harp

NASA Astrophysics Data System (ADS)

Quinn, Daniel B.; Rosenberg, Brian J.

2015-08-01

We present an analytical treatment of the acoustics of liquid-filled wine glasses, or "glass harps." The solution is generalized such that under certain assumptions it reduces to previous glass harp models, but also leads to a proposed musical instrument, the "inverted glass harp," in which an empty glass is submerged in a liquid-filled basin. The versatility of the solution demonstrates that all glass harps are governed by a family of solutions to Laplace's equation around a vibrating disk. Tonal analyses of recordings for a sample glass are offered as confirmation of the scaling predictions.

Applications of He's semi-inverse method, ITEM and GGM to the Davey-Stewartson equation

NASA Astrophysics Data System (ADS)

Zinati, Reza Farshbaf; Manafian, Jalil

2017-04-01

We investigate the Davey-Stewartson (DS) equation. Travelling wave solutions were found. In this paper, we demonstrate the effectiveness of the analytical methods, namely, He's semi-inverse variational principle method (SIVPM), the improved tan(φ/2)-expansion method (ITEM) and generalized G'/G-expansion method (GGM) for seeking more exact solutions via the DS equation. These methods are direct, concise and simple to implement compared to other existing methods. The exact solutions containing four types solutions have been achieved. The results demonstrate that the aforementioned methods are more efficient than the Ansatz method applied by Mirzazadeh (2015). Abundant exact travelling wave solutions including solitons, kink, periodic and rational solutions have been found by the improved tan(φ/2)-expansion and generalized G'/G-expansion methods. By He's semi-inverse variational principle we have obtained dark and bright soliton wave solutions. Also, the obtained semi-inverse variational principle has profound implications in physical understandings. These solutions might play important role in engineering and physics fields. Moreover, by using Matlab, some graphical simulations were done to see the behavior of these solutions.

Hydrostatic equilibrium of stars without electroneutrality constraint

NASA Astrophysics Data System (ADS)

Krivoruchenko, M. I.; Nadyozhin, D. K.; Yudin, A. V.

2018-04-01

The general solution of hydrostatic equilibrium equations for a two-component fluid of ions and electrons without a local electroneutrality constraint is found in the framework of Newtonian gravity theory. In agreement with the Poincaré theorem on analyticity and in the context of Dyson's argument, the general solution is demonstrated to possess a fixed (essential) singularity in the gravitational constant G at G =0 . The regular component of the general solution can be determined by perturbation theory in G starting from a locally neutral solution. The nonperturbative component obtained using the method of Wentzel, Kramers and Brillouin is exponentially small in the inner layers of the star and grows rapidly in the outward direction. Near the surface of the star, both components are comparable in magnitude, and their nonlinear interplay determines the properties of an electro- or ionosphere. The stellar charge varies within the limits of -0.1 to 150 C per solar mass. The properties of electro- and ionospheres are exponentially sensitive to variations of the fluid densities in the central regions of the star. The general solutions of two exactly solvable stellar models without a local electroneutrality constraint are also presented.

Complete factorisation and analytic solutions of generalized Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Brenig, L.

1988-11-01

It is shown that many systems of nonlinear differential equations of interest in various fields are naturally imbedded in a new family of differential equations. This family is invariant under nonlinear transformations based on the concept of matrix power of a vector. Each equation belonging to that family can be brought into a factorized canonical form for which integrable cases can be easily identified and solutions can be found by quadratures.

Statistical theory on the analytical form of cloud particle size distributions

NASA Astrophysics Data System (ADS)

Wu, Wei; McFarquhar, Greg

2017-11-01

Several analytical forms of cloud particle size distributions (PSDs) have been used in numerical modeling and remote sensing retrieval studies of clouds and precipitation, including exponential, gamma, lognormal, and Weibull distributions. However, there is no satisfying physical explanation as to why certain distribution forms preferentially occur instead of others. Theoretically, the analytical form of a PSD can be derived by directly solving the general dynamic equation, but no analytical solutions have been found yet. Instead of using a process level approach, the use of the principle of maximum entropy (MaxEnt) for determining the analytical form of PSDs from the perspective of system is examined here. Here, the issue of variability under coordinate transformations that arises using the Gibbs/Shannon definition of entropy is identified, and the use of the concept of relative entropy to avoid these problems is discussed. Focusing on cloud physics, the four-parameter generalized gamma distribution is proposed as the analytical form of a PSD using the principle of maximum (relative) entropy with assumptions on power law relations between state variables, scale invariance and a further constraint on the expectation of one state variable (e.g. bulk water mass). DOE ASR.

General two-species interacting Lotka-Volterra system: Population dynamics and wave propagation

NASA Astrophysics Data System (ADS)

Zhu, Haoqi; Wang, Mao-Xiang; Lai, Pik-Yin

2018-05-01

The population dynamics of two interacting species modeled by the Lotka-Volterra (LV) model with general parameters that can promote or suppress the other species is studied. It is found that the properties of the two species' isoclines determine the interaction of species, leading to six regimes in the phase diagram of interspecies interaction; i.e., there are six different interspecific relationships described by the LV model. Four regimes allow for nontrivial species coexistence, among which it is found that three of them are stable, namely, weak competition, mutualism, and predator-prey scenarios can lead to win-win coexistence situations. The Lyapunov function for general nontrivial two-species coexistence is also constructed. Furthermore, in the presence of spatial diffusion of the species, the dynamics can lead to steady wavefront propagation and can alter the population map. Propagating wavefront solutions in one dimension are investigated analytically and by numerical solutions. The steady wavefront speeds are obtained analytically via nonlinear dynamics analysis and verified by numerical solutions. In addition to the inter- and intraspecific interaction parameters, the intrinsic speed parameters of each species play a decisive role in species populations and wave properties. In some regimes, both species can copropagate with the same wave speeds in a finite range of parameters. Our results are further discussed in the light of possible biological relevance and ecological implications.

Four-dimensional black holes in Einsteinian cubic gravity

NASA Astrophysics Data System (ADS)

Bueno, Pablo; Cano, Pablo A.

2016-12-01

We construct static and spherically symmetric generalizations of the Schwarzschild- and Reissner-Nordström-(anti-)de Sitter [RN-(A)dS] black-hole solutions in four-dimensional Einsteinian cubic gravity (ECG). The solutions are characterized by a single function which satisfies a nonlinear second-order differential equation. Interestingly, we are able to compute independently the Hawking temperature T , the Wald entropy S and the Abbott-Deser mass M of the solutions analytically as functions of the horizon radius and the ECG coupling constant λ . Using these we show that the first law of black-hole mechanics is exactly satisfied. Some of the solutions have positive specific heat, which makes them thermodynamically stable, even in the uncharged and asymptotically flat case. Further, we claim that, up to cubic order in curvature, ECG is the most general four-dimensional theory of gravity which allows for nontrivial generalizations of Schwarzschild- and RN-(A)dS characterized by a single function which reduce to the usual Einstein gravity solutions when the corresponding higher-order couplings are set to zero.

Semi-analytical solution for flow in a leaky unconfined aquifer toward a partially penetrating pumping well

NASA Astrophysics Data System (ADS)

Malama, Bwalya; Kuhlman, Kristopher L.; Barrash, Warren

2008-07-01

SummaryA semi-analytical solution is presented for the problem of flow in a system consisting of unconfined and confined aquifers, separated by an aquitard. The unconfined aquifer is pumped continuously at a constant rate from a well of infinitesimal radius that partially penetrates its saturated thickness. The solution is termed semi-analytical because the exact solution obtained in double Laplace-Hankel transform space is inverted numerically. The solution presented here is more general than similar solutions obtained for confined aquifer flow as we do not adopt the assumption of unidirectional flow in the confined aquifer (typically assumed to be horizontal) and the aquitard (typically assumed to be vertical). Model predicted results show significant departure from the solution that does not take into account the effect of leakage even for cases where aquitard hydraulic conductivities are two orders of magnitude smaller than those of the aquifers. The results show low sensitivity to changes in radial hydraulic conductivities for aquitards that are two or more orders of magnitude smaller than those of the aquifers, in conformity to findings of earlier workers that radial flow in aquitards may be neglected under such conditions. Hence, for cases were aquitard hydraulic conductivities are two or more orders of magnitude smaller than aquifer conductivities, the simpler models that restrict flow to the radial direction in aquifers and to the vertical direction in aquitards may be sufficient. However, the model developed here can be used to model flow in aquifer-aquitard systems where radial flow is significant in aquitards.

An analytically solvable three-body break-up model problem in hyperspherical coordinates

NASA Astrophysics Data System (ADS)

Ancarani, L. U.; Gasaneo, G.; Mitnik, D. M.

2012-10-01

An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrödinger equation where the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The closed form solution is derived in hyperspherical coordinates leading to an analytic expression for the associated scattering transition amplitude. The proposed scattering model contains most of the difficulties encountered in real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behavior. Since the coordinates' coupling is completely different, the model provides an alternative test to that given by the Temkin-Poet model. The knowledge of the analytic solution provides an interesting benchmark to test numerical methods dealing with the double continuum, in particular in the asymptotic regions. An hyperspherical Sturmian approach recently developed for three-body collisional problems is used to reproduce to high accuracy the analytical results. In addition to this, we generalized the model generating an approximate wave function possessing the correct radial asymptotic behavior corresponding to an S-wave three-body Coulomb problem. The model allows us to explore the typical structure of the solution of a three-body driven equation, to identify three regions (the driven, the Coulombic and the asymptotic), and to analyze how far one has to go to extract the transition amplitude.

Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics

NASA Astrophysics Data System (ADS)

Denicol, Gabriel S.; Noronha, Jorge

2018-03-01

We find the general analytical solution of the viscous relativistic hydrodynamic equations (in the absence of bulk viscosity and chemical potential) for a Bjorken expanding fluid with an ideal gas equation of state and a constant shear viscosity relaxation time. We analytically determine the hydrodynamic attractor of this fluid and discuss its properties. We show for the first time that the slow-roll expansion, a commonly used approach to characterize the attractor, diverges. This is shown to hold also in a conformal plasma. The gradient expansion is found to converge in an example where causality and stability are violated.

VERTPAK1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golis, M.J.

1983-04-01

VERTPAK1 is a package of analytical solutions used in verification of numerical codes that simulate fluid flow, rock deformation, and solute transport in fractured and unfractured porous media. VERTPAK1 contains the following: BAREN, an analytical solution developed by Barenblatt, Zhelton and Kochina (1960) for describing transient flow to a well penetrating a (double porosity) confined aquifer; GIBMAC, an analytical solution developed by McNamee and Gibson (1960) for describing consolidation of a semi-infinite soil medium subject to a strip (plane strain) or cylindrical (axisymmetric) loading; GRINRH, an analytical solution developed by Gringarten (1971) for describing transient flow to a partially penetratingmore » well in a confined aquifer containing a single horizontal fracture; GRINRV, an analytical solution developed by Gringarten, Ramey, and Raghavan (1974) for describing transient flow to a fully penetrating well in a confined aquifer containing a single vertical fracture; HART, an analytical solution given by Nowacki (1962) and implemented by HART (1981) for describing the elastic behavior of an infinite solid subject to a line heat source; LESTER, an analytical solution presented by Lester, Jansen, and Burkholder (1975) for describing one-dimensional transport of radionuclide chains through an adsorbing medium; STRELT, an analytical solution presented by Streltsova-Adams (1978) for describing transient flow to a fully penetrating well in a (double porosity) confined aquifer; and TANG, an analytical solution developed by Tang, Frind, and Sudicky (1981) for describing solute transport in a porous medium containing a single fracture.« less

Kinematics and dynamics of robotic systems with multiple closed loops

NASA Astrophysics Data System (ADS)

Zhang, Chang-De

The kinematics and dynamics of robotic systems with multiple closed loops, such as Stewart platforms, walking machines, and hybrid manipulators, are studied. In the study of kinematics, focus is on the closed-form solutions of the forward position analysis of different parallel systems. A closed-form solution means that the solution is expressed as a polynomial in one variable. If the order of the polynomial is less than or equal to four, the solution has analytical closed-form. First, the conditions of obtaining analytical closed-form solutions are studied. For a Stewart platform, the condition is found to be that one rotational degree of freedom of the output link is decoupled from the other five. Based on this condition, a class of Stewart platforms which has analytical closed-form solution is formulated. Conditions of analytical closed-form solution for other parallel systems are also studied. Closed-form solutions of forward kinematics for walking machines and multi-fingered grippers are then studied. For a parallel system with three three-degree-of-freedom subchains, there are 84 possible ways to select six independent joints among nine joints. These 84 ways can be classified into three categories: Category 3:3:0, Category 3:2:1, and Category 2:2:2. It is shown that the first category has no solutions; the solutions of the second category have analytical closed-form; and the solutions of the last category are higher order polynomials. The study is then extended to a nearly general Stewart platform. The solution is a 20th order polynomial and the Stewart platform has a maximum of 40 possible configurations. Also, the study is extended to a new class of hybrid manipulators which consists of two serially connected parallel mechanisms. In the study of dynamics, a computationally efficient method for inverse dynamics of manipulators based on the virtual work principle is developed. Although this method is comparable with the recursive Newton-Euler method for serial manipulators, its advantage is more noteworthy when applied to parallel systems. An approach of inverse dynamics of a walking machine is also developed, which includes inverse dynamic modeling, foot force distribution, and joint force/torque allocation.

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

NASA Technical Reports Server (NTRS)

Chen, C.-J.; Naseri-Neshat, H.; Ho, K.-S.

1981-01-01

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Ding, Xiao-Li; Nieto, Juan J.

2017-11-01

In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

Application of an Extended Parabolic Equation to the Calculation of the Mean Field and the Transverse and Longitudinal Mutual Coherence Functions Within Atmospheric Turbulence

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2005-01-01

Solutions are derived for the generalized mutual coherence function (MCF), i.e., the second order moment, of a random wave field propagating through a random medium within the context of the extended parabolic equation. Here, "generalized" connotes the consideration of both the transverse as well as the longitudinal second order moments (with respect to the direction of propagation). Such solutions will afford a comparison between the results of the parabolic equation within the pararaxial approximation and those of the wide-angle extended theory. To this end, a statistical operator method is developed which gives a general equation for an arbitrary spatial statistical moment of the wave field. The generality of the operator method allows one to obtain an expression for the second order field moment in the direction longitudinal to the direction of propagation. Analytical solutions to these equations are derived for the Kolmogorov and Tatarskii spectra of atmospheric permittivity fluctuations within the Markov approximation.

A new approach to study cadmium complexes with oxalic acid in soil solution.

PubMed

Dytrtová, Jana Jaklová; Jakl, Michal; Sestáková, Ivana; Zins, Emilie-Laure; Schröder, Detlef; Navrátil, Tomáš

2011-05-05

This study presents a new analytical approach for the determination of heavy metals complexed to low-molecular-weight-organic acids in soil solutions, which combines the sensitivity of differential pulse anodic stripping voltammetry (DPASV) with the molecular insight gained by electrospray ionization mass spectrometry (ESI-MS). The combination of these analytical methods allows the investigation of such complexes in complex matrixes. On the voltammograms of the soil solutions, in addition to the expected complexes of oxalic acid with cadmium and lead, respectively, also peaks belonging to mixed complexes of cadmium, lead, and oxalic acid (OAH(2)) were observed. In order to verify the possible formation of complexes with OAH(2), aqueous solutions of OAH(2) with traces of Cd(II) were investigated as model systems. Signals corresponding to several distinct molecular complexes between cadmium and oxalic acid were detected in the model solutions using negative-ion ESI-MS, which follow the general formula [Cd(n)(X,Y)((2n+1))](-), where n is the number of cadmium atoms, X=Cl(-), and Y=OAH(-). Some of these complexes were also identified in the ESI mass spectra taken from the soil solutions. Copyright © 2011 Elsevier B.V. All rights reserved.

Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas

NASA Astrophysics Data System (ADS)

Hu, Wen-Qiang; Gao, Yi-Tian; Jia, Shu-Liang; Huang, Qian-Min; Lan, Zhong-Zhou

2016-11-01

In this paper, a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation is investigated, which has been presented as a model for the shallow water wave in fluids or the electrostatic wave potential in plasmas. By virtue of the binary Bell polynomials, the bilinear form of this equation is obtained. With the aid of the bilinear form, N -soliton solutions are obtained by the Hirota method, periodic wave solutions are constructed via the Riemann theta function, and breather wave solutions are obtained according to the extended homoclinic test approach. Travelling waves are constructed by the polynomial expansion method as well. Then, the relations between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure. Furthermore, we obtain some new solutions of this equation by the standard extended homoclinic test approach. Finally, we give a generalized form of this equation, and find that similar analytical solutions can be obtained from the generalized equation with arbitrary coefficients.

Optimization techniques applied to passive measures for in-orbit spacecraft survivability

NASA Technical Reports Server (NTRS)

Mog, Robert A.; Price, D. Marvin

1991-01-01

Spacecraft designers have always been concerned about the effects of meteoroid impacts on mission safety. The engineering solution to this problem has generally been to erect a bumper or shield placed outboard from the spacecraft wall to disrupt/deflect the incoming projectiles. Spacecraft designers have a number of tools at their disposal to aid in the design process. These include hypervelocity impact testing, analytic impact predictors, and hydrodynamic codes. Analytic impact predictors generally provide the best quick-look estimate of design tradeoffs. The most complete way to determine the characteristics of an analytic impact predictor is through optimization of the protective structures design problem formulated with the predictor of interest. Space Station Freedom protective structures design insight is provided through the coupling of design/material requirements, hypervelocity impact phenomenology, meteoroid and space debris environment sensitivities, optimization techniques and operations research strategies, and mission scenarios. Major results are presented.

Theory of precipitation effects on dead cylindrical fuels

Treesearch

Michael A. Fosberg

1972-01-01

Numerical and analytical solutions of the Fickian diffusion equation were used to determine the effects of precipitation on dead cylindrical forest fuels. The analytical solution provided a physical framework. The numerical solutions were then used to refine the analytical solution through a similarity argument. The theoretical solutions predicted realistic rates of...

Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation.

PubMed

Hu, Xiao-Rui; Lou, Sen-Yue; Chen, Yong

2012-05-01

In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painlevé waves. Actually, even if for the most well-known prototypical models such as the Kortewet-de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetries which are related to Darboux transformation for the well-known KdV equation. The same approach also yields some other types of interaction solutions among different types of solutions such as solitary waves, rational solutions, Bessel function solutions, and/or general Painlevé II solutions.

General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van Gorder, Robert A., E-mail: rav@knights.ucf.edu

2014-06-15

In his study of superfluid turbulence in the low-temperature limit, Svistunov [“Superfluid turbulence in the low-temperature limit,” Phys. Rev. B 52, 3647 (1995)] derived a Hamiltonian equation for the self-induced motion of a vortex filament. Under the local induction approximation (LIA), the Svistunov formulation is equivalent to a nonlinear dispersive partial differential equation. In this paper, we consider a family of rotating vortex filament solutions for the LIA reduction of the Svistunov formulation, which we refer to as the 2D LIA (since it permits a potential formulation in terms of two of the three Cartesian coordinates). This class of solutionsmore » holds the well-known Hasimoto-type planar vortex filament [H. Hasimoto, “Motion of a vortex filament and its relation to elastica,” J. Phys. Soc. Jpn. 31, 293 (1971)] as one reduction and helical solutions as another. More generally, we obtain solutions which are periodic in the space variable. A systematic analytical study of the behavior of such solutions is carried out. In the case where vortex filaments have small deviations from the axis of rotation, closed analytical forms of the filament solutions are given. A variety of numerical simulations are provided to demonstrate the wide range of rotating filament behaviors possible. Doing so, we are able to determine a number of vortex filament structures not previously studied. We find that the solution structure progresses from planar to helical, and then to more intricate and complex filament structures, possibly indicating the onset of superfluid turbulence.« less

Thin airfoil theory based on approximate solution of the transonic flow equation

NASA Technical Reports Server (NTRS)

Spreiter, John R; Alksne, Alberta Y

1957-01-01

A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.

Exploratory Bifactor Analysis: The Schmid-Leiman Orthogonalization and Jennrich-Bentler Analytic Rotations

PubMed Central

Mansolf, Maxwell; Reise, Steven P.

2017-01-01

Analytic bifactor rotations (Jennrich & Bentler, 2011, 2012) have been recently developed and made generally available, but are not well understood. The Jennrich-Bentler analytic bifactor rotations (bi-quartimin and bi-geomin) are an alternative to, and arguably an improvement upon, the less technically sophisticated Schmid-Leiman orthogonalization (Schmid & Leiman, 1957). We review the technical details that underlie the Schmid-Leiman and Jennrich-Bentler bifactor rotations, using simulated data structures to illustrate important features and limitations. For the Schmid-Leiman, we review the problem of inaccurate parameter estimates caused by the linear dependencies, sometimes called “proportionality constraints,” that are required to expand a p correlated factors solution into a (p+1) (bi)factor space. We also review the complexities involved when the data depart from perfect cluster structure (e.g., item cross-loading on group factors). For the Jennrich-Bentler rotations, we describe problems in parameter estimation caused by departures from perfect cluster structure. In addition, we illustrate the related problems of: (a) solutions that are not invariant under different starting values (i.e., local minima problems); and, (b) group factors collapsing onto the general factor. Recommendations are made for substantive researchers including examining all local minima and applying multiple exploratory techniques in an effort to identify an accurate model. PMID:27612521

An extension of the Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

Bordenave, Charles; Germain, Pierre; Trogdon, Thomas

2015-12-01

We show how the derivation of the Derrida-Lebowitz-Speer-Spohn equation can be prolonged to obtain a new equation, generalizing the models obtained in the paper by these authors. We then investigate its properties from both an analytical and numerical perspective. Specifically, a numerical method is presented to approximate solutions of the prolonged equation. Using this method, we investigate the relationship between the solutions of the prolonged equation and the Tracy-Widom GOE distribution.

Insight solutions are correct more often than analytic solutions

PubMed Central

Salvi, Carola; Bricolo, Emanuela; Kounios, John; Bowden, Edward; Beeman, Mark

2016-01-01

How accurate are insights compared to analytical solutions? In four experiments, we investigated how participants’ solving strategies influenced their solution accuracies across different types of problems, including one that was linguistic, one that was visual and two that were mixed visual-linguistic. In each experiment, participants’ self-judged insight solutions were, on average, more accurate than their analytic ones. We hypothesised that insight solutions have superior accuracy because they emerge into consciousness in an all-or-nothing fashion when the unconscious solving process is complete, whereas analytic solutions can be guesses based on conscious, prematurely terminated, processing. This hypothesis is supported by the finding that participants’ analytic solutions included relatively more incorrect responses (i.e., errors of commission) than timeouts (i.e., errors of omission) compared to their insight responses. PMID:27667960

Solving vertical and horizontal well hydraulics problems analytically in Cartesian coordinates with vertical and horizontal anisotropies

NASA Astrophysics Data System (ADS)

Batu, Vedat

2012-01-01

SummaryA new generalized three-dimensional analytical solution is developed for a partially-penetrating vertical rectangular parallelepiped well screen in a confined aquifer by solving the three-dimensional transient ground water flow differential equation in x- y- z Cartesian coordinates system for drawdown by taking into account the three principal hydraulic conductivities ( Kx, Ky, and Kz) along the x- y- z coordinate directions. The fully penetrating screen case becomes equivalent to the single vertical fracture case of Gringarten and Ramey (1973). It is shown that the new solution and Gringarten and Ramey solution (1973) match very well. Similarly, it is shown that this new solution for a horizontally tiny fully penetrating parallelepiped rectangular parallelepiped screen case match very well with Theis (1935) solution. Moreover, it is also shown that the horizontally tiny partially-penetrating parallelepiped rectangular well screen case of this new solution match very well with Hantush (1964) solution. This new analytical solution can also cover a partially-penetrating horizontal well by representing its screen interval with vertically tiny rectangular parallelepiped. Also the solution takes into account both the vertical anisotropy ( azx = Kz/ Kx) as well as the horizontal anisotropy ( ayx = Ky/ Kx) and has potential application areas to analyze pumping test drawdown data from partially-penetrating vertical and horizontal wells by representing them as tiny rectangular parallelepiped as well as line sources. The solution has also potential application areas for a partially-penetrating parallelepiped rectangular vertical fracture. With this new solution, the horizontal anisotropy ( ayx = Ky/ Kx) in addition to the vertical anisotropy ( azx = Kz/ Kx) can also be determined using observed drawdown data. Most importantly, with this solution, to the knowledge of the author, it has been shown the first time in the literature that some well-known well hydraulics problems can also be solved in Cartesian coordinates with some additional advantages other than the conventional cylindrical coordinates method.

Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

NASA Astrophysics Data System (ADS)

Minesaki, Yukitaka

2018-04-01

We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

Implementation of Finite Volume based Navier Stokes Algorithm Within General Purpose Flow Network Code

NASA Technical Reports Server (NTRS)

Schallhorn, Paul; Majumdar, Alok

2012-01-01

This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.

Development of a solution adaptive unstructured scheme for quasi-3D inviscid flows through advanced turbomachinery cascades

NASA Technical Reports Server (NTRS)

Usab, William J., Jr.; Jiang, Yi-Tsann

1991-01-01

The objective of the present research is to develop a general solution adaptive scheme for the accurate prediction of inviscid quasi-three-dimensional flow in advanced compressor and turbine designs. The adaptive solution scheme combines an explicit finite-volume time-marching scheme for unstructured triangular meshes and an advancing front triangular mesh scheme with a remeshing procedure for adapting the mesh as the solution evolves. The unstructured flow solver has been tested on a series of two-dimensional airfoil configurations including a three-element analytic test case presented here. Mesh adapted quasi-three-dimensional Euler solutions are presented for three spanwise stations of the NASA rotor 67 transonic fan. Computed solutions are compared with available experimental data.

Analytic Analysis of Convergent Shocks to Multi-Gigabar Conditions

NASA Astrophysics Data System (ADS)

Ruby, J. J.; Rygg, J. R.; Collins, G. W.; Bachmann, B.; Doeppner, T.; Ping, Y.; Gaffney, J.; Lazicki, A.; Kritcher, A. L.; Swift, D.; Nilsen, J.; Landen, O. L.; Hatarik, R.; Masters, N.; Nagel, S.; Sterne, P.; Pardini, T.; Khan, S.; Celliers, P. M.; Patel, P.; Gericke, D.; Falcone, R.

2017-10-01

The gigabar experimental platform at the National Ignition Facility is designed to increase understanding of the physical states and processes that dominate in the hydrogen at pressures from several hundreds of Mbar to tens of Gbar. Recent experiments using a solid CD2 ball reached temperatures and densities of order 107 K and several tens of g/cm3 , respectively. These conditions lead to the production of D-D fusion neutrons and x-ray bremsstrahlung photons, which allow us to place constraints on the thermodynamic states at peak compression. We use an analytic model to connect the neutron and x-ray emission with the state variables at peak compression. This analytic model is based on the self-similar Guderley solution of an imploding shock wave and the self-similar solution of the point explosion with heat conduction from Reinicke. Work is also being done to create a fully self-similar solution of an imploding shock wave coupled with heat conduction and radiation transport using a general equation of state. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.

Bessel Fourier orientation reconstruction: an analytical EAP reconstruction using multiple shell acquisitions in diffusion MRI.

PubMed

Hosseinbor, Ameer Pasha; Chung, Moo K; Wu, Yu-Chien; Alexander, Andrew L

2011-01-01

The estimation of the ensemble average propagator (EAP) directly from q-space DWI signals is an open problem in diffusion MRI. Diffusion spectrum imaging (DSI) is one common technique to compute the EAP directly from the diffusion signal, but it is burdened by the large sampling required. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed. One, in particular, is Diffusion Propagator Imaging (DPI) which is based on the Laplace's equation estimation of diffusion signal for each shell acquisition. Viewed intuitively in terms of the heat equation, the DPI solution is obtained when the heat distribution between temperatuere measurements at each shell is at steady state. We propose a generalized extension of DPI, Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition. That is, the heat distribution between shell measurements is no longer at steady state. In addition to being analytical, the BFOR solution also includes an intrinsic exponential smootheing term. We illustrate the effectiveness of the proposed method by showing results on both synthetic and real MR datasets.

Numerical and Analytical Solutions of Hypersonic Interactions Involving Surface Property Discontinuities

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.; Inger, George R.

1999-01-01

The local viscous-inviscid interaction field generated by a wall temperature jump on a flat plate in supersonic flow and on the windside of a Reusable Launch Vehicle in hypersonic flow is studied in detail by both a Navier-Stokes numerical code and an analytical triple-deck model. Treatment of the rapid heat transfer changes both upstream and downstream of the jump is included. Closed form relationships derived from the triple-deck theory are presented. The analytically predicted pressure and heating variations including upstream influence are found to be in generally good agreement with the Computational Fluid Dynamic (CFD) predictions. These analyses not only clarify the interactive physics involved but also are useful in preliminary design of thermal protection systems and as an insertable module to improve CFD code efficiency when applied to such small-scale interaction problems. The analyses only require conditions at the wall and boundary-layer edge which are easily extracted from a baseline, constant wall temperature, CFD solution.

Stable static structures in models with higher-order derivatives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bazeia, D., E-mail: bazeia@fisica.ufpb.br; Departamento de Física, Universidade Federal de Campina Grande, 58109-970 Campina Grande, PB; Lobão, A.S.

2015-09-15

We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space–time. We study models in which the scalar field engenders higher-order derivatives and spontaneous symmetry breaking, inducing the presence of domain walls. Despite the presence of higher-order derivatives, the models keep to equations of motion second-order differential equations, so we focus on the presence of first-order equations that help us to obtain analytical solutions and investigate linear stability on general grounds. We then illustrate the general results with some specific examples, showing that the domain wall may become compact and that themore » zero mode may split. Moreover, if the model is further generalized to include k-field behavior, it may contribute to split the static structure itself.« less

Modeling mass transfer and reaction of dilute solutes in a ternary phase system by the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Fu, Yu-Hang; Bai, Lin; Luo, Kai-Hong; Jin, Yong; Cheng, Yi

2017-04-01

In this work, we propose a general approach for modeling mass transfer and reaction of dilute solute(s) in incompressible three-phase flows by introducing a collision operator in lattice Boltzmann (LB) method. An LB equation was used to simulate the solute dynamics among three different fluids, in which the newly expanded collision operator was used to depict the interface behavior of dilute solute(s). The multiscale analysis showed that the presented model can recover the macroscopic transport equations derived from the Maxwell-Stefan equation for dilute solutes in three-phase systems. Compared with the analytical equation of state of solute and dynamic behavior, these results are proven to constitute a generalized framework to simulate solute distributions in three-phase flows, including compound soluble in one phase, compound adsorbed on single-interface, compound in two phases, and solute soluble in three phases. Moreover, numerical simulations of benchmark cases, such as phase decomposition, multilayered planar interfaces, and liquid lens, were performed to test the stability and efficiency of the model. Finally, the multiphase mass transfer and reaction in Janus droplet transport in a straight microchannel were well reproduced.

A closed-form solution for steady-state coupled phloem/xylem flow using the Lambert-W function.

PubMed

Hall, A J; Minchin, P E H

2013-12-01

A closed-form solution for steady-state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert-W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time-dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed-form solution, and is expected to be useful as a component part of larger numerical models of entire plants. © 2013 John Wiley & Sons Ltd.

Nonlinear storage models of unconfined flow through a shallow aquifer on an inclined base and their quasi-steady flow application

NASA Astrophysics Data System (ADS)

Varvaris, Ioannis; Gravanis, Elias; Koussis, Antonis; Akylas, Evangelos

2013-04-01

Hillslope processes involving flow through an inclined shallow aquifer range from subsurface stormflow to stream base flow (drought flow, or groundwater recession flow). In the case of recharge, the infiltrating water moves vertically as unsaturated flow until it reaches the saturated groundwater, where the flow is approximately parallel to the base of the aquifer. Boussinesq used the Dupuit-Forchheimer (D-F) hydraulic theory to formulate unconfined groundwater flow through a soil layer resting on an impervious inclined bed, deriving a nonlinear equation for the flow rate that consists of a linear gravity-driven component and a quadratic pressure-gradient component. Inserting that flow rate equation into the differential storage balance equation (volume conservation) Boussinesq obtained a nonlinear second-order partial differential equation for the depth. So far however, only few special solutions have been advanced for that governing equation. The nonlinearity of the equation of Boussinesq is the major obstacle to deriving a general analytical solution for the depth profile of unconfined flow on a sloping base with recharge (from which the discharges could be then determined). Henderson and Wooding (1964) were able to obtain an exact analytical solution for steady unconfined flow on a sloping base, with recharge, and their work deserves special note in the realm of solutions of the nonlinear equation of Boussinesq. However, the absence of a general solution for the transient case, which is of practical interest to hydrologists, has been the motivation for developing approximate solutions of the non-linear equation of Boussinesq. In this work, we derive the aquifer storage function by integrating analytically over the aquifer base the depth profiles resulting from the complete nonlinear Boussinesq equation for steady flow. This storage function consists of a linear and a nonlinear outflow-dependent term. Then, we use this physics-based storage function in the transient storage balance over the hillslope, obtaining analytical solutions of the outflow and the storage, for recharge and drainage, via a quasi-steady flow calculation. The hydraulically derived storage model is thus embedded in a quasi-steady approximation of transient unconfined flow in sloping aquifers. We generalise this hydrologic model of groundwater flow by modifying the storage function to be the weighted sum of the linear and the nonlinear storage terms, determining the weighting factor objectively from a known integral quantity of the flow (either an initial volume of water stored in the aquifer or a drained water volume). We demonstrate the validity of this model through comparisons with experimental data and simulation results.

Comparison of particle tracking algorithms in commercial CFD packages: sedimentation and diffusion.

PubMed

Robinson, Risa J; Snyder, Pam; Oldham, Michael J

2007-05-01

Computational fluid dynamic modeling software has enabled microdosimetry patterns of inhaled toxins and toxicants to be predicted and visualized, and is being used in inhalation toxicology and risk assessment. These predicted microdosimetry patterns in airway structures are derived from predicted airflow patterns within these airways and particle tracking algorithms used in computational fluid dynamics (CFD) software packages. Although these commercial CFD codes have been tested for accuracy under various conditions, they have not been well tested for respiratory flows in general. Nor has their particle tracking algorithm accuracy been well studied. In this study, three software packages, Fluent Discrete Phase Model (DPM), Fluent Fine Particle Model (FPM), and ANSYS CFX, were evaluated. Sedimentation and diffusion were each isolated in a straight tube geometry and tested for accuracy. A range of flow rates corresponding to adult low activity (minute ventilation = 10 L/min) and to heavy exertion (minute ventilation = 60 L/min) were tested by varying the range of dimensionless diffusion and sedimentation parameters found using the Weibel symmetric 23 generation lung morphology. Numerical results for fully developed parabolic and uniform (slip) profiles were compared respectively, to Pich (1972) and Yu (1977) analytical sedimentation solutions. Schum and Yeh (1980) equations for sedimentation were also compared. Numerical results for diffusional deposition were compared to analytical solutions of Ingham (1975) for parabolic and uniform profiles. Significant differences were found among the various CFD software packages and between numerical and analytical solutions. Therefore, it is prudent to validate CFD predictions against analytical solutions in idealized geometry before tackling the complex geometries of the respiratory tract.

Surface tension effects on fully developed liquid layer flow over a convex corner

NASA Astrophysics Data System (ADS)

Bhatti, Ifrah; Farid, Saadia; Ullah, Saif; Riaz, Samia; Faryad, Maimoona

2018-04-01

This investigation deals with the study of fully developed liquid layer flow along with surface tension effects, confronting a convex corner in the direction of fluid flow. At the point of interaction, the related equations are formulated using double deck structure and match asymptotic techniques. Linearized solutions for small angle are obtained analytically. The solutions corresponding to similar flow neglecting surface tension effects are also recovered as special case of our general solutions. Finally, the influence of pertinent parameters on the flow, as well as a comparison between models, are shown by graphical illustration.

Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

NASA Astrophysics Data System (ADS)

Terasaki, J.; Smetana, A.; Šimkovic, F.; Krivoruchenko, M. I.

2017-10-01

It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number N = 2 and numerically for N = 8. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation.

Multichoice minority game.

PubMed

Ein-Dor, L; Metzler, R; Kanter, I; Kinzel, W

2001-06-01

The generalization of the problem of adaptive competition, known as the minority game, to the case of K possible choices for each player, is addressed, and applied to a system of interacting perceptrons with input and output units of a type of K-state Potts spins. An optimal solution of this minority game, as well as the dynamic evolution of the adaptive strategies of the players, are solved analytically for a general K and compared with numerical simulations.

The MCNP6 Analytic Criticality Benchmark Suite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Forrest B.

2016-06-16

Analytical benchmarks provide an invaluable tool for verifying computer codes used to simulate neutron transport. Several collections of analytical benchmark problems [1-4] are used routinely in the verification of production Monte Carlo codes such as MCNP® [5,6]. Verification of a computer code is a necessary prerequisite to the more complex validation process. The verification process confirms that a code performs its intended functions correctly. The validation process involves determining the absolute accuracy of code results vs. nature. In typical validations, results are computed for a set of benchmark experiments using a particular methodology (code, cross-section data with uncertainties, and modeling)more » and compared to the measured results from the set of benchmark experiments. The validation process determines bias, bias uncertainty, and possibly additional margins. Verification is generally performed by the code developers, while validation is generally performed by code users for a particular application space. The VERIFICATION_KEFF suite of criticality problems [1,2] was originally a set of 75 criticality problems found in the literature for which exact analytical solutions are available. Even though the spatial and energy detail is necessarily limited in analytical benchmarks, typically to a few regions or energy groups, the exact solutions obtained can be used to verify that the basic algorithms, mathematics, and methods used in complex production codes perform correctly. The present work has focused on revisiting this benchmark suite. A thorough review of the problems resulted in discarding some of them as not suitable for MCNP benchmarking. For the remaining problems, many of them were reformulated to permit execution in either multigroup mode or in the normal continuous-energy mode for MCNP. Execution of the benchmarks in continuous-energy mode provides a significant advance to MCNP verification methods.« less

Development of an analytical solution for the Budyko watershed parameter in terms of catchment physical features

NASA Astrophysics Data System (ADS)

Reaver, N.; Kaplan, D. A.; Jawitz, J. W.

2017-12-01

The Budyko hypothesis states that a catchment's long-term water and energy balances are dependent on two relatively easy to measure quantities: rainfall depth and potential evaporation. This hypothesis is expressed as a simple function, the Budyko equation, which allows for the prediction of a catchment's actual evapotranspiration and discharge from measured rainfall depth and potential evaporation, data which are widely available. However, the two main analytically derived forms of the Budyko equation contain a single unknown watershed parameter, whose value varies across catchments; variation in this parameter has been used to explain the hydrological behavior of different catchments. The watershed parameter is generally thought of as a lumped quantity that represents the influence of all catchment biophysical features (e.g. soil type and depth, vegetation type, timing of rainfall, etc). Previous work has shown that the parameter is statistically correlated with catchment properties, but an explicit expression has been elusive. While the watershed parameter can be determined empirically by fitting the Budyko equation to measured data in gauged catchments where actual evapotranspiration can be estimated, this limits the utility of the framework for predicting impacts to catchment hydrology due to changing climate and land use. In this study, we developed an analytical solution for the lumped catchment parameter for both forms of the Budyko equation. We combined these solutions with a statistical soil moisture model to obtain analytical solutions for the Budyko equation parameter as a function of measurable catchment physical features, including rooting depth, soil porosity, and soil wilting point. We tested the predictive power of these solutions using the U.S. catchments in the MOPEX database. We also compared the Budyko equation parameter estimates generated from our analytical solutions (i.e. predicted parameters) with those obtained through the calibration of the Budyko equation to discharge data (i.e. empirical parameters), and found good agreement. These results suggest that it is possible to predict the Budyko equation watershed parameter directly from physical features, even for ungauged catchments.

The mathematical research for the Kuramoto model of the describing neuronal synchrony in the brain

NASA Astrophysics Data System (ADS)

Lin, Chang; Lin, Mai-mai

2009-08-01

The Kuramoto model of the describing neuronal synchrony is mathematically investigated in the brain. A general analytical solutions (the most sententious description) for the Kuramoto model, incorporating the inclusion of a Ki,j (t) term to represent time-varying coupling strengths, have been obtained by using the precise mathematical approach. We derive an exact analytical expression, opening out the connotative and latent linear relation, for the mathematical character of the phase configurations in the Kuramoto model of the describing neuronal synchrony in the brain.

Estimation on nonlinear damping in second order distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1989-01-01

An approximation and convergence theory for the identification of nonlinear damping in abstract wave equations is developed. It is assumed that the unknown dissipation mechanism to be identified can be described by a maximal monotone operator acting on the generalized velocity. The stiffness is assumed to be linear and symmetric. Functional analytic techniques are used to establish that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem.

GHM method for obtaining rationalsolutions of nonlinear differential equations.

PubMed

Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo

2015-01-01

In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.

Properties of finite difference models of non-linear conservative oscillators

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1988-01-01

Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.

Dynamics of nonautonomous rogue waves in Bose-Einstein condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Li-Chen, E-mail: zhaolichen3@163.com

2013-02-15

We study rogue waves of Bose-Einstein condensate (BEC) analytically in a time-dependent harmonic trap with a complex potential. Properties of the nonautonomous rogue waves are investigated analytically. It is reported that there are possibilities to 'catch' rogue waves through manipulating nonlinear interaction properly. The results provide many possibilities to manipulate rogue waves experimentally in a BEC system. - Highlights: Black-Right-Pointing-Pointer One more generalized rogue wave solutions are presented. Black-Right-Pointing-Pointer Present one possible way to catch a rouge wave. Black-Right-Pointing-Pointer Properties of rogue waves are investigated analytically for the first time. Black-Right-Pointing-Pointer Provide many possibilities to manipulate rogue waves in BEC.

Analytical solutions by squeezing to the anisotropic Rabi model in the nonperturbative deep-strong-coupling regime

NASA Astrophysics Data System (ADS)

Zhang, Yu-Yu; Chen, Xiang-You

2017-12-01

An unexplored nonperturbative deep strong coupling (npDSC) achieved in superconducting circuits has been studied in the anisotropic Rabi model by the generalized squeezing rotating-wave approximation. Energy levels are evaluated analytically from the reformulated Hamiltonian and agree well with numerical ones in a wide range of coupling strength. Such improvement ascribes to deformation effects in the displaced-squeezed state presented by the squeezed momentum variance, which are omitted in previous displaced states. The atom population dynamics confirms the validity of our approach for the npDSC strength. Our approach offers the possibility to explore interesting phenomena analytically in the npDSC regime in qubit-oscillator experiments.

A multi-species reactive transport model to estimate biogeochemical rates based on single-well push-pull test data

NASA Astrophysics Data System (ADS)

Phanikumar, Mantha S.; McGuire, Jennifer T.

2010-08-01

Push-pull tests are a popular technique to investigate various aquifer properties and microbial reaction kinetics in situ. Most previous studies have interpreted push-pull test data using approximate analytical solutions to estimate (generally first-order) reaction rate coefficients. Though useful, these analytical solutions may not be able to describe important complexities in rate data. This paper reports the development of a multi-species, radial coordinate numerical model (PPTEST) that includes the effects of sorption, reaction lag time and arbitrary reaction order kinetics to estimate rates in the presence of mixing interfaces such as those created between injected "push" water and native aquifer water. The model has the ability to describe an arbitrary number of species and user-defined reaction rate expressions including Monod/Michelis-Menten kinetics. The FORTRAN code uses a finite-difference numerical model based on the advection-dispersion-reaction equation and was developed to describe the radial flow and transport during a push-pull test. The accuracy of the numerical solutions was assessed by comparing numerical results with analytical solutions and field data available in the literature. The model described the observed breakthrough data for tracers (chloride and iodide-131) and reactive components (sulfate and strontium-85) well and was found to be useful for testing hypotheses related to the complex set of processes operating near mixing interfaces.

Variational method enabling simplified solutions to the linearized Boltzmann equation for oscillatory gas flows

NASA Astrophysics Data System (ADS)

Ladiges, Daniel R.; Sader, John E.

2018-05-01

Nanomechanical resonators and sensors, operated in ambient conditions, often generate low-Mach-number oscillating rarefied gas flows. Cercignani [C. Cercignani, J. Stat. Phys. 1, 297 (1969), 10.1007/BF01007482] proposed a variational principle for the linearized Boltzmann equation, which can be used to derive approximate analytical solutions of steady (time-independent) flows. Here we extend and generalize this principle to unsteady oscillatory rarefied flows and thus accommodate resonating nanomechanical devices. This includes a mathematical approach that facilitates its general use and allows for systematic improvements in accuracy. This formulation is demonstrated for two canonical flow problems: oscillatory Couette flow and Stokes' second problem. Approximate analytical formulas giving the bulk velocity and shear stress, valid for arbitrary oscillation frequency, are obtained for Couette flow. For Stokes' second problem, a simple system of ordinary differential equations is derived which may be solved to obtain the desired flow fields. Using this framework, a simple and accurate formula is provided for the shear stress at the oscillating boundary, again for arbitrary frequency, which may prove useful in application. These solutions are easily implemented on any symbolic or numerical package, such as Mathematica or matlab, facilitating the characterization of flows produced by nanomechanical devices and providing insight into the underlying flow physics.

Bending analysis of a general cross-ply laminate using 3D elasticity solution and layerwise theory

NASA Astrophysics Data System (ADS)

Yazdani Sarvestani, H.; Naghashpour, A.; Heidari-Rarani, M.

2015-12-01

In this study, the analytical solution of interlaminar stresses near the free edges of a general (symmetric and unsymmetric layups) cross-ply composite laminate subjected to pure bending loading is presented based on Reddy's layerwise theory (LWT) for the first time. First, the reduced form of displacement field is obtained for a general cross-ply composite laminate subjected to a bending moment by elasticity theory. Then, first-order shear deformation theory of plates and LWT is utilized to determine the global and local deformation parameters appearing in the displacement fields, respectively. One of the main advantages of the developed solution based on the LWT is exact prediction of interlaminar stresses at the boundary layer regions. To show the accuracy of this solution, three-dimensional elasticity bending problem of a laminated composite is solved for special set of boundary conditions as well. Finally, LWT results are presented for edge-effect problems of several symmetric and unsymmetric cross-ply laminates under the bending moment. The obtained results indicate high stress gradients of interlaminar stresses near the edges of laminates.

Front and pulse solutions for the complex Ginzburg-Landau equation with higher-order terms.

PubMed

Tian, Huiping; Li, Zhonghao; Tian, Jinping; Zhou, Guosheng

2002-12-01

We investigate one-dimensional complex Ginzburg-Landau equation with higher-order terms and discuss their influences on the multiplicity of solutions. An exact analytic front solution is presented. By stability analysis for the original partial differential equation, we derive its necessary stability condition for amplitude perturbations. This condition together with the exact front solution determine the region of parameter space where the uniformly translating front solution can exist. In addition, stable pulses, chaotic pulses, and attenuation pulses appear generally if the parameters are out of the range. Finally, applying these analysis into the optical transmission system numerically we find that the stable transmission of optical pulses can be achieved if the parameters are appropriately chosen.

Analytical techniques for characterization of cyclodextrin complexes in aqueous solution: a review.

PubMed

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. Copyright © 2014 Elsevier B.V. All rights reserved.

Anisotropic charged generalized polytropic models

NASA Astrophysics Data System (ADS)

Nasim, A.; Azam, M.

2018-06-01

In this paper, we found some new anisotropic charged models admitting generalized polytropic equation of state with spherically symmetry. An analytic solution of the Einstein-Maxwell field equations is obtained through the transformation introduced by Durgapal and Banerji (Phys. Rev. D 27:328, 1983). The physical viability of solutions corresponding to polytropic index η =1/2, 2/3, 1, 2 is analyzed graphically. For this, we plot physical quantities such as radial and tangential pressure, anisotropy, speed of sound which demonstrated that these models achieve all the considerable physical conditions required for a relativistic star. Further, it is mentioned here that previous results for anisotropic charged matter with linear, quadratic and polytropic equation of state can be retrieved.

Second virial coefficient of a generalized Lennard-Jones potential.

PubMed

González-Calderón, Alfredo; Rocha-Ichante, Adrián

2015-01-21

We present an exact analytical solution for the second virial coefficient of a generalized Lennard-Jones type of pair potential model. The potential can be reduced to the Lennard-Jones, hard-sphere, and sticky hard-sphere models by tuning the potential parameters corresponding to the width and depth of the well. Thus, the second virial solution can also regain the aforementioned cases. Moreover, the obtained expression strongly resembles the one corresponding to the Kihara potential. In fact, the Fk functions are the same. Furthermore, for these functions, the complete expansions at low and high temperature are given. Additionally, we propose an alternative stickiness parameter based on the obtained second virial coefficient.

Diffusion Influenced Adsorption Kinetics.

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.

Space-charge-limited currents for cathodes with electric field enhanced geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lai, Dingguo, E-mail: laidingguo@nint.ac.cn; Qiu, Mengtong; Xu, Qifu

This paper presents the approximate analytic solutions of current density for annulus and circle cathodes. The current densities of annulus and circle cathodes are derived approximately from first principles, which are in agreement with simulation results. The large scaling laws can predict current densities of high current vacuum diodes including annulus and circle cathodes in practical applications. In order to discuss the relationship between current density and electric field on cathode surface, the existing analytical solutions of currents for concentric cylinder and sphere diodes are fitted from existing solutions relating with electric field enhancement factors. It is found that themore » space-charge-limited current density for the cathode with electric-field enhanced geometry can be written in a general form of J = g(β{sub E}){sup 2}J{sub 0}, where J{sub 0} is the classical (1D) Child-Langmuir current density, β{sub E} is the electric field enhancement factor, and g is the geometrical correction factor depending on the cathode geometry.« less

An exact solution for a rotating black hole in modified gravity

NASA Astrophysics Data System (ADS)

Filippini, Francesco; Tasinato, Gianmassimo

2018-01-01

Exact solutions describing rotating black holes can offer important tests for alternative theories of gravity, motivated by the dark energy and dark matter problems. We present an analytic rotating black hole solution for a class of vector-tensor theories of modified gravity, valid for arbitrary values of the rotation parameter. The new configuration is characterised by parametrically large deviations from the Kerr-Newman geometry, controlled by non-minimal couplings between vectors and gravity. It has an oblate horizon in Boyer-Lindquist coordinates, and it can rotate more rapidly and have a larger ergosphere than black holes in General Relativity (GR) with the same asymptotic properties. We analytically investigate the features of the innermost stable circular orbits for massive objects on the equatorial plane, and show that stable orbits lie further away from the black hole horizon with respect to rotating black holes in GR. We also comment on possible applications of our findings for the extraction of rotational energy from the black hole.

Analytical and numerical solutions for mass diffusion in a composite cylindrical body

NASA Astrophysics Data System (ADS)

Kumar, A.

1980-12-01

The analytical and numerical solution techniques were investigated to study moisture diffusion problems in cylindrical bodies that are assumed to be composed of a finite number of layers of different materials. A generalized diffusion model for an n-layer cylindrical body with discontinuous moisture content at the interfaces was developed and the formal solutions were obtained. The model is to be used for describing mass transfer rates of any composite body, such as an ear of corn which could be assumed of consisting two different layers: the inner core represents the woody cob and the outer cylinder represents the kernel layer. Data describing the fully exposed drying characteristics of ear corn at high air velocity were obtained under different drying conditions. Ear corns were modeled as homogeneous bodies since composite model did not improve the fit substantially. A computer program using multidimensional optimization technique showed that diffusivity was an exponential function of moisture content and an arrhenius function of temperature of drying air.

Maximally multipartite entangled states

NASA Astrophysics Data System (ADS)

Facchi, Paolo; Florio, Giuseppe; Parisi, Giorgio; Pascazio, Saverio

2008-06-01

We introduce the notion of maximally multipartite entangled states of n qubits as a generalization of the bipartite case. These pure states have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. They are solutions of a minimization problem. Examples for small n are investigated, both analytically and numerically.

Teacher Efficacy: A Study of Construct Dimensions.

ERIC Educational Resources Information Center

Guskey, Thomas R.; Passaro, Perry

The structure of a concept generally labeled "teacher efficacy" is examined. A sample of 342 prospective and experienced teachers was administered an efficacy questionnaire adapted from the research of S. Gibson and M. H. Dembo (1984). Factor analytic procedures with varimax rotation were used to generate a 2-factor solution that accounted for 32…

Comparison of adjoint and analytical Bayesian inversion methods for constraining Asian sources of carbon monoxide using satellite (MOPITT) measurements of CO columns

NASA Astrophysics Data System (ADS)

Kopacz, Monika; Jacob, Daniel J.; Henze, Daven K.; Heald, Colette L.; Streets, David G.; Zhang, Qiang

2009-02-01

We apply the adjoint of an atmospheric chemical transport model (GEOS-Chem CTM) to constrain Asian sources of carbon monoxide (CO) with 2° × 2.5° spatial resolution using Measurement of Pollution in the Troposphere (MOPITT) satellite observations of CO columns in February-April 2001. Results are compared to the more common analytical method for solving the same Bayesian inverse problem and applied to the same data set. The analytical method is more exact but because of computational limitations it can only constrain emissions over coarse regions. We find that the correction factors to the a priori CO emission inventory from the adjoint inversion are generally consistent with those of the analytical inversion when averaged over the large regions of the latter. The adjoint solution reveals fine-scale variability (cities, political boundaries) that the analytical inversion cannot resolve, for example, in the Indian subcontinent or between Korea and Japan, and some of that variability is of opposite sign which points to large aggregation errors in the analytical solution. Upward correction factors to Chinese emissions from the prior inventory are largest in central and eastern China, consistent with a recent bottom-up revision of that inventory, although the revised inventory also sees the need for upward corrections in southern China where the adjoint and analytical inversions call for downward correction. Correction factors for biomass burning emissions derived from the adjoint and analytical inversions are consistent with a recent bottom-up inventory on the basis of MODIS satellite fire data.

Ground state sign-changing solutions for fractional Kirchhoff equations in bounded domains

NASA Astrophysics Data System (ADS)

Luo, Huxiao; Tang, Xianhua; Gao, Zu

2018-03-01

We study the existence of ground state sign-changing solutions for the fractional Kirchhoff problem. Under mild assumptions on the nonlinearity, by using some new analytical skills and the non-Nehari manifold method, we prove that the fractional Kirchhoff problem possesses a ground state sign-changing solution ub. Moreover, we show that the energy of ub is strictly larger than twice that of the ground state solutions of Nehari-type. Finally, we establish the convergence property of ub as the parameter b ↘ 0. Our results generalize some results obtained by Shuai [J. Differ. Equations 259, 1256 (2015)] and Tang and Cheng [J. Differ. Equations 261, 2384 (2016)].

Long term cavity closure in salt using a Carreau viscosity model.

NASA Astrophysics Data System (ADS)

Cornet, Jan; Dabrowski, Marcin; Schmid, Daniel

2017-04-01

The problem of a pressurized hole in an infinite homogenous body is one of the most classical problems in geoscience. The solution is well-known when the rheology is linear but becomes much more complicated when applied to formations such as salt that can behave nonlinearly. Defining a constitutive law for the steady state deformation of salt is already a challenge and we rely on two deformation mechanisms - dislocation creep and pressure solution - to do that. More precisely, we use a Carreau model for viscosity to take into account in a single and smooth manner a linear and a nonlinear process. We use this rheology to revisit the classical two-dimensional problem of a pressurized cylindrical hole in an infinite and homogeneous body under general far field loads. We are interested in characterizing the maximum closure velocity at the rim. We provide analytical solutions for pressure and far field pure shear loads and we give a proxy for the general case based on the two end members. Using this general approach, we show that adding pressure solution to the constitutive law is especially important when studying long term hole closure under low pressure loads or when the grain size is in the order of 0.1 mm. Only considering dislocation creep can lead to underestimating the closure velocity by several orders of magnitude. Adding far field shear stress also dramatically enhances hole closure. The stress situation in salt bodies is often considered as isotropic but some shear exists at the interface between moving salt bodies and cap rock so pressurized holes in these regions experience increased closure. The analytical approach adopted in this study enables us to better understand the influence of all the input parameters on hole closure in salt.

DL_MG: A Parallel Multigrid Poisson and Poisson-Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution.

PubMed

Womack, James C; Anton, Lucian; Dziedzic, Jacek; Hasnip, Phil J; Probert, Matt I J; Skylaris, Chris-Kriton

2018-03-13

The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential-a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the Poisson equation, featuring nonhomogeneous dielectric permittivities, ionic concentrations with nonlinear dependencies, and diverse boundary conditions. The analytic solutions generally used to solve the Poisson equation in vacuum (or with homogeneous permittivity) are not applicable in these circumstances, and numerical methods must be used. In this work, we present DL_MG, a flexible, scalable, and accurate solver library, developed specifically to tackle the challenges of solving the Poisson equation in modern large-scale electronic structure calculations on parallel computers. Our solver is based on the multigrid approach and uses an iterative high-order defect correction method to improve the accuracy of solutions. Using two chemically relevant model systems, we tested the accuracy and computational performance of DL_MG when solving the generalized Poisson and Poisson-Boltzmann equations, demonstrating excellent agreement with analytic solutions and efficient scaling to ∼10 9 unknowns and 100s of CPU cores. We also applied DL_MG in actual large-scale electronic structure calculations, using the ONETEP linear-scaling electronic structure package to study a 2615 atom protein-ligand complex with routinely available computational resources. In these calculations, the overall execution time with DL_MG was not significantly greater than the time required for calculations using a conventional FFT-based solver.

Extremal black holes in dynamical Chern-Simons gravity

NASA Astrophysics Data System (ADS)

McNees, Robert; Stein, Leo C.; Yunes, Nicolás

2016-12-01

Rapidly rotating black hole (BH) solutions in theories beyond general relativity (GR) play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of GR. Such solutions are often difficult to find in beyond-general-relativity theories due to the inclusion of additional fields that couple to the metric nonlinearly and non-minimally. In this paper, we consider rotating BH solutions in one such theory, dynamical Chern-Simons (dCS) gravity, where the Einstein-Hilbert action is modified by the introduction of a dynamical scalar field that couples to the metric through the Pontryagin density. We treat dCS gravity as an effective field theory and work in the decoupling limit, where corrections are treated as small perturbations from GR. We perturb about the maximally rotating Kerr solution, the so-called extremal limit, and develop mathematical insight into the analysis techniques needed to construct solutions for generic spin. First we find closed-form, analytic expressions for the extremal scalar field, and then determine the trace of the metric perturbation, giving both in terms of Legendre decompositions. Retaining only the first three and four modes in the Legendre representation of the scalar field and the trace, respectively, suffices to ensure a fidelity of over 99% relative to full numerical solutions. The leading-order mode in the Legendre expansion of the trace of the metric perturbation contains a logarithmic divergence at the extremal Kerr horizon, which is likely to be unimportant as it occurs inside the perturbed dCS horizon. The techniques employed here should enable the construction of analytic, closed-form expressions for the scalar field and metric perturbations on a background with arbitrary rotation.

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Transport of a decay chain in homogenous porous media: analytical solutions.

PubMed

Bauer, P; Attinger, S; Kinzelbach, W

2001-06-01

With the aid of integral transforms, analytical solutions for the transport of a decay chain in homogenous porous media are derived. Unidirectional steady-state flow and radial steady-state flow in single and multiple porosity media are considered. At least in Laplace domain, all solutions can be written in closed analytical formulae. Partly, the solutions can also be inverted analytically. If not, analytical calculation of the steady-state concentration distributions, evaluation of temporal moments and numerical inversion are still possible. Formulae for several simple boundary conditions are given and visualized in this paper. The derived novel solutions are widely applicable and are very useful for the validation of numerical transport codes.

Exact and Approximate Solutions for Transient Squeezing Flow

NASA Astrophysics Data System (ADS)

Lang, Ji; Santhanam, Sridhar; Wu, Qianhong

2017-11-01

In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration is negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear, and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process, and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity of the analytical approaches. The study presented herein fills the gap in the literature, and will have a broad impact in industrial and biomedical applications. This work is supported by National Science Foundation CBET Fluid Dynamics Program under Award #1511096, and supported by the Seed Grant from The Villanova Center for the Advancement of Sustainability in Engineering (VCASE).

Quaternion regularization in celestial mechanics, astrodynamics, and trajectory motion control. III

NASA Astrophysics Data System (ADS)

Chelnokov, Yu. N.

2015-09-01

The present paper1 analyzes the basic problems arising in the solution of problems of the optimum control of spacecraft (SC) trajectory motion (including the Lyapunov instability of solutions of conjugate equations) using the principle of the maximum. The use of quaternion models of astrodynamics is shown to allow: (1) the elimination of singular points in the differential phase and conjugate equations and in their partial analytical solutions; (2) construction of the first integrals of the new quaternion; (3) a considerable decrease of the dimensions of systems of differential equations of boundary value optimization problems with their simultaneous simplification by using the new quaternion variables related with quaternion constants of motion by rotation transformations; (4) construction of general solutions of differential equations for phase and conjugate variables on the sections of SC passive motion in the simplest and most convenient form, which is important for the solution of optimum pulse SC transfers; (5) the extension of the possibilities of the analytical investigation of differential equations of boundary value problems with the purpose of identifying the basic laws of optimum control and motion of SC; (6) improvement of the computational stability of the solution of boundary value problems; (7) a decrease in the required volume of computation.

Metric of two balancing Kerr particles in physical parametrization

NASA Astrophysics Data System (ADS)

Manko, V. S.; Ruiz, E.

2015-11-01

The present paper aims at elaborating a completely physical representation for the general 4-parameter family of the extended double-Kerr spacetimes describing two spinning sources in gravitational equilibrium. This involved problem is solved in a concise analytical form by using the individual Komar masses and angular momenta as arbitrary parameters, and the simplest equatorially symmetric specialization of the general expressions obtained by us yields the physical representation for the well-known Dietz-Hoenselaers superextreme case of two balancing identical Kerr constituents. The existence of the physically meaningful "black-hole-superextreme-object" equilibrium configurations permitted by the general solution may be considered as a clear indication that the spin-spin repulsion force might actually be by far stronger than expected earlier, when only the balance between two superextreme Kerr sources was thought possible. We also present the explicit analytical formulas relating the equilibrium states in the double-Kerr and double-Reissner-Nordström configurations.

A transient laboratory method for determining the hydraulic properties of 'tight' rocks-II. Application

USGS Publications Warehouse

Neuzil, C.E.; Cooley, C.; Silliman, Stephen E.; Bredehoeft, J.D.; Hsieh, P.A.

1981-01-01

In Part I a general analytical solution for the transient pulse test was presented. Part II presents a graphical method for analyzing data from a test to obtain the hydraulic properties of the sample. The general solution depends on both hydraulic conductivity and specific storage and, in theory, analysis of the data can provide values for both of these hydraulic properties. However, in practice, one of two limiting cases may apply in which case it is possible to calculate only hydraulic conductivity or the product of hydraulic conductivity times specific storage. In this paper we examine the conditions when both hydraulic parameters can be calculated. The analyses of data from two tests are presented. In Appendix I the general solution presented in Part I is compared with an earlier analysis, in which compressive storage in the sample is assumed negligible, and the error in calculated hydraulic conductivity due to this simplifying assumption is examined. ?? 1981.

General relativistic electromagnetic fields of a slowly rotating magnetized neutron star - I. Formulation of the equations

NASA Astrophysics Data System (ADS)

Rezzolla, L.; Ahmedov, B. J.; Miller, J. C.

2001-04-01

We present analytic solutions of Maxwell equations in the internal and external background space-time of a slowly rotating magnetized neutron star. The star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. With respect to a flat space-time solution, general relativity introduces corrections related both to the monopolar and the dipolar parts of the gravitational field. In particular, we show that in the case of infinite electrical conductivity general relativistic corrections resulting from the dragging of reference frames are present, but only in the expression for the electric field. In the case of finite electrical conductivity, however, corrections resulting from both the space-time curvature and the dragging of reference frames are shown to be present in the induction equation. These corrections could be relevant for the evolution of the magnetic fields of pulsars and magnetars. The solutions found, while obtained through some simplifying assumption, reflect a rather general physical configuration and could therefore be used in a variety of astrophysical situations.

Deformation of extremal black holes from stringy interactions

NASA Astrophysics Data System (ADS)

Chen, Baoyi; Stein, Leo C.

2018-04-01

Black holes are a powerful setting for studying general relativity and theories beyond GR. However, analytical solutions for rotating black holes in beyond-GR theories are difficult to find because of the complexity of such theories. In this paper, we solve for the deformation to the near-horizon extremal Kerr metric due to two example string-inspired beyond-GR theories: Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons theory. We accomplish this by making use of the enhanced symmetry group of NHEK and the weak-coupling limit of EdGB and dCS. We find that the EdGB metric deformation has a curvature singularity, while the dCS metric is regular. From these solutions, we compute orbital frequencies, horizon areas, and entropies. This sets the stage for analytically understanding the microscopic origin of black hole entropy in beyond-GR theories.

A thermoelastic transversely isotropic thick walled cylinder/disk application: An analytical solution and study

NASA Technical Reports Server (NTRS)

Arnold, S. M.

1989-01-01

A continuum theory is utilized to represent the thermoelastic behavior of a thick walled composite cylinder that can be idealized as transversely isotropic. A multiaxial statement of the constitutive theory employed is presented, as well as the out of the plane of isotropy, plane stress, and plane strain reductions. The derived analytical solution presented is valid for a cylindrical tube or thin disk with a concentric hole, subjected to internal and/or external pressure and a general radial temperature distribution. A specific problem examined is that of a thick walled cylinder subjected to an internal and external pressure loading and a linear radial temperature distribution. The results are expressed in nondimensional form and the effects on the response behavior are examined for various material properties, fiber orientation and types of loadings.

Primer vector theory applied to the linear relative-motion equations. [for N-impulse space trajectory optimization

NASA Technical Reports Server (NTRS)

Jezewski, D.

1980-01-01

Prime vector theory is used in analyzing a set of linear relative-motion equations - the Clohessy-Wiltshire (C/W) equations - to determine the criteria and necessary conditions for an optimal N-impulse trajectory. The analysis develops the analytical criteria for improving a solution by: (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of: (1) fixed-end conditions, two impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized renezvous problem.

Approximated analytical solution to an Ebola optimal control problem

NASA Astrophysics Data System (ADS)

Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.

2016-11-01

An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.

3D Tensorial Elastodynamics for Isotropic Media on Vertically Deformed Meshes

NASA Astrophysics Data System (ADS)

Shragge, J. C.

2017-12-01

Solutions of the 3D elastodynamic wave equation are sometimes required in industrial and academic applications of elastic reverse-time migration (E-RTM) and full waveform inversion (E-FWI) that involve vertically deformed meshes. Examples include incorporating irregular free-surface topography and handling internal boundaries (e.g., water bottom) directly into the computational meshes. In 3D E-RTM and E-FWI applications, the number of forward modeling simulations can number in the tens of thousands (per iteration), which necessitates the development of stable, accurate and efficient 3D elastodynamics solvers. For topographic scenarios, most finite-difference solution approaches use a change-of-variable strategy that has a number of associated computational challenges, including difficulties in handling of the free-surface boundary condition. In this study, I follow a tensorial approach and use a generalized family of analytic transforms to develop a set of analytic equations for 3D elastodynamics that directly incorporates vertical grid deformations. Importantly, this analytic approach allows for the specification of an analytic free-surface boundary condition appropriate for vertically deformed meshes. These equations are both straightforward and efficient to solve using a velocity-stress formulation with finite-difference (MFD) operators implemented on a fully staggered grid. Moreover, I demonstrate that the use of mimetic finite difference (MFD) methods allows stable, accurate, and efficient numerical solutions to be simulated for typical topographic scenarios. Examples demonstrate that high-quality elastic wavefields can be generated for topographic surfaces exhibiting significant topographic relief.

New analytical solutions to the two-phase water faucet problem

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-06-17

Here, the one-dimensional water faucet problem is one of the classical benchmark problems originally proposed by Ransom to study the two-fluid two-phase flow model. With certain simplifications, such as massless gas phase and no wall and interfacial frictions, analytical solutions had been previously obtained for the transient liquid velocity and void fraction distribution. The water faucet problem and its analytical solutions have been widely used for the purposes of code assessment, benchmark and numerical verifications. In our previous study, the Ransom’s solutions were used for the mesh convergence study of a high-resolution spatial discretization scheme. It was found that, atmore » the steady state, an anticipated second-order spatial accuracy could not be achieved, when compared to the existing Ransom’s analytical solutions. A further investigation showed that the existing analytical solutions do not actually satisfy the commonly used two-fluid single-pressure two-phase flow equations. In this work, we present a new set of analytical solutions of the water faucet problem at the steady state, considering the gas phase density’s effect on pressure distribution. This new set of analytical solutions are used for mesh convergence studies, from which anticipated second-order of accuracy is achieved for the 2nd order spatial discretization scheme. In addition, extended Ransom’s transient solutions for the gas phase velocity and pressure are derived, with the assumption of decoupled liquid and gas pressures. Numerical verifications on the extended Ransom’s solutions are also presented.« less

Analytical solutions to optimal underactuated spacecraft formation reconfiguration

NASA Astrophysics Data System (ADS)

Huang, Xu; Yan, Ye; Zhou, Yang

2015-11-01

Underactuated systems can generally be defined as systems with fewer number of control inputs than that of the degrees of freedom to be controlled. In this paper, analytical solutions to optimal underactuated spacecraft formation reconfiguration without either the radial or the in-track control are derived. By using a linear dynamical model of underactuated spacecraft formation in circular orbits, controllability analysis is conducted for either underactuated case. Indirect optimization methods based on the minimum principle are then introduced to generate analytical solutions to optimal open-loop underactuated reconfiguration problems. Both fixed and free final conditions constraints are considered for either underactuated case and comparisons between these two final conditions indicate that the optimal control strategies with free final conditions require less control efforts than those with the fixed ones. Meanwhile, closed-loop adaptive sliding mode controllers for both underactuated cases are designed to guarantee optimal trajectory tracking in the presence of unmatched external perturbations, linearization errors, and system uncertainties. The adaptation laws are designed via a Lyapunov-based method to ensure the overall stability of the closed-loop system. The explicit expressions of the terminal convergent regions of each system states have also been obtained. Numerical simulations demonstrate the validity and feasibility of the proposed open-loop and closed-loop control schemes for optimal underactuated spacecraft formation reconfiguration in circular orbits.

Achromatic-chromatic colorimetric sensors for on-off type detection of analytes.

PubMed

Heo, Jun Hyuk; Cho, Hui Hun; Lee, Jin Woong; Lee, Jung Heon

2014-12-21

We report the development of achromatic colorimetric sensors; sensors changing their colors from achromatic black to other chromatic colors. An achromatic colorimetric sensor was prepared by mixing a general colorimetric indicator, whose color changes between chromatic colors, and a complementary colored dye with no reaction to the targeted analyte. As the color of an achromatic colorimetric sensor changes from black to a chromatic color, the color change could be much easily recognized than general colorimetric sensors with naked eyes. More importantly, the achromatic colorimetric sensors enable on-off type recognition of the presence of analytes, which have not been achieved from most colorimetric sensors. In addition, the color changes from some achromatic colorimetric sensors (achromatic Eriochrome Black T and achromatic Benedict's solution) could be recognized with naked eyes at much lower concentration ranges than normal chromatic colorimetric sensors. These results provide new opportunities in the use of colorimetric sensors for diverse applications, such as harsh industrial, environmental, and biological detection.

Solving the Schroedinger Equation of Atoms and Molecules without Analytical Integration Based on the Free Iterative-Complement-Interaction Wave Function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakatsuji, H.; Nakashima, H.; Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510

2007-12-14

A local Schroedinger equation (LSE) method is proposed for solving the Schroedinger equation (SE) of general atoms and molecules without doing analytic integrations over the complement functions of the free ICI (iterative-complement-interaction) wave functions. Since the free ICI wave function is potentially exact, we can assume a flatness of its local energy. The variational principle is not applicable because the analytic integrations over the free ICI complement functions are very difficult for general atoms and molecules. The LSE method is applied to several 2 to 5 electron atoms and molecules, giving an accuracy of 10{sup -5} Hartree in total energy.more » The potential energy curves of H{sub 2} and LiH molecules are calculated precisely with the free ICI LSE method. The results show the high potentiality of the free ICI LSE method for developing accurate predictive quantum chemistry with the solutions of the SE.« less

Analytical solutions for efficient interpretation of single-well push-pull tracer tests

EPA Science Inventory

Single-well push-pull tracer tests have been used to characterize the extent, fate, and transport of subsurface contamination. Analytical solutions provide one alternative for interpreting test results. In this work, an exact analytical solution to two-dimensional equations descr...

ANALYTICAL SOLUTION TO SATURATED FLOW IN A FINITE STRATIFIED AQUIFER

EPA Science Inventory

An analytical solution for the flow of water in a saturated-stratified aquitard-aquifer-aquitard system of finite length is presented. The analytical solution assumes one-dimensional horizontal flow in the aquifer and two-dimensional flow in the aquitards. Several examples are gi...

Analytical Investigation of Elastic Thin-Walled Cylinder and Truncated Cone Shell Intersection Under Internal Pressure.

PubMed

Zamani, J; Soltani, B; Aghaei, M

2014-10-01

An elastic solution of cylinder-truncated cone shell intersection under internal pressure is presented. The edge solution theory that has been used in this study takes bending moments and shearing forces into account in the thin-walled shell of revolution element. The general solution of the cone equations is based on power series method. The effect of cone apex angle on the stress distribution in conical and cylindrical parts of structure is investigated. In addition, the effect of the intersection and boundary locations on the circumferential and longitudinal stresses is evaluated and it is shown that how quantitatively they are essential.

Metrics on the relative spacecraft motion invariant manifold.

PubMed

Gurfil, P; Kholshevnikov, Konstantin V

2005-12-01

This paper establishes a methodology for obtaining the general solution to the spacecraft relative motion problem by utilizing Cartesian configuration space in conjunction with classical orbital elements. The geometry of the relative motion configuration space is analyzed, and the relative motion invariant manifold is determined. Most importantly, the geometric structure of the relative motion problem is used to derive useful metrics for quantification of the minimum, maximum, and mean distance between spacecraft for commensurable and non-commensurable mean motions. A number of analytic solutions, as well as useful examples, are provided, illustrating the calculated bounds. A few particular cases are given that yield simple solutions.

Space Trajectories Error Analysis (STEAP) Programs. Volume 1: Analytic manual, update

NASA Technical Reports Server (NTRS)

1971-01-01

Manual revisions are presented for the modified and expanded STEAP series. The STEAP 2 is composed of three independent but related programs: NOMAL for the generation of n-body nominal trajectories performing a number of deterministic guidance events; ERRAN for the linear error analysis and generalized covariance analysis along specific targeted trajectories; and SIMUL for testing the mathematical models used in the navigation and guidance process. The analytic manual provides general problem description, formulation, and solution and the detailed analysis of subroutines. The programmers' manual gives descriptions of the overall structure of the programs as well as the computational flow and analysis of the individual subroutines. The user's manual provides information on the input and output quantities of the programs. These are updates to N69-36472 and N69-36473.

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

Analytical Approach to Large Deformation Problems of Frame Structures

NASA Astrophysics Data System (ADS)

Ohtsuki, Atsumi; Ellyin, Fernand

In elements used as flexible linking devices and structures, the main characteristic is a fairly large deformation without exceeding the elastic limit of the material. This property is of both analytical and technological interests. Previous studies of large deformation have been generally concerned with a single member (e.g. a cantilever beam, a simply supported beam, etc.). However, there are very few large deformation studies of assembled members such as frames. This paper deals with a square frame with rigid joints, loaded diagonally in either tension or compression by a pair of opposite forces. Analytical solutions for large deformation are obtained in terms of elliptic integrals, and are compared with the experimental data. The agreement is found to be fairly close.

Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

NASA Astrophysics Data System (ADS)

Bervillier, C.; Boisseau, B.; Giacomini, H.

2008-02-01

The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).

The use of an analytic Hamiltonian matrix for solving the hydrogenic atom

NASA Astrophysics Data System (ADS)

Bhatti, Mohammad

2001-10-01

The non-relativistic Hamiltonian corresponding to the Shrodinger equation is converted into analytic Hamiltonian matrix using the kth order B-splines functions. The Galerkin method is applied to the solution of the Shrodinger equation for bound states of hydrogen-like systems. The program Mathematica is used to create analytic matrix elements and exact integration is performed over the knot-sequence of B-splines and the resulting generalized eigenvalue problem is solved on a specified numerical grid. The complete basis set and the energy spectrum is obtained for the coulomb potential for hydrogenic systems with Z less than 100 with B-splines of order eight. Another application is given to test the Thomas-Reiche-Kuhn sum rule for the hydrogenic systems.

An analytical theory of radio-wave scattering from meteoric ionization - I. Basic equation

NASA Astrophysics Data System (ADS)

Pecina, P.

2016-01-01

We have developed an analytical theory of radio-wave scattering from ionization of meteoric origin. It is based on an integro-differential equation for the polarization vector, P, inside the meteor trail, representing an analytical solution of the set of Maxwell equations, in combination with a generalized radar equation involving an integral of the trail volume electron density, Ne, and P represented by an auxiliary vector, Q, taken over the whole trail volume. During the derivation of the final formulae, the following assumptions were applied: transversal as well as longitudinal dimensions of the meteor trail are small compared with the distances of the relevant trail point to both the transmitter and receiver and the ratio of these distances to the wavelength of the wave emitted by the radar is very large, so that the stationary-phase method can be employed for evaluation of the relevant integrals. Further, it is shown that in the case of sufficiently low electron density, Ne, corresponding to the case of underdense trails, the classical McKinley's radar equation results as a special case of the general theory. The same also applies regarding the Fresnel characteristics. Our approach is also capable of yielding solutions to the problems of the formation of Fresnel characteristics on trails having any electron density, forward scattering and scattering on trails immersed in the magnetic field. However, we have also shown that the geomagnetic field can be removed from consideration, due to its low strength. The full solution of the above integro-differential equation, valid for any electron volume densities, has been left to subsequent works dealing with this particular problem, due to its complexity.

Interactive Visualization of a Thin Disc around a Schwarzschild Black Hole

ERIC Educational Resources Information Center

Muller, Thomas; Frauendiener, Jorg

2012-01-01

In a first course in general relativity, the Schwarzschild spacetime is the most discussed analytic solution to Einstein's field equations. Unfortunately, there is rarely enough time to study the optical consequences of the bending of light for some advanced examples. In this paper, we present how the visual appearance of a thin disc around a…

Global stability and exact solution of an arbitrary-solute nonlinear cellular mass transport system.

PubMed

Benson, James D

2014-12-01

The prediction of the cellular state as a function of extracellular concentrations and temperatures has been of interest to physiologists for nearly a century. One of the most widely used models in the field is one where mass flux is linearly proportional to the concentration difference across the membrane. These fluxes define a nonlinear differential equation system for the intracellular state, which when coupled with appropriate initial conditions, define the intracellular state as a function of the extracellular concentrations of both permeating and nonpermeating solutes. Here we take advantage of a reparametrization scheme to extend existing stability results to a more general setting and to a develop analytical solutions to this model for an arbitrary number of extracellular solutes. Copyright © 2014 Elsevier Inc. All rights reserved.

General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks.

PubMed

Reis, Matthias; Kromer, Justus A; Klipp, Edda

2018-01-20

Multimodality is a phenomenon which complicates the analysis of statistical data based exclusively on mean and variance. Here, we present criteria for multimodality in hierarchic first-order reaction networks, consisting of catalytic and splitting reactions. Those networks are characterized by independent and dependent subnetworks. First, we prove the general solvability of the Chemical Master Equation (CME) for this type of reaction network and thereby extend the class of solvable CME's. Our general solution is analytical in the sense that it allows for a detailed analysis of its statistical properties. Given Poisson/deterministic initial conditions, we then prove the independent species to be Poisson/binomially distributed, while the dependent species exhibit generalized Poisson/Khatri Type B distributions. Generalized Poisson/Khatri Type B distributions are multimodal for an appropriate choice of parameters. We illustrate our criteria for multimodality by several basic models, as well as the well-known two-stage transcription-translation network and Bateman's model from nuclear physics. For both examples, multimodality was previously not reported.

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Ma, Wen-Xiu; Zhou, Yuan

2018-02-01

Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u = 2(ln ⁡ f) x and u = 2(ln ⁡ f) xx, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations.

On analytic modeling of lunar perturbations of artificial satellites of the earth

NASA Astrophysics Data System (ADS)

Lane, M. T.

1989-06-01

Two different procedures for analytically modeling the effects of the moon's direct gravitational force on artificial earth satellites are discussed from theoretical and numerical viewpoints. One is developed using classical series expansions of inclination and eccentricity for both the satellite and the moon, and the other employs the method of averaging. Both solutions are seen to have advantages, but it is shown that while the former is more accurate in special situations, the latter is quicker and more practical for the general orbit determination problem where observed data are used to correct the orbit in near real time.

Many-body delocalization in a strongly disordered system with long-range interactions: Finite-size scaling

NASA Astrophysics Data System (ADS)

Burin, Alexander L.

2015-03-01

Many-body localization in a disordered system of interacting spins coupled by the long-range interaction 1 /Rα is investigated combining analytical theory considering resonant interactions and a finite-size scaling of exact numerical solutions with number of spins N . The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for a d -dimensional system including the absence of localization in the infinite system at α <2 d and a universal scaling of a critical energy disordering Wc∝N2/d -α d .

Generalised quasiprobability distribution for Hermite polynomial squeezed states

NASA Astrophysics Data System (ADS)

Datta, Sunil; D'Souza, Richard

1996-02-01

Generalized quasiprobability distributions (QPD) for Hermite polynomial states are presented. These states are solutions of an eigenvalue equation which is quadratic in creation and annihilation operators. Analytical expressions for the QPD are presented for some special cases of the eigenvalues. For large squeezing these analytical expressions for the QPD take the form of a finite series in even Hermite functions. These expressions very transparently exhibit the transition between, P, Q and W functions corresponding to the change of the s-parameter of the QPD. Further, they clearly show the two-photon nature of the processes involved in the generation of these states.

Numerical realization of the variational method for generating self-trapped beams

NASA Astrophysics Data System (ADS)

Duque, Erick I.; Lopez-Aguayo, Servando; Malomed, Boris A.

2018-03-01

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schr\\"odinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Nonequilibrium Entropy in a Shock

DOE PAGES

Margolin, Len G.

2017-07-19

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies themore » Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.« less

The mode branching route to localization of the finite-length floating elastica

NASA Astrophysics Data System (ADS)

Rivetti, Marco; Neukirch, Sébastien

2014-09-01

The beam on elastic foundation is a general model used in physical, biological, and technological problems to study delamination, wrinkling, or pattern formation. Recent focus has been given to the buckling of beams deposited on liquid baths, and in the regime where the beam is soft compared to hydrostatic forces the wrinkling pattern observed at buckling has been shown to lead to localization of the deformation when the confinement is increased. Here we perform a global study of the general case where the intensity of the liquid foundation and the confinement are both varied. We compute equilibrium and stability of the solutions and unravel secondary bifurcations that play a major role in the route to localization. Moreover we classify the post-buckling solutions and shed light on the mechanism leading to localization. Finally, using an asymptotic technique imported from fluid mechanics, we derive an approximated analytical solution to the problem.

Nonequilibrium Entropy in a Shock

DOE Office of Scientific and Technical Information (OSTI.GOV)

Margolin, Len G.

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies themore » Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.« less

Analytical Solution for Flow to a Partially Penetrating Well with Storage in a Confined Aquifer

NASA Astrophysics Data System (ADS)

Vesselinov, V. V.; Mishra, P. K.; Neuman, S. P.

2009-12-01

Analytical solutions for radial flow toward a pumping well are commonly applied to analyze pumping tests conducted in confined aquifers. However, the existing analytical solutions are not capable to simultaneously take into account aquifer anisotropy, partial penetration, and wellbore storage capacity of pumping well. Ignoring these effects may have important impact on the estimated aquifer properties. We present a new analytical solution for three-dimensional, axially symmetric flow to a pumping well in confined aquifer that accouts for aquifer anisotropy, partial penetration and wellbore storage capacity of pumping well. Our analytical reduces to that of Papadopulos et.al. [1967] when the pumping well is fully penetrating, Hantush [1964] when the pumping well has no wellbore storage, and Theis [1935] when both conditions are fulfilled. The solution is evaluated through numerical inversion of its Laplace transform. We use our new solution to analyze data from synthetic and real pumping tests.

Error analysis of analytic solutions for self-excited near-symmetric rigid bodies - A numerical study

NASA Technical Reports Server (NTRS)

Kia, T.; Longuski, J. M.

1984-01-01

Analytic error bounds are presented for the solutions of approximate models for self-excited near-symmetric rigid bodies. The error bounds are developed for analytic solutions to Euler's equations of motion. The results are applied to obtain a simplified analytic solution for Eulerian rates and angles. The results of a sample application of the range and error bound expressions for the case of the Galileo spacecraft experiencing transverse torques demonstrate the use of the bounds in analyses of rigid body spin change maneuvers.

Method and apparatus for simultaneous spectroelectrochemical analysis

DOEpatents

Chatterjee, Sayandev; Bryan, Samuel A; Schroll, Cynthia A; Heineman, William R

2013-11-19

An apparatus and method of simultaneous spectroelectrochemical analysis is disclosed. A transparent surface is provided. An analyte solution on the transparent surface is contacted with a working electrode and at least one other electrode. Light from a light source is focused on either a surface of the working electrode or the analyte solution. The light reflected from either the surface of the working electrode or the analyte solution is detected. The potential of the working electrode is adjusted, and spectroscopic changes of the analyte solution that occur with changes in thermodynamic potentials are monitored.

Study of transient behavior of finned coil heat exchangers

NASA Technical Reports Server (NTRS)

Rooke, S. P.; Elissa, M. G.

1993-01-01

The status of research on the transient behavior of finned coil cross-flow heat exchangers using single phase fluids is reviewed. Applications with available analytical or numerical solutions are discussed. Investigation of water-to-air type cross-flow finned tube heat exchangers is examined through the use of simplified governing equations and an up-wind finite difference scheme. The degenerate case of zero air-side capacitance rate is compared with available exact solution. Generalization of the numerical model is discussed for application to multi-row multi-circuit heat exchangers.

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases.

PubMed

D'Amico, María Belén; Calandrini, Guillermo L

2015-11-01

Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases

NASA Astrophysics Data System (ADS)

D'Amico, María Belén; Calandrini, Guillermo L.

2015-11-01

Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

NASA Astrophysics Data System (ADS)

Dutykh, Denys; Hoefer, Mark; Mitsotakis, Dimitrios

2018-04-01

Some effects of surface tension on fully nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order 4.

Inflation and acceleration of the universe by nonlinear magnetic monopole fields

NASA Astrophysics Data System (ADS)

Övgün, A.

2017-02-01

Despite impressive phenomenological success, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. In the context of Friedmann-Robertson-Walker (FRW) spacetime, we show that singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory for strong fields. A new mathematical model is proposed for which the analytical nonsingular extension of FRW solutions is obtained by using the nonlinear magnetic monopole fields.

Approximate solutions to Mathieu's equation

NASA Astrophysics Data System (ADS)

Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

2018-06-01

Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

Analytical approach for the fractional differential equations by using the extended tanh method

NASA Astrophysics Data System (ADS)

Pandir, Yusuf; Yildirim, Ayse

2018-07-01

In this study, we consider analytical solutions of space-time fractional derivative foam drainage equation, the nonlinear Korteweg-de Vries equation with time and space-fractional derivatives and time-fractional reaction-diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann-Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained.

On the motion of a quantum particle in the spinning cosmic string space–time

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hassanabadi, H., E-mail: h.hasanabadi@shahroodut.ac.ir; Afshardoost, A.; Zarrinkamar, S.

2015-05-15

We analyze the energy spectrum and the wave function of a particle subjected to magnetic field in the spinning cosmic string space–time and investigate the influence of the spinning reference frame and topological defect on the system. To do this we solve Schrödinger equation in the spinning cosmic string background. In our work, instead of using an approximation in the calculations, we use the quasi-exact ansatz approach which gives the exact solutions for some primary levels. - Highlights: • Solving the Schrödinger equation in the spinning cosmic string space time. • Proposing a quasi-exact analytical solution to the general formmore » of the corresponding equation. • Generalizing the previous works.« less

A finite element analysis of viscoelastically damped sandwich plates

NASA Astrophysics Data System (ADS)

Ma, B.-A.; He, J.-F.

1992-01-01

A finite element analysis associated with an asymptotic solution method for the harmonic flexural vibration of viscoelastically damped unsymmetrical sandwich plates is given. The element formulation is based on generalization of the discrete Kirchhoff theory (DKT) element formulation. The results obtained with the first order approximation of the asymptotic solution presented here are the same as those obtained by means of the modal strain energy (MSE) method. By taking more terms of the asymptotic solution, with successive calculations and use of the Padé approximants method, accuracy can be improved. The finite element computation has been verified by comparison with an analytical exact solution for rectangular plates with simply supported edges. Results for the same plates with clamped edges are also presented.

The “2T” ion-electron semi-analytic shock solution for code-comparison with xRAGE: A report for FY16

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferguson, Jim Michael

2016-10-05

This report documents an effort to generate the semi-analytic "2T" ion-electron shock solution developed in the paper by Masser, Wohlbier, and Lowrie, and the initial attempts to understand how to use this solution as a code-verification tool for one of LANL's ASC codes, xRAGE. Most of the work so far has gone into generating the semi-analytic solution. Considerable effort will go into understanding how to write the xRAGE input deck that both matches the boundary conditions imposed by the solution, and also what physics models must be implemented within the semi-analytic solution itself to match the model assumptions inherit withinmore » xRAGE. Therefore, most of this report focuses on deriving the equations for the semi-analytic 1D-planar time-independent "2T" ion-electron shock solution, and is written in a style that is intended to provide clear guidance for anyone writing their own solver.« less

Competition Between Transients in the Rate of Approach to a Fixed Point

NASA Astrophysics Data System (ADS)

Day, Judy; Rubin, Jonathan E.; Chow, Carson C.

2009-01-01

The goal of this paper is to provide and apply tools for analyzing a specific aspect of transient dynamics not covered by previous theory. The question we address is whether one component of a perturbed solution to a system of differential equations can overtake the corresponding component of a reference solution as both converge to a stable node at the origin, given that the perturbed solution was initially farther away and that both solutions are nonnegative for all time. We call this phenomenon tolerance, for its relation to a biological effect. We show using geometric arguments that tolerance will exist in generic linear systems with a complete set of eigenvectors and in excitable nonlinear systems. We also define a notion of inhibition that may constrain the regions in phase space where the possibility of tolerance arises in general systems. However, these general existence theorems do not not yield an assessment of tolerance for specific initial conditions. To address that issue, we develop some analytical tools for determining if particular perturbed and reference solution initial conditions will exhibit tolerance.

Analytical solutions of one-dimensional multispecies reactive transport in a permeable reactive barrier-aquifer system

NASA Astrophysics Data System (ADS)

Mieles, John; Zhan, Hongbin

2012-06-01

The permeable reactive barrier (PRB) remediation technology has proven to be more cost-effective than conventional pump-and-treat systems, and has demonstrated the ability to rapidly reduce the concentrations of specific chemicals of concern (COCs) by up to several orders of magnitude in some scenarios. This study derives new steady-state analytical solutions to multispecies reactive transport in a PRB-aquifer (dual domain) system. The advantage of the dual domain model is that it can account for the potential existence of natural degradation in the aquifer, when designing the required PRB thickness. The study focuses primarily on the steady-state analytical solutions of the tetrachloroethene (PCE) serial degradation pathway and secondly on the analytical solutions of the parallel degradation pathway. The solutions in this study can also be applied to other types of dual domain systems with distinct flow and transport properties. The steady-state analytical solutions are shown to be accurate and the numerical program RT3D is selected for comparison. The results of this study are novel in that the solutions provide improved modeling flexibility including: 1) every species can have unique first-order reaction rates and unique retardation factors, and 2) daughter species can be modeled with their individual input concentrations or solely as byproducts of the parent species. The steady-state analytical solutions exhibit a limitation that occurs when interspecies reaction rate factors equal each other, which result in undefined solutions. Excel spreadsheet programs were created to facilitate prompt application of the steady-state analytical solutions, for both the serial and parallel degradation pathways.

Matrix precipitation: a general strategy to eliminate matrix interference for pharmaceutical toxic impurities analysis.

PubMed

Yang, Xiaojing; Xiong, Xuewu; Cao, Ji; Luan, Baolei; Liu, Yongjun; Liu, Guozhu; Zhang, Lei

2015-01-30

Matrix interference, which can lead to false positive/negative results, contamination of injector or separation column, incompatibility between sample solution and the selected analytical instrument, and response inhibition or even quenching, is commonly suffered for the analysis of trace level toxic impurities in drug substance. In this study, a simple matrix precipitation strategy is proposed to eliminate or minimize the above stated matrix interference problems. Generally, a sample of active pharmaceutical ingredients (APIs) is dissolved in an appropriate solvent to achieve the desired high concentration and then an anti-solvent is added to precipitate the matrix substance. As a result, the target analyte is extracted into the mixed solution with very less residual of APIs. This strategy has the characteristics of simple manipulation, high recovery and excellent anti-interference capability. It was found that the precipitation ratio (R, representing the ability to remove matrix substance) and the proportion of solvent (the one used to dissolve APIs) in final solution (P, affecting R and also affecting the method sensitivity) are two important factors of the precipitation process. The correlation between R and P was investigated by performing precipitation with various APIs in different solvent/anti-solvent systems. After a detailed mathematical reasoning process, P=20% was proved to be an effective and robust condition to perform the precipitation strategy. The precipitation method with P=20% can be used as a general strategy for toxic impurity analysis in APIs. Finally, several typical examples are described in this article, where the challenging matrix interference issues have been resolved successfully. Copyright © 2014 Elsevier B.V. All rights reserved.

Exact solutions for kinetic models of macromolecular dynamics.

PubMed

Chemla, Yann R; Moffitt, Jeffrey R; Bustamante, Carlos

2008-05-15

Dynamic biological processes such as enzyme catalysis, molecular motor translocation, and protein and nucleic acid conformational dynamics are inherently stochastic processes. However, when such processes are studied on a nonsynchronized ensemble, the inherent fluctuations are lost, and only the average rate of the process can be measured. With the recent development of methods of single-molecule manipulation and detection, it is now possible to follow the progress of an individual molecule, measuring not just the average rate but the fluctuations in this rate as well. These fluctuations can provide a great deal of detail about the underlying kinetic cycle that governs the dynamical behavior of the system. However, extracting this information from experiments requires the ability to calculate the general properties of arbitrarily complex theoretical kinetic schemes. We present here a general technique that determines the exact analytical solution for the mean velocity and for measures of the fluctuations. We adopt a formalism based on the master equation and show how the probability density for the position of a molecular motor at a given time can be solved exactly in Fourier-Laplace space. With this analytic solution, we can then calculate the mean velocity and fluctuation-related parameters, such as the randomness parameter (a dimensionless ratio of the diffusion constant and the velocity) and the dwell time distributions, which fully characterize the fluctuations of the system, both commonly used kinetic parameters in single-molecule measurements. Furthermore, we show that this formalism allows calculation of these parameters for a much wider class of general kinetic models than demonstrated with previous methods.

Simulation and analysis of airborne antenna radiation patterns

NASA Technical Reports Server (NTRS)

Kim, J. J.; Burnside, Walter D.

1984-01-01

The objective is to develop an accurate and efficient analytic solution for predicting high frequency radiation patterns of fuselage-mounted airborne antennas. This is an analytic study of airborne antenna patterns using the Uniform Geometrical Theory of Diffraction (UTD). The aircraft is modeled in its most basic form so that the solution is applicable to general-type aircraft. The fuselage is modeled as a perfectly conducting composite ellipsoid; whereas, the wings, stabilizers, nose, fuel tanks, and engines, are simulated as perfectly conducting flat plates that can be attached to the fuselage and/or to each other. The composite-ellipsoid fuselage model is necessary to successfully simulate the wide variety of real world fuselage shapes. Since the antenna is mounted on the fuselage, it has a dominant effect on the resulting radiation pattern so it must be simulated accurately, especially near the antenna. Various radiation patterns are calculated for commercial, private, and military aircraft, and the Space Shuttle Orbiter. The application of this solution to numerous practical airborne antenna problems illustrates its versatility and design capability. In most cases, the solution accuracy is verified by the comparisons between the calculated and measured data.

Cross reactive arrays of three-way junction sensors for steroid determination

NASA Technical Reports Server (NTRS)

Stojanovic, Milan N. (Inventor); Nikic, Dragan B. (Inventor); Landry, Donald (Inventor)

2008-01-01

This invention provides analyte sensitive oligonucleotide compositions for detecting and analyzing analytes in solution, including complex solutions using cross reactive arrays of analyte sensitive oligonucleotide compositions.

A strategy for reducing gross errors in the generalized Born models of implicit solvation

PubMed Central

Onufriev, Alexey V.; Sigalov, Grigori

2011-01-01

The “canonical” generalized Born (GB) formula [C. Still, A. Tempczyk, R. C. Hawley, and T. Hendrickson, J. Am. Chem. Soc. 112, 6127 (1990)] is known to provide accurate estimates for total electrostatic solvation energies ΔGel of biomolecules if the corresponding effective Born radii are accurate. Here we show that even if the effective Born radii are perfectly accurate, the canonical formula still exhibits significant number of gross errors (errors larger than 2kBT relative to numerical Poisson equation reference) in pairwise interactions between individual atomic charges. Analysis of exact analytical solutions of the Poisson equation (PE) for several idealized nonspherical geometries reveals two distinct spatial modes of the PE solution; these modes are also found in realistic biomolecular shapes. The canonical GB Green function misses one of two modes seen in the exact PE solution, which explains the observed gross errors. To address the problem and reduce gross errors of the GB formalism, we have used exact PE solutions for idealized nonspherical geometries to suggest an alternative analytical Green function to replace the canonical GB formula. The proposed functional form is mathematically nearly as simple as the original, but depends not only on the effective Born radii but also on their gradients, which allows for better representation of details of nonspherical molecular shapes. In particular, the proposed functional form captures both modes of the PE solution seen in nonspherical geometries. Tests on realistic biomolecular structures ranging from small peptides to medium size proteins show that the proposed functional form reduces gross pairwise errors in all cases, with the amount of reduction varying from more than an order of magnitude for small structures to a factor of 2 for the largest ones. PMID:21528947

Comparison between numeric and approximate analytic solutions for the prediction of soil metal uptake by roots. Example of cadmium.

PubMed

Schneider, André; Lin, Zhongbing; Sterckeman, Thibault; Nguyen, Christophe

2018-04-01

The dissociation of metal complexes in the soil solution can increase the availability of metals for root uptake. When it is accounted for in models of bioavailability of soil metals, the number of partial differential equations (PDEs) increases and the computation time to numerically solve these equations may be problematic when a large number of simulations are required, for example for sensitivity analyses or when considering root architecture. This work presents analytical solutions for the set of PDEs describing the bioavailability of soil metals including the kinetics of complexation for three scenarios where the metal complex in solution was fully inert, fully labile, or partially labile. The analytical solutions are only valid i) at steady-state when the PDEs become ordinary differential equations, the transient phase being not covered, ii) when diffusion is the major mechanism of transport and therefore, when convection is negligible, iii) when there is no between-root competition. The formulation of the analytical solutions is for cylindrical geometry but the solutions rely on the spread of the depletion profile around the root, which was modelled assuming a planar geometry. The analytical solutions were evaluated by comparison with the corresponding PDEs for cadmium in the case of the French agricultural soils. Provided that convection was much lower than diffusion (Péclet's number<0.02), the cumulative uptakes calculated from the analytic solutions were in very good agreement with those calculated from the PDEs, even in the case of a partially labile complex. The analytic solutions can be used instead of the PDEs to predict root uptake of metals. The analytic solutions were also used to build an indicator of the contribution of a complex to the uptake of the metal by roots, which can be helpful to predict the effect of soluble organic matter on the bioavailability of soil metals. Copyright © 2017 Elsevier B.V. All rights reserved.

A novel analytical description of periodic volume coil geometries in MRI

NASA Astrophysics Data System (ADS)

Koh, D.; Felder, J.; Shah, N. J.

2018-03-01

MRI volume coils can be represented by equivalent lumped element circuits and for a variety of these circuit configurations analytical design equations have been presented. The unification of several volume coil topologies results in a two-dimensional gridded equivalent lumped element circuit which compromises the birdcage resonator, its multiple endring derivative but also novel structures like the capacitive coupled ring resonator. The theory section analyzes a general two-dimensional circuit by noting that its current distribution can be decomposed into a longitudinal and an azimuthal dependency. This can be exploited to compare the current distribution with a transfer function of filter circuits along one direction. The resonances of the transfer function coincide with the resonance of the volume resonator and the simple analytical solution can be used as a design equation. The proposed framework is verified experimentally against a novel capacitive coupled ring structure which was derived from the general circuit formulation and is proven to exhibit a dominant homogeneous mode. In conclusion, a unified analytical framework is presented that allows determining the resonance frequency of any volume resonator that can be represented by a two dimensional meshed equivalent circuit.

Analytical solutions for coagulation and condensation kinetics of composite particles

NASA Astrophysics Data System (ADS)

Piskunov, Vladimir N.

2013-04-01

The processes of composite particles formation consisting of a mixture of different materials are essential for many practical problems: for analysis of the consequences of accidental releases in atmosphere; for simulation of precipitation formation in clouds; for description of multi-phase processes in chemical reactors and industrial facilities. Computer codes developed for numerical simulation of these processes require optimization of computational methods and verification of numerical programs. Kinetic equations of composite particle formation are given in this work in a concise form (impurity integrated). Coagulation, condensation and external sources associated with nucleation are taken into account. Analytical solutions were obtained in a number of model cases. The general laws for fraction redistribution of impurities were defined. The results can be applied to develop numerical algorithms considerably reducing the simulation effort, as well as to verify the numerical programs for calculation of the formation kinetics of composite particles in the problems of practical importance.

Investigation of aerodynamic characteristics of subsonic wings

NASA Technical Reports Server (NTRS)

Dejarnette, F. R.; Frink, N. T.

1979-01-01

An analytical strake design procedure is investigated. A numerical solution to the governing strake design equation is used to generate a series of strakes which are tested in a water tunnel to study their vortex breakdown characteristics. The strakes are scaled for use on a half-scale model of the NASA-LaRC general research fuselage with a 44 degrees trapezoidal wing. An analytical solution to the governing design equation is obtained. The strake design procedure relates the potential-flow leading-edge suction and pressure distributions to vortex stability. Several suction distributions are studied and those which are more triangular and peak near the tip generate strakes that reach higher angles of attack before vortex breakdown occurs at the wing trailing edge. For the same suction distribution, a conical rather than three dimensional pressure specification results in a better strake shape as judged from its vortex breakdown characteristics.

Symmetric tridiagonal structure preserving finite element model updating problem for the quadratic model

NASA Astrophysics Data System (ADS)

Rakshit, Suman; Khare, Swanand R.; Datta, Biswa Nath

2018-07-01

One of the most important yet difficult aspect of the Finite Element Model Updating Problem is to preserve the finite element inherited structures in the updated model. Finite element matrices are in general symmetric, positive definite (or semi-definite) and banded (tridiagonal, diagonal, penta-diagonal, etc.). Though a large number of papers have been published in recent years on various aspects of solutions of this problem, papers dealing with structure preservation almost do not exist. A novel optimization based approach that preserves the symmetric tridiagonal structures of the stiffness and damping matrices is proposed in this paper. An analytical expression for the global minimum solution of the associated optimization problem along with the results of numerical experiments obtained by both the analytical expressions and by an appropriate numerical optimization algorithm are presented. The results of numerical experiments support the validity of the proposed method.

Numerical analysis of two-fluid tearing mode instability in a finite aspect ratio cylinder

NASA Astrophysics Data System (ADS)

Ito, Atsushi; Ramos, Jesús J.

2018-01-01

The two-fluid resistive tearing mode instability in a periodic plasma cylinder of finite aspect ratio is investigated numerically for parameters such that the cylindrical aspect ratio and two-fluid effects are of order unity, hence the real and imaginary parts of the mode eigenfunctions and growth rate are comparable. Considering a force-free equilibrium, numerical solutions of the complete eigenmode equations for general aspect ratios and ion skin depths are compared and found to be in very good agreement with the corresponding analytic solutions derived by means of the boundary layer theory [A. Ito and J. J. Ramos, Phys. Plasmas 24, 072102 (2017)]. Scaling laws for the growth rate and the real frequency of the mode are derived from the analytic dispersion relation by using Taylor expansions and Padé approximations. The cylindrical finite aspect ratio effect is inferred from the scaling law for the real frequency of the mode.

CTEPP STANDARD OPERATING PROCEDURE FOR PREPARATION OF SURROGATE RECOVERY STANDARD AND INTERNAL STANDARD SOLUTIONS FOR POLAR TARGET ANALYTES (SOP-5.26)

EPA Science Inventory

This SOP describes the method used for preparing surrogate recovery standard and internal standard solutions for the analysis of polar target analytes. It also describes the method for preparing calibration standard solutions for polar analytes used for gas chromatography/mass sp...

Analytical model for the radio-frequency sheath

NASA Astrophysics Data System (ADS)

Czarnetzki, Uwe

2013-12-01

A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.

Analytical model for the radio-frequency sheath.

PubMed

Czarnetzki, Uwe

2013-12-01

A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.

Heat addition to a subsonic boundary layer: A preliminary analytical study

NASA Technical Reports Server (NTRS)

Macha, J. M.; Norton, D. J.

1971-01-01

A preliminary analytical study of the effects of heat addition to the subsonic boundary layer flow over a typical airfoil shape is presented. This phenomenon becomes of interest in the space shuttle mission since heat absorbed by the wing structure during re-entry will be rejected to the boundary layer during the subsequent low speed maneuvering and landing phase. A survey of existing literature and analytical solutions for both laminar and turbulent flow indicate that a heated surface generally destabilizes the boundary layer. Specifically, the boundary layer thickness is increased, the skin friction at the surface is decreased and the point of flow separation is moved forward. In addition, limited analytical results predict that the angle of attack at which a heated airfoil will stall is significantly less than the stall angle of an unheated wing. These effects could adversely affect the lift and drag, and thus the maneuvering capabilities of booster and orbiter shuttle vehicles.

Semi-analytical solutions of the Schnakenberg model of a reaction-diffusion cell with feedback

NASA Astrophysics Data System (ADS)

Al Noufaey, K. S.

2018-06-01

This paper considers the application of a semi-analytical method to the Schnakenberg model of a reaction-diffusion cell. The semi-analytical method is based on the Galerkin method which approximates the original governing partial differential equations as a system of ordinary differential equations. Steady-state curves, bifurcation diagrams and the region of parameter space in which Hopf bifurcations occur are presented for semi-analytical solutions and the numerical solution. The effect of feedback control, via altering various concentrations in the boundary reservoirs in response to concentrations in the cell centre, is examined. It is shown that increasing the magnitude of feedback leads to destabilization of the system, whereas decreasing this parameter to negative values of large magnitude stabilizes the system. The semi-analytical solutions agree well with numerical solutions of the governing equations.

Decisions through data: analytics in healthcare.

PubMed

Wills, Mary J

2014-01-01

The amount of data in healthcare is increasing at an astonishing rate. However, in general, the industry has not deployed the level of data management and analysis necessary to make use of those data. As a result, healthcare executives face the risk of being overwhelmed by a flood of unusable data. In this essay I argue that, in order to extract actionable information, leaders must take advantage of the promise of data analytics. Small data, predictive modeling expansion, and real-time analytics are three forms of data analytics. On the basis of my analysis for this study, I recommend all three for adoption. Recognizing the uniqueness of each organization's situation, I also suggest that practices, hospitals, and healthcare systems examine small data and conduct real-time analytics and that large-scale organizations managing populations of patients adopt predictive modeling. I found that all three solutions assist in the collection, management, and analysis of raw data to improve the quality of care and decrease costs.

Spinning solutions in general relativity with infinite central density

NASA Astrophysics Data System (ADS)

Flammer, P. D.

2018-05-01

This paper presents general relativistic numerical simulations of uniformly rotating polytropes. Equations are developed using MSQI coordinates, but taking a logarithm of the radial coordinate. The result is relatively simple elliptical differential equations. Due to the logarithmic scale, we can resolve solutions with near-singular mass distributions near their center, while the solution domain extends many orders of magnitude larger than the radius of the distribution (to connect with flat space-time). Rotating solutions are found with very high central energy densities for a range of adiabatic exponents. Analytically, assuming the pressure is proportional to the energy density (which is true for polytropes in the limit of large energy density), we determine the small radius behavior of the metric potentials and energy density. This small radius behavior agrees well with the small radius behavior of large central density numerical results, lending confidence to our numerical approach. We compare results with rotating solutions available in the literature, which show good agreement. We study the stability of spherical solutions: instability sets in at the first maximum in mass versus central energy density; this is also consistent with results in the literature, and further lends confidence to the numerical approach.

Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension

NASA Astrophysics Data System (ADS)

Brihaye, Yves; Herdeiro, Carlos; Radu, Eugen; Tchrakian, D. H.

2017-11-01

We consider a class of generalizations of the Skyrme model to five spacetime dimensions ( d = 5), which is defined in terms of an O(5) sigma model. A special ansatz for the Skyrme field allows angular momentum to be present and equations of motion with a radial dependence only. Using it, we obtain: 1) everywhere regular solutions describing localised energy lumps ( Skyrmions); 2) Self-gravitating, asymptotically flat, everywhere non-singular solitonic solutions ( Skyrme stars), upon minimally coupling the model to Einstein's gravity; 3) both static and spinning black holes with Skyrme hair, the latter with rotation in two orthogonal planes, with both angular momenta of equal magnitude. In the absence of gravity we present an analytic solution that satisfies a BPS-type bound and explore numerically some of the non-BPS solutions. In the presence of gravity, we contrast the solutions to this model with solutions to a complex scalar field model, namely boson stars and black holes with synchronised hair. Remarkably, even though the two models present key differences, and in particular the Skyrme model allows static hairy black holes, when introducing rotation, the synchronisation condition becomes mandatory, providing further evidence for its generality in obtaining rotating hairy black holes.

A globally convergent and closed analytical solution of the Blasius equation with beneficial applications

NASA Astrophysics Data System (ADS)

Zheng, Jun; Han, Xinyue; Wang, ZhenTao; Li, Changfeng; Zhang, Jiazhong

2017-06-01

For about a century, people have been trying to seek for a globally convergent and closed analytical solution (CAS) of the Blasius Equation (BE). In this paper, we proposed a formally satisfied solution which could be parametrically expressed by two power series. Some analytical results of the laminar boundary layer of a flat plate, that were not analytically given in former studies, e.g. the thickness of the boundary layer and higher order derivatives, could be obtained based on the solution. Besides, the heat transfer in the laminar boundary layer of a flat plate with constant temperature could also be analytically formulated. Especially, the solution of the singular situation with Prandtl number Pr=0, which seems impossible to be analyzed in prior studies, could be given analytically. The method for finding the CAS of Blasius equation was also utilized in the problem of the boundary layer regulation through wall injection and slip velocity on the wall surface.

Firing the Executive: When an Analytic Approach to Problem Solving Helps and Hurts

ERIC Educational Resources Information Center

Aiello, Daniel A.; Jarosz, Andrew F.; Cushen, Patrick J.; Wiley, Jennifer

2012-01-01

There is a general assumption that a more controlled or more focused attentional state is beneficial for most cognitive tasks. However, there has been a growing realization that creative problem solving tasks, such as the Remote Associates Task (RAT), may benefit from a less controlled solution approach. To test this hypothesis, in a 2x2 design,…

Multipolar electromagnetic fields around neutron stars: general-relativistic vacuum solutions

NASA Astrophysics Data System (ADS)

Pétri, J.

2017-12-01

Magnetic fields inside and around neutron stars are at the heart of pulsar magnetospheric activity. Strong magnetic fields are responsible for quantum effects, an essential ingredient to produce leptonic pairs and the subsequent broad-band radiation. The variety of electromagnetic field topologies could lead to the observed diversity of neutron star classes. Thus, it is important to include multipolar components to a presumably dominant dipolar magnetic field. Exact analytical solutions for these multipoles in Newtonian gravity have been computed in recent literature. However, flat space-time is not adequate to describe physics in the immediate surroundings of neutron stars. We generalize the multipole expressions to the strong gravity regime by using a slowly rotating metric approximation such as the one expected around neutron stars. Approximate formulae for the electromagnetic field including frame dragging are computed from which we estimate the Poynting flux and the braking index. Corrections to leading order in compactness and spin parameter are presented. As far as spin-down luminosity is concerned, it is shown that frame dragging remains irrelevant. For high-order multipoles starting from the quadrupole, the electric part can radiate more efficiently than the magnetic part. Both analytical and numerical tools are employed.

Development and application of a unified balancing approach with multiple constraints

NASA Technical Reports Server (NTRS)

Zorzi, E. S.; Lee, C. C.; Giordano, J. C.

1985-01-01

The development of a general analytic approach to constrained balancing that is consistent with past influence coefficient methods is described. The approach uses Lagrange multipliers to impose orbit and/or weight constraints; these constraints are combined with the least squares minimization process to provide a set of coupled equations that result in a single solution form for determining correction weights. Proper selection of constraints results in the capability to: (1) balance higher speeds without disturbing previously balanced modes, thru the use of modal trial weight sets; (2) balance off-critical speeds; and (3) balance decoupled modes by use of a single balance plane. If no constraints are imposed, this solution form reduces to the general weighted least squares influence coefficient method. A test facility used to examine the use of the general constrained balancing procedure and application of modal trial weight ratios is also described.

The primer vector in linear, relative-motion equations. [spacecraft trajectory optimization

NASA Technical Reports Server (NTRS)

1980-01-01

Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.

Holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole

NASA Astrophysics Data System (ADS)

Ishibashi, Akihiro; Maeda, Kengo; Mefford, Eric

2017-07-01

We investigate a stress-energy tensor for a conformal field theory (CFT) at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the "derivative expansion" method, generalizing the work of Haddad [Classical Quantum Gravity 29, 245001 (2012), 10.1088/0264-9381/29/24/245001] and analytically compute the holographic stress-energy tensor for our solution. We find that the stress-energy tensor is finite at both the future and past outer (event) horizons and that the energy density is negative just outside the event horizons due to the Hawking effect. Furthermore, we apply the holographic method to the question of quantum instability of the Cauchy horizon since, by construction, our black droplet solution also admits a Cauchy horizon inside. We analytically show that the null-null component of the holographic stress-energy tensor negatively diverges at the Cauchy horizon, suggesting that a singularity appears there, in favor of strong cosmic censorship.

Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: one-dimensional soil thaw with conduction and advection

USGS Publications Warehouse

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.

ANALYTICAL ASSESSMENT OF THE IMPACTS OF PARTIAL MASS DEPLETION IN DNAPL SOURCE ZONES (SAN FRANCISCO, CA)

EPA Science Inventory

Analytical solutions describing the time-dependent DNAPL source-zone mass and contaminant discharge rate are used as a flux-boundary condition in a semi-analytical contaminant transport model. These analytical solutions assume a power relationship between the flow-averaged sourc...

Nonlinear electroelastic deformations of dielectric elastomer composites: II - Non-Gaussian elastic dielectrics

NASA Astrophysics Data System (ADS)

Lefèvre, Victor; Lopez-Pamies, Oscar

2017-02-01

This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response - under finite deformations and finite electric fields - of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method - this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics - to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi-)conducting/high-permittivity particles to dielectric elastomers does not lead to the extreme electrostriction enhancements observed in experiments. It is posited that such extreme enhancements are the manifestation of interphasial phenomena.

A Family of Vortices to Study Axisymmetric Vortex Breakdown and Reconnection

NASA Technical Reports Server (NTRS)

Young, Larry A.

2007-01-01

A new analytic model describing a family of vortices has been developed to study some of the axisymmetric vortex breakdown and reconnection fluid dynamic processes underlying body-vortex interactions that are frequently manifested in rotorcraft and propeller-driven fixed-wing aircraft wakes. The family of vortices incorporates a wide range of prescribed initial vorticity distributions -- including single or dual-core vorticity distributions. The result is analytical solutions for the vorticity and velocities for each member of the family of vortices. This model is of sufficient generality to further illustrate the dependence of vortex reconnection and breakdown on initial vorticity distribution as was suggested by earlier analytical work. This family of vortices, though laminar in nature, is anticipated to provide valuable insight into the vortical evolution of large-scale rotor and propeller wakes.

A stationary bulk planar ideal flow solution for the double shearing model

NASA Astrophysics Data System (ADS)

Lyamina, E. A.; Kalenova, N. V.; Date, P. P.

2018-04-01

This paper provides a general ideal flow solution for the double shearing model of pressure-dependent plasticity. This new solution is restricted to a special class of stationary planar flows. A distinguished feature of this class of solutions is that one family of characteristic lines is straight. The solution is analytic. The mapping between Cartesian and principal lines based coordinate systems is given in parametric form with characteristic coordinates being the parameters. A simple relation that connects the scale factor for one family of coordinate curves of the principal lines based coordinate system and the magnitude of velocity is derived. The original ideal flow theory is widely used as the basis for inverse methods for the preliminary design of metal forming processes driven by minimum plastic work. The new theory extends this area of application to granular materials.

A Semianalytical Model for Pumping Tests in Finite Heterogeneous Confined Aquifers With Arbitrarily Shaped Boundary

NASA Astrophysics Data System (ADS)

Wang, Lei; Dai, Cheng; Xue, Liang

2018-04-01

This study presents a Laplace-transform-based boundary element method to model the groundwater flow in a heterogeneous confined finite aquifer with arbitrarily shaped boundaries. The boundary condition can be Dirichlet, Neumann or Robin-type. The derived solution is analytical since it is obtained through the Green's function method within the domain. However, the numerical approximation is required on the boundaries, which essentially renders it a semi-analytical solution. The proposed method can provide a general framework to derive solutions for zoned heterogeneous confined aquifers with arbitrarily shaped boundary. The requirement of the boundary element method presented here is that the Green function must exist for a specific PDE equation. In this study, the linear equations for the two-zone and three-zone confined aquifers with arbitrarily shaped boundary is established in Laplace space, and the solution can be obtained by using any linear solver. Stehfest inversion algorithm can be used to transform it back into time domain to obtain the transient solution. The presented solution is validated in the two-zone cases by reducing the arbitrarily shaped boundaries to circular ones and comparing it with the solution in Lin et al. (2016, https://doi.org/10.1016/j.jhydrol.2016.07.028). The effect of boundary shape and well location on dimensionless drawdown in two-zone aquifers is investigated. Finally the drawdown distribution in three-zone aquifers with arbitrarily shaped boundary for constant-rate tests (CRT) and flow rate distribution for constant-head tests (CHT) are analyzed.

Hybrid Numerical-Analytical Scheme for Calculating Elastic Wave Diffraction in Locally Inhomogeneous Waveguides

NASA Astrophysics Data System (ADS)

Glushkov, E. V.; Glushkova, N. V.; Evdokimov, A. A.

2018-01-01

Numerical simulation of traveling wave excitation, propagation, and diffraction in structures with local inhomogeneities (obstacles) is computationally expensive due to the need for mesh-based approximation of extended domains with the rigorous account for the radiation conditions at infinity. Therefore, hybrid numerical-analytic approaches are being developed based on the conjugation of a numerical solution in a local vicinity of the obstacle and/or source with an explicit analytic representation in the remaining semi-infinite external domain. However, in standard finite-element software, such a coupling with the external field, moreover, in the case of multimode expansion, is generally not provided. This work proposes a hybrid computational scheme that allows realization of such a conjugation using a standard software. The latter is used to construct a set of numerical solutions used as the basis for the sought solution in the local internal domain. The unknown expansion coefficients on this basis and on normal modes in the semi-infinite external domain are then determined from the conditions of displacement and stress continuity at the boundary between the two domains. We describe the implementation of this approach in the scalar and vector cases. To evaluate the reliability of the results and the efficiency of the algorithm, we compare it with a semianalytic solution to the problem of traveling wave diffraction by a horizontal obstacle, as well as with a finite-element solution obtained for a limited domain artificially restricted using absorbing boundaries. As an example, we consider the incidence of a fundamental antisymmetric Lamb wave onto surface and partially submerged elastic obstacles. It is noted that the proposed hybrid scheme can also be used to determine the eigenfrequencies and eigenforms of resonance scattering, as well as the characteristics of traveling waves in embedded waveguides.

Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

PubMed

Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke

2018-02-01

In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models

NASA Astrophysics Data System (ADS)

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.

Analytical solution for the transient wave propagation of a buried cylindrical P-wave line source in a semi-infinite elastic medium with a fluid surface layer

NASA Astrophysics Data System (ADS)

Shan, Zhendong; Ling, Daosheng

2018-02-01

This article develops an analytical solution for the transient wave propagation of a cylindrical P-wave line source in a semi-infinite elastic solid with a fluid layer. The analytical solution is presented in a simple closed form in which each term represents a transient physical wave. The Scholte equation is derived, through which the Scholte wave velocity can be determined. The Scholte wave is the wave that propagates along the interface between the fluid and solid. To develop the analytical solution, the wave fields in the fluid and solid are defined, their analytical solutions in the Laplace domain are derived using the boundary and interface conditions, and the solutions are then decomposed into series form according to the power series expansion method. Each item of the series solution has a clear physical meaning and represents a transient wave path. Finally, by applying Cagniard's method and the convolution theorem, the analytical solutions are transformed into the time domain. Numerical examples are provided to illustrate some interesting features in the fluid layer, the interface and the semi-infinite solid. When the P-wave velocity in the fluid is higher than that in the solid, two head waves in the solid, one head wave in the fluid and a Scholte wave at the interface are observed for the cylindrical P-wave line source.

Analytical study on the generalized Davydov model in the alpha helical proteins

NASA Astrophysics Data System (ADS)

Wang, Pan; Xiao, Shu-Hong; Chen, Li; Yang, Gang

2017-06-01

In this paper, we investigate the dynamics of a generalized Davydov model derived from an infinite chain of alpha helical protein molecules which contain three hydrogen bonding spines running almost parallel to the helical axis. Through the introduction of the auxiliary function, the bilinear form, one-, two- and three-soliton solutions for the generalized Davydov model are obtained firstly. Propagation and interactions of solitons have been investigated analytically and graphically. The amplitude of the soliton is only related to the complex parameter μ and real parameter 𝜃 with a range of [0, 2π]. The velocity of the soliton is only related to the complex parameter μ, real parameter 𝜃, lattice parameter 𝜀, and physical parameters β1, β3 and β4. Overtaking and head-on interactions of two and three solitons are presented. The common in the interactions of three solitons is the directions of the solitons change after the interactions. The soliton derived in this paper is expected to have potential applications in the alpha helical proteins.

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra ismore » later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a rotating quadrupole field ion trap are presented. •Exact solutions for magneto-transport in variable electromagnetic fields are shown.« less

The analysis of solutions behaviour of Van der Pol Duffing equation describing local brain hemodynamics

NASA Astrophysics Data System (ADS)

Cherevko, A. A.; Bord, E. E.; Khe, A. K.; Panarin, V. A.; Orlov, K. J.

2017-10-01

This article proposes the generalized model of Van der Pol — Duffing equation for describing the relaxation oscillations in local brain hemodynamics. This equation connects the velocity and pressure of blood flow in cerebral vessels. The equation is individual for each patient, since the coefficients are unique. Each set of coefficients is built based on clinical data obtained during neurosurgical operation in Siberian Federal Biomedical Research Center named after Academician E. N. Meshalkin. The equation has solutions of different structure defined by the coefficients and right side. We investigate the equations for different patients considering peculiarities of their vessel systems. The properties of approximate analytical solutions are studied. Amplitude-frequency and phase-frequency characteristics are built for the small-dimensional solution approximations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

Here, the one-dimensional water faucet problem is one of the classical benchmark problems originally proposed by Ransom to study the two-fluid two-phase flow model. With certain simplifications, such as massless gas phase and no wall and interfacial frictions, analytical solutions had been previously obtained for the transient liquid velocity and void fraction distribution. The water faucet problem and its analytical solutions have been widely used for the purposes of code assessment, benchmark and numerical verifications. In our previous study, the Ransom’s solutions were used for the mesh convergence study of a high-resolution spatial discretization scheme. It was found that, atmore » the steady state, an anticipated second-order spatial accuracy could not be achieved, when compared to the existing Ransom’s analytical solutions. A further investigation showed that the existing analytical solutions do not actually satisfy the commonly used two-fluid single-pressure two-phase flow equations. In this work, we present a new set of analytical solutions of the water faucet problem at the steady state, considering the gas phase density’s effect on pressure distribution. This new set of analytical solutions are used for mesh convergence studies, from which anticipated second-order of accuracy is achieved for the 2nd order spatial discretization scheme. In addition, extended Ransom’s transient solutions for the gas phase velocity and pressure are derived, with the assumption of decoupled liquid and gas pressures. Numerical verifications on the extended Ransom’s solutions are also presented.« less

Analytical description of the ternary melt and solution crystallization with a non-linear phase diagram

NASA Astrophysics Data System (ADS)

Toropova, L. V.; Alexandrov, D. V.

2018-05-01

The directional solidification of a ternary system with an extended phase transition region is theoretically studied. A mathematical model is developed to describe quasi-stationary solidification, and its analytical solution is constructed with allowance for a nonlinear liquids line equation. We demonstrate that the phase diagram nonlinearity leads to substantial changes of analytical solutions.

Exact analytical solution of a classical Josephson tunnel junction problem

NASA Astrophysics Data System (ADS)

Kuplevakhsky, S. V.; Glukhov, A. M.

2010-10-01

We give an exact and complete analytical solution of the classical problem of a Josephson tunnel junction of arbitrary length W ɛ(0,∞) in the presence of external magnetic fields and transport currents. Contrary to a wide-spread belief, the exact analytical solution unambiguously proves that there is no qualitative difference between so-called "small" (W≪1) and "large" junctions (W≫1). Another unexpected physical implication of the exact analytical solution is the existence (in the current-carrying state) of unquantized Josephson vortices carrying fractional flux and located near one of the edges of the junction. We also refine the mathematical definition of critical transport current.

Further studies on liquid sloshing

NASA Astrophysics Data System (ADS)

Lou, Y. K.; Wu, M. C.; Lee, C. K.

1985-03-01

Sloshing is especially of concern for LNG Carriers and large oil tankers because of their tank size and geometrical configurations and the likelihood of near resonant excitation of the contained liquid. When a tank is under multidegree of freedom excitations the phase relationships among the excitations might have a significant effect on sloshing loads. An analytical solution is obtained for liquid sloshing under combined excitations with phase difference. A series of physical model tests has also been conducted to investigate the effects of the phase angle on liquid sloshing loads for tanks under combined roll and sway and roll and heave excitations. The experimental results are in general agreement with the analytical findings.

Crew appliance computer program manual, volume 1

NASA Technical Reports Server (NTRS)

Russell, D. J.

1975-01-01

Trade studies of numerous appliance concepts for advanced spacecraft galley, personal hygiene, housekeeping, and other areas were made to determine which best satisfy the space shuttle orbiter and modular space station mission requirements. Analytical models of selected appliance concepts not currently included in the G-189A Generalized Environmental/Thermal Control and Life Support Systems (ETCLSS) Computer Program subroutine library were developed. The new appliance subroutines are given along with complete analytical model descriptions, solution methods, user's input instructions, and validation run results. The appliance components modeled were integrated with G-189A ETCLSS models for shuttle orbiter and modular space station, and results from computer runs of these systems are presented.

Solar neutrino masses and mixing from bilinear R-parity broken supersymmetry: Analytical versus numerical results

NASA Astrophysics Data System (ADS)

Díaz, M.; Hirsch, M.; Porod, W.; Romão, J.; Valle, J.

2003-07-01

We give an analytical calculation of solar neutrino masses and mixing at one-loop order within bilinear R-parity breaking supersymmetry, and compare our results to the exact numerical calculation. Our method is based on a systematic perturbative expansion of R-parity violating vertices to leading order. We find in general quite good agreement between the approximate and full numerical calculations, but the approximate expressions are much simpler to implement. Our formalism works especially well for the case of the large mixing angle Mikheyev-Smirnov-Wolfenstein solution, now strongly favored by the recent KamLAND reactor neutrino data.

Random variable transformation for generalized stochastic radiative transfer in finite participating slab media

NASA Astrophysics Data System (ADS)

El-Wakil, S. A.; Sallah, M.; El-Hanbaly, A. M.

2015-10-01

The stochastic radiative transfer problem is studied in a participating planar finite continuously fluctuating medium. The problem is considered for specular- and diffusly-reflecting boundaries with linear anisotropic scattering. Random variable transformation (RVT) technique is used to get the complete average for the solution functions, that are represented by the probability-density function (PDF) of the solution process. In the RVT algorithm, a simple integral transformation to the input stochastic process (the extinction function of the medium) is applied. This linear transformation enables us to rewrite the stochastic transport equations in terms of the optical random variable (x) and the optical random thickness (L). Then the transport equation is solved deterministically to get a closed form for the solution as a function of x and L. So, the solution is used to obtain the PDF of the solution functions applying the RVT technique among the input random variable (L) and the output process (the solution functions). The obtained averages of the solution functions are used to get the complete analytical averages for some interesting physical quantities, namely, reflectivity and transmissivity at the medium boundaries. In terms of the average reflectivity and transmissivity, the average of the partial heat fluxes for the generalized problem with internal source of radiation are obtained and represented graphically.

Global Properties of Fully Convective Accretion Disks from Local Simulations

NASA Astrophysics Data System (ADS)

Bodo, G.; Cattaneo, F.; Mignone, A.; Ponzo, F.; Rossi, P.

2015-08-01

We present an approach to deriving global properties of accretion disks from the knowledge of local solutions derived from numerical simulations based on the shearing box approximation. The approach consists of a two-step procedure. First, a local solution valid for all values of the disk height is constructed by piecing together an interior solution obtained numerically with an analytical exterior radiative solution. The matching is obtained by assuming hydrostatic balance and radiative equilibrium. Although in principle the procedure can be carried out in general, it simplifies considerably when the interior solution is fully convective. In these cases, the construction is analogous to the derivation of the Hayashi tracks for protostars. The second step consists of piecing together the local solutions at different radii to obtain a global solution. Here we use the symmetry of the solutions with respect to the defining dimensionless numbers—in a way similar to the use of homology relations in stellar structure theory—to obtain the scaling properties of the various disk quantities with radius.

An investigation on the motion and deformation of viscoelastic drops descending in another viscoelastic media

NASA Astrophysics Data System (ADS)

Davoodi, M.; Norouzi, M.

2016-10-01

In the present study, an investigation of the motion and shape deformation of drops is carried out in creeping flow to highlight the effect of viscoelastic properties on the problem. A perturbation method is employed to derive an analytical solution for the general case that both interior and exterior fluids are viscoelastic, both fluids obeying the Giesekus model. An experiment is also performed for the limiting case of an immiscible drop of a 0.03% (w/w) polyacrylamide in an 80:20 glycerol/water solution falling through a viscous Newtonian silicon oil (410 cP polydimethylsiloxane oil) in order to check the accuracy of the analytical solution. It is shown that the addition of elastic properties to the interior fluid may cause a decrease in the terminal velocity of the droplet while an increase in the elastic properties of the exterior fluid results in the opposite behavior and increases the terminal velocity. The well-known spherical shape of creeping drops for Newtonian fluids is modified by elasticity into either prolate or oblate shapes. Using the analytical solution, it is shown that normal stresses play a key role on the final steady-state shape of the drops. To keep the drops spherical in viscoelastic phases, it is shown that the effect of normal stresses on the interior and exterior media can cancel out under certain conditions. The results presented here may be of interest to industries dealing with petroleum and medicine processing, paint and power-plant related fields where knowledge of the shape and terminal velocity of descending droplets is of great importance.

Solid Rocket Fuel Constitutive Theory and Polymer Cure

NASA Technical Reports Server (NTRS)

Ream, Robert

2006-01-01

Solid Rocket Fuel is a complex composite material for which no general constitutive theory, based on first principles, has been developed. One of the principles such a relation would depend on is the morphology of the binder. A theory of polymer curing is required to determine this morphology. During work on such a theory an algorithm was developed for counting the number of ways a polymer chain could assemble. The methods used to develop and check this algorithm led to an analytic solution to the problem. This solution is used in a probability distribution function which characterizes the morphology of the polymer.

Moment distributions around holes in symmetric composite laminates subjected to bending moments

NASA Technical Reports Server (NTRS)

Prasad, C. B.; Shuart, M. J.

1989-01-01

An analytical investigation of the effects of holes on the moment distribution of symmetric composite laminates subjected to bending moments is described. A general, closed-form solution for the moment distribution of an infinite anisotropic plate is derived, and this solution is used to determine stress distributions both on the hole boundary and throughout the plate. Results are presented for several composite laminates that have holes and are subjected to either pure bending or cylindrical bending. Laminates with a circular hole or with an elliptical hole are studied. Laminate moment distributions are discussed, and ply stresses are described.

Probing quantum gravity through exactly soluble midi-superspaces I

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ashtekar, A.; Pierri, M.

1996-12-01

It is well-known that the Einstein-Rosen solutions to the 3+1- dimensional vacuum Einstein{close_quote}s equations are in one to one correspondence with solutions of 2+1-dimensional general relativity coupled to axi-symmetric, zero rest mass scalar fields. We first re-examine the quantization of this midi-superspace paying special attention to the asymptotically flat boundary conditions and to certain functional analytic subtleties associated with regularization. We then use the resulting quantum theory to analyze several conceptual and technical issues of quantum gravity. {copyright} {ital 1996 American Institute of Physics.}

Dynamics of generalized sine-Gordon soliton in inhomogeneous media

NASA Astrophysics Data System (ADS)

Gharaati, A.; Khordad, R.

2011-03-01

In this paper we introduce a few novel generalized sine-Gordon equations and study the dynamics of its solitons in inhomogeneous media. We consider length, mass, gravitational acceleration and spring stiffness of a coupled pendulums chain as a function of position x. Then in the continuum limit we derive semi-analytical and numerical soliton solutions of the modified sine-Gordon equation in the inhomogeneous media. The obtained results confirm that the behavior of solitons in these media is similar to that of a classical point particle moved in an external potential.

Numerical realization of the variational method for generating self-trapped beams.

PubMed

Duque, Erick I; Lopez-Aguayo, Servando; Malomed, Boris A

2018-03-19

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schrödinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Scattering From the Finite-Length, Dielectric Circular Cylinder. Part 2 - On the Validity of an Analytical Solution for Characterizing Backscattering from Tree Trunks at P-Band

DTIC Science & Technology

2015-09-01

accuracy of an analytical solution for characterizing the backscattering responses of circular cylindrical tree trunks located above a dielectric ground...Figures iv 1. Introduction 1 2. Analytical Solution 2 3. Validation with Full-Wave Solution 4 3.1 Untapered Circular Cylindrical Trunk 5 3.2...Linearly Tapered Circular Cylindrical Trunk 13 3.3 Nonlinearly Tapered Circular Cylindrical Trunk 18 4. Conclusions 22 5. References 23 Appendix

Studies of Fundamental Particle Dynamics in Microgravity

NASA Technical Reports Server (NTRS)

Rangel, Roger; Trolinger, James D.; Coimbra, Carlos F. M.; Witherow, William; Rogers, Jan; Rose, M. Franklin (Technical Monitor)

2001-01-01

This work summarizes theoretical and experimental concepts used to design the flight experiment mission for SHIVA - Spaceflight Holography Investigation in a Virtual Apparatus. SHIVA is a NASA project that exploits a unique, holography-based, diagnostics tool to understand the behavior of small particles subjected to transient accelerations. The flight experiments are designed for testing model equations, measuring g, g-jitter, and other microgravity phenomena. Data collection will also include experiments lying outside of the realm of existing theory. The regime under scrutiny is the low Reynolds number, Stokes regime or creeping flow, which covers particles and bubbles moving at very low velocity. The equations describing this important regime have been under development and investigation for over 100 years and yet a complete analytical solution of the general equation had remained elusive yielding only approximations and numerical solutions. In the course of the ongoing NASA NRA, the first analytical solution of the general equation was produced by members of the investigator team using the mathematics of fractional derivatives. This opened the way to an even more insightful and important investigation of the phenomena in microgravity. Recent results include interacting particles, particle-wall interactions, bubbles, and Reynolds numbers larger than unity. The Space Station provides an ideal environment for SHIVA. Limited ground experiments have already confirmed some aspects of the theory. In general the space environment is required for the overall experiment, especially for cases containing very heavy particles, very light particles, bubbles, collections of particles and for characterization of the space environment and its effect on particle experiments. Lightweight particles and bubbles typically rise too fast in a gravitational field and heavy particles sink too fast. In a microgravity environment, heavy and light particles can be studied side-by-side for long periods of time.

Prediction of pressure drop in fluid tuned mounts using analytical and computational techniques

NASA Technical Reports Server (NTRS)

Lasher, William C.; Khalilollahi, Amir; Mischler, John; Uhric, Tom

1993-01-01

A simplified model for predicting pressure drop in fluid tuned isolator mounts was developed. The model is based on an exact solution to the Navier-Stokes equations and was made more general through the use of empirical coefficients. The values of these coefficients were determined by numerical simulation of the flow using the commercial computational fluid dynamics (CFD) package FIDAP.

Overdetermined elliptic problems in topological disks

NASA Astrophysics Data System (ADS)

Mira, Pablo

2018-06-01

We introduce a method, based on the Poincaré-Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk. Applications to some well-known nonlinear elliptic PDEs are provided. Our result can be seen as the analogue of Hopf's uniqueness theorem for constant mean curvature spheres, but for the general analytic context of overdetermined elliptic problems.

Time Domain Version of the Uniform Geometrical Theory of Diffraction

NASA Astrophysics Data System (ADS)

Rousseau, Paul R.

1995-01-01

A time domain (TD) version of the uniform geometrical theory of diffraction which is referred to as the TD-UTD is developed to analyze the transient electromagnetic scattering from perfectly conducting objects that are large in terms of pulse width. In particular, the scattering from a perfectly conducting arbitrary curved wedge and an arbitrary smooth convex surface are treated in detail. Note that the canonical geometries of a circular cylinder and a sphere are special cases of the arbitrary smooth convex surface. These TD -UTD solutions are obtained in the form of relatively simple analytical expressions valid for early to intermediate times. The geometries treated here can be used to build up a transient solution to more complex radiating objects via space-time localization, in exactly the same way as is done by invoking spatial localization properties in the frequency domain UTD. The TD-UTD provides the response due to an excitation of a general astigmatic impulsive wavefront with any polarization. This generalized impulse response may then be convolved with other excitation time pulses, to find even more general solutions due to other excitation pulses. Since the TD-UTD uses the same rays as the frequency domain UTD, it provides a simple picture for transient radiation or scattering and is therefore just as physically appealing as the frequency domain UTD. The formulation of an analytic time transform (ATT), which produces an analytic time signal given a frequency response function, is given here. This ATT is used because it provides a very efficient method of inverting the asymptotic high frequency UTD representations to obtain the corresponding TD-UTD expressions even when there are special UTD transition functions which may not be well behaved at the low frequencies; also, using the ATT avoids the difficulties associated with the inversion of UTD ray fields that traverse line or smooth caustics. Another useful aspect of the ATT is the ability to perform an efficient convolution with a broad class of excitation pulse functions, where the frequency response of the excitation function must be expressed as a summation of complex exponential functions.

Analytical Solution of the Radiative Transfer Equation in a Thin Dusty Circumstellar Shell

NASA Astrophysics Data System (ADS)

Cruzalèbes, P.; Sacuto, S.

The radiative transfer equation can be solved analytically for optically thin shells. The solution leads to a semi-analytical expression of the visibility function, which can be compared to the numerical solution given by the DUSTY code. Best-fit model parameters are given using real measurements of ISO fluxes, ISI and VLTI-MIDI visibilities for 3 late-type stars.

Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach

NASA Astrophysics Data System (ADS)

Trinkle, Dallas R.

2017-10-01

A general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the vacancy lattice Green function reduces to the sum of a few analytic functions and numerical integration of a smooth function over the Brillouin zone for arbitrary crystals. The Dyson equation solves for the Green function in the presence of a solute with arbitrary but finite interaction range to compute the transport coefficients accurately, efficiently and automatically, including cases with very large differences in solute-vacancy exchange rates. The methodology takes advantage of the space group symmetry of a crystal to reduce the complexity of the matrix inversion in the Dyson equation. An open-source implementation of the algorithm is available, and numerical results are presented for the convergence of the integration error of the bare vacancy Green function, and tracer correlation factors for a variety of crystals including wurtzite (hexagonal diamond) and garnet.

A new analytical solution solved by triple series equations method for constant-head tests in confined aquifers

NASA Astrophysics Data System (ADS)

Chang, Ya-Chi; Yeh, Hund-Der

2010-06-01

The constant-head pumping tests are usually employed to determine the aquifer parameters and they can be performed in fully or partially penetrating wells. Generally, the Dirichlet condition is prescribed along the well screen and the Neumann type no-flow condition is specified over the unscreened part of the test well. The mathematical model describing the aquifer response to a constant-head test performed in a fully penetrating well can be easily solved by the conventional integral transform technique under the uniform Dirichlet-type condition along the rim of wellbore. However, the boundary condition for a test well with partial penetration should be considered as a mixed-type condition. This mixed boundary value problem in a confined aquifer system of infinite radial extent and finite vertical extent is solved by the Laplace and finite Fourier transforms in conjunction with the triple series equations method. This approach provides analytical results for the drawdown in a partially penetrating well for arbitrary location of the well screen in a finite thickness aquifer. The semi-analytical solutions are particularly useful for the practical applications from the computational point of view.

Apparent Mass Nonlinearity for Paired Oscillating Plates

NASA Astrophysics Data System (ADS)

Granlund, Kenneth; Ol, Michael

2014-11-01

The classical potential-flow problem of a plate oscillating sinusoidally at small amplitude, in a direction normal to its plane, has a well-known analytical solution of a fluid ``mass,'' multiplied by plate acceleration, being equal to the force on the plate. This so-called apparent-mass is analytically equal to that of a cylinder of fluid, with diameter equal to plate chord. The force is directly proportional to frequency squared. Here we consider experimentally a generalization, where two coplanar plates of equal chord are placed at some lateral distance apart. For spacing of ~0.5 chord and larger between the two plates, the analytical solution for a single plate can simply be doubled. Zero spacing means a plate of twice the chord and therefore a heuristic cylinder of fluid of twice the cross-sectional area. This limit is approached for plate spacing <0.5c. For a spacing of 0.1-0.2c, the force due to apparent mass was found to increase with frequency, when normalized by frequency squared; this is a nonlinearity and a departure from the classical theory. Flow visualization in a water-tank suggests that such departure can be imputed to vortex shedding from the plates' edges inside the inter-plate gap.

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Baumeister, Joseph F.

1994-01-01

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

Kinetic modeling of electro-Fenton reaction in aqueous solution.

PubMed

Liu, H; Li, X Z; Leng, Y J; Wang, C

2007-03-01

To well describe the electro-Fenton (E-Fenton) reaction in aqueous solution, a new kinetic model was established according to the generally accepted mechanism of E-Fenton reaction. The model has special consideration on the rates of hydrogen peroxide (H(2)O(2)) generation and consumption in the reaction solution. The model also embraces three key operating factors affecting the organic degradation in the E-Fenton reaction, including current density, dissolved oxygen concentration and initial ferrous ion concentration. This analytical model was then validated by the experiments of phenol degradation in aqueous solution. The experiments demonstrated that the H(2)O(2) gradually built up with time and eventually approached its maximum value in the reaction solution. The experiments also showed that phenol was degraded at a slow rate at the early stage of the reaction, a faster rate during the middle stage, and a slow rate again at the final stage. It was confirmed in all experiments that the curves of phenol degradation (concentration vs. time) appeared to be an inverted "S" shape. The experimental data were fitted using both the normal first-order model and our new model, respectively. The goodness of fittings demonstrated that the new model could better fit the experimental data than the first-order model appreciably, which indicates that this analytical model can better describe the kinetics of the E-Fenton reaction mathematically and also chemically.

An analytical model for solute transport in an infiltration tracer test in soil with a shallow groundwater table

NASA Astrophysics Data System (ADS)

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 solution against the approximate solutions that derived from the previous analytical solution and has been suggested to serve as fast tools for simultaneously estimating the longitudinal and transverse dispersion coefficients. The results indicate that the approximate solutions offer predictions that are markedly distinct from our solution for the entire range of dispersion coefficient values. Thus, it is not appropriate to use the approximate solution for interpreting the results of an infiltration tracer test.

Overloaded elution band profiles of ionizable compounds in reversed-phase liquid chromatography: Influence of the competition between the neutral and the ionic species

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gritti, Fabrice; Guiochon, Georges A

2008-01-01

The parameters that affect the shape of the band profiles of acido-basic compounds under moderately overloaded conditions (sample size less than 500 nmol for a conventional column) in RPLC are discussed. Only analytes that have a single pK{sub a} are considered. In the buffer mobile phase used for their elution, their dissociation may, under certain conditions, cause a significant pH perturbation during the passage of the band. Two consecutive injections (3.3 and 10 {micro}L) of each one of three sample solutions (0.5, 5, and 50 mM) of ten compounds were injected on five C{sub 18}-bonded packing materials, including the 5more » {micro}m Xterra-C{sub 18} (121 {angstrom}), 5 {micro}m Gemini-C{sub 18} (110 {angstrom}), 5 {micro}m Luna-C{sub 18}(2) (93 {angstrom}), 3.5 {micro}m Extend-C{sub 18} (80 {angstrom}), and 2.7 {micro}m Halo-C{sub 18} (90 {angstrom}). The mobile phase was an aqueous solution of methanol buffered at a constant {sub W}{sup W}pH of 6, with a phosphate buffer. The total concentration of the phosphate groups was constant at 50 mM. The methanol concentration was adjusted to keep all the retention factors between 1 and 10. The compounds injected were phenol, caffeine, 3-phenyl 1-propanol, 2-phenyl butyric acid, amphetamine, aniline, benzylamine, p-toluidine, procainamidium chloride, and propranololium chloride. Depending on the relative values of the analyte pK{sub a} and the buffer solution pH, these analytes elute as the neutral, the cationic, or the anionic species. The influence of structural parameters such as the charge, the size, and the hydrophobicity of the analytes on the shape of its overloaded band profile is discussed. Simple but general rules predict these shapes. An original adsorption model is proposed that accounts for the unusual peak shapes observed when the analyte is partially dissociated in the buffer solution during its elution.« less

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

Analytic Theory and Control of the Motion of Spinning Rigid Bodies

NASA Technical Reports Server (NTRS)

Tsiotras, Panagiotis

1993-01-01

Numerical simulations are often resorted to, in order to understand the attitude response and control characteristics of a rigid body. However, this approach in performing sensitivity and/or error analyses may be prohibitively expensive and time consuming, especially when a large number of problem parameters are involved. Thus, there is an important role for analytical models in obtaining an understanding of the complex dynamical behavior. In this dissertation, new analytic solutions are derived for the complete attitude motion of spinning rigid bodies, under minimal assumptions. Hence, we obtain the most general solutions reported in the literature so far. Specifically, large external torques and large asymmetries are included in the problem statement. Moreover, problems involving large angular excursions are treated in detail. A new tractable formulation of the kinematics is introduced which proves to be extremely helpful in the search for analytic solutions of the attitude history of such kinds of problems. The main utility of the new formulation becomes apparent however, when searching for feedback control laws for stabilization and/or reorientation of spinning spacecraft. This is an inherently nonlinear problem, where standard linear control techniques fail. We derive a class of control laws for spin axis stabilization of symmetric spacecraft using only two pairs of gas jet actuators. Practically, this could correspond to a spacecraft operating in failure mode, for example. Theoretically, it is also an important control problem which, because of its difficulty, has received little, if any, attention in the literature. The proposed control laws are especially simple and elegant. A feedback control law that achieves arbitrary reorientation of the spacecraft is also derived, using ideas from invariant manifold theory. The significance of this research is twofold. First, it provides a deeper understanding of the fundamental behavior of rigid bodies subject to body-fixed torques. Assessment of the analytic solutions reveals that they are very accurate; for symmetric bodies the solutions of Euler's equations of motion are, in fact, exact. Second, the results of this research have a fundamental impact on practical scientific and mechanical applications in terms of the analysis and control of all finite-sized rigid bodies ranging from nanomachines to very large bodies, both man made and natural. After all, Euler's equations of motion apply to all physical bodies, barring only the extreme limits of quantum mechanics and relativity.

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

Secular dynamics of multiplanetary circumbinary systems: stationary solutions and binary-planet secular resonance

NASA Astrophysics Data System (ADS)

Andrade-Ines, Eduardo; Robutel, Philippe

2018-01-01

We present an analytical formalism to study the secular dynamics of a system consisting of N-2 planets orbiting a binary star in outer orbits. We introduce a canonical coordinate system and expand the disturbing function in terms of canonical elliptic elements, combining both Legendre polynomials and Laplace coefficients, to obtain a general formalism for the secular description of this type of configuration. With a quadratic approximation of the development, we present a simplified analytical solution for the planetary orbits for both the single planet and the two-planet cases. From the two-planet model, we show that the inner planet accelerates the precession rate of the binary pericenter, which, in turn, may enter in resonance with the secular frequency of the outer planet, characterizing a secular resonance. We calculate an analytical expression for the approximate location of this resonance and apply it to known circumbinary systems, where we show that it can occur at relatively close orbits, for example at 2.4 au for the Kepler-38 system. With a more refined model, we analyse the dynamics of this secular resonance and we show that a bifurcation of the corresponding fixed points can affect the long- term evolution and stability of planetary systems. By comparing our results with complete integrations of the exact equations of motion, we verified the accuracy of our analytical model.

Transient well flow in vertically heterogeneous aquifers

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1999-11-01

A solution for the general problem of computing well flow in vertically heterogeneous aquifers is found by an integration of both analytical and numerical techniques. The radial component of flow is treated analytically; the drawdown is a continuous function of the distance to the well. The finite-difference technique is used for the vertical flow component only. The aquifer is discretized in the vertical dimension and the heterogeneous aquifer is considered to be a layered (stratified) formation with a finite number of homogeneous sublayers, where each sublayer may have different properties. The transient part of the differential equation is solved with Stehfest's algorithm, a numerical inversion technique of the Laplace transform. The well is of constant discharge and penetrates one or more of the sublayers. The effect of wellbore storage on early drawdown data is taken into account. In this way drawdowns are found for a finite number of sublayers as a continuous function of radial distance to the well and of time since the pumping started. The model is verified by comparing results with published analytical and numerical solutions for well flow in homogeneous and heterogeneous, confined and unconfined aquifers. Instantaneous and delayed drainage of water from above the water table are considered, combined with the effects of partially penetrating and finite-diameter wells. The model is applied to demonstrate that the transient effects of wellbore storage in unconfined aquifers are less pronounced than previous numerical experiments suggest. Other applications of the presented solution technique are given for partially penetrating wells in heterogeneous formations, including a demonstration of the effect of decreasing specific storage values with depth in an otherwise homogeneous aquifer. The presented solution can be a powerful tool for the analysis of drawdown from pumping tests, because hydraulic properties of layered heterogeneous aquifer systems with partially penetrating wells may be estimated without the need to construct transient numerical models. A computer program based on the hybrid analytical-numerical technique is available from the author.

Analytical solutions for one-, two-, and three-dimensional solute transport in ground-water systems with uniform flow

USGS Publications Warehouse

Wexler, Eliezer J.

1992-01-01

Analytical solutions to the advective-dispersive solute-transport equation are useful in predicting the fate of solutes in ground water. Analytical solutions compiled from available literature or derived by the author are presented for a variety of boundary condition types and solute-source configurations in one-, two-, and three-dimensional systems having uniform ground-water flow. A set of user-oriented computer programs was created to evaluate these solutions and to display the results in tabular and computer-graphics format. These programs incorporate many features that enhance their accuracy, ease of use, and versatility. Documentation for the programs describes their operation and required input data, and presents the results of sample problems. Derivations of selected solutions, source codes for the computer programs, and samples of program input and output also are included.

Analytical approaches to optimizing system "Semiconductor converter-electric drive complex"

NASA Astrophysics Data System (ADS)

Kormilicin, N. V.; Zhuravlev, A. M.; Khayatov, E. S.

2018-03-01

In the electric drives of the machine-building industry, the problem of optimizing the drive in terms of mass-size indicators is acute. The article offers analytical methods that ensure the minimization of the mass of a multiphase semiconductor converter. In multiphase electric drives, the form of the phase current at which the best possible use of the "semiconductor converter-electric drive complex" for active materials is different from the sinusoidal form. It is shown that under certain restrictions on the phase current form, it is possible to obtain an analytical solution. In particular, if one assumes the shape of the phase current to be rectangular, the optimal shape of the control actions will depend on the width of the interpolar gap. In the general case, the proposed algorithm can be used to solve the problem under consideration by numerical methods.

New generalized Noh solutions for HEDP hydrocode verification

NASA Astrophysics Data System (ADS)

Velikovich, A. L.; Giuliani, J. L.; Zalesak, S. T.; Tangri, V.

2017-10-01

The classic Noh solution describing stagnation of a cold ideal gas in a strong accretion shock wave has been the workhorse of compressible hydrocode verification for over three decades. We describe a number of its generalizations available for HEDP code verification. First, for an ideal gas, we have obtained self-similar solutions that describe adiabatic convergence either of a finite-pressure gas into an empty cavity or of a finite-amplitude sound wave into a uniform resting gas surrounding the center or axis of symmetry. At the moment of collapse such a flow produces a uniform gas whose velocity at each point is constant and directed towards the axis or the center, i. e. the initial condition similar to the classic solution but with a finite pressure of the converging gas. After that, a constant-velocity accretion shock propagates into the incident gas whose pressure and velocity profiles are not flat, in contrast with the classic solution. Second, for an arbitrary equation of state, we demonstrate the existence of self-similar solutions of the Noh problem in cylindrical and spherical geometry. Examples of such solutions with a three-term equation of state that includes cold, thermal ion/lattice, and thermal electron contributions are presented for aluminum and copper. These analytic solutions are compared to our numerical simulation results as an example of their use for code verification. Work supported by the US DOE/NNSA.

HART-II: Prediction of Blade-Vortex Interaction Loading

DTIC Science & Technology

2003-09-01

14:30 (2) Improvement of DLR Rotor Aero- acoustic Code ( APSIM ) and its Valida- tion with Analytic Solution J. Yin, J. Delfs (5...of DLR Rotor Aero- acoustic Code ( APSIM ) and its Valida- tion with Analytic Solution J. Yin, J. Delfs (5) Aeroelastic Stability Analysis of...of DLR Rotor Aero- acoustic Code ( APSIM ) and its Valida- tion with Analytic Solution J. Yin, J. Delfs (5) Aeroelastic Stability Analysis of

Physical models for the normal YORP and diurnal Yarkovsky effects

NASA Astrophysics Data System (ADS)

Golubov, O.; Kravets, Y.; Krugly, Yu. N.; Scheeres, D. J.

2016-06-01

We propose an analytic model for the normal Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) and diurnal Yarkovsky effects experienced by a convex asteroid. Both the YORP torque and the Yarkovsky force are expressed as integrals of a universal function over the surface of an asteroid. Although in general this function can only be calculated numerically from the solution of the heat conductivity equation, approximate solutions can be obtained in quadratures for important limiting cases. We consider three such simplified models: Rubincam's approximation (zero heat conductivity), low thermal inertia limit (including the next order correction and thus valid for small heat conductivity), and high thermal inertia limit (valid for large heat conductivity). All three simplified models are compared with the exact solution.

Effect of triangular element orientation on finite element solutions of the Helmholtz equation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1986-01-01

The Galerkin finite element solutions for the scalar homogeneous Helmholtz equation are presented for no reflection, hard wall, and potential relief exit terminations with a variety of triangular element orientations. For this group of problems, the correlation between the accuracy of the solution and the orientation of the linear triangle is examined. Nonsymmetric element patterns are found to give generally poor results in the model problems investigated, particularly for cases where standing waves exist. For a fixed number of vertical elements, the results showed that symmetric element patterns give much better agreement with corresponding exact analytical results. In laminated wave guide application, the symmetric pyramid pattern is convenient to use and is shown to give excellent results.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prakash, S. Arun; Malathi, V.; Mani Rajan, M. S., E-mail: senthilmanirajanofc@gmail.com

We obtain the bright similariton solutions for generalized inhomogeneous nonlinear Schrödinger equation (GINLSE) which governs the pulse propagation in a tapered graded index diffraction decreasing waveguide (DDW). The exact solutions have been worked out by employing similarity transformations which involve the mapping of the GINLSE to standard NLSE for the certain conditions of the parameters. By making use of the exact analytical solutions, we have investigated the dynamical behavior of optical similariton pairs and have suggested the methods to control them as they propagate through DDW. Moreover, pulse width of similariton is controlled through various profiles. These results are helpfulmore » to understand the similaritons in DDW and can be potentially useful for future experiments in optical communications which involve optical amplifiers and long-haul telecommunication networks.« less

Steady-state protein focusing in carrier ampholyte based isoelectric focusing: Part I-Analytical solution.

PubMed

Shim, Jaesool; Yoo, Kisoo; Dutta, Prashanta

2017-03-01

The determination of an analytical solution to find the steady-state protein concentration distribution in IEF is very challenging due to the nonlinear coupling between mass and charge conservation equations. In this study, approximate analytical solutions are obtained for steady-state protein distribution in carrier ampholyte based IEF. Similar to the work of Svensson, the final concentration profile for proteins is assumed to be Gaussian, but appropriate expressions are presented in order to obtain the effective electric field and pH gradient in the focused protein band region. Analytical results are found from iterative solutions of a system of coupled algebraic equations using only several iterations for IEF separation of three plasma proteins: albumin, cardiac troponin I, and hemoglobin. The analytical results are compared with numerically predicted results for IEF, showing excellent agreement. Analytically obtained electric field and ionic conductivity distributions show significant deviation from their nominal values, which is essential in finding the protein focusing behavior at isoelectric points. These analytical solutions can be used to determine steady-state protein concentration distribution for experiment design of IEF considering any number of proteins and ampholytes. Moreover, the model presented herein can be used to find the conductivity, electric field, and pH field. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Analytical solutions to dissolved contaminant plume evolution with source depletion during carbon dioxide storage.

PubMed

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. Copyright © 2016 Elsevier B.V. All rights reserved.

Analytical solutions of the one-dimensional advection-dispersion solute transport equation subject to time-dependent boundary conditions

USDA-ARS?s Scientific Manuscript database

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...

An approximate analytical solution for interlaminar stresses in angle-ply laminates

NASA Technical Reports Server (NTRS)

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.

Magnetohydrodynamic Jump Conditions for Oblique Relativistic Shocks with Gyrotropic Pressure

NASA Technical Reports Server (NTRS)

Double, Glen P.; Baring, Matthew G.; Jones, Frank C.; Ellison, Donald C.

2003-01-01

Shock jump conditions, i.e., the specification of the downstream parameters of the gas in terms of the upstream parameters, are obtained for steady-state, plane shocks with oblique magnetic fields and arbitrary flow speeds. This is done by combining the continuity of particle number flux and the electromagnetic boundary conditions at the shock with the magnetohydrodynamic conservation laws derived from the stress-energy tensor. For ultrarelativistic and nonrelativistic shocks, the jump conditions may be solved analytically. For mildly relativistic shocks, analytic solutions are obtained for isotropic pressure using an approximation for the adiabatic index that is valid in high sonic Mach number cases. Examples assuming isotropic pressure illustrate how the shock compression ratio depends on the shock speed and obliquity. In the more general case of gyrotropic pressure, the jump conditions cannot be solved analytically with- out additional assumptions, and the effects of gyrotropic pressure are investigated by parameterizing the distribution of pressure parallel and perpendicular to the magnetic field. Our numerical solutions reveal that relatively small departures from isotropy (e.g., approximately 20%) produce significant changes in the shock compression ratio, r , at all shock Lorentz factors, including ultrarelativistic ones, where an analytic solution with gyrotropic pressure is obtained. In particular, either dynamically important fields or significant pressure anisotropies can incur marked departures from the canonical gas dynamic value of r = 3 for a shocked ultrarelativistic flow and this may impact models of particle acceleration in gamma-ray bursts and other environments where relativistic shocks are inferred. The jump conditions presented apply directly to test-particle acceleration, and will facilitate future self-consistent numerical modeling of particle acceleration at oblique, relativistic shocks; such models include the modification of the fluid velocity profile due to the contribution of energetic particles to the momentum and energy fluxes.

Studies on transport phenomena in electrothermal vaporization sample introduction applied to inductively coupled plasma for optical emission and mass spectrometry

NASA Astrophysics Data System (ADS)

Kántor, T.; Maestre, S.; de Loos-Vollebregt, M. T. C.

2005-10-01

In the present work electrothermal vaporization (ETV) was used in both inductively coupled plasma mass spectrometry (ICP-MS) and optical emission spectrometry (OES) for sample introduction of solution samples. The effect of (Pd + Mg)-nitrate modifier and CaCl 2 matrix/modifier of variable amounts were studied on ETV-ICP-MS signals of Cr, Cu, Fe, Mn and Pb and on ETV-ICP-OES signals of Ag, Cd, Co, Cu, Fe, Ga, Mn and Zn. With the use of matrix-free standard solutions the analytical curves were bent to the signal axes (as expected from earlier studies), which was observed in the 20-800 pg mass range by ICP-MS and in the 1-50 ng mass range by ICP-OES detection. The degree of curvature was, however, different with the use of single element and multi-element standards. When applying the noted chemical modifiers (aerosol carriers) in microgram amounts, linear analytical curves were found in the nearly two orders of magnitude mass ranges. Changes of the CaCl 2 matrix concentration (loaded amount of 2-10 μg Ca) resulted in less than 5% changes in MS signals of 5 elements (each below 1 ng) and OES signals of 22 analytes (each below 15 ng). Exceptions were Pb (ICP-MS) and Cd (ICP-OES), where the sensitivity increase by Pd + Mg modifier was much larger compared to other elements studied. The general conclusions suggest that quantitative analysis with the use of ETV sample introduction requires matrix matching or matrix replacement by appropriate chemical modifier to the specific concentration ranges of analytes. This is a similar requirement to that claimed also by the most commonly used pneumatic nebulization of solutions, if samples with high matrix concentration are concerned.

A thin-walled pressurized sphere exposed to external general corrosion and nonuniform heating

NASA Astrophysics Data System (ADS)

Sedova, Olga S.; Pronina, Yulia G.; Kuchin, Nikolai L.

2018-05-01

A thin-walled spherical shell subjected to simultaneous action of internal and external pressure, nonuniform heating and outside mechanochemical corrosion is considered. It is assumed that the shell is homogeneous, isotropic and linearly elastic. The rate of corrosion is linearly dependent on the equivalent stress, which is the sum of mechanical and temperature stress components. Paper presents a new analytical solution, which takes into account the effect of the internal and external pressure values themselves, not only their difference. At the same time, the new solution has a rather simple form as compared to the results based on the solution to the Lame problem for a thick-walled sphere under pressure. The solution obtained can serve as a benchmark for numerical analysis and for a qualitative forecast of durability of the vessel.

Numerically calibrated model for propagation of a relativistic unmagnetized jet in dense media

NASA Astrophysics Data System (ADS)

Harrison, Richard; Gottlieb, Ore; Nakar, Ehud

2018-06-01

Relativistic jets reside in high-energy astrophysical systems of all scales. Their interaction with the surrounding media is critical as it determines the jet evolution, observable signature, and feedback on the environment. During its motion, the interaction of the jet with the ambient media inflates a highly pressurized cocoon, which under certain conditions collimates the jet and strongly affects its propagation. Recently, Bromberg et al. derived a general simplified (semi-)analytic solution for the evolution of the jet and the cocoon in case of an unmagnetized jet that propagates in a medium with a range of density profiles. In this work we use a large suite of 2D and 3D relativistic hydrodynamic simulations in order to test the validity and accuracy of this model. We discuss the similarities and differences between the analytic model and numerical simulations and also, to some extent, between 2D and 3D simulations. Our main finding is that although the analytic model is highly simplified, it properly predicts the evolution of the main ingredients of the jet-cocoon system, including its temporal evolution and the transition between various regimes (e.g. collimated to uncollimated). The analytic solution predicts a jet head velocity that is faster by a factor of about 3 compared to the simulations, as long as the head velocity is Newtonian. We use the results of the simulations to calibrate the analytic model which significantly increases its accuracy. We provide an applet that calculates semi-analytically the propagation of a jet in an arbitrary density profile defined by the user at http://www.astro.tau.ac.il/˜ore/propagation.html.

An integral equation-based numerical solver for Taylor states in toroidal geometries

NASA Astrophysics Data System (ADS)

O'Neil, Michael; Cerfon, Antoine J.

2018-04-01

We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.

Multi-analyte validation in heterogeneous solution by ELISA.

PubMed

Lakshmipriya, Thangavel; Gopinath, Subash C B; Hashim, Uda; Murugaiyah, Vikneswaran

2017-12-01

Enzyme Linked Immunosorbent Assay (ELISA) is a standard assay that has been used widely to validate the presence of analyte in the solution. With the advancement of ELISA, different strategies have shown and became a suitable immunoassay for a wide range of analytes. Herein, we attempted to provide additional evidence with ELISA, to show its suitability for multi-analyte detection. To demonstrate, three clinically relevant targets have been chosen, which include 16kDa protein from Mycobacterium tuberculosis, human blood clotting Factor IXa and a tumour marker Squamous Cell Carcinoma antigen. Indeed, we adapted the routine steps from the conventional ELISA to validate the occurrence of analytes both in homogeneous and heterogeneous solutions. With the homogeneous and heterogeneous solutions, we could attain the sensitivity of 2, 8 and 1nM for the targets 16kDa protein, FIXa and SSC antigen, respectively. Further, the specific multi-analyte validations were evidenced with the similar sensitivities in the presence of human serum. ELISA assay in this study has proven its applicability for the genuine multiple target validation in the heterogeneous solution, can be followed for other target validations. Copyright © 2017 Elsevier B.V. All rights reserved.

The behavior of beams of relativistic non-thermal electrons under the influence of collisions and synchrotron losses

NASA Technical Reports Server (NTRS)

Mctiernan, James M.; Petrosian, Vahe

1989-01-01

For many astrophysical situations, such as in solar flares or cosmic gamma-ray bursts, continuum gamma rays with energies up to hundreds of MeV were observed, and can be interpreted to be due to bremsstrahlung radiation by relativistic electrons. The region of acceleration for these particles is not necessarily the same as the region in which the radiation is produced, and the effects of the transport of the electrons must be included in the general problem. Hence it is necessary to solve the kinetic equation for relativistic electrons, including all the interactions and loss mechanisms relevant at such energies. The resulting kinetic equation for non-thermal electrons, including the effects of Coulomb collisions and losses due to synchrotron emission, was solved analytically in some simple limiting cases, and numerically for the general cases including constant and varying background plasma density and magnetic field. New approximate analytic solutions are presented for collision dominated cases, for small pitch angles and all energies, synchrotron dominated cases, both steady-state and time dependent, for all pitch angles and energies, and for cases when both synchrotron and collisional energy losses are important, but for relativistic electrons. These analytic solutions are compared to the full numerical results in the proper limits. These results will be useful for calculation of spectra and angular distribution of the radiation (x rays, gamma-rays, and microwaves) emitted via synchrotron or bremsstrahlung processes by the electrons. These properties and their relevance to observations will be observed in subsequent papers.

Determination of linear short chain aliphatic aldehyde and ketone vapors in air using a polystyrene-coated quartz crystal nanobalance sensor.

PubMed

Mirmohseni, Abdolreza; Olad, Ali

2010-01-01

A polystyrene coated quartz crystal nanobalance (QCN) sensor was developed for use in the determination of a number of linear short-chain aliphatic aldehyde and ketone vapors contained in air. The quartz crystal was modified by a thin-layer coating of a commercial grade general purpose polystyrene (GPPS) from Tabriz petrochemical company using a solution casting method. Determination was based on frequency shifts of the modified quartz crystal due to the adsorption of analytes at the surface of modified electrode in exposure to various concentrations of analytes. The frequency shift was found to have a linear relation to the concentration of analytes. Linear calibration curves were obtained for 7-70 mg l(-1) of analytes with correlation coefficients in the range of 0.9935-0.9989 and sensitivity factors in the range of 2.07-6.74 Hz/mg l(-1). A storage period of over three months showed no loss in the sensitivity and performance of the sensor.

Colorimetric and Fluorescent Biosensors Based on Directed Assembly of Nanomaterials with Functional DNA

NASA Astrophysics Data System (ADS)

Liu, Juewen; Lu, Yi

This chapter reviews recent progress in the interface between functional nucleic acids and nanoscale science and technology, and its analytical applications. In particular, the use of metallic nanoparticles as the color reporting groups for the action (binding, catalysis, or both) of aptamers, DNAzymes, and aptazymes is described in detail. Because metallic nanoparticles possess high extinction coefficients and distance-dependent optical properties, they allow highly sensitive detections with minimal consumption of materials. The combination of quantum dots (QDs) with functional nucleic acids as fluorescent sensors is also described. The chapter starts with the design of colorimetric and fluorescent sensors responsive to single analytes, followed by sensors responsive to multiple analytes with controllable cooperativity and multiplex detection using both colorimetric and fluorescent signals in one pot, and ends by transferring solution-based detections into litmus paper type of tests, making them generally applicable and usable for a wide range of on-site and real-time analytical applications such as household tests, environmental monitoring, and clinical diagnostics.

A Proof of Friedman's Ergosphere Instability for Scalar Waves

NASA Astrophysics Data System (ADS)

Moschidis, Georgios

2018-03-01

Let {(M^{3+1},g)} be a real analytic, stationary and asymptotically flat spacetime with a non-empty ergoregion E and no future event horizon H}^{+. In Friedman (Commun Math Phys 63(3):243-255, 1978), Friedman observed that, on such spacetimes, there exist solutions φ to the wave equation \\squaregφ=0 such that their local energy does not decay to 0 as time increases. In addition, Friedman provided a heuristic argument that the energy of such solutions actually grows to +∞. In this paper, we provide a rigorous proof of Friedman's instability. Our setting is, in fact, more general. We consider smooth spacetimes {(M^{d+1},g)}, for any {d≥2}, not necessarily globally real analytic. We impose only a unique continuation condition for the wave equation across the boundary partial{E} of E on a small neighborhood of a point p\\inpartialE. This condition always holds if {(M,g)} is analytic in that neighborhood of p, but it can also be inferred in the case when {(M,g)} possesses a second Killing field {Φ} such that the span of {Φ} and the stationary Killing field T is timelike on partial{E}. We also allow the spacetimes {(M,g)} under consideration to possess a (possibly empty) future event horizon H}^{+, such that, however, {H+\\cap E=\\emptyset} (excluding, thus, the Kerr exterior family). As an application of our theorem, we infer an instability result for the acoustical wave equation on the hydrodynamic vortex, a phenomenon first investigated numerically by Oliveira et al. in (Phys Rev D 89(12):124008, 2014). Furthermore, as a side benefit of our proof, we provide a derivation, based entirely on the vector field method, of a Carleman-type estimate on the exterior of the ergoregion for a general class of stationary and asymptotically flat spacetimes. Applications of this estimate include a Morawetz-type bound for solutions φ of \\squaregφ=0 with frequency support bounded away from {{ω}=0} and {{ω}=±∞}.

Back analysis of geomechanical parameters in underground engineering using artificial bee colony.

PubMed

Zhu, Changxing; Zhao, Hongbo; Zhao, Ming

2014-01-01

Accurate geomechanical parameters are critical in tunneling excavation, design, and supporting. In this paper, a displacements back analysis based on artificial bee colony (ABC) algorithm is proposed to identify geomechanical parameters from monitored displacements. ABC was used as global optimal algorithm to search the unknown geomechanical parameters for the problem with analytical solution. To the problem without analytical solution, optimal back analysis is time-consuming, and least square support vector machine (LSSVM) was used to build the relationship between unknown geomechanical parameters and displacement and improve the efficiency of back analysis. The proposed method was applied to a tunnel with analytical solution and a tunnel without analytical solution. The results show the proposed method is feasible.

Analytical solution and simplified analysis of coupled parent-daughter steady-state transport with multirate mass transfer

Treesearch

R. Haggerty

2013-01-01

In this technical note, a steady-state analytical solution of concentrations of a parent solute reacting to a daughter solute, both of which are undergoing transport and multirate mass transfer, is presented. Although the governing equations are complicated, the resulting solution can be expressed in simple terms. A function of the ratio of concentrations, In (daughter...

AN ANALYTICAL SOLUTION TO RICHARDS' EQUATIONS FOR A DRAINING SOIL PROFILE

EPA Science Inventory

Analytical solutions are developed for the Richards' equation following the analysis of Broadbridge and White. Included here is the solution for drainage and redistribution of a partially or deeply wetted profile. Additionally, infiltration for various initial conditions is exami...

Symmetry breaking in optimal timing of traffic signals on an idealized two-way street.

PubMed

Panaggio, Mark J; Ottino-Löffler, Bertand J; Hu, Peiguang; Abrams, Daniel M

2013-09-01

Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal world, traffic signals would be timed such that consecutive lights turned green just as vehicles arrived, eliminating the need to stop at each block. Unfortunately, this "green-wave" scenario is generally unworkable due to frustration imposed by competing demands of traffic moving in different directions. Until now this has typically been resolved by numerical simulation and optimization. Here, we develop a theory for the flow in an idealized system consisting of a long two-way road with periodic intersections. We show that optimal signal timing can be understood analytically and that there are counterintuitive asymmetric solutions to this signal coordination problem. We further explore how these theoretical solutions degrade as traffic conditions vary and automotive density increases.

Application of conformal transformation to elliptic geometry for electric impedance tomography.

PubMed

Yilmaz, Atila; Akdoğan, Kurtuluş E; Saka, Birsen

2008-03-01

Electrical impedance tomography (EIT) is a medical imaging modality that is used to compute the conductivity distribution through measurements on the cross-section of a body part. An elliptic geometry model, which defines a more general frame, ensures more accurate results in reconstruction and assessment of inhomogeneities inside. This study provides a link between the analytical solutions defined in circular and elliptical geometries on the basis of the computation of conformal mapping. The results defined as voltage distributions for the homogeneous case in elliptic and circular geometries have been compared with those obtained by the use of conformal transformation between elliptical and well-known circular geometry. The study also includes the results of the finite element method (FEM) as another approach for more complex geometries for the comparison of performance in other complex scenarios for eccentric inhomogeneities. The study emphasizes that for the elliptic case the analytical solution with conformal transformation is a reliable and useful tool for developing insight into more complex forms including eccentric inhomogeneities.

Symmetry breaking in optimal timing of traffic signals on an idealized two-way street

NASA Astrophysics Data System (ADS)

Panaggio, Mark J.; Ottino-Löffler, Bertand J.; Hu, Peiguang; Abrams, Daniel M.

2013-09-01

Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal world, traffic signals would be timed such that consecutive lights turned green just as vehicles arrived, eliminating the need to stop at each block. Unfortunately, this “green-wave” scenario is generally unworkable due to frustration imposed by competing demands of traffic moving in different directions. Until now this has typically been resolved by numerical simulation and optimization. Here, we develop a theory for the flow in an idealized system consisting of a long two-way road with periodic intersections. We show that optimal signal timing can be understood analytically and that there are counterintuitive asymmetric solutions to this signal coordination problem. We further explore how these theoretical solutions degrade as traffic conditions vary and automotive density increases.

Indentation theory on a half-space of transversely isotropic multi-ferroic composite medium: sliding friction effect

NASA Astrophysics Data System (ADS)

Wu, F.; Wu, T.-H.; Li, X.-Y.

2018-03-01

This article aims to present a systematic indentation theory on a half-space of multi-ferroic composite medium with transverse isotropy. The effect of sliding friction between the indenter and substrate is taken into account. The cylindrical flat-ended indenter is assumed to be electrically/magnetically conducting or insulating, which leads to four sets of mixed boundary-value problems. The indentation forces in the normal and tangential directions are related to the Coulomb friction law. For each case, the integral equations governing the contact behavior are developed by means of the generalized method of potential theory, and the corresponding coupling field is obtained in terms of elementary functions. The effect of sliding on the contact behavior is investigated. Finite element method (FEM) in the context of magneto-electro-elasticity is developed to discuss the validity of the analytical solutions. The obtained analytical solutions may serve as benchmarks to various simplified analyses and numerical codes and as a guide for future experimental studies.

New solutions to the constant-head test performed at a partially penetrating well

NASA Astrophysics Data System (ADS)

Chang, Y. C.; Yeh, H. D.

2009-05-01

SummaryThe mathematical model describing the aquifer response to a constant-head test performed at a fully penetrating well can be easily solved by the conventional integral transform technique. In addition, the Dirichlet-type condition should be chosen as the boundary condition along the rim of wellbore for such a test well. However, the boundary condition for a test well with partial penetration must be considered as a mixed-type condition. Generally, the Dirichlet condition is prescribed along the well screen and the Neumann type no-flow condition is specified over the unscreened part of the test well. The model for such a mixed boundary problem in a confined aquifer system of infinite radial extent and finite vertical extent is solved by the dual series equations and perturbation method. This approach provides analytical results for the drawdown in the partially penetrating well and the well discharge along the screen. The semi-analytical solutions are particularly useful for the practical applications from the computational point of view.

Electrochemically Initiated Tagging of Thiols Using an Electrospray Ionization-Based Liquid Microjunction Surface Sampling Probe Two-Electrode Cell

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van Berkel, Gary J; Kertesz, Vilmos

2009-01-01

This paper reports on the conversion of a liquid microjunction surface sampling probe (LMJ-SSP) into a two electrode electrochemical cell using a conductive sample surface and the probe as the two electrodes with an appropriate battery powered circuit. With this LMJ-SSP, two-electrode cell arrangement, tagging of analyte thiol functionalities (in this case peptide cysteine residues) with hydroquinone tags was initiated electrochemically using a hydroquinone doped solution when the analyte either was initially in solution or was sampled from a surface. Efficient tagging (~90%), at flow rates of 5-10 L/min, could be achieved for up to at least two cysteines onmore » a peptide. The high tagging efficiency observed was explained with a simple kinetic model. In general, the incorporation of a two-electrode electrochemical cell, or other multiple electrode arrangement, into the LMJ-SSP is expected to add to the versatility of this approach for surface sampling and ionization coupled with mass spectrometric detection.« less

Thermal drilling in planetary ices: an analytic solution with application to planetary protection problems of radioisotope power sources.

PubMed

Lorenz, Ralph D

2012-08-01

Thermal drilling has been applied to studies of glaciers on Earth and proposed for study of the martian ice caps and the crust of Europa. Additionally, inadvertent thermal drilling by radioisotope sources released from the breakup of a space vehicle is of astrobiological concern in that this process may form a downward-propagating "warm little pond" that could convey terrestrial biota to a habitable environment. A simple analytic solution to the asymptotic slow-speed case of thermal drilling is noted and used to show that the high thermal conductivity of the low-temperature ice on Europa and Titan makes thermal drilling qualitatively more difficult than at Mars. It is shown that an isolated General Purpose Heat Source (GPHS) "brick" can drill effectively on Earth or Mars, whereas on Titan or Europa with ice at 100 K, the source would stall and become stuck in the ice with a surface temperature of <200 K.

Spacecraft drag-free technology development: On-board estimation and control synthesis

NASA Technical Reports Server (NTRS)

Key, R. W.; Mettler, E.; Milman, M. H.; Schaechter, D. B.

1982-01-01

Estimation and control methods for a Drag-Free spacecraft are discussed. The functional and analytical synthesis of on-board estimators and controllers for an integrated attitude and translation control system is represented. The framework for detail definition and design of the baseline drag-free system is created. The techniques for solution of self-gravity and electrostatic charging problems are applicable generally, as is the control system development.

Installation Restoration Program. Phase I. Records Search, Vance Air Force Base, Oklahoma.

DTIC Science & Technology

1984-07-01

cadmium , and descaling solutions. The general trend in waste disposal over the years since VAFB first began operation has been from 3 largely unsegregated...generated at the jet engine shop and metal plating shops and consists of phosphoric acid, chromic acid, potassium permanganate, cadmium , and descaling...benzene, MIBK, carbon tetrachloride, MEK, methylene chloride, and acetone. The metal analytes should include cadmium , chromium, copper, iron, lead

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result.

PubMed

Wu, Yang; Kelly, Damien P

2014-12-12

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of [Formula: see text] and [Formula: see text] type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Formula: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Formula: see text], where [Formula: see text] is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result

NASA Astrophysics Data System (ADS)

Wu, Yang; Kelly, Damien P.

2014-12-01

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 ? and ? 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 ? 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 ?, where ? is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Electroosmotic flow in microchannels with arbitrary geometry and arbitrary distribution of wall charge.

PubMed

Xuan, Xiangchun; Li, Dongqing

2005-09-01

General solutions are developed for direct current (DC) and alternating current (AC) electroosmotic flows in microfluidic channels with arbitrary cross-sectional geometry and arbitrary distribution of wall charge (zeta potential). The applied AC electric field can also be of arbitrary waveform. By proposing a nondimensional time scale varpi defined as the ratio of the diffusion time of momentum across the electric double-layer thickness to the period of the applied electric field, we demonstrate analytically that the Helmholtz-Smoluchowski electroosmotic velocity is an appropriate slip condition for AC electroosmotic flows in typical microfluidic applications. With this slip condition approach, electroosmotic flows in rectangular and asymmetric trapezoidal microchannels with nonuniform wall charge, as examples, are investigated. The unknown constants in the proposed general solutions are numerically determined with a least-squares method through matching the boundary conditions. We find that the wall charge affects significantly the electroosmotic flow while the channel geometry does not. Moreover, the flow feature is characterized by another nondimensional time scale Omega defined as the ratio of the diffusion time of momentum across the channel hydraulic radius to the period of the applied electric field. The onset of phase shift between AC electroosmotic velocity and applied electric field is also examined analytically.

Analysis of Transient Shear Wave in Lossy Media.

PubMed

Parker, Kevin J; Ormachea, Juvenal; Will, Scott; Hah, Zaegyoo

2018-07-01

The propagation of shear waves from impulsive forces is an important topic in elastography. Observations of shear wave propagation can be obtained with numerous clinical imaging systems. Parameter estimations of the shear wave speed in tissues, and more generally the viscoelastic parameters of tissues, are based on some underlying models of shear wave propagation. The models typically include specific choices of the spatial and temporal shape of the impulsive force and the elastic or viscoelastic properties of the medium. In this work, we extend the analytical treatment of 2-D shear wave propagation in a biomaterial. The approach applies integral theorems relevant to the solution of the generalized Helmholtz equation, and does not depend on a specific rheological model of the tissue's viscoelastic properties. Estimators of attenuation and shear wave speed are derived from the analytical solutions, and these are applied to an elastic phantom, a viscoelastic phantom and in vivo liver using a clinical ultrasound scanner. In these samples, estimated shear wave group velocities ranged from 1.7 m/s in the liver to 2.5 m/s in the viscoelastic phantom, and these are lower-bounded by independent measurements of phase velocity. Copyright © 2018 World Federation for Ultrasound in Medicine and Biology. Published by Elsevier Inc. All rights reserved.

Analytical solutions for one-, two-, and three-dimensional solute transport in ground-water systems with uniform flow

USGS Publications Warehouse

Wexler, Eliezer J.

1989-01-01

Analytical solutions to the advective-dispersive solute-transport equation are useful in predicting the fate of solutes in ground water. Analytical solutions compiled from available literature or derived by the author are presented in this report for a variety of boundary condition types and solute-source configurations in one-, two-, and three-dimensional systems with uniform ground-water flow. A set of user-oriented computer programs was created to evaluate these solutions and to display the results in tabular and computer-graphics format. These programs incorporate many features that enhance their accuracy, ease of use, and versatility. Documentation for the programs describes their operation and required input data, and presents the results of sample problems. Derivations of select solutions, source codes for the computer programs, and samples of program input and output also are included.

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

PubMed

Gai, Litao; Bilige, Sudao; Jie, Yingmo

2016-01-01

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

Full analytical solution of the bloch equation when using a hyperbolic-secant driving function.

PubMed

Zhang, Jinjin; Garwood, Michael; Park, Jang-Yeon

2017-04-01

The frequency-swept pulse known as the hyperbolic-secant (HS) pulse is popular in NMR for achieving adiabatic spin inversion. The HS pulse has also shown utility for achieving excitation and refocusing in gradient-echo and spin-echo sequences, including new ultrashort echo-time imaging (e.g., Sweep Imaging with Fourier Transform, SWIFT) and B 1 mapping techniques. To facilitate the analysis of these techniques, the complete theoretical solution of the Bloch equation, as driven by the HS pulse, was derived for an arbitrary state of initial magnetization. The solution of the Bloch-Riccati equation for transverse and longitudinal magnetization for an arbitrary initial state was derived analytically in terms of HS pulse parameters. The analytical solution was compared with the solutions using both the Runge-Kutta method and the small-tip approximation. The analytical solution was demonstrated on different initial states at different frequency offsets with/without a combination of HS pulses. Evolution of the transverse magnetization was influenced significantly by the choice of HS pulse parameters. The deviation of the magnitude of the transverse magnetization, as obtained by comparing the small-tip approximation to the analytical solution, was < 5% for flip angles < 30 °, but > 10% for the flip angles > 40 °. The derived analytical solution provides insights into the influence of HS pulse parameters on the magnetization evolution. Magn Reson Med 77:1630-1638, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

NASA Astrophysics Data System (ADS)

Bodin, Jacques

2015-03-01

In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

Continuum description of ionic and dielectric shielding for molecular-dynamics simulations of proteins in solution

NASA Astrophysics Data System (ADS)

Egwolf, Bernhard; Tavan, Paul

2004-01-01

We extend our continuum description of solvent dielectrics in molecular-dynamics (MD) simulations [B. Egwolf and P. Tavan, J. Chem. Phys. 118, 2039 (2003)], which has provided an efficient and accurate solution of the Poisson equation, to ionic solvents as described by the linearized Poisson-Boltzmann (LPB) equation. We start with the formulation of a general theory for the electrostatics of an arbitrarily shaped molecular system, which consists of partially charged atoms and is embedded in a LPB continuum. This theory represents the reaction field induced by the continuum in terms of charge and dipole densities localized within the molecular system. Because these densities cannot be calculated analytically for systems of arbitrary shape, we introduce an atom-based discretization and a set of carefully designed approximations. This allows us to represent the densities by charges and dipoles located at the atoms. Coupled systems of linear equations determine these multipoles and can be rapidly solved by iteration during a MD simulation. The multipoles yield the reaction field forces and energies. Finally, we scrutinize the quality of our approach by comparisons with an analytical solution restricted to perfectly spherical systems and with results of a finite difference method.

Closed, analytic, boson realizations for Sp(4)

NASA Astrophysics Data System (ADS)

Klein, Abraham; Zhang, Qing-Ying

1986-08-01

The problem of determing a boson realization for an arbitrary irrep of the unitary simplectic algebra Sp(2d) [or of the corresponding discrete unitary irreps of the unbounded algebra Sp(2d,R)] has been solved completely in recent papers by Deenen and Quesne [J. Deenen and C. Quesne, J. Math. Phys. 23, 878, 2004 (1982); 25, 1638 (1984); 26, 2705 (1985)] and by Moshinsky and co-workers [O. Castaños, E. Chacón, M. Moshinsky, and C. Quesne, J. Math. Phys. 26, 2107 (1985); M. Moshinsky, ``Boson realization of symplectic algebras,'' to be published]. This solution is not known in closed analytic form except for d=1 and for special classes of irreps for d>1. A different method of obtaining a boson realization that solves the full problem for Sp(4) is described. The method utilizes the chain Sp(2d)⊇SU(2)×SU(2) ×ṡṡṡ×SU(2) (d times), which, for d≥4, does not provide a complete set of quantum numbers. Though a simple solution of the missing label problem can be given, this solution does not help in the construction of a mapping algorithm for general d.

Analytical Solutions for Rumor Spreading Dynamical Model in a Social Network

NASA Astrophysics Data System (ADS)

Fallahpour, R.; Chakouvari, S.; Askari, H.

2015-03-01

In this paper, Laplace Adomian decomposition method is utilized for evaluating of spreading model of rumor. Firstly, a succinct review is constructed on the subject of using analytical methods such as Adomian decomposion method, Variational iteration method and Homotopy Analysis method for epidemic models and biomathematics. In continue a spreading model of rumor with consideration of forgetting mechanism is assumed and subsequently LADM is exerted for solving of it. By means of the aforementioned method, a general solution is achieved for this problem which can be readily employed for assessing of rumor model without exerting any computer program. In addition, obtained consequences for this problem are discussed for different cases and parameters. Furthermore, it is shown the method is so straightforward and fruitful for analyzing equations which have complicated terms same as rumor model. By employing numerical methods, it is revealed LADM is so powerful and accurate for eliciting solutions of this model. Eventually, it is concluded that this method is so appropriate for this problem and it can provide researchers a very powerful vehicle for scrutinizing rumor models in diverse kinds of social networks such as Facebook, YouTube, Flickr, LinkedIn and Tuitor.

Solitons in Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Carr, Lincoln D.

2003-05-01

The stationary form, dynamical properties, and experimental criteria for creation of matter-wave bright and dark solitons, both singly and in trains, are studied numerically and analytically in the context of Bose-Einstein condensates [1]. The full set of stationary solutions in closed analytic form to the mean field model in the quasi-one-dimensional regime, which is a nonlinear Schrodinger equation equally relevant in nonlinear optics, is developed under periodic and box boundary conditions [2]. These solutions are extended numerically into the two and three dimensional regimes, where it is shown that dark solitons can be used to create vortex-anti-vortex pairs under realistic conditions. Specific experimental prescriptions for creating viable dark and bright solitons in the quasi-one-dimensional regime are provided. These analytic methods are then extended to treat the nonlinear Schrodinger equation with a generalized lattice potential, which models a Bose-Einstein condensate trapped in the potential generated by a standing light wave. A novel solution family is developed and stability criterion are presented. Experiments which successfully carried out these ideas are briefly discussed [3]. [1] Dissertation research completed at the University of Washington Physics Department under the advisorship of Prof. William P. Reinhardt. [2] L. D. Carr, C. W. Clark, and W. P. Reinhardt, Phys. Rev. A v. 62 p. 063610-1--10 and Phys. Rev. A v.62, p.063611-1--10 (2000). [3] L. Khaykovich, F. Schreck, T. Bourdel, J. Cubizolles, G. Ferrari, L. D. Carr, Y. Castin, and C. Salomon, Science v. 296, p.1290--1293 (2002).

Isothermal Bondi Accretion in Jaffe and Hernquist Galaxies with a Central Black Hole: Fully Analytical Solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ciotti, Luca; Pellegrini, Silvia, E-mail: luca.ciotti@unibo.it

One of the most active fields of research of modern-day astrophysics is that of massive black hole formation and coevolution with the host galaxy. In these investigations, ranging from cosmological simulations, to semi-analytical modeling, to observational studies, the Bondi solution for accretion on a central point-mass is widely adopted. In this work we generalize the classical Bondi accretion theory to take into account the effects of the gravitational potential of the host galaxy, and of radiation pressure in the optically thin limit. Then, we present the fully analytical solution, in terms of the Lambert–Euler W -function, for isothermal accretion inmore » Jaffe and Hernquist galaxies with a central black hole. The flow structure is found to be sensitive to the shape of the mass profile of the host galaxy. These results and the formulae that are provided, most importantly, the one for the critical accretion parameter, allow for a direct evaluation of all flow properties, and are then useful for the abovementioned studies. As an application, we examine the departure from the true mass accretion rate of estimates obtained using the gas properties at various distances from the black hole, under the hypothesis of classical Bondi accretion. An overestimate is obtained from regions close to the black hole, and an underestimate outside a few Bondi radii; the exact position of the transition between the two kinds of departure depends on the galaxy model.« less

On analyticity of linear waves scattered by a layered medium

NASA Astrophysics Data System (ADS)

Nicholls, David P.

2017-10-01

The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High-Order Perturbation of Surfaces methods for simulating such waves. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions. This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.

Analytical and numerical study of electroosmotic slip flows of fractional second grade fluids

NASA Astrophysics Data System (ADS)

Wang, Xiaoping; Qi, Haitao; Yu, Bo; Xiong, Zhen; Xu, Huanying

2017-09-01

This work investigates the unsteady electroosmotic slip flow of viscoelastic fluid through a parallel plate micro-channel under combined influence of electroosmotic and pressure gradient forcings with asymmetric zeta potentials at the walls. The generalized second grade fluid with fractional derivative was used for the constitutive equation. The Navier slip model with different slip coefficients at both walls was also considered. By employing the Debye-Hückel linearization and the Laplace and sin-cos-Fourier transforms, the analytical solutions for the velocity distribution are derived. And the finite difference method for this problem was also given. Finally, the influence of pertinent parameters on the generation of flow is presented graphically.

A Comprehensive Analytical Solution of the Nonlinear Pendulum

ERIC Educational Resources Information Center

Ochs, Karlheinz

2011-01-01

In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions…

Influence of distributed delays on the dynamics of a generalized immune system cancerous cells interactions model

NASA Astrophysics Data System (ADS)

Piotrowska, M. J.; Bodnar, M.

2018-01-01

We present a generalisation of the mathematical models describing the interactions between the immune system and tumour cells which takes into account distributed time delays. For the analytical study we do not assume any particular form of the stimulus function describing the immune system reaction to presence of tumour cells but we only postulate its general properties. We analyse basic mathematical properties of the considered model such as existence and uniqueness of the solutions. Next, we discuss the existence of the stationary solutions and analytically investigate their stability depending on the forms of considered probability densities that is: Erlang, triangular and uniform probability densities separated or not from zero. Particular instability results are obtained for a general type of probability densities. Our results are compared with those for the model with discrete delays know from the literature. In addition, for each considered type of probability density, the model is fitted to the experimental data for the mice B-cell lymphoma showing mean square errors at the same comparable level. For estimated sets of parameters we discuss possibility of stabilisation of the tumour dormant steady state. Instability of this steady state results in uncontrolled tumour growth. In order to perform numerical simulation, following the idea of linear chain trick, we derive numerical procedures that allow us to solve systems with considered probability densities using standard algorithm for ordinary differential equations or differential equations with discrete delays.

Sedimentary Geothermal Feasibility Study: October 2016

DOE Office of Scientific and Technical Information (OSTI.GOV)

Augustine, Chad; Zerpa, Luis

The objective of this project is to analyze the feasibility of commercial geothermal projects using numerical reservoir simulation, considering a sedimentary reservoir with low permeability that requires productivity enhancement. A commercial thermal reservoir simulator (STARS, from Computer Modeling Group, CMG) is used in this work for numerical modeling. In the first stage of this project (FY14), a hypothetical numerical reservoir model was developed, and validated against an analytical solution. The following model parameters were considered to obtain an acceptable match between the numerical and analytical solutions: grid block size, time step and reservoir areal dimensions; the latter related to boundarymore » effects on the numerical solution. Systematic model runs showed that insufficient grid sizing generates numerical dispersion that causes the numerical model to underestimate the thermal breakthrough time compared to the analytic model. As grid sizing is decreased, the model results converge on a solution. Likewise, insufficient reservoir model area introduces boundary effects in the numerical solution that cause the model results to differ from the analytical solution.« less

Geometric model of pseudo-distance measurement in satellite location systems

NASA Astrophysics Data System (ADS)

Panchuk, K. L.; Lyashkov, A. A.; Lyubchinov, E. V.

2018-04-01

The existing mathematical model of pseudo-distance measurement in satellite location systems does not provide a precise solution of the problem, but rather an approximate one. The existence of such inaccuracy, as well as bias in measurement of distance from satellite to receiver, results in inaccuracy level of several meters. Thereupon, relevance of refinement of the current mathematical model becomes obvious. The solution of the system of quadratic equations used in the current mathematical model is based on linearization. The objective of the paper is refinement of current mathematical model and derivation of analytical solution of the system of equations on its basis. In order to attain the objective, geometric analysis is performed; geometric interpretation of the equations is given. As a result, an equivalent system of equations, which allows analytical solution, is derived. An example of analytical solution implementation is presented. Application of analytical solution algorithm to the problem of pseudo-distance measurement in satellite location systems allows to improve the accuracy such measurements.

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

On the nonlinear dynamics of trolling-mode AFM: Analytical solution using multiple time scales method

NASA Astrophysics Data System (ADS)

Sajjadi, Mohammadreza; Pishkenari, Hossein Nejat; Vossoughi, Gholamreza

2018-06-01

Trolling mode atomic force microscopy (TR-AFM) has resolved many imaging problems by a considerable reduction of the liquid-resonator interaction forces in liquid environments. The present study develops a nonlinear model of the meniscus force exerted to the nanoneedle of TR-AFM and presents an analytical solution to the distributed-parameter model of TR-AFM resonator utilizing multiple time scales (MTS) method. Based on the developed analytical solution, the frequency-response curves of the resonator operation in air and liquid (for different penetration length of the nanoneedle) are obtained. The closed-form analytical solution and the frequency-response curves are validated by the comparison with both the finite element solution of the main partial differential equations and the experimental observations. The effect of excitation angle of the resonator on horizontal oscillation of the probe tip and the effect of different parameters on the frequency-response of the system are investigated.

Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells.

PubMed

Ahmadi, S M; Campoli, G; Amin Yavari, S; Sajadi, B; Wauthle, R; Schrooten, J; Weinans, H; Zadpoor, A A

2014-06-01

Cellular structures with highly controlled micro-architectures are promising materials for orthopedic applications that require bone-substituting biomaterials or implants. The availability of additive manufacturing techniques has enabled manufacturing of biomaterials made of one or multiple types of unit cells. The diamond lattice unit cell is one of the relatively new types of unit cells that are used in manufacturing of regular porous biomaterials. As opposed to many other types of unit cells, there is currently no analytical solution that could be used for prediction of the mechanical properties of cellular structures made of the diamond lattice unit cells. In this paper, we present new analytical solutions and closed-form relationships for predicting the elastic modulus, Poisson׳s ratio, critical buckling load, and yield (plateau) stress of cellular structures made of the diamond lattice unit cell. The mechanical properties predicted using the analytical solutions are compared with those obtained using finite element models. A number of solid and porous titanium (Ti6Al4V) specimens were manufactured using selective laser melting. A series of experiments were then performed to determine the mechanical properties of the matrix material and cellular structures. The experimentally measured mechanical properties were compared with those obtained using analytical solutions and finite element (FE) models. It has been shown that, for small apparent density values, the mechanical properties obtained using analytical and numerical solutions are in agreement with each other and with experimental observations. The properties estimated using an analytical solution based on the Euler-Bernoulli theory markedly deviated from experimental results for large apparent density values. The mechanical properties estimated using FE models and another analytical solution based on the Timoshenko beam theory better matched the experimental observations. Copyright © 2014 Elsevier Ltd. All rights reserved.

Stochastic modeling of the migration of Cs-137 in the soil considering a power law tailing in space

NASA Astrophysics Data System (ADS)

Oka, Hiroki; Hatano, Yuko

2016-04-01

We develop a theoretical model to reproduce the measured data of Cs-137 in the soil due to the Fukushima Daiichi NPP accident. In our past study, we derived the analytic solution under the generalized Robin boundary condition (Oka-Yamamoto solution). This is a generalization of the He-Walling solution (1996). We compared our solution with the Fukushima soil data of for 3 years after the accident and found that the concentration of Cs-137 has a discrepancy from our solution, specifically in a deep part because the depth profiles have a power law tailing. Therefore, we improved our model in the following aspect. When Cs particle (or Cs solution) migrate in the soil, the diffusion coefficient should be the results of many processes in the soil. These processes include the effect of various materials which constitute the soil (clay, litter, sand), or the variations of pore size in the soil. Hence we regard the diffusion coefficient as the stochastic variable, we derive the model. Specifically, we consider the solution of ADE to be the conditional probability C(x,t|D) in terms of the diffusion coefficient D and calculate C(x,t)=∫_(0~∞) C(x,t|D)*f(D)*dD, where f(D) is the probability density function of D. This model has a power law tailing in space like the space-fractional ADE.

Recursive-operator method in vibration problems for rod systems

NASA Astrophysics Data System (ADS)

Rozhkova, E. V.

2009-12-01

Using linear differential equations with constant coefficients describing one-dimensional dynamical processes as an example, we show that the solutions of these equations and systems are related to the solution of the corresponding numerical recursion relations and one does not have to compute the roots of the corresponding characteristic equations. The arbitrary functions occurring in the general solution of the homogeneous equations are determined by the initial and boundary conditions or are chosen from various classes of analytic functions. The solutions of the inhomogeneous equations are constructed in the form of integro-differential series acting on the right-hand side of the equation, and the coefficients of the series are determined from the same recursion relations. The convergence of formal solutions as series of a more general recursive-operator construction was proved in [1]. In the special case where the solutions of the equation can be represented in separated variables, the power series can be effectively summed, i.e., expressed in terms of elementary functions, and coincide with the known solutions. In this case, to determine the natural vibration frequencies, one obtains algebraic rather than transcendental equations, which permits exactly determining the imaginary and complex roots of these equations without using the graphic method [2, pp. 448-449]. The correctness of the obtained formulas (differentiation formulas, explicit expressions for the series coefficients, etc.) can be verified directly by appropriate substitutions; therefore, we do not prove them here.

PFLOTRAN Verification: Development of a Testing Suite to Ensure Software Quality

NASA Astrophysics Data System (ADS)

Hammond, G. E.; Frederick, J. M.

2016-12-01

In scientific computing, code verification ensures the reliability and numerical accuracy of a model simulation by comparing the simulation results to experimental data or known analytical solutions. The model is typically defined by a set of partial differential equations with initial and boundary conditions, and verification ensures whether the mathematical model is solved correctly by the software. Code verification is especially important if the software is used to model high-consequence systems which cannot be physically tested in a fully representative environment [Oberkampf and Trucano (2007)]. Justified confidence in a particular computational tool requires clarity in the exercised physics and transparency in its verification process with proper documentation. We present a quality assurance (QA) testing suite developed by Sandia National Laboratories that performs code verification for PFLOTRAN, an open source, massively-parallel subsurface simulator. PFLOTRAN solves systems of generally nonlinear partial differential equations describing multiphase, multicomponent and multiscale reactive flow and transport processes in porous media. PFLOTRAN's QA test suite compares the numerical solutions of benchmark problems in heat and mass transport against known, closed-form, analytical solutions, including documentation of the exercised physical process models implemented in each PFLOTRAN benchmark simulation. The QA test suite development strives to follow the recommendations given by Oberkampf and Trucano (2007), which describes four essential elements in high-quality verification benchmark construction: (1) conceptual description, (2) mathematical description, (3) accuracy assessment, and (4) additional documentation and user information. Several QA tests within the suite will be presented, including details of the benchmark problems and their closed-form analytical solutions, implementation of benchmark problems in PFLOTRAN simulations, and the criteria used to assess PFLOTRAN's performance in the code verification procedure. References Oberkampf, W. L., and T. G. Trucano (2007), Verification and Validation Benchmarks, SAND2007-0853, 67 pgs., Sandia National Laboratories, Albuquerque, NM.

Unsteady free convection flow of viscous fluids with analytical results by employing time-fractional Caputo-Fabrizio derivative (without singular kernel)

NASA Astrophysics Data System (ADS)

Ali Shah, Nehad; Mahsud, Yasir; Ali Zafar, Azhar

2017-10-01

This article introduces a theoretical study for unsteady free convection flow of an incompressible viscous fluid. The fluid flows near an isothermal vertical plate. The plate has a translational motion with time-dependent velocity. The equations governing the fluid flow are expressed in fractional differential equations by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Explicit solutions for velocity, temperature and solute concentration are obtained by applying the Laplace transform technique. As the fractional parameter approaches to one, solutions for the ordinary fluid model are extracted from the general solutions of the fractional model. The results showed that, for the fractional model, the obtained solutions for velocity, temperature and concentration exhibit stationary jumps discontinuity across the plane at t=0 , while the solutions are continuous functions in the case of the ordinary model. Finally, numerical results for flow features at small-time are illustrated through graphs for various pertinent parameters.

A mean spherical model for soft potentials: The hard core revealed as a perturbation

NASA Technical Reports Server (NTRS)

Rosenfeld, Y.; Ashcroft, N. W.

1978-01-01

The mean spherical approximation for fluids is extended to treat the case of dense systems interacting via soft-potentials. The extension takes the form of a generalized statement concerning the behavior of the direct correlation function c(r) and radial distribution g(r). From a detailed analysis that views the hard core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions.

Laminar film condensation along a vertical plate embedded in an anisotropic porous medium with oblique principal axes

NASA Astrophysics Data System (ADS)

Degan, Gérard; Sanya, Arthur; Akowanou, Christian

2016-10-01

This work analytically investigates the problem of steady film condensation along a vertical surface embedded in an anisotropic porous medium filled with a dry saturated vapor. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction which is oblique to the gravity vector. On the basis of the generalized Darcy's law and within the boundary layer approximations, similar solutions have been obtained for the temperature and flow patterns in the condensate. Moreover, closed form solutions for the boundary layer thickness and heat transfer rate have been obtained in terms of the governing parameters of the problem.

Multigrid methods for a semilinear PDE in the theory of pseudoplastic fluids

NASA Technical Reports Server (NTRS)

Henson, Van Emden; Shaker, A. W.

1993-01-01

We show that by certain transformations the boundary layer equations for the class of non-Newtonian fluids named pseudoplastic can be generalized in the form the vector differential operator(u) + p(x)u(exp -lambda) = 0, where x is a member of the set Omega and Omega is a subset of R(exp n), n is greater than or equal to 1 under the classical conditions for steady flow over a semi-infinite flat plate. We provide a survey of the existence, uniqueness, and analyticity of the solutions for this problem. We also establish numerical solutions in one- and two-dimensional regions using multigrid methods.

Solution of D dimensional Dirac equation for coulombic potential using NU method and its thermodynamics properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cari, C., E-mail: cari@staff.uns.ac.id; Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Yunianto, M., E-mail: muhtaryunianto@staff.uns.ac.id

2016-02-08

The analytical solution of Ddimensional Dirac equation for Coulombic potential is investigated using Nikiforov-Uvarov method. The D dimensional relativistic energy spectra are obtained from relativistic energy eigenvalue equation by using Mat Lab software.The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi and Laguerre Polynomials. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy which will be applied to determine some thermodynamical properties of the system. The thermodynamical properties of the system are expressed in terms of error function and imaginary error function.

Analytical solution for the normal emission portion of the averaged Yarkovsky-O'Keefe-Radzvieskii-Paddack coefficient for a single facet

NASA Astrophysics Data System (ADS)

Albuja, Antonella A.; Scheeres, Daniel J.

2015-02-01

The Yarkovsky-O'Keefe-Radzvieskii-Paddack (YORP) effect has been well studied for asteroids. This paper develops an analytic solution to find the normal emission YORP component for a single facet. The solution presented here does not account for self-shadowing or self-heating. The YORP coefficient for all facets can be summed together to find the total coefficient of the asteroid. The normal emission component of YORP has been shown to be the most important for asteroids and it directly affects the rate of change of the asteroid's spin period. The analytical solution found is a sole function of the facet's geometry and the obliquity of the asteroid. This solution is universal for any facet and its orientation. The behaviour of the coefficient is analysed with this analytical solution. The closed-form solution is used to find the total YORP coefficient for the asteroids Apollo and 1998 ML14 whose shape models are composed of different numbers of facets. The results are then compared to published results and those obtained through numerical quadrature for validation.

Parametric study of minimum reactor mass in energy-storage dc-to-dc converters

NASA Technical Reports Server (NTRS)

Wong, R. C.; Owen, H. A., Jr.; Wilson, T. G.

1981-01-01

Closed-form analytical solutions for the design equations of a minimum-mass reactor for a two-winding voltage-or-current step-up converter are derived. A quantitative relationship between the three parameters - minimum total reactor mass, maximum output power, and switching frequency - is extracted from these analytical solutions. The validity of the closed-form solution is verified by a numerical minimization procedure. A computer-aided design procedure using commercially available toroidal cores and magnet wires is also used to examine how the results from practical designs follow the predictions of the analytical solutions.

On the first crossing distributions in fractional Brownian motion and the mass function of dark matter haloes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hiotelis, Nicos; Popolo, Antonino Del, E-mail: adelpopolo@oact.inaf.it, E-mail: hiotelis@ipta.demokritos.gr

We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions derived by simulating paths from fractional Brownian motion. We compare the results of the analytical solutions with both those of simulations and those of some approximated solutions which have been used in the literature. Finally, we present multiplicity functions for dark matter structures resulting from our analytical approach and we compare with those resulting from N-body simulations. We show that the results of analytical solutions aremore » in good agreement with those of path simulations but differ significantly from those derived from approximated solutions. Additionally, multiplicity functions derived from fractional Brownian motion are poor fits of the those which result from N-body simulations. We also present comparisons with other models which are exist in the literature and we discuss different ways of improving the agreement between analytical results and N-body simulations.« less

An analytical solution for Dean flow in curved ducts with rectangular cross section

NASA Astrophysics Data System (ADS)

Norouzi, M.; Biglari, N.

2013-05-01

In this paper, a full analytical solution for incompressible flow inside the curved ducts with rectangular cross-section is presented for the first time. The perturbation method is applied to solve the governing equations and curvature ratio is considered as the perturbation parameter. The previous perturbation solutions are usually restricted to the flow in curved circular or annular pipes related to the overly complex form of solutions or singularity situation for flow in curved ducts with non-circular shapes of cross section. This issue specifies the importance of analytical studies in the field of Dean flow inside the non-circular ducts. In this study, the main flow velocity, stream function of lateral velocities (secondary flows), and flow resistance ratio in rectangular curved ducts are obtained analytically. The effect of duct curvature and aspect ratio on flow field is investigated as well. Moreover, it is important to mention that the current analytical solution is able to simulate the Taylor-Görtler and Dean vortices (vortices in stable and unstable situations) in curved channels.

Using emergent order to shape a space society

NASA Technical Reports Server (NTRS)

Graps, Amara L.

1993-01-01

A fast-growing movement in the scientific community is reshaping the way that we view the world around us. The short-hand name for this movement is 'chaos'. Chaos is a science of the global, nonlinear nature of systems. The center of this set of ideas is that simple, deterministic systems can breed complexity. Systems as complex as the human body, ecology, the mind or a human society. While it is true that simple laws can breed complexity, the other side is that complex systems can breed order. It is the latter that I will focus on in this paper. In the past, nonlinear was nearly synonymous with unsolvable because no general analytic solutions exist. Mathematically, an essential difference exists between linear and nonlinear systems. For linear systems, you just break up the complicated system into many simple pieces and patch together the separated solutions for each piece to form a solution to the full problem. In contrast, solutions to a nonlinear system cannot be added to form a new solution. The system must be treated in its full complexity. While it is true that no general analytical approach exists for reducing a complex system such as a society, it can be modeled. The technical involves a mathematical construct called phase space. In this space stable structures can appear which I use as analogies for the stable structures that appear in a complex system such as an ecology, the mind or a society. The common denominator in all of these systems is that they rely on a process called feedback loops. Feedback loops link the microscopic (individual) parts to the macroscopic (global) parts. The key, then, in shaping a space society, is in effectively using feedback loops. This paper will illustrate how one can model a space society by using methods that chaoticists have developed over the last hundred years. And I will show that common threads exist in the modeling of biological, economical, philosophical, and sociological systems.

Analytical and Numerical Solutions of Generalized Fokker-Planck Equations - Final Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prinja, Anil K.

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 aremore » 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 multigroup transport setting, and (ii) two unique families of discontinuous finite element schemes, one linear and the other nonlinear.« less

On a class of integrals of Legendre polynomials with complicated arguments--with applications in electrostatics and biomolecular modeling.

PubMed

Yu, Yi-Kuo

2003-08-15

The exact analytical result for a class of integrals involving (associated) Legendre polynomials of complicated argument is presented. The method employed can in principle be generalized to integrals involving other special functions. This class of integrals also proves useful in the electrostatic problems in which dielectric spheres are involved, which is of importance in modeling the dynamics of biological macromolecules. In fact, with this solution, a more robust foundation is laid for the Generalized Born method in modeling the dynamics of biomolecules. c2003 Elsevier B.V. All rights reserved.

A Quantum-Like View to a Generalized Two Players Game

NASA Astrophysics Data System (ADS)

Bagarello, F.

2015-10-01

This paper consider the possibility of using some quantum tools in decision making strategies. In particular, we consider here a dynamical open quantum system helping two players, and , to take their decisions in a specific context. We see that, within our approach, the final choices of the players do not depend in general on their initial mental states, but they are driven essentially by the environment which interacts with them. The model proposed here also considers interactions of different nature between the two players, and it is simple enough to allow for an analytical solution of the equations of motion.

Regge calculus and observations. II. Further applications.

NASA Astrophysics Data System (ADS)

Williams, Ruth M.; Ellis, G. F. R.

1984-11-01

The method, developed in an earlier paper, for tracing geodesies of particles and light rays through Regge calculus space-times, is applied to a number of problems in the Schwarzschild geometry. It is possible to obtain accurate predictions of light bending by taking sufficiently small Regge blocks. Calculations of perihelion precession, Thomas precession, and the distortion of a ball of fluid moving on a geodesic can also show good agreement with the analytic solution. However difficulties arise in obtaining accurate predictions for general orbits in these space-times. Applications to other problems in general relativity are discussed briefly.

Analytical study of exact solutions of the nonlinear Korteweg-de Vries equation with space-time fractional derivatives

NASA Astrophysics Data System (ADS)

Liu, Jiangen; Zhang, Yufeng

2018-01-01

This paper gives an analytical study of dynamic behavior of the exact solutions of nonlinear Korteweg-de Vries equation with space-time local fractional derivatives. By using the improved (G‧ G )-expansion method, the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solutions and soliton-like solutions, are obtained for the first time. They can better help us further understand the physical phenomena and provide a strong basis. Meanwhile, some solutions are presented through 3D-graphs.

Analytic regularization of uniform cubic B-spline deformation fields.

PubMed

Shackleford, James A; Yang, Qi; Lourenço, Ana M; Shusharina, Nadya; Kandasamy, Nagarajan; Sharp, Gregory C

2012-01-01

Image registration is inherently ill-posed, and lacks a unique solution. In the context of medical applications, it is desirable to avoid solutions that describe physically unsound deformations within the patient anatomy. Among the accepted methods of regularizing non-rigid image registration to provide solutions applicable to medical practice is the penalty of thin-plate bending energy. In this paper, we develop an exact, analytic method for computing the bending energy of a three-dimensional B-spline deformation field as a quadratic matrix operation on the spline coefficient values. Results presented on ten thoracic case studies indicate the analytic solution is between 61-1371x faster than a numerical central differencing solution.

Quantum cluster theory for the polarizable continuum model. I. The CCSD level with analytical first and second derivatives.

PubMed

Cammi, R

2009-10-28

We present a general formulation of the coupled-cluster (CC) theory for a molecular solute described within the framework of the polarizable continuum model (PCM). The PCM-CC theory is derived in its complete form, called PTDE scheme, in which the correlated electronic density is used to have a self-consistent reaction field, and in an approximate form, called PTE scheme, in which the PCM-CC equations are solved assuming the fixed Hartree-Fock solvent reaction field. Explicit forms for the PCM-CC-PTDE equations are derived at the single and double (CCSD) excitation level of the cluster operator. At the same level, explicit equations for the analytical first derivatives of the PCM basic energy functional are presented, and analytical second derivatives are also discussed. The corresponding PCM-CCSD-PTE equations are given as a special case of the full theory.

Analysis of Mathematical Modelling on Potentiometric Biosensors

PubMed Central

Mehala, N.; Rajendran, L.

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

Analysis of mathematical modelling on potentiometric biosensors.

PubMed

Mehala, N; Rajendran, L

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

Relating the microscopic rules in coalescence-fragmentation models to the cluster-size distribution

NASA Astrophysics Data System (ADS)

Ruszczycki, B.; Burnett, B.; Zhao, Z.; Johnson, N. F.

2009-11-01

Coalescence-fragmentation problems are now of great interest across the physical, biological, and social sciences. They are typically studied from the perspective of rate equations, at the heart of which are the rules used for coalescence and fragmentation. Here we discuss how changes in these microscopic rules affect the macroscopic cluster-size distribution which emerges from the solution to the rate equation. Our analysis elucidates the crucial role that the fragmentation rule can play in such dynamical grouping models. We focus our discussion on two well-known models whose fragmentation rules lie at opposite extremes. In particular, we provide a range of generalizations and new analytic results for the well-known model of social group formation developed by Eguíluz and Zimmermann, [Phys. Rev. Lett. 85, 5659 (2000)]. We develop analytic perturbation treatments of this original model, and extend the analytic analysis to the treatment of growing and declining populations.

Analytical solutions for solute transport in groundwater and riverine flow using Green's Function Method and pertinent coordinate transformation method

NASA Astrophysics Data System (ADS)

Sanskrityayn, Abhishek; Suk, Heejun; Kumar, Naveen

2017-04-01

In this study, analytical solutions of one-dimensional pollutant transport originating from instantaneous and continuous point sources were developed in groundwater and riverine flow using both Green's Function Method (GFM) and pertinent coordinate transformation method. Dispersion coefficient and flow velocity are considered spatially and temporally dependent. The spatial dependence of the velocity is linear, non-homogeneous and that of dispersion coefficient is square of that of velocity, while the temporal dependence is considered linear, exponentially and asymptotically decelerating and accelerating. Our proposed analytical solutions are derived for three different situations depending on variations of dispersion coefficient and velocity, respectively which can represent real physical processes occurring in groundwater and riverine systems. First case refers to steady solute transport situation in steady flow in which dispersion coefficient and velocity are only spatially dependent. The second case represents transient solute transport in steady flow in which dispersion coefficient is spatially and temporally dependent while the velocity is spatially dependent. Finally, the third case indicates transient solute transport in unsteady flow in which both dispersion coefficient and velocity are spatially and temporally dependent. The present paper demonstrates the concentration distribution behavior from a point source in realistically occurring flow domains of hydrological systems including groundwater and riverine water in which the dispersivity of pollutant's mass is affected by heterogeneity of the medium as well as by other factors like velocity fluctuations, while velocity is influenced by water table slope and recharge rate. Such capabilities give the proposed method's superiority about application of various hydrological problems to be solved over other previously existing analytical solutions. Especially, to author's knowledge, any other solution doesn't exist for both spatially and temporally variations of dispersion coefficient and velocity. In this study, the existing analytical solutions from previous widely known studies are used for comparison as validation tools to verify the proposed analytical solution as well as the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) code and the developed 1D finite difference code (FDM). All such solutions show perfect match with the respective proposed solutions.

GLOBAL PROPERTIES OF FULLY CONVECTIVE ACCRETION DISKS FROM LOCAL SIMULATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bodo, G.; Ponzo, F.; Rossi, P.

2015-08-01

We present an approach to deriving global properties of accretion disks from the knowledge of local solutions derived from numerical simulations based on the shearing box approximation. The approach consists of a two-step procedure. First, a local solution valid for all values of the disk height is constructed by piecing together an interior solution obtained numerically with an analytical exterior radiative solution. The matching is obtained by assuming hydrostatic balance and radiative equilibrium. Although in principle the procedure can be carried out in general, it simplifies considerably when the interior solution is fully convective. In these cases, the construction ismore » analogous to the derivation of the Hayashi tracks for protostars. The second step consists of piecing together the local solutions at different radii to obtain a global solution. Here we use the symmetry of the solutions with respect to the defining dimensionless numbers—in a way similar to the use of homology relations in stellar structure theory—to obtain the scaling properties of the various disk quantities with radius.« less

Comparison of Analytical and Experimental Effectiveness of Four-Row Plate-Fin-Tube Heat Exchangers with Water, R-22, and R-410A

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baxter, V.D.; Chen, T.D.; Conklin, J.C.

1998-11-15

The analytical solutions of heat exchanger effectiveness for four-row crcmilow, cross-countertlow and cross-paralleltlow have been derived in the recent study. The main objective of this study is to investigate the etlkct of heat exchawger tlow conllguration on thermal performance with refrigerant mixtures. Difference of heat exchanger effectiveness for all flow arrangements relative to an analytical many-row solution has been analyzed. A comparison of four-row cross cou~ltet-ilow heat exchanger effectiveness between analytical solutions and experimental data with water, R-22, and R-4 10A is presented.

Analytical solution for multi-species contaminant transport in finite media with time-varying boundary conditions

USDA-ARS?s Scientific Manuscript database

Most analytical solutions available for the equations governing the advective-dispersive transport of multiple solutes undergoing sequential first-order decay reactions have been developed for infinite or semi-infinite spatial domains and steady-state boundary conditions. In this work we present an ...

APPROXIMATE AND ANALYTICAL SOLUTIONS FOR SOLUTE TRANSPORT FROM AN INJECTION WELL INTO A SINGLE FRACTURE

EPA Science Inventory

In dealing with problems related to land-based nuclear waste management, a number of analytical and approximate solutions were developed to quantify radionuclide transport through fractures contained in the porous formation. t has been reported that by treating the radioactive de...

Analytical solution for vacuum preloading considering the nonlinear distribution of horizontal permeability within the smear zone.

PubMed

Peng, Jie; He, Xiang; Ye, Hanming

2015-01-01

The vacuum preloading is an effective method which is widely used in ground treatment. In consolidation analysis, the soil around prefabricated vertical drain (PVD) is traditionally divided into smear zone and undisturbed zone, both with constant permeability. In reality, the permeability of soil changes continuously within the smear zone. In this study, the horizontal permeability coefficient of soil within the smear zone is described by an exponential function of radial distance. A solution for vacuum preloading consolidation considers the nonlinear distribution of horizontal permeability within the smear zone is presented and compared with previous analytical results as well as a numerical solution, the results show that the presented solution correlates well with the numerical solution, and is more precise than previous analytical solution.

Analytical solution for vacuum preloading considering the nonlinear distribution of horizontal permeability within the smear zone

PubMed Central

Peng, Jie; He, Xiang; Ye, Hanming

2015-01-01

The vacuum preloading is an effective method which is widely used in ground treatment. In consolidation analysis, the soil around prefabricated vertical drain (PVD) is traditionally divided into smear zone and undisturbed zone, both with constant permeability. In reality, the permeability of soil changes continuously within the smear zone. In this study, the horizontal permeability coefficient of soil within the smear zone is described by an exponential function of radial distance. A solution for vacuum preloading consolidation considers the nonlinear distribution of horizontal permeability within the smear zone is presented and compared with previous analytical results as well as a numerical solution, the results show that the presented solution correlates well with the numerical solution, and is more precise than previous analytical solution. PMID:26447973

Analytic solution and pulse area theorem for three-level atoms

NASA Astrophysics Data System (ADS)

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.

Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

PubMed

Hasegawa, Chihiro; Duffull, Stephen B

2018-02-01

Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

NASA Astrophysics Data System (ADS)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

Potential profile near singularity point in kinetic Tonks-Langmuir discharges as a function of the ion sources temperature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kos, L.; Tskhakaya, D. D.; Jelic, N.

2011-05-15

A plasma-sheath transition analysis requires a reliable mathematical expression for the plasma potential profile {Phi}(x) near the sheath edge x{sub s} in the limit {epsilon}{identical_to}{lambda}{sub D}/l=0 (where {lambda}{sub D} is the Debye length and l is a proper characteristic length of the discharge). Such expressions have been explicitly calculated for the fluid model and the singular (cold ion source) kinetic model, where exact analytic solutions for plasma equation ({epsilon}=0) are known, but not for the regular (warm ion source) kinetic model, where no analytic solution of the plasma equation has ever been obtained. For the latter case, Riemann [J. Phys.more » D: Appl. Phys. 24, 493 (1991)] only predicted a general formula assuming relatively high ion-source temperatures, i.e., much higher than the plasma-sheath potential drop. Riemann's formula, however, according to him, never was confirmed in explicit solutions of particular models (e.g., that of Bissell and Johnson [Phys. Fluids 30, 779 (1987)] and Scheuer and Emmert [Phys. Fluids 31, 3645 (1988)]) since ''the accuracy of the classical solutions is not sufficient to analyze the sheath vicinity''[Riemann, in Proceedings of the 62nd Annual Gaseous Electronic Conference, APS Meeting Abstracts, Vol. 54 (APS, 2009)]. Therefore, for many years, there has been a need for explicit calculation that might confirm the Riemann's general formula regarding the potential profile at the sheath edge in the cases of regular very warm ion sources. Fortunately, now we are able to achieve a very high accuracy of results [see, e.g., Kos et al., Phys. Plasmas 16, 093503 (2009)]. We perform this task by using both the analytic and the numerical method with explicit Maxwellian and ''water-bag'' ion source velocity distributions. We find the potential profile near the plasma-sheath edge in the whole range of ion source temperatures of general interest to plasma physics, from zero to ''practical infinity.'' While within limits of ''very low'' and ''relatively high'' ion source temperatures, the potential is proportional to the space coordinate powered by rational numbers {alpha}=1/2 and {alpha}=2/3, with medium ion source temperatures. We found {alpha} between these values being a non-rational number strongly dependent on the ion source temperature. The range of the non-rational power-law turns out to be a very narrow one, at the expense of the extension of {alpha}=2/3 region towards unexpectedly low ion source temperatures.« less

Magnetic iron oxide and manganese-doped iron oxide nanoparticles for the collection of alpha-emitting radionuclides from aqueous solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Hara, Matthew J.; Carter, Jennifer C.; Warner, Cynthia L.

Magnetic nanoparticles are well known to possess chemically active surfaces and high surface areas that can be employed to extract a range of ions from aqueous solutions. Additionally, their paramagnetic property provides a convenient means for bulk collection of the material from solution after the targeted ions have been adsorbed. Herein, two nanoscale amphoteric metal oxides, each possessing useful magnetic attributes, were evaluated for their ability to collect both naturally occurring radioactive isotopes (polonium (Po), radium (Ra), and uranium (U)) as well as the transuranic element americium (Am) from a suite of naturally occurring aqueous matrices. The nanomaterials include commerciallymore » available paramagnetic magnetite (Fe3O4) and magnetite that was modified to incorporate manganese (Mn) into the crystal structure. The chemical stability of these nanomaterials was evaluated in Hanford Site, WA ground water between the natural pH (~8) and pH 1 (acidified with HCl). Whereas the magnetite was observed to have good stability over the pH range, the Mn-doped material was observed to leach Mn at low pH. The materials were evaluated in parallel to characterize their uptake performance of the aforementioned alpha-emitting radionuclide spikes from Hanford Site ground water across a range of pH (from ~8 down to 2). In addition, radiotracer uptake experiments were performed on Columbia River water, seawater, and human urine at their natural pH and at pH 2. Despite the observed leaching of Mn from the Mn-doped nanomaterial in the lower pH range, it exhibited generally superior analyte extraction performance compared to the magnetite, and analyte uptake was observed across a broader pH range. The uptake behavior of the various radiotracers on these two materials at different pH levels can generally be explained by the amphoteric nature of the nanoparticle surfaces. Finally, the rate of sorption of the radiotracers on the two materials in unacidified groundwater was evaluated. The uptake curves generally indicate that equilibrium is obtained within a few minutes, which is attributed to the high surface areas of the nanomaterials and the high level of dispersion in the liquids. Overall, the results indicate that these nanomaterials may have the potential to be employed for a range of applications to extract radionuclides from aqueous solutions. These applications may include analytical chemistry, waste water treatment and remediation, mining, and in vitro radiobioassay.« less

Analytical Solution for Transport with Bimolecular Reactions in Fracture-Matrix Systems with Application to In-Situ Chemical Oxidation

NASA Astrophysics Data System (ADS)

Rajaram, H.; Arshadi, M.

2016-12-01

In-situ chemical oxidation (ISCO) is an effective strategy for remediation of DNAPL contamination in fractured rock. During ISCO, an oxidant (e.g. permanganate) is typically injected through fractures and is consumed by bimolecular reactions with DNAPLs such as TCE and natural organic matter in the fracture and the adjacent rock matrix. Under these conditions, moving reaction fronts form and propagate along the fracture and into the rock matrix. The propagation of these reaction fronts is strongly influenced by the heterogeneity/discontinuity across the fracture-matrix interface (advective transport dominates in the fractures, while diffusive transport dominates in the rock matrix). We present analytical solutions for the concentrations of the oxidant, TCE and natural organic matter; and the propagation of the reaction fronts in a fracture-matrix system. Our approximate analytical solutions assume advection and reaction dominate over diffusion/dispersion in the fracture and neglect the latter. Diffusion and reaction with both TCE and immobile natural organic matter in the rock matrix are considered. The behavior of the reaction-diffusion equations in the rock matrix is posed as a Stefan problem where the diffusing oxidant reacts with both diffusing (TCE) and immobile (natural organic matter) reductants. Our analytical solutions establish that the reaction fronts propagate diffusively (i.e. as the square root of time) in both the matrix and the fracture. Our analytical solutions agree very well with numerical simulations for the case of uniform advection in the fracture. We also present extensions of our analytical solutions to non-uniform flows in the fracture by invoking a travel-time transformation. The non-uniform flow solutions are relevant to field applications of ISCO. The approximate analytical solutions are relevant to a broad class of reactive transport problems in fracture-matrix systems where moving reaction fronts occur.

Calculating corner singularities by boundary integral equations.

PubMed

Shi, Hualiang; Lu, Ya Yan; Du, Qiang

2017-06-01

Accurate numerical solutions for electromagnetic fields near sharp corners and edges are important for nanophotonics applications that rely on strong near fields to enhance light-matter interactions. For cylindrical structures, the singularity exponents of electromagnetic fields near sharp edges can be solved analytically, but in general the actual fields can only be calculated numerically. In this paper, we use a boundary integral equation method to compute electromagnetic fields near sharp edges, and construct the leading terms in asymptotic expansions based on numerical solutions. Our integral equations are formulated for rescaled unknown functions to avoid unbounded field components, and are discretized with a graded mesh and properly chosen quadrature schemes. The numerically found singularity exponents agree well with the exact values in all the test cases presented here, indicating that the numerical solutions are accurate.

Rogue-wave solutions of the Zakharov equation

NASA Astrophysics Data System (ADS)

Rao, Jiguang; Wang, Lihong; Liu, Wei; He, Jingsong

2017-12-01

Using the bilinear transformation method, we derive general rogue-wave solutions of the Zakharov equation. We present these Nth-order rogue-wave solutions explicitly in terms of Nth-order determinants whose matrix elements have simple expressions. We show that the fundamental rogue wave is a line rogue wave with a line profile on the plane ( x, y) arising from a constant background at t ≪ 0 and then gradually tending to the constant background for t ≫ 0. Higher-order rogue waves arising from a constant background and later disappearing into it describe the interaction of several fundamental line rogue waves. We also consider different structures of higher-order rogue waves. We present differences between rogue waves of the Zakharov equation and of the first type of the Davey-Stewartson equation analytically and graphically.

Quantum Dynamics of Solitons in Strongly Interacting Systems on Optical Lattices

NASA Astrophysics Data System (ADS)

Rubbo, Chester; Balakrishnan, Radha; Reinhardt, William; Satija, Indubala; Rey, Ana; Manmana, Salvatore

2012-06-01

We present results of the quantum dynamics of solitons in XXZ spin-1/2 systems which in general can be derived from a system of spinless fermions or hard-core bosons (HCB) with nearest neighbor interaction on a lattice. A mean-field treatment using spin-coherent states revealed analytic solutions of both bright and dark solitons [1]. We take these solutions and apply a full quantum evolution using the adaptive time-dependent density matrix renormalization group method (adaptive t-DMRG), which takes into account the effect of strong correlations. We use local spin observables, correlations functions, and entanglement entropies as measures for the stability of these soliton solutions over the simulation times. [4pt] [1] R. Balakrishnan, I.I. Satija, and C.W. Clark, Phys. Rev. Lett. 103, 230403 (2009).

Nonsingular solutions and instabilities in Einstein-scalar-Gauss-Bonnet cosmology

NASA Astrophysics Data System (ADS)

Sberna, Laura; Pani, Paolo

2017-12-01

It is generically believed that higher-order curvature corrections to the Einstein-Hilbert action might cure the curvature singularities that plague general relativity. Here we consider Einstein-scalar-Gauss-Bonnet gravity, the only four-dimensional, ghost-free theory with quadratic curvature terms. For any choice of the coupling function and of the scalar potential, we show that the theory does not allow for bouncing solutions in the flat and open Friedmann universe. For the case of a closed universe, using a reverse-engineering method, we explicitly provide a bouncing solution which is nevertheless linearly unstable in the scalar gravitational sector. Moreover, we show that the expanding, singularity-free, early-time cosmologies allowed in the theory are unstable. These results rely only on analyticity and finiteness of cosmological variables at early times.

On square-integrability of solutions of the stationary Schrödinger equation for the quantum harmonic oscillator in two dimensional constant curvature spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noguera, Norman, E-mail: norman.noguera@ucr.ac.cr; Rózga, Krzysztof, E-mail: krzysztof.rozga@upr.edu

In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case ofmore » a slightly more general potential than the one for harmonic oscillator.« less

Link between alginate reaction front propagation and general reaction diffusion theory.

PubMed

Braschler, Thomas; Valero, Ana; Colella, Ludovica; Pataky, Kristopher; Brugger, Jürgen; Renaud, Philippe

2011-03-15

We provide a common theoretical framework reuniting specific models for the Ca(2+)-alginate system and general reaction diffusion theory along with experimental validation on a microfluidic chip. As a starting point, we use a set of nonlinear, partial differential equations that are traditionally solved numerically: the Mikkelsen-Elgsaeter model. Applying the traveling-wave hypothesis as a major simplification, we obtain an analytical solution. The solution indicates that the fundamental properties of the alginate reaction front are governed by a single dimensionless parameter λ. For small λ values, a large depletion zone accompanies the reaction front. For large λ values, the alginate reacts before having the time to diffuse significantly. We show that the λ parameter is of general importance beyond the alginate model system, as it can be used to classify known solutions for second-order reaction diffusion schemes, along with the novel solution presented here. For experimental validation, we develop a microchip model system, in which the alginate gel formation can be carried out in a highly controlled, essentially 1D environment. The use of a filter barrier enables us to rapidly renew the CaCl(2) solution, while maintaining flow speeds lower than 1 μm/s for the alginate compartment. This allows one to impose an exactly known bulk CaCl(2) concentration and diffusion resistance. This experimental model system, taken together with the theoretical development, enables the determination of the entire set of physicochemical parameters governing the alginate reaction front in a single experiment.

The long-solved problem of the best-fit straight line: application to isotopic mixing lines

NASA Astrophysics Data System (ADS)

Wehr, Richard; Saleska, Scott R.

2017-01-01

It has been almost 50 years since York published an exact and general solution for the best-fit straight line to independent points with normally distributed errors in both x and y. York's solution is highly cited in the geophysical literature but almost unknown outside of it, so that there has been no ebb in the tide of books and papers wrestling with the problem. Much of the post-1969 literature on straight-line fitting has sown confusion not merely by its content but by its very existence. The optimal least-squares fit is already known; the problem is already solved. Here we introduce the non-specialist reader to York's solution and demonstrate its application in the interesting case of the isotopic mixing line, an analytical tool widely used to determine the isotopic signature of trace gas sources for the study of biogeochemical cycles. The most commonly known linear regression methods - ordinary least-squares regression (OLS), geometric mean regression (GMR), and orthogonal distance regression (ODR) - have each been recommended as the best method for fitting isotopic mixing lines. In fact, OLS, GMR, and ODR are all special cases of York's solution that are valid only under particular measurement conditions, and those conditions do not hold in general for isotopic mixing lines. Using Monte Carlo simulations, we quantify the biases in OLS, GMR, and ODR under various conditions and show that York's general - and convenient - solution is always the least biased.

The Analytical Solution of the Transient Radial Diffusion Equation with a Nonuniform Loss Term.

NASA Astrophysics Data System (ADS)

Loridan, V.; Ripoll, J. F.; De Vuyst, F.

2017-12-01

Many works have been done during the past 40 years to perform the analytical solution of the radial diffusion equation that models the transport and loss of electrons in the magnetosphere, considering a diffusion coefficient proportional to a power law in shell and a constant loss term. Here, we propose an original analytical method to address this challenge with a nonuniform loss term. The strategy is to match any L-dependent electron losses with a piecewise constant function on M subintervals, i.e., dealing with a constant lifetime on each subinterval. Applying an eigenfunction expansion method, the eigenvalue problem becomes presently a Sturm-Liouville problem with M interfaces. Assuming the continuity of both the distribution function and its first spatial derivatives, we are able to deal with a well-posed problem and to find the full analytical solution. We further show an excellent agreement between both the analytical solutions and the solutions obtained directly from numerical simulations for different loss terms of various shapes and with a diffusion coefficient DLL L6. We also give two expressions for the required number of eigenmodes N to get an accurate snapshot of the analytical solution, highlighting that N is proportional to 1/√t0, where t0 is a time of interest, and that N increases with the diffusion power. Finally, the equilibrium time, defined as the time to nearly reach the steady solution, is estimated by a closed-form expression and discussed. Applications to Earth and also Jupiter and Saturn are discussed.

Closed form solution for a double quantum well using Gröbner basis

NASA Astrophysics Data System (ADS)

Acus, A.; Dargys, A.

2011-07-01

Analytical expressions for the spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and the effective masses are different. This was achieved by using a Gröbner basis algorithm that allowed us to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation.

Wave Functions for Time-Dependent Dirac Equation under GUP

NASA Astrophysics Data System (ADS)

Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen

2018-04-01

In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009

DOE Office of Scientific and Technical Information (OSTI.GOV)

Afonso, V.I.; Olmo, Gonzalo J.; Rubiera-Garcia, D., E-mail: viafonso@df.ufcg.edu.br, E-mail: gonzalo.olmo@uv.es, E-mail: drgarcia@fc.ul.pt

The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at r ≈ 2 Mmore » , while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.« less

Spherically symmetric vacuum solutions arising from trace dynamics modifications to gravitation

NASA Astrophysics Data System (ADS)

Adler, Stephen L.; Ramazanoğlu, Fethi M.

2015-12-01

We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action (derived from trace dynamics) that gives an alternative explanation of the origin of "dark energy". We give analytic and numerical results for the solutions of these equations, first in polar coordinates, and then in isotropic coordinates. General features of the static case are that: (i) there is no horizon, since g00 is nonvanishing for finite values of the polar radius, and only vanishes (in isotropic coordinates) at the internal singularity, (ii) the Ricci scalar R vanishes identically, and (iii) there is a physical singularity at cosmological distances. The large distance singularity may be an artifact of the static restriction, since we find that the behavior at large distances is altered in a time-dependent solution using the McVittie Ansatz.

Assessment of ALEGRA Computation for Magnetostatic Configurations

DOE PAGES

Grinfeld, Michael; Niederhaus, John Henry; Porwitzky, Andrew

2016-03-01

Here, a closed-form solution is described here for the equilibrium configurations of the magnetic field in a simple heterogeneous domain. This problem and its solution are used for rigorous assessment of the accuracy of the ALEGRA code in the quasistatic limit. By the equilibrium configuration we understand the static condition, or the stationary states without macroscopic current. The analysis includes quite a general class of 2D solutions for which a linear isotropic metallic matrix is placed inside a stationary magnetic field approaching a constant value H i° at infinity. The process of evolution of the magnetic fields inside and outsidemore » the inclusion and the parameters for which the quasi-static approach provides for self-consistent results is also explored. Lastly, it is demonstrated that under spatial mesh refinement, ALEGRA converges to the analytic solution for the interior of the inclusion at the expected rate, for both body-fitted and regular rectangular meshes.« less

Solution of the Eshelby problem in gradient elasticity for multilayer spherical inclusions

NASA Astrophysics Data System (ADS)

Volkov-Bogorodskii, D. B.; Lurie, S. A.

2016-03-01

We consider gradient models of elasticity which permit taking into account the characteristic scale parameters of the material. We prove the Papkovich-Neuber theorems, which determine the general form of the gradient solution and the structure of scale effects. We derive the Eshelby integral formula for the gradient moduli of elasticity, which plays the role of the closing equation in the self-consistent three-phase method. In the gradient theory of deformations, we consider the fundamental Eshelby-Christensen problem of determining the effective elastic properties of dispersed composites with spherical inclusions; the exact solution of this problem for classical models was obtained in 1976. This paper is the first to present the exact analytical solution of the Eshelby-Christensen problem for the gradient theory, which permits estimating the influence of scale effects on the stress state and the effective properties of the dispersed composites under study.We also analyze the influence of scale factors.

Exact BPS domain walls at finite gauge coupling

NASA Astrophysics Data System (ADS)

Blaschke, Filip

2017-01-01

Bogomol'nyi-Prasad-Sommerfield solitons in models with spontaneously broken gauge symmetry have been intensively studied at the infinite gauge coupling limit, where the governing equation-the so-called master equation-is exactly solvable. Except for a handful of special solutions, the standing impression is that analytic results at finite coupling are generally unavailable. The aim of this paper is to demonstrate, using domain walls in Abelian-Higgs models as the simplest example, that exact solitons at finite gauge coupling can be readily obtained if the number of Higgs fields (NF ) is large enough. In particular, we present a family of exact solutions, describing N domain walls at arbitrary positions in models with at least NF≥2 N +1 . We have also found that adding together any pair of solutions can produce a new exact solution if the combined tension is below a certain limit.

Convective heat transfer for a gaseous slip flow in micropipe and parallel-plate microchannel with uniform wall heat flux: effect of axial heat conduction

NASA Astrophysics Data System (ADS)

Haddout, Y.; Essaghir, E.; Oubarra, A.; Lahjomri, J.

2017-12-01

Thermally developing laminar slip flow through a micropipe and a parallel plate microchannel, with axial heat conduction and uniform wall heat flux, is studied analytically by using a powerful method of self-adjoint formalism. This method results from a decomposition of the elliptic energy equation into a system of two first-order partial differential equations. The advantage of this method over other methods, resides in the fact that the decomposition procedure leads to a selfadjoint problem although the initial problem is apparently not a self-adjoint one. The solution is an extension of prior studies and considers a first order slip model boundary conditions at the fluid-wall interface. The analytical expressions for the developing temperature and local Nusselt number in the thermal entrance region are obtained in the general case. Therefore, the solution obtained could be extended easily to any hydrodynamically developed flow and arbitrary heat flux distribution. The analytical results obtained are compared for select simplified cases with available numerical calculations and they both agree. The results show that the heat transfer characteristics of flow in the thermal entrance region are strongly influenced by the axial heat conduction and rarefaction effects which are respectively characterized by Péclet and Knudsen numbers.

Convective heat transfer for a gaseous slip flow in micropipe and parallel-plate microchannel with uniform wall heat flux: effect of axial heat conduction

NASA Astrophysics Data System (ADS)

Haddout, Y.; Essaghir, E.; Oubarra, A.; Lahjomri, J.

2018-06-01

Thermally developing laminar slip flow through a micropipe and a parallel plate microchannel, with axial heat conduction and uniform wall heat flux, is studied analytically by using a powerful method of self-adjoint formalism. This method results from a decomposition of the elliptic energy equation into a system of two first-order partial differential equations. The advantage of this method over other methods, resides in the fact that the decomposition procedure leads to a selfadjoint problem although the initial problem is apparently not a self-adjoint one. The solution is an extension of prior studies and considers a first order slip model boundary conditions at the fluid-wall interface. The analytical expressions for the developing temperature and local Nusselt number in the thermal entrance region are obtained in the general case. Therefore, the solution obtained could be extended easily to any hydrodynamically developed flow and arbitrary heat flux distribution. The analytical results obtained are compared for select simplified cases with available numerical calculations and they both agree. The results show that the heat transfer characteristics of flow in the thermal entrance region are strongly influenced by the axial heat conduction and rarefaction effects which are respectively characterized by Péclet and Knudsen numbers.

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

NASA Astrophysics Data System (ADS)

Liu, X.; Banerjee, J. R.

2017-03-01

A highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J0) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.

A Semi-Analytical Model for Dispersion Modelling Studies in the Atmospheric Boundary Layer

NASA Astrophysics Data System (ADS)

Gupta, A.; Sharan, M.

2017-12-01

The severe impact of harmful air pollutants has always been a cause of concern for a wide variety of air quality analysis. The analytical models based on the solution of the advection-diffusion equation have been the first and remain the convenient way for modeling air pollutant dispersion as it is easy to handle the dispersion parameters and related physics in it. A mathematical model describing the crosswind integrated concentration is presented. The analytical solution to the resulting advection-diffusion equation is limited to a constant and simple profiles of eddy diffusivity and wind speed. In practice, the wind speed depends on the vertical height above the ground and eddy diffusivity profiles on the downwind distance from the source as well as the vertical height. In the present model, a method of eigen-function expansion is used to solve the resulting partial differential equation with the appropriate boundary conditions. This leads to a system of first order ordinary differential equations with a coefficient matrix depending on the downwind distance. The solution of this system, in general, can be expressed in terms of Peano-baker series which is not easy to compute, particularly when the coefficient matrix becomes non-commutative (Martin et al., 1967). An approach based on Taylor's series expansion is introduced to find the numerical solution of first order system. The method is applied to various profiles of wind speed and eddy diffusivities. The solution computed from the proposed methodology is found to be efficient and accurate in comparison to those available in the literature. The performance of the model is evaluated with the diffusion datasets from Copenhagen (Gryning et al., 1987) and Hanford (Doran et al., 1985). In addition, the proposed method is used to deduce three dimensional concentrations by considering the Gaussian distribution in crosswind direction, which is also evaluated with diffusion data corresponding to a continuous point source.

Padé approximant for normal stress differences in large-amplitude oscillatory shear flow

NASA Astrophysics Data System (ADS)

Poungthong, P.; Saengow, C.; Giacomin, A. J.; Kolitawong, C.; Merger, D.; Wilhelm, M.

2018-04-01

Analytical solutions for the normal stress differences in large-amplitude oscillatory shear flow (LAOS), for continuum or molecular models, normally take the inexact form of the first few terms of a series expansion in the shear rate amplitude. Here, we improve the accuracy of these truncated expansions by replacing them with rational functions called Padé approximants. The recent advent of exact solutions in LAOS presents an opportunity to identify accurate and useful Padé approximants. For this identification, we replace the truncated expansion for the corotational Jeffreys fluid with its Padé approximants for the normal stress differences. We uncover the most accurate and useful approximant, the [3,4] approximant, and then test its accuracy against the exact solution [C. Saengow and A. J. Giacomin, "Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow," Phys. Fluids 29, 121601 (2017)]. We use Ewoldt grids to show the stunning accuracy of our [3,4] approximant in LAOS. We quantify this accuracy with an objective function and then map it onto the Pipkin space. Our two applications illustrate how to use our new approximant reliably. For this, we use the Spriggs relations to generalize our best approximant to multimode, and then, we compare with measurements on molten high-density polyethylene and on dissolved polyisobutylene in isobutylene oligomer.

Limitless Analytic Elements

NASA Astrophysics Data System (ADS)

Strack, O. D. L.

2018-02-01

We present equations for new limitless analytic line elements. These elements possess a virtually unlimited number of degrees of freedom. We apply these new limitless analytic elements to head-specified boundaries and to problems with inhomogeneities in hydraulic conductivity. Applications of these new analytic elements to practical problems involving head-specified boundaries require the solution of a very large number of equations. To make the new elements useful in practice, an efficient iterative scheme is required. We present an improved version of the scheme presented by Bandilla et al. (2007), based on the application of Cauchy integrals. The limitless analytic elements are useful when modeling strings of elements, rivers for example, where local conditions are difficult to model, e.g., when a well is close to a river. The solution of such problems is facilitated by increasing the order of the elements to obtain a good solution. This makes it unnecessary to resort to dividing the element in question into many smaller elements to obtain a satisfactory solution.

Damage states in laminated composite three-point bend specimens: An experimental-analytical correlation study

NASA Technical Reports Server (NTRS)

Starbuck, J. Michael; Guerdal, Zafer; Pindera, Marek-Jerzy; Poe, Clarence C.

1990-01-01

Damage states in laminated composites were studied by considering the model problem of a laminated beam subjected to three-point bending. A combination of experimental and theoretical research techniques was used to correlate the experimental results with the analytical stress distributions. The analytical solution procedure was based on the stress formulation approach of the mathematical theory of elasticity. The solution procedure is capable of calculating the ply-level stresses and beam displacements for any laminated beam of finite length using the generalized plane deformation or plane stress state assumption. Prior to conducting the experimental phase, the results from preliminary analyses were examined. Significant effects in the ply-level stress distributions were seen depending on the fiber orientation, aspect ratio, and whether or not a grouped or interspersed stacking sequence was used. The experimental investigation was conducted to determine the different damage modes in laminated three-point bend specimens. The test matrix consisted of three-point bend specimens of 0 deg unidirectional, cross-ply, and quasi-isotropic stacking sequences. The dependence of the damage initiation loads and ultimate failure loads were studied, and their relation to damage susceptibility and damage tolerance of the mean configuration was discussed. Damage modes were identified by visual inspection of the damaged specimens using an optical microscope. The four fundamental damage mechanisms identified were delaminations, matrix cracking, fiber breakage, and crushing. The correlation study between the experimental results and the analytical results were performed for the midspan deflection, indentation, damage modes, and damage susceptibility.

Users manual for Streamtube Curvature Analysis: Analytical method for predicting the pressure distribution about a nacelle at transonic speeds, volume 1

NASA Technical Reports Server (NTRS)

Keith, J. S.; Ferguson, D. R.; Heck, P. H.

1972-01-01

The computer program, Streamtube Curvature Analysis, is described for the engineering user and for the programmer. The user oriented documentation includes a description of the mathematical governing equations, their use in the solution, and the method of solution. The general logical flow of the program is outlined and detailed instructions for program usage and operation are explained. General procedures for program use and the program capabilities and limitations are described. From the standpoint of the grammar, the overlay structure of the program is described. The various storage tables are defined and their uses explained. The input and output are discussed in detail. The program listing includes numerous comments so that the logical flow within the program is easily followed. A test case showing input data and output format is included as well as an error printout description.

The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

NASA Technical Reports Server (NTRS)

Hoots, F. R.; Fitzpatrick, P. M.

1979-01-01

The classical Poisson equations of rotational motion are used to study the attitude motions of an earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the earth. A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Long-term solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.

Shadows, signals, and stability in Einsteinian cubic gravity

NASA Astrophysics Data System (ADS)

Hennigar, Robie A.; Jahani Poshteh, Mohammad Bagher; Mann, Robert B.

2018-03-01

We conduct a preliminary investigation into the phenomenological implications of Einsteinian cubic gravity (ECG), a four-dimensional theory of gravity cubic in curvature of interest for its unique formulation and properties. We find an analytic approximation for a spherically symmetric black hole solution to this theory using a continued fraction ansatz. This approximate solution is valid everywhere outside of the horizon and we use it to study the orbit of massive test bodies near a black hole, specifically computing the innermost stable circular orbit. We compute constraints on the ECG coupling parameter imposed by Shapiro time delay. We then compute the shadow of an ECG black hole and find it to be larger than its Einsteinian counterpart in general relativity for the same value of the mass. Applying our results to Sgr A*, we find that departures from general relativity are small but in principle distinguishable.

A general low frequency acoustic radiation capability for NASTRAN

NASA Technical Reports Server (NTRS)

Everstine, G. C.; Henderson, F. M.; Schroeder, E. A.; Lipman, R. R.

1986-01-01

A new capability called NASHUA is described for calculating the radiated acoustic sound pressure field exterior to a harmonically-excited arbitrary submerged 3-D elastic structure. The surface fluid pressures and velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior fluid. After the fluid impedance is calculated, most of the required matrix operations are performed using the general matrix manipulation package (DMAP) available in NASTRAN. Far field radiated pressures are then calculated from the surface solution using the Helmholtz exterior integral equation. Other output quantities include the maximum sound pressure levels in each of the three coordinate planes, the rms and average surface pressures and normal velocities, the total radiated power and the radiation efficiency. The overall approach is illustrated and validated using known analytic solutions for submerged spherical shells subjected to both uniform and nonuniform applied loads.

Hydraulic modeling of riverbank filtration systems with curved boundaries using analytic elements and series solutions

NASA Astrophysics Data System (ADS)

Bakker, Mark

2010-08-01

A new analytic solution approach is presented for the modeling of steady flow to pumping wells near rivers in strip aquifers; all boundaries of the river and strip aquifer may be curved. The river penetrates the aquifer only partially and has a leaky stream bed. The water level in the river may vary spatially. Flow in the aquifer below the river is semi-confined while flow in the aquifer adjacent to the river is confined or unconfined and may be subject to areal recharge. Analytic solutions are obtained through superposition of analytic elements and Fourier series. Boundary conditions are specified at collocation points along the boundaries. The number of collocation points is larger than the number of coefficients in the Fourier series and a solution is obtained in the least squares sense. The solution is analytic while boundary conditions are met approximately. Very accurate solutions are obtained when enough terms are used in the series. Several examples are presented for domains with straight and curved boundaries, including a well pumping near a meandering river with a varying water level. The area of the river bottom where water infiltrates into the aquifer is delineated and the fraction of river water in the well water is computed for several cases.

Improved partition equilibrium model for predicting analyte response in electrospray ionization mass spectrometry.

PubMed

Du, Lihong; White, Robert L

2009-02-01

A previously proposed partition equilibrium model for quantitative prediction of analyte response in electrospray ionization mass spectrometry is modified to yield an improved linear relationship. Analyte mass spectrometer response is modeled by a competition mechanism between analyte and background electrolytes that is based on partition equilibrium considerations. The correlation between analyte response and solution composition is described by the linear model over a wide concentration range and the improved model is shown to be valid for a wide range of experimental conditions. The behavior of an analyte in a salt solution, which could not be explained by the original model, is correctly predicted. The ion suppression effects of 16:0 lysophosphatidylcholine (LPC) on analyte signals are attributed to a combination of competition for excess charge and reduction of total charge due to surface tension effects. In contrast to the complicated mathematical forms that comprise the original model, the simplified model described here can more easily be employed to predict analyte mass spectrometer responses for solutions containing multiple components. Copyright (c) 2008 John Wiley & Sons, Ltd.

Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere

NASA Technical Reports Server (NTRS)

Weinman, J. A.; Twitty, J. T.; Browning, S. R.; Herman, B. M.

1975-01-01

The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical small-angle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosol-laden model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few per cent. The analytical solution to the problem which considers an aerosol-laden atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.

Modelling shoreline evolution in the vicinity of a groyne and a river

NASA Astrophysics Data System (ADS)

Valsamidis, Antonios; Reeve, Dominic E.

2017-01-01

Analytical solutions to the equations governing shoreline evolution are well-known and have value both as pedagogical tools and for conceptual design. Nevertheless, solutions have been restricted to a fairly narrow class of conditions with limited applicability to real-life situations. We present a new analytical solution for a widely encountered situation where a groyne is constructed close to a river to control sediment movement. The solution, which employs Laplace transforms, has the advantage that a solution for time-varying conditions may be constructed from the solution for constant conditions by means of the Heaviside procedure. Solutions are presented for various combinations of wave conditions and sediment supply/removal by the river. An innovation introduced in this work is the capability to provide an analytical assessment of the accretion or erosion caused near the groyne due to its proximity to the river which may act either as a source or a sink of sediment material.

A Quantum Dot with Spin-Orbit Interaction--Analytical Solution

ERIC Educational Resources Information Center

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.

Analytic solution of magnetic induction distribution of ideal hollow spherical field sources

NASA Astrophysics Data System (ADS)

Xu, Xiaonong; Lu, Dingwei; Xu, Xibin; Yu, Yang; Gu, Min

2017-12-01

The Halbach type hollow spherical permanent magnet arrays (HSPMA) are volume compacted, energy efficient field sources, and capable of producing multi-Tesla field in the cavity of the array, which have attracted intense interests in many practical applications. Here, we present analytical solutions of magnetic induction to the ideal HSPMA in entire space, outside of array, within the cavity of array, and in the interior of the magnet. We obtain solutions using concept of magnetic charge to solve the Poisson's and Laplace's equations for the HSPMA. Using these analytical field expressions inside the material, a scalar demagnetization function is defined to approximately indicate the regions of magnetization reversal, partial demagnetization, and inverse magnetic saturation. The analytical field solution provides deeper insight into the nature of HSPMA and offer guidance in designing optimized one.

Development of an analytical solution for thermal single-well injection-withdrawal tests in horizontally fractured reservoirs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jung, Yoojin

In this study, we have developed an analytical solution for thermal single-well injection-withdrawal tests in horizontally fractured reservoirs where fluid flow through the fracture is radial. The dimensionless forms of the governing equations and the initial and boundary conditions in the radial flow system can be written in a form identical to those in the linear flow system developed by Jung and Pruess [Jung, Y., and K. Pruess (2012), A Closed-Form Analytical Solution for Thermal Single-Well Injection-Withdrawal Tests, Water Resour. Res., 48, W03504, doi:10.1029/2011WR010979], and therefore the analytical solutions developed in Jung and Pruess (2012) can be applied to computemore » the time dependence of temperature recovery at the injection/withdrawal well in a horizontally oriented fracture with radial flow.« less