Elegant Ince—Gaussian breathers in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Bai, Zhi-Yong; Deng, Dong-Mei; Guo, Qi

2012-06-01

A novel class of optical breathers, called elegant Ince—Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell's mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schrödinger equation.

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.

Homoclinic accretion solutions in the Schwarzschild-anti-de Sitter space-time

NASA Astrophysics Data System (ADS)

Mach, Patryk

2015-04-01

The aim of this paper is to clarify the distinction between homoclinic and standard (global) Bondi-type accretion solutions in the Schwarzschild-anti-de Sitter space-time. The homoclinic solutions have recently been discovered numerically for polytropic equations of state. Here I show that they exist also for certain isothermal (linear) equations of state, and an analytic solution of this type is obtained. It is argued that the existence of such solutions is generic, although for sufficiently relativistic matter models (photon gas, ultrahard equation of state) there exist global solutions that can be continued to infinity, similarly to standard Michel's solutions in the Schwarzschild space-time. In contrast to that global solutions should not exist for matter models with a nonvanishing rest-mass component, and this is demonstrated for polytropes. For homoclinic isothermal solutions I derive an upper bound on the mass of the black hole for which stationary transonic accretion is allowed.

Big data analytics as a service infrastructure: challenges, desired properties and solutions

NASA Astrophysics Data System (ADS)

Martín-Márquez, Manuel

2015-12-01

CERN's accelerator complex generates a very large amount of data. A large volumen of heterogeneous data is constantly generated from control equipment and monitoring agents. These data must be stored and analysed. Over the decades, CERN's researching and engineering teams have applied different approaches, techniques and technologies for this purpose. This situation has minimised the necessary collaboration and, more relevantly, the cross data analytics over different domains. These two factors are essential to unlock hidden insights and correlations between the underlying processes, which enable better and more efficient daily-based accelerator operations and more informed decisions. The proposed Big Data Analytics as a Service Infrastructure aims to: (1) integrate the existing developments; (2) centralise and standardise the complex data analytics needs for CERN's research and engineering community; (3) deliver real-time, batch data analytics and information discovery capabilities; and (4) provide transparent access and Extract, Transform and Load (ETL), mechanisms to the various and mission-critical existing data repositories. This paper presents the desired objectives and properties resulting from the analysis of CERN's data analytics requirements; the main challenges: technological, collaborative and educational and; potential solutions.

Bernstein-Greene-Kruskal Modes in a Three-Dimensional Plasma

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

Ng, C.S.; Bhattacharjee, A.

2005-12-09

Bernstein-Greene-Kruskal modes in a three-dimensional (3D) unmagnetized plasma are constructed. It is shown that 3D solutions that depend only on energy do not exist. However, 3D solutions that depend on energy and additional constants of motion (such as angular momentum) do exist. Exact analytical as well as numerical solutions are constructed assuming spherical symmetry, and their properties are contrasted with those of 1D solutions. Possible extensions to solutions with cylindrical symmetry with or without a finite magnetic guide field are discussed.

Development and application of a gradient method for solving differential games

NASA Technical Reports Server (NTRS)

Roberts, D. A.; Montgomery, R. C.

1971-01-01

A technique for solving n-dimensional games is developed and applied to two pursuit-evasion games. The first is a two-dimensional game similar to the homicidal chauffeur but modified to resemble an airplane-helicopter engagement. The second is a five-dimensional game of two airplanes at constant altitude and with thrust and turning controls. The performance function to be optimized by the pursuer and evader was the distance between the evader and a given target point in front of the pursuer. The analytic solution to the first game reveals that both unique and nonunique solutions exist. A comparison between the gradient results and the analytic solution shows a dependence on the nominal controls in regions where nonunique solutions exist. In the unique solution region, the results from the two methods agree closely. The results for the five-dimensional two-airplane game are also shown to be dependent on the nominal controls selected and indicate that initial conditions are in a region of nonunique solutions.

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.

Simulation and statistics: Like rhythm and song

NASA Astrophysics Data System (ADS)

Othman, Abdul Rahman

2013-04-01

Simulation has been introduced to solve problems in the form of systems. By using this technique the following two problems can be overcome. First, a problem that has an analytical solution but the cost of running an experiment to solve is high in terms of money and lives. Second, a problem exists but has no analytical solution. In the field of statistical inference the second problem is often encountered. With the advent of high-speed computing devices, a statistician can now use resampling techniques such as the bootstrap and permutations to form pseudo sampling distribution that will lead to the solution of the problem that cannot be solved analytically. This paper discusses how a Monte Carlo simulation was and still being used to verify the analytical solution in inference. This paper also discusses the resampling techniques as simulation techniques. The misunderstandings about these two techniques are examined. The successful usages of both techniques are also explained.

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

Reply to ``Comment on `Free surface Hele-Shaw flows around an obstacle: A random walk simulation' ''

NASA Astrophysics Data System (ADS)

Bogoyavlenskiy, Vladislav A.; Cotts, Eric J.

2007-09-01

As pointed out by Vasconcelos in his Comment, our computer simulations of Hele-Shaw flows around series of wedges differ from analytical solutions existing for this problem. We attribute the discrepancy to the notion that these analytical solutions correspond to ideal, steady-state flow regimes which are hardly applicable when a rigid obstacle interacts with a moving liquid-gas interface.

Modified harmonic balance method for the solution of nonlinear jerk equations

NASA Astrophysics Data System (ADS)

Rahman, M. Saifur; Hasan, A. S. M. Z.

2018-03-01

In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

Physics of heat pipe rewetting

NASA Technical Reports Server (NTRS)

Chan, S. H.

1992-01-01

Although several studies have been made to determine the rewetting characteristics of liquid films on heated rods, tubes, and flat plates, no solutions are yet available to describe the rewetting process of a hot plate subjected to a uniform heating. A model is presented to analyze the rewetting process of such plates with and without grooves. Approximate analytical solutions are presented for the prediction of the rewetting velocity and the transient temperature profiles of the plates. It is shown that the present rewetting velocity solution reduces correctly to the existing solution for the rewetting of an initially hot isothermal plate without heating from beneath the plate. Numerical solutions have also been obtained to validate the analytical solutions.

Continuous-time safety-first portfolio selection with jump-diffusion processes

NASA Astrophysics Data System (ADS)

Yan, Wei

2012-04-01

This article is concerned with continuous-time portfolio selection based on a safety-first criterion under discontinuous price processes (jump-diffusion processes). The solution of the corresponding Hamilton-Jacobi-Bellman equation of the problem is demonstrated. The analytical solutions are presented when there does not exist any riskless asset. Moreover, the problem is also discussed while there exists one riskless asset.

Stationary and moving solitons in spin-orbit-coupled spin-1 Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Li, Yu-E.; Xue, Ju-Kui

2018-04-01

We investigate the matter-wave solitons in a spin-orbit-coupled spin-1 Bose-Einstein condensate using a multiscale perturbation method. Beginning with the one-dimensional spin-orbit-coupled threecomponent Gross-Pitaevskii equations, we derive a single nonlinear Schrödinger equation, which allows determination of the analytical soliton solutions of the system. Stationary and moving solitons in the system are derived. In particular, a parameter space for different existing soliton types is provided. It is shown that there exist only dark or bright solitons when the spin-orbit coupling is weak, with the solitons depending on the atomic interactions. However, when the spin-orbit coupling is strong, both dark and bright solitons exist, being determined by the Raman coupling. Our analytical solutions are confirmed by direct numerical simulations.

Study of tethered satellite active attitude control

NASA Technical Reports Server (NTRS)

Colombo, G.

1982-01-01

Existing software was adapted for the study of tethered subsatellite rotational dynamics, an analytic solution for a stable configuration of a tethered subsatellite was developed, the analytic and numerical integrator (computer) solutions for this "test case' was compared in a two mass tether model program (DUMBEL), the existing multiple mass tether model (SKYHOOK) was modified to include subsatellite rotational dynamics, the analytic "test case,' was verified, and the use of the SKYHOOK rotational dynamics capability with a computer run showing the effect of a single off axis thruster on the behavior of the subsatellite was demonstrated. Subroutines for specific attitude control systems are developed and applied to the study of the behavior of the tethered subsatellite under realistic on orbit conditions. The effect of all tether "inputs,' including pendular oscillations, air drag, and electrodynamic interactions, on the dynamic behavior of the tether are included.

Sierra/Aria 4.48 Verification Manual.

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

Sierra Thermal Fluid Development Team

Presented in this document is a portion of the tests that exist in the Sierra Thermal/Fluids verification test suite. Each of these tests is run nightly with the Sierra/TF code suite and the results of the test checked under mesh refinement against the correct analytic result. For each of the tests presented in this document the test setup, derivation of the analytic solution, and comparison of the code results to the analytic solution is provided. This document can be used to confirm that a given code capability is verified or referenced as a compilation of example problems.

Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. Part 1: Velocity selection

NASA Technical Reports Server (NTRS)

Tanveer, Saleh

1989-01-01

An asymptotic theory is presented for the determination of velocity and linear stability of a steady symmetric bubble in a Hele-Shaw cell for small surface tension. In the first part, the bubble velocity U relative to the fluid velocity at infinity is determined for small surface tension T by determining transcendentally small correction to the asymptotic series solution. It is found that for any relative bubble velocity U in the interval (U(c),2), solutions exist at a countably infinite set of values of T (which has zero as its limit point) corresponding to the different branches of bubble solutions. U(c) decreases monotonically from 2 to 1 as the bubble area increases from 0 to infinity. However, for a bubble of arbitrarily given size, as T approaches 0, solution exists on any given branch with relative bubble velocity U satisfying the relation 2-U = cT to the 2/3 power, where c depends on the branch but is independent of the bubble area. The analytical evidence further suggests that there are no solutions for U greater than 2. These results are in agreement with earlier analytical results for a finger. In Part 2, an analytic theory is presented for the determination of the linear stability of the bubble in the limit of zero surface tension. Only the solution branch corresponding to the largest possible U for given surface tension is found to be stable, while all the others are unstable, in accordance with earlier numerical results.

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.

The impact of capillary backpressure on spontaneous counter-current imbibition in porous media

NASA Astrophysics Data System (ADS)

Foley, Amir Y.; Nooruddin, Hasan A.; Blunt, Martin J.

2017-09-01

We investigate the impact of capillary backpressure on spontaneous counter-current imbibition. For such displacements in strongly water-wet systems, the non-wetting phase is forced out through the inlet boundary as the wetting phase imbibes into the rock, creating a finite capillary backpressure. Under the assumption that capillary backpressure depends on the water saturation applied at the inlet boundary of the porous medium, its impact is determined using the continuum modelling approach by varying the imposed inlet saturation in the analytical solution. We present analytical solutions for the one-dimensional incompressible horizontal displacement of a non-wetting phase by a wetting phase in a porous medium. There exists an inlet saturation value above which any change in capillary backpressure has a negligible impact on the solutions. Above this threshold value, imbibition rates and front positions are largely invariant. A method for identifying this inlet saturation is proposed using an analytical procedure and we explore how varying multiphase flow properties affects the analytical solutions and this threshold saturation. We show the value of this analytical approach through the analysis of previously published experimental data.

Spherical indentation of a freestanding circular membrane revisited: Analytical solutions and experiments

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

Jin, Congrui; Davoodabadi, Ali; Li, Jianlin

Because of the development of novel micro-fabrication techniques to produce ultra-thin materials and increasing interest in thin biological membranes, in recent years, the mechanical characterization of thin films has received a significant amount of attention. To provide a more accurate solution for the relationship among contact radius, load and deflection, the fundamental and widely applicable problem of spherical indentation of a freestanding circular membrane have been revisited. The work presented here significantly extends the previous contributions by providing an exact analytical solution to the governing equations of Föppl–Hecky membrane indented by a frictionless spherical indenter. In this study, experiments ofmore » spherical indentation has been performed, and the exact analytical solution presented in this article is compared against experimental data from existing literature as well as our own experimental results.« less

Spherical indentation of a freestanding circular membrane revisited: Analytical solutions and experiments

DOE PAGES

Jin, Congrui; Davoodabadi, Ali; Li, Jianlin; ...

2017-01-11

Because of the development of novel micro-fabrication techniques to produce ultra-thin materials and increasing interest in thin biological membranes, in recent years, the mechanical characterization of thin films has received a significant amount of attention. To provide a more accurate solution for the relationship among contact radius, load and deflection, the fundamental and widely applicable problem of spherical indentation of a freestanding circular membrane have been revisited. The work presented here significantly extends the previous contributions by providing an exact analytical solution to the governing equations of Föppl–Hecky membrane indented by a frictionless spherical indenter. In this study, experiments ofmore » spherical indentation has been performed, and the exact analytical solution presented in this article is compared against experimental data from existing literature as well as our own experimental results.« less

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.

Sierra/SolidMechanics 4.48 Verification Tests Manual.

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

Plews, Julia A.; Crane, Nathan K; de Frias, Gabriel Jose

2018-03-01

Presented in this document is a small portion of the tests that exist in the Sierra / SolidMechanics (Sierra / SM) verification test suite. Most of these tests are run nightly with the Sierra / SM code suite, and the results of the test are checked versus the correct analytical result. For each of the tests presented in this document, the test setup, a description of the analytic solution, and comparison of the Sierra / SM code results to the analytic solution is provided. Mesh convergence is also checked on a nightly basis for several of these tests. This documentmore » can be used to confirm that a given code capability is verified or referenced as a compilation of example problems. Additional example problems are provided in the Sierra / SM Example Problems Manual. Note, many other verification tests exist in the Sierra / SM test suite, but have not yet been included in this manual.« less

Sierra/SolidMechanics 4.48 Verification Tests Manual.

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

Plews, Julia A.; Crane, Nathan K.; de Frias, Gabriel Jose

Presented in this document is a small portion of the tests that exist in the Sierra / SolidMechanics (Sierra / SM) verification test suite. Most of these tests are run nightly with the Sierra / SM code suite, and the results of the test are checked versus the correct analytical result. For each of the tests presented in this document, the test setup, a description of the analytic solution, and comparison of the Sierra / SM code results to the analytic solution is provided. Mesh convergence is also checked on a nightly basis for several of these tests. This documentmore » can be used to confirm that a given code capability is verified or referenced as a compilation of example problems. Additional example problems are provided in the Sierra / SM Example Problems Manual. Note, many other verification tests exist in the Sierra / SM test suite, but have not yet been included in this manual.« less

Existence and numerical simulation of periodic traveling wave solutions to the Casimir equation for the Ito system

NASA Astrophysics Data System (ADS)

Abbasbandy, S.; Van Gorder, R. A.; Hajiketabi, M.; Mesrizadeh, M.

2015-10-01

We consider traveling wave solutions to the Casimir equation for the Ito system (a two-field extension of the KdV equation). These traveling waves are governed by a nonlinear initial value problem with an interesting nonlinearity (which actually amplifies in magnitude as the size of the solution becomes small). The nonlinear problem is parameterized by two initial constant values, and we demonstrate that the existence of solutions is strongly tied to these parameter values. For our interests, we are concerned with positive, bounded, periodic wave solutions. We are able to classify parameter regimes which admit such solutions in full generality, thereby obtaining a nice existence result. Using the existence result, we are then able to numerically simulate the positive, bounded, periodic solutions. We elect to employ a group preserving scheme in order to numerically study these solutions, and an outline of this approach is provided. The numerical simulations serve to illustrate the properties of these solutions predicted analytically through the existence result. Physically, these results demonstrate the existence of a type of space-periodic structure in the Casimir equation for the Ito model, which propagates as a traveling wave.

Existence Regions of Shock Wave Triple Configurations

ERIC Educational Resources Information Center

Bulat, Pavel V.; Chernyshev, Mikhail V.

2016-01-01

The aim of the research is to create the classification for shock wave triple configurations and their existence regions of various types: type 1, type 2, type 3. Analytical solutions for limit Mach numbers and passing shock intensity that define existence region of every type of triple configuration have been acquired. The ratios that conjugate…

Singular eigenstates in the even(odd) length Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Ranjan Giri, Pulak; Deguchi, Tetsuo

2015-05-01

We study the implications of the regularization for the singular solutions on the even(odd) length spin-1/2 XXX chains in some specific down-spin sectors. In particular, the analytic expressions of the Bethe eigenstates for three down-spin sector have been obtained along with their numerical forms in some fixed length chains. For an even-length chain if the singular solutions \\{{{λ }α }\\} are invariant under the sign changes of their rapidities \\{{{λ }α }\\}=\\{-{{λ }α }\\}, then the Bethe ansatz equations are reduced to a system of (M-2)/2((M-3)/2) equations in an even (odd) down-spin sector. For an odd N length chain in the three down-spin sector, it has been analytically shown that there exist singular solutions in any finite length of the spin chain of the form N=3(2k+1) with k=1,2,3,\\cdots . It is also shown that there exist no singular solutions in the four down-spin sector for some odd-length spin-1/2 XXX chains.

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.

Kinks in higher derivative scalar field theory

NASA Astrophysics Data System (ADS)

Zhong, Yuan; Guo, Rong-Zhen; Fu, Chun-E.; Liu, Yu-Xiao

2018-07-01

We study static kink configurations in a type of two-dimensional higher derivative scalar field theory whose Lagrangian contains second-order derivative terms of the field. The linear fluctuation around arbitrary static kink solutions is analyzed. We find that, the linear spectrum can be described by a supersymmetric quantum mechanics problem, and the criteria for stable static solutions can be given analytically. We also construct a superpotential formalism for finding analytical static kink solutions. Using this formalism we first reproduce some existed solutions and then offer a new solution. The properties of our solution is studied and compared with those preexisted. We also show the possibility in constructing twinlike model in the higher derivative theory, and give the consistency conditions for twinlike models corresponding to the canonical scalar field theory.

Hip-hop solutions of the 2N-body problem

NASA Astrophysics Data System (ADS)

Barrabés, Esther; Cors, Josep Maria; Pinyol, Conxita; Soler, Jaume

2006-05-01

Hip-hop solutions of the 2N-body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2N-gon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are three-dimensional choreographies, with all the bodies moving along the same closed curve in the inertial frame.

Novel asymmetric representation method for solving the higher-order Ginzburg-Landau equation

PubMed Central

Wong, Pring; Pang, Lihui; Wu, Ye; Lei, Ming; Liu, Wenjun

2016-01-01

In ultrafast optics, optical pulses are generated to be of shorter pulse duration, which has enormous significance to industrial applications and scientific research. The ultrashort pulse evolution in fiber lasers can be described by the higher-order Ginzburg-Landau (GL) equation. However, analytic soliton solutions for this equation have not been obtained by use of existing methods. In this paper, a novel method is proposed to deal with this equation. The analytic soliton solution is obtained for the first time, and is proved to be stable against amplitude perturbations. Through the split-step Fourier method, the bright soliton solution is studied numerically. The analytic results here may extend the integrable methods, and could be used to study soliton dynamics for some equations in other disciplines. It may also provide the other way to obtain two-soliton solutions for higher-order GL equations. PMID:27086841

Closed-form analytical solutions incorporating pumping and tidal effects in various coastal aquifer systems

NASA Astrophysics Data System (ADS)

Wang, Chaoyue; Li, Hailong; Wan, Li; Wang, Xusheng; Jiang, Xiaowei

2014-07-01

Pumping wells are common in coastal aquifers affected by tides. Here we present analytical solutions of groundwater table or head variations during a constant rate pumping from a single, fully-penetrating well in coastal aquifer systems comprising an unconfined aquifer, a confined aquifer and semi-permeable layer between them. The unconfined aquifer terminates at the coastline (or river bank) and the other two layers extend under tidal water (sea or tidal river) for a certain distance L. Analytical solutions are derived for 11 reasonable combinations of different situations of the L-value (zero, finite, and infinite), of the middle layer's permeability (semi-permeable and impermeable), of the boundary condition at the aquifer's submarine terminal (Dirichlet describing direct connection with seawater and no-flow describing the existence of an impermeable capping), and of the tidal water body (sea and tidal river). Solutions are discussed with application examples in fitting field observations and parameter estimations.

Semianalytical solutions for transport in aquifer and fractured clay matrix system

NASA Astrophysics Data System (ADS)

Huang, Junqi; Goltz, Mark N.

2015-09-01

A three-dimensional mathematical model that describes transport of contaminant in a horizontal aquifer with simultaneous diffusion into a fractured clay formation is proposed. A group of semianalytical solutions is derived based on specific initial and boundary conditions as well as various source functions. The analytical model solutions are evaluated by numerical Laplace inverse transformation and analytical Fourier inverse transformation. The model solutions can be used to study the fate and transport in a three-dimensional spatial domain in which a nonaqueous phase liquid exists as a pool atop a fractured low-permeability clay layer. The nonaqueous phase liquid gradually dissolves into the groundwater flowing past the pool, while simultaneously diffusing into the fractured clay formation below the aquifer. Mass transfer of the contaminant into the clay formation is demonstrated to be significantly enhanced by the existence of the fractures, even though the volume of fractures is relatively small compared to the volume of the clay matrix. The model solution is a useful tool in assessing contaminant attenuation processes in a confined aquifer underlain by a fractured clay formation.

Existence of a coupled system of fractional differential equations

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

Ibrahim, Rabha W.; Siri, Zailan

2015-10-22

We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.

Automatic differentiation for Fourier series and the radii polynomial approach

NASA Astrophysics Data System (ADS)

Lessard, Jean-Philippe; Mireles James, J. D.; Ransford, Julian

2016-11-01

In this work we develop a computer-assisted technique for proving existence of periodic solutions of nonlinear differential equations with non-polynomial nonlinearities. We exploit ideas from the theory of automatic differentiation in order to formulate an augmented polynomial system. We compute a numerical Fourier expansion of the periodic orbit for the augmented system, and prove the existence of a true solution nearby using an a-posteriori validation scheme (the radii polynomial approach). The problems considered here are given in terms of locally analytic vector fields (i.e. the field is analytic in a neighborhood of the periodic orbit) hence the computer-assisted proofs are formulated in a Banach space of sequences satisfying a geometric decay condition. In order to illustrate the use and utility of these ideas we implement a number of computer-assisted existence proofs for periodic orbits of the Planar Circular Restricted Three-Body Problem (PCRTBP).

Analytical Methods of Decoupling the Automotive Engine Torque Roll Axis

NASA Astrophysics Data System (ADS)

JEONG, TAESEOK; SINGH, RAJENDRA

2000-06-01

This paper analytically examines the multi-dimensional mounting schemes of an automotive engine-gearbox system when excited by oscillating torques. In particular, the issue of torque roll axis decoupling is analyzed in significant detail since it is poorly understood. New dynamic decoupling axioms are presented an d compared with the conventional elastic axis mounting and focalization methods. A linear time-invariant system assumption is made in addition to a proportionally damped system. Only rigid-body modes of the powertrain are considered and the chassis elements are assumed to be rigid. Several simplified physical systems are considered and new closed-form solutions for symmetric and asymmetric engine-mounting systems are developed. These clearly explain the design concepts for the 4-point mounting scheme. Our analytical solutions match with the existing design formulations that are only applicable to symmetric geometries. Spectra for all six rigid-body motions are predicted using the alternate decoupling methods and the closed-form solutions are verified. Also, our method is validated by comparing modal solutions with prior experimental and analytical studies. Parametric design studies are carried out to illustrate the methodology. Chief contributions of this research include the development of new or refined analytical models and closed-form solutions along with improved design strategies for the torque roll axis decoupling.

Locations of stationary/periodic solutions in mean motion resonances according to the properties of dust grains

NASA Astrophysics Data System (ADS)

Pástor, P.

2016-07-01

The equations of secular evolution for dust grains in mean motion resonances with a planet are solved for stationary points. Non-gravitational effects caused by stellar radiation (the Poynting-Robertson effect and the stellar wind) are taken into account. The solutions are stationary in the semimajor axis, eccentricity and resonant angle, but allow the pericentre to advance. The semimajor axis of stationary solutions can be slightly shifted from the exact resonant value. The periodicity of the stationary solutions in a reference frame orbiting with the planet is proved analytically. The existence of periodic solutions in mean motion resonances means that analytical theory enables infinitely long capture times for dust particles. The stationary solutions are periodic motions to which the eccentricity asymptotically approaches and around which the libration occurs. Initial conditions corresponding to the stationary solutions are successfully found by numerically integrating the equation of motion. Numerically and analytically determined shifts of the semimajor axis from the exact resonance for the stationary solutions are in excellent agreement. The stationary solutions can be plotted by the locations of pericentres in the reference frame orbiting with the planet. The pericentres are distributed in space according to the properties of the dust particles.

A nonequilibrium model for reactive contaminant transport through fractured porous media: Model development and semianalytical solution

NASA Astrophysics Data System (ADS)

Joshi, Nitin; Ojha, C. S. P.; Sharma, P. K.

2012-10-01

In this study a conceptual model that accounts for the effects of nonequilibrium contaminant transport in a fractured porous media is developed. Present model accounts for both physical and sorption nonequilibrium. Analytical solution was developed using the Laplace transform technique, which was then numerically inverted to obtain solute concentration in the fracture matrix system. The semianalytical solution developed here can incorporate both semi-infinite and finite fracture matrix extent. In addition, the model can account for flexible boundary conditions and nonzero initial condition in the fracture matrix system. The present semianalytical solution was validated against the existing analytical solutions for the fracture matrix system. In order to differentiate between various sorption/transport mechanism different cases of sorption and mass transfer were analyzed by comparing the breakthrough curves and temporal moments. It was found that significant differences in the signature of sorption and mass transfer exists. Applicability of the developed model was evaluated by simulating the published experimental data of Calcium and Strontium transport in a single fracture. The present model simulated the experimental data reasonably well in comparison to the model based on equilibrium sorption assumption in fracture matrix system, and multi rate mass transfer model.

Singular perturbation of smoothly evolving Hele-Shaw solutions

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

Siegel, M.; Tanveer, S.

1996-01-01

We present analytical scaling results, confirmed by accurate numerics, to show that there exists a class of smoothly evolving zero surface tension solutions to the Hele-Shaw problem that are significantly perturbed by an arbitrarily small amount of surface tension in order one time. {copyright} {ital 1996 The American Physical Society.}

Polynomial solutions of the Monge-Ampère equation

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

Aminov, Yu A

2014-11-30

The question of the existence of polynomial solutions to the Monge-Ampère equation z{sub xx}z{sub yy}−z{sub xy}{sup 2}=f(x,y) is considered in the case when f(x,y) is a polynomial. It is proved that if f is a polynomial of the second degree, which is positive for all values of its arguments and has a positive squared part, then no polynomial solution exists. On the other hand, a solution which is not polynomial but is analytic in the whole of the x, y-plane is produced. Necessary and sufficient conditions for the existence of polynomial solutions of degree up to 4 are found and methods for the construction ofmore » such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.« less

An efficient closed-form solution for acoustic emission source location in three-dimensional structures

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

Li, Xibing; Dong, Longjun, E-mail: csudlj@163.com; Australian Centre for Geomechanics, The University of Western Australia, Crawley, 6009

This paper presents an efficient closed-form solution (ECS) for acoustic emission(AE) source location in three-dimensional structures using time difference of arrival (TDOA) measurements from N receivers, N ≥ 6. The nonlinear location equations of TDOA are simplified to linear equations. The unique analytical solution of AE sources for unknown velocity system is obtained by solving the linear equations. The proposed ECS method successfully solved the problems of location errors resulting from measured deviations of velocity as well as the existence and multiplicity of solutions induced by calculations of square roots in existed close-form methods.

Solar flare particle propagation: Comparision of a new analytic solution with spacecraft measurements. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lupton, J. E.

1972-01-01

An analytic solution was obtained to the complete Fokker-Planck equation for solar flare particle propagation including the effects of convection, energy-change, corotation, and diffusion. It is assumed that the particles are injected impulsively at a single point in space, and that a boundary exists beyond which the particles are free to escape. Several solar flare particle events were observed with solar and galactic cosmic ray experiment aboard OGO 6. Detailed comparisons of the predictions of the solution with observations of 1 to 70 MeV protons show that the model adequately describes both the rise and decay times. The solution also yields a time evolution for the vector anisotropy which agrees well with reported observations.

Dispersion relations for 1D high-gain FELs

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

Webb, S.D.; Litvinenko, V.N.

2010-08-23

We present analytical results for the one-dimensional dispersion relation for high-gain FELs. Using kappa-n distributions, we obtain analytical relations between the dispersion relations for various order kappa distributions. Since an exact solution exists for the kappa-1 (Lorentzian) distribution, this provides some insight into the number of modes on the way to the Gaussian distribution.

On the motion of viscous fluids in the presence of diffusion

NASA Astrophysics Data System (ADS)

Secchi, Paolo

1988-01-01

The flow of a viscous incompressible two-component fluid with Fick's-law diffusion is investigated analytically. The existence of a unique global solution for small values of the diffusion coefficient (lambda) is proved for two-dimensional flow. The two- and three-dimensional solutions are also shown to converge toward the solutions of the Navier-Stokes equations for inhomogeneous fluids as lambda approaches zero.

An analytic, approximate method for modeling steady, three-dimensional flow to partially penetrating wells

NASA Astrophysics Data System (ADS)

Bakker, Mark

2001-05-01

An analytic, approximate solution is derived for the modeling of three-dimensional flow to partially penetrating wells. The solution is written in terms of a correction on the solution for a fully penetrating well and is obtained by dividing the aquifer up, locally, in a number of aquifer layers. The resulting system of differential equations is solved by application of the theory for multiaquifer flow. The presented approach has three major benefits. First, the solution may be applied to any groundwater model that can simulate flow to a fully penetrating well; the solution may be superimposed onto the solution for the fully penetrating well to simulate the local three-dimensional drawdown and flow field. Second, the approach is applicable to isotropic, anisotropic, and stratified aquifers and to both confined and unconfined flow. Third, the solution extends over a small area around the well only; outside this area the three-dimensional effect of the partially penetrating well is negligible, and no correction to the fully penetrating well is needed. A number of comparisons are made to existing three-dimensional, analytic solutions, including radial confined and unconfined flow and a well in a uniform flow field. It is shown that a subdivision in three layers is accurate for many practical cases; very accurate solutions are obtained with more layers.

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

Analysis of user equilibrium for staggered shifts in a single-entry traffic corridor with no late arrivals

NASA Astrophysics Data System (ADS)

Li, Chuan-Yao; Huang, Hai-Jun; Tang, Tie-Qiao

2017-05-01

In this paper, we investigate the effects of staggered shifts on the user equilibrium (UE) state in a single-entry traffic corridor with no late arrivals from the analytical and numerical perspective. The LWR (Lighthill-Whitham-Richards) model and the Greenshields' velocity-density function are used to describe the dynamic properties of traffic flow. Propositions for the properties of flow patterns in UE, and the quasi-analytic solutions for three possible situations in UE are deduced. Numerical tests are carried out to testify the analytical results, where the three-dimensional evolution diagram of traffic flow illustrates that shock and rarefaction wave exist in UE and the space-time diagram indicates that UE solutions satisfy the propagation properties of traffic flow. In addition, the cost curves show that the UE solutions satisfy the UE trip-timing condition.

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.

The dynamics of a delayed predator-prey model with state dependent feedback control

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

Singh, Anuraj; Gakkhar, Sunita

2011-11-30

A delayed prey-predator model with state-dependent impulses is investigated. The sufficient conditions of existence and stability of semi-trivial solution and positive period-1 solution are obtained by using the Poincare map and analogue of the Poincare Criterion. The qualitative analysis shows that the positive period-one solution bifurcates from the semi-trivial solution through a fold bifurcation. The complex dynamics including chaos is obtained and numerical simulations substantiate the analytical results.

Modulational Instability and Quantum Discrete Breather States of Cold Bosonic Atoms in a Zig-Zag Optical Lattice

NASA Astrophysics Data System (ADS)

Chang, Xia; Xie, Jiayu; Wu, Tianle; Tang, Bing

2018-07-01

A theoretical study on modulational instability and quantum discrete breather states in a system of cold bosonic atoms in zig-zag optical lattices is presented in this work. The time-dependent Hartree approximation is employed to deal with the multiple body problem. By means of a linear stability analysis, we analytically study the modulational instability, and estimate existence conditions of the bright stationary localized solutions for different values of the second-neighbor hopping constant. On the other hand, we get analytical bright stationary localized solutions, and analyze the influence of the second-neighbor hopping on their existence conditions. The predictions of the modulational instability analysis are shown to be reliable. Using these stationary localized single-boson wave functions, the quantum breather states corresponding to the system with different types of nonlinearities are constructed.

Solubility Limits of Dibutyl Phosphoric Acid in Uranium Solutions at SRS

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

Thompson, M.C.; Pierce, R.A.; Ray, R.J.

1998-06-01

The Savannah River Site has enriched uranium (EU) solution which has been stored for almost 10 years since being purified in the second uranium cycle of the H area solvent extraction process. The concentrations in solution are {tilde 6} g/L U and about 0.1 M nitric acid. Residual tributylphosphate in the solutions has slowly hydrolyzed to form dibutyl phosphoric acid (HDBP) at concentrations averaging 50 mg/L. Uranium is known to form compounds with DBP which have limited solubility. The potential to form uranium-DBP solids raises a nuclear criticality safety issue. SRTC tests have shown that U-DBP solids will precipitate atmore » concentrations potentially attainable during storage of enriched uranium solutions. Evaporation of the existing EUS solution without additional acidification could result in the precipitation of U-DBP solids if DBP concentration in the resulting solution exceeds 110 ppm at ambient temperature. The same potential exists for evaporation of unwashed 1CU solutions. The most important variables of interest for present plant operations are HNO{sub 3} and DBP concentrations. Temperature is also an important variable controlling precipitation. The data obtained in these tests can be used to set operating and safety limits for the plant. It is recommended that the data for 0 degrees C with 0.5 M HNO{sub 3} be used for setting the limits. The limit would be 80 mg/L which is 3 standard deviations below the average of 86 observed in the tests. The data shows that super-saturation can occur when the DBP concentration is as much as 50 percent above the solubility limit. However, super-saturation cannot be relied on for maintaining nuclear criticality safety. The analytical method for determining DBP concentration in U solutions was improved so that analyses for a solution are accurate to within 10 percent. However, the overall uncertainty of results for periodic samples of the existing EUS solutions was only reduced slightly. Thus, sampling appears to be the largest portion of the uncertainty for EUS sample results, although the number of samples analyzed here is low which could contribution to higher uncertainty. The analytical method can be transferred to the plant analytical labs for more routine analysis of samples.« less

Analytical formulation of selected activities of the remote manipulator system

NASA Technical Reports Server (NTRS)

Zimmerman, K. J.

1977-01-01

Existing analysis of Orbiter-RMS-Payload kinematics were surveyed, including equations dealing with the two body kinematics in the presence of a massless RMS and compares analytical explicit solutions with numerical solutions. For the following operational phases of the RMS numerical demonstration, problems are provided: (1) payload capture; (2) payload stowage and removal from cargo bay; and (3) payload deployment. The equation of motion provided accounted for RMS control forces and torque moments and could be extended to RMS flexibility and control loop simulation without increasing the degrees of freedom of the two body system.

Review of Thawing Time Prediction Models Depending
on Process Conditions and Product Characteristics

PubMed Central

Kluza, Franciszek; Spiess, Walter E. L.; Kozłowicz, Katarzyna

2016-01-01

Summary Determining thawing times of frozen foods is a challenging problem as the thermophysical properties of the product change during thawing. A number of calculation models and solutions have been developed. The proposed solutions range from relatively simple analytical equations based on a number of assumptions to a group of empirical approaches that sometimes require complex calculations. In this paper analytical, empirical and graphical models are presented and critically reviewed. The conditions of solution, limitations and possible applications of the models are discussed. The graphical and semi--graphical models are derived from numerical methods. Using the numerical methods is not always possible as running calculations takes time, whereas the specialized software and equipment are not always cheap. For these reasons, the application of analytical-empirical models is more useful for engineering. It is demonstrated that there is no simple, accurate and feasible analytical method for thawing time prediction. Consequently, simplified methods are needed for thawing time estimation of agricultural and food products. The review reveals the need for further improvement of the existing solutions or development of new ones that will enable accurate determination of thawing time within a wide range of practical conditions of heat transfer during processing. PMID:27904387

Novel approach for dam break flow modeling using computational intelligence

NASA Astrophysics Data System (ADS)

Seyedashraf, Omid; Mehrabi, Mohammad; Akhtari, Ali Akbar

2018-04-01

A new methodology based on the computational intelligence (CI) system is proposed and tested for modeling the classic 1D dam-break flow problem. The reason to seek for a new solution lies in the shortcomings of the existing analytical and numerical models. This includes the difficulty of using the exact solutions and the unwanted fluctuations, which arise in the numerical results. In this research, the application of the radial-basis-function (RBF) and multi-layer-perceptron (MLP) systems is detailed for the solution of twenty-nine dam-break scenarios. The models are developed using seven variables, i.e. the length of the channel, the depths of the up-and downstream sections, time, and distance as the inputs. Moreover, the depths and velocities of each computational node in the flow domain are considered as the model outputs. The models are validated against the analytical, and Lax-Wendroff and MacCormack FDM schemes. The findings indicate that the employed CI models are able to replicate the overall shape of the shock- and rarefaction-waves. Furthermore, the MLP system outperforms RBF and the tested numerical schemes. A new monolithic equation is proposed based on the best fitting model, which can be used as an efficient alternative to the existing piecewise analytic equations.

The PAC-MAN model: Benchmark case for linear acoustics in computational physics

NASA Astrophysics Data System (ADS)

Ziegelwanger, Harald; Reiter, Paul

2017-10-01

Benchmark cases in the field of computational physics, on the one hand, have to contain a certain complexity to test numerical edge cases and, on the other hand, require the existence of an analytical solution, because an analytical solution allows the exact quantification of the accuracy of a numerical simulation method. This dilemma causes a need for analytical sound field formulations of complex acoustic problems. A well known example for such a benchmark case for harmonic linear acoustics is the ;Cat's Eye model;, which describes the three-dimensional sound field radiated from a sphere with a missing octant analytically. In this paper, a benchmark case for two-dimensional (2D) harmonic linear acoustic problems, viz., the ;PAC-MAN model;, is proposed. The PAC-MAN model describes the radiated and scattered sound field around an infinitely long cylinder with a cut out sector of variable angular width. While the analytical calculation of the 2D sound field allows different angular cut-out widths and arbitrarily positioned line sources, the computational cost associated with the solution of this problem is similar to a 1D problem because of a modal formulation of the sound field in the PAC-MAN model.

Well-posedness and continuity properties of the Fornberg-Whitham equation in Besov spaces

NASA Astrophysics Data System (ADS)

Holmes, John; Thompson, Ryan C.

2017-10-01

In this paper, we prove well-posedness of the Fornberg-Whitham equation in Besov spaces B2,rs in both the periodic and non-periodic cases. This will imply the existence and uniqueness of solutions in the aforementioned spaces along with the continuity of the data-to-solution map provided that the initial data belongs to B2,rs. We also establish sharpness of continuity on the data-to-solution map by showing that it is not uniformly continuous from any bounded subset of B2,rs to C ([ - T , T ] ;B2,rs). Furthermore, we prove a Cauchy-Kowalevski type theorem for this equation that establishes the existence and uniqueness of real analytic solutions and also provide blow-up criterion for solutions.

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

Pal, Ritu, E-mail: maan.ritupal@gmail.com; Kumar, C. N.; Loomba, Shally

We present the exact analytical solutions of cubic-quintic nonlinear Schrödinger equation with localized gain. We have demonstrated that the bright and dark solitons exist for the repulsive cubic and attractive quintic nonlinearity. These solutions have been obtained for those values of parameters which support the formation of solitons in Yttrium iron garnet thin films. Our results may be useful to understand the nonlinear pulse excitations in thin films.

Group invariant solution for a pre-existing fracture driven by a power-law fluid in permeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2016-06-01

Group invariant analytical and numerical solutions for the evolution of a two-dimensional fracture with nonzero initial length in permeable rock and driven by an incompressible non-Newtonian fluid of power-law rheology are obtained. The effect of fluid leak-off on the evolution of the power-law fluid fracture is investigated.

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.

Analysis of modal behavior at frequency cross-over

NASA Astrophysics Data System (ADS)

Costa, Robert N., Jr.

1994-11-01

The existence of the mode crossing condition is detected and analyzed in the Active Control of Space Structures Model 4 (ACOSS4). The condition is studied for its contribution to the inability of previous algorithms to successfully optimize the structure and converge to a feasible solution. A new algorithm is developed to detect and correct for mode crossings. The existence of the mode crossing condition is verified in ACOSS4 and found not to have appreciably affected the solution. The structure is then successfully optimized using new analytic methods based on modal expansion. An unrelated error in the optimization algorithm previously used is verified and corrected, thereby equipping the optimization algorithm with a second analytic method for eigenvector differentiation based on Nelson's Method. The second structure is the Control of Flexible Structures (COFS). The COFS structure is successfully reproduced and an initial eigenanalysis completed.

Comparing (semi-) analytic solutions used to model the impact of deep carbon injection on the displacement and pressurization of the resident brine

NASA Astrophysics Data System (ADS)

Bandilla, K.; Kraemer, S. R.

2009-12-01

Injection of carbon dioxide into deep saline formations is seen as one possible technology for mitigating carbon emissions from utilities. The safety of the sequestered carbon dioxide is the focus of many studies with leakage through faults or abandoned wells as some of the main failure mechanisms. The focus of this study is on the displacement of resident brine and the resulting changes in pressure due to the injection of large volumes of super-critical phase carbon dioxide into the subsurface. The movement of brine becomes important if it travels vertically and reaches an existing or potential underground source of drinking water where an increase in salt content may threaten the viability of the drinking water source. Vertical displacement of brine may occur slowly through confining layers, or more rapidly through faults and abandoned wells. This presentation compares several (semi-) analytic solutions to determine their applicability to the problem of brine pressurization and displacement. The goal is to find ranges of formation parameters (e.g., formation seal conductivity, distance to lateral boundary, … ) for which simplifying assumption are justifiable Each simplification in the conceptual model (e.g., neglecting the lateral boundary turns a bounded domain into an infinite one) leads to a simpler (semi-) analytic solution. The process involves a solution hierarchy from the most complex solution down to the basic Theis solution. A software tool-kit implementing several (semi-) analytic solutions was developed for this study to facilitate the comparison of the solutions.

Attainment of unstable β nucleation of glycine in presence of L-tyrosine and its analytical interpretation-A combined approach

NASA Astrophysics Data System (ADS)

Renuka Devi, K.; Srinivasan, K.

2015-05-01

The ability of L-tyrosine molecules to act as a template and to facilitate the nucleation of unstable β polymorph in the solution has been revealed through in-situ nucleation study. This nucleation of β occurs along with the existing α nucleation at the critical concentration of additive in the solution. The presence of L-tyrosine molecules lowers the inherent barrier that exists for β nucleation in the solution. No nucleation of γ was observed over the entire range of concentrations studied. The molecular recognition capability and stereo selective inhibitory action of the added L-tyrosine molecules towards glycine molecule have been successfully revealed in terms of habit modification observed in the nucleated polymorphs. In the case of α polymorph, L-tyrosine induces a change in the morphology along the enantiopolar -b direction while in the case of β polymorph, habit modification from needle to plate like structure is observed. With the increase in time span, solution mediated phase transformation from β to α polymorph has been observed in the solution. Analytically the nucleation parameters of α and β polymorphs were estimated based on Classical Nucleation Theory. Form of crystallization of the nucleated polymorphs of glycine was confirmed by a powder x-ray diffraction analysis.

The role of membrane-like stresses in determining the stability and sensitivity of the Antarctic ice sheets: back pressure and grounding line motion.

PubMed

Hindmarsh, Richard C A

2006-07-15

Membrane stresses act along thin bodies which are relatively well lubricated on both surfaces. They operate in ice sheets because the bottom is either sliding, or is much less viscous than the top owing to stress and heat softening of the basal ice. Ice streams flow over very well lubricated beds, and are restrained at their sides. The ideal of the perfectly slippery bed is considered in this paper, and the propagation of mechanical effects along an ice stream considered by applying spatially varying horizontal body forces. Propagation distances depend sensitively on the rheological index, and can be very large for ice-type rheologies.A new analytical solution for ice-shelf profiles and grounded tractionless stream profiles is presented, which show blow up of the profile in a finite distance upstream at locations where the flux is non-zero. This is a feature of an earlier analytical solution for a floating shelf.The length scale of decay of membrane stresses from the grounding line is investigated through scale analysis. In ice sheets, such effects decay over distances of several tens of kilometres, creating a vertical boundary layer between sheet flow and shelf flow, where membrane stresses adjust. Bounded, physically reasonable steady surface profiles only exist conditionally in this boundary layer. Where bounded steady profiles exist, adjacent profile equilibria for the whole ice sheet corresponding to different grounded areas occur (neutral equilibrium). If no solution in the boundary layer can exist, the ice-sheet profile must change.The conditions for existence can be written in terms of whether the basal rate factor (sliding or internal deformation) is too large to permit a steady solution. The critical value depends extremely sensitively on ice velocity and the back stress applied at the grounding line. High ice velocity and high stress both favour the existence of solutions and stability. Changes in these parameters can cause the steady solution existence criterion to be traversed, and the ice-sheet dynamics to change.A finite difference model which represents both neutral equilibrium and the dynamical transition is presented, and preliminary investigations into its numerical sensitivity are carried out. Evidence for the existence of a long wavelength instability is presented through the solution of a numerical eigenproblem, which will hamper predictability.

Soliton-type solutions for two models in mathematical physics

NASA Astrophysics Data System (ADS)

Al-Ghafri, K. S.

2018-04-01

In this paper, the generalised Klein-Gordon and Kadomtsov-Petviashvili Benjamin-Bona-Mahony equations with power law nonlinearity are investigated. Our study is based on reducing the form of both equations to a first-order ordinary differential equation having the travelling wave solutions. Subsequently, soliton-type solutions such as compacton and solitary pattern solutions are obtained analytically. Additionally, the peaked soliton has been derived where it exists under a specific restrictions. In addition to the soliton solutions, the mathematical method which is exploited in this work also creates a few amount of travelling wave solutions.

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).

Phases and stability of non-uniform black strings

NASA Astrophysics Data System (ADS)

Emparan, Roberto; Luna, Raimon; Martínez, Marina; Suzuki, Ryotaku; Tanabe, Kentaro

2018-05-01

We construct solutions of non-uniform black strings in dimensions from D ≈ 9 all the way up to D = ∞, and investigate their thermodynamics and dynamical stability. Our approach employs the large- D perturbative expansion beyond the leading order, including corrections up to 1 /D 4. Combining both analytical techniques and relatively simple numerical solution of ODEs, we map out the ranges of parameters in which non-uniform black strings exist in each dimension and compute their thermodynamics and quasinormal modes with accuracy. We establish with very good precision the existence of Sorkin's critical dimension and we prove that not only the thermodynamic stability, but also the dynamic stability of the solutions changes at it.

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

Saturated-unsaturated flow in a compressible leaky-unconfined aquifer

NASA Astrophysics Data System (ADS)

Mishra, Phoolendra K.; Vesselinov, Velimir V.; Kuhlman, Kristopher L.

2012-06-01

An analytical solution is developed for three-dimensional flow towards a partially penetrating large-diameter well in an unconfined aquifer bounded below by a leaky aquitard of finite or semi-infinite extent. The analytical solution is derived using Laplace and Hankel transforms, then inverted numerically. Existing solutions for flow in leaky unconfined aquifers neglect the unsaturated zone following an assumption of instantaneous drainage due to Neuman. We extend the theory of leakage in unconfined aquifers by (1) including water flow and storage in the unsaturated zone above the water table, and (2) allowing the finite-diameter pumping well to partially penetrate the aquifer. The investigation of model-predicted results shows that aquitard leakage leads to significant departure from the unconfined solution without leakage. The investigation of dimensionless time-drawdown relationships shows that the aquitard drawdown also depends on unsaturated zone properties and the pumping-well wellbore storage effects.

Radial flow towards well in leaky unconfined aquifer

NASA Astrophysics Data System (ADS)

Mishra, P. K.; Kuhlman, K. L.

2012-12-01

An analytical solution is developed for three-dimensional flow towards a partially penetrating large- diameter well in an unconfined aquifer bounded below by a leaky aquitard of finite or semi-infinite extent. The analytical solution is derived using Laplace and Hankel transforms, then inverted numerically. Existing solutions for flow in leaky unconfined aquifers neglect the unsaturated zone following an assumption of instantaneous drainage due to Neuman. We extend the theory of leakage in unconfined aquifers by (1) including water flow and storage in the unsaturated zone above the water table, and (2) allowing the finite-diameter pumping well to partially penetrate the aquifer. The investigation of model-predicted results shows that aquitard leakage leads to significant departure from the unconfined solution without leakage. The investigation of dimensionless time-drawdown relationships shows that the aquitard drawdown also depends on unsaturated zone properties and the pumping-well wellbore storage effects.

An Experimental and Analytical Study of TIP Clearance Effects in Axial Flow Compressors

DTIC Science & Technology

1991-12-01

increasingly being used for design insight into the flow field. Implementations of the Navier Stokes equations using interacting grids or similar schemes...analytical reason for the existence of a pressure minimum locus lving away from the suction corner is provided by Barclay (1982) in a solution for the...relief at the leading edge on the suction side, grid Sensitivity and similar computational concerns, the computations predict %khat the blade loading

Algorithms and analytical solutions for rapidly approximating long-term dispersion from line and area sources

NASA Astrophysics Data System (ADS)

Barrett, Steven R. H.; Britter, Rex E.

Predicting long-term mean pollutant concentrations in the vicinity of airports, roads and other industrial sources are frequently of concern in regulatory and public health contexts. Many emissions are represented geometrically as ground-level line or area sources. Well developed modelling tools such as AERMOD and ADMS are able to model dispersion from finite (i.e. non-point) sources with considerable accuracy, drawing upon an up-to-date understanding of boundary layer behaviour. Due to mathematical difficulties associated with line and area sources, computationally expensive numerical integration schemes have been developed. For example, some models decompose area sources into a large number of line sources orthogonal to the mean wind direction, for which an analytical (Gaussian) solution exists. Models also employ a time-series approach, which involves computing mean pollutant concentrations for every hour over one or more years of meteorological data. This can give rise to computer runtimes of several days for assessment of a site. While this may be acceptable for assessment of a single industrial complex, airport, etc., this level of computational cost precludes national or international policy assessments at the level of detail available with dispersion modelling. In this paper, we extend previous work [S.R.H. Barrett, R.E. Britter, 2008. Development of algorithms and approximations for rapid operational air quality modelling. Atmospheric Environment 42 (2008) 8105-8111] to line and area sources. We introduce approximations which allow for the development of new analytical solutions for long-term mean dispersion from line and area sources, based on hypergeometric functions. We describe how these solutions can be parameterized from a single point source run from an existing advanced dispersion model, thereby accounting for all processes modelled in the more costly algorithms. The parameterization method combined with the analytical solutions for long-term mean dispersion are shown to produce results several orders of magnitude more efficiently with a loss of accuracy small compared to the absolute accuracy of advanced dispersion models near sources. The method can be readily incorporated into existing dispersion models, and may allow for additional computation time to be expended on modelling dispersion processes more accurately in future, rather than on accounting for source geometry.

Non-existence of time-periodic solutions of the Dirac equation in a Reissner-Nordström black hole background

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

2000-04-01

It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a Reissner-Nordström black hole background; in particular, there are no static solutions of the Dirac equation in such a background metric. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit around the black hole.

a Bounded Finite-Difference Discretization of a Two-Dimensional Diffusion Equation with Logistic Nonlinear Reaction

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

In the present manuscript, we introduce a finite-difference scheme to approximate solutions of the two-dimensional version of Fisher's equation from population dynamics, which is a model for which the existence of traveling-wave fronts bounded within (0,1) is a well-known fact. The method presented here is a nonstandard technique which, in the linear regime, approximates the solutions of the original model with a consistency of second order in space and first order in time. The theory of M-matrices is employed here in order to elucidate conditions under which the method is able to preserve the positivity and the boundedness of solutions. In fact, our main result establishes relatively flexible conditions under which the preservation of the positivity and the boundedness of new approximations is guaranteed. Some simulations of the propagation of a traveling-wave solution confirm the analytical results derived in this work; moreover, the experiments evince a good agreement between the numerical result and the analytical solutions.

Discrete breathers in an array of self-excited oscillators: Exact solutions and stability.

PubMed

Shiroky, I B; Gendelman, O V

2016-10-01

We consider dynamics of array of coupled self-excited oscillators. The model of Franklin bell is adopted as a mechanism for the self-excitation. The model allows derivation of exact analytic solutions for discrete breathers (DBs) and exploration of their stability in the space of parameters. The DB solutions exist for all frequencies in the attenuation zone but lose stability via Neimark-Sacker bifurcation in the vicinity of the bandgap boundary. Besides the well-known DBs with exponential localization, the considered system possesses novel type of solutions-discrete breathers with main frequency in the propagation zone of the chain. In these regimes, the energy irradiation into the chain is balanced by the self-excitation. The amplitude of oscillations is maximal at the localization site and then exponentially approaches constant value at infinity. We also derive these solutions in the closed analytic form. They are stable in a narrow region of system parameters bounded by Neimark-Sacker and pitchfork bifurcations.

A Generic analytical solution for modelling pumping tests in wells intersecting fractures

NASA Astrophysics Data System (ADS)

Dewandel, Benoît; Lanini, Sandra; Lachassagne, Patrick; Maréchal, Jean-Christophe

2018-04-01

The behaviour of transient flow due to pumping in fractured rocks has been studied for at least the past 80 years. Analytical solutions were proposed for solving the issue of a well intersecting and pumping from one vertical, horizontal or inclined fracture in homogeneous aquifers, but their domain of application-even if covering various fracture geometries-was restricted to isotropic or anisotropic aquifers, whose potential boundaries had to be parallel or orthogonal to the fracture direction. The issue thus remains unsolved for many field cases. For example, a well intersecting and pumping a fracture in a multilayer or a dual-porosity aquifer, where intersected fractures are not necessarily parallel or orthogonal to aquifer boundaries, where several fractures with various orientations intersect the well, or the effect of pumping not only in fractures, but also in the aquifer through the screened interval of the well. Using a mathematical demonstration, we show that integrating the well-known Theis analytical solution (Theis, 1935) along the fracture axis is identical to the equally well-known analytical solution of Gringarten et al. (1974) for a uniform-flux fracture fully penetrating a homogeneous aquifer. This result implies that any existing line- or point-source solution can be used for implementing one or more discrete fractures that are intersected by the well. Several theoretical examples are presented and discussed: a single vertical fracture in a dual-porosity aquifer or in a multi-layer system (with a partially intersecting fracture); one and two inclined fractures in a leaky-aquifer system with pumping either only from the fracture(s), or also from the aquifer between fracture(s) in the screened interval of the well. For the cases with several pumping sources, analytical solutions of flowrate contribution from each individual source (fractures and well) are presented, and the drawdown behaviour according to the length of the pumped screened interval of the well is discussed. Other advantages of this proposed generic analytical solution are also given. The application of this solution to field data should provide additional field information on fracture geometry, as well as identifying the connectivity between the pumped fractures and other aquifers.

Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Alal Hosen, Md.; Chowdhury, M. S. H.; Yeakub Ali, Mohammad; Faris Ismail, Ahmad

2017-12-01

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.

Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin

NASA Astrophysics Data System (ADS)

Baronio, Fabio; Wabnitz, Stefan; Kodama, Yuji

2016-04-01

There is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave solutions of the (2 +1 )D nonlinear Schrödinger equation. Dark lumps represent multidimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2 +1 )D shallow water Kadomtsev-Petviashvili model, inheriting their complex interaction properties. This finding opens a novel path for the excitation and control of optical spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave phenomena.

Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin.

PubMed

Baronio, Fabio; Wabnitz, Stefan; Kodama, Yuji

2016-04-29

There is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave solutions of the (2+1)D nonlinear Schrödinger equation. Dark lumps represent multidimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2+1)D shallow water Kadomtsev-Petviashvili model, inheriting their complex interaction properties. This finding opens a novel path for the excitation and control of optical spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave phenomena.

Complete set of homogeneous isotropic analytic solutions in scalar-tensor cosmology with radiation and curvature

NASA Astrophysics Data System (ADS)

Bars, Itzhak; Chen, Shih-Hung; Steinhardt, Paul J.; Turok, Neil

2012-10-01

We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the Universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the Universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null-energy condition. There is a special subset of geodesically complete nongeneric solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine-tuning the initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained.

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.

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

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

Messaris, Gerasimos A. T., E-mail: messaris@upatras.gr; School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras; Hadjinicolaou, Maria

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient inmore » a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the arterial system and the possible malfunction of the aorta.« less

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

NASA Astrophysics Data System (ADS)

Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.

2016-08-01

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the arterial system and the possible malfunction of the aorta.

Semi-analytical solution of flow to a well in an unconfined-fractured aquifer system separated by an aquitard

NASA Astrophysics Data System (ADS)

Sedghi, Mohammad M.; Samani, Nozar; Barry, D. A.

2018-04-01

Semi-analytical solutions are presented for flow to a well in an extensive homogeneous and anisotropic unconfined-fractured aquifer system separated by an aquitard. The pumping well is of infinitesimal radius and screened in either the overlying unconfined aquifer or the underlying fractured aquifer. An existing linearization method was used to determine the watertable drainage. The solution was obtained via Laplace and Hankel transforms, with results calculated by numerical inversion. The main findings are presented in the form of non-dimensional drawdown-time curves, as well as scaled sensitivity-dimensionless time curves. The new solution permits determination of the influence of fractures, matrix blocks and watertable drainage parameters on the aquifer drawdown. The effect of the aquitard on the drawdown response of the overlying unconfined aquifer and the underlying fractured aquifer was also explored. The results permit estimation of the unconfined and fractured aquifer hydraulic parameters via type-curve matching or coupling of the solution with a parameter estimation code. The solution can also be used to determine aquifer hydraulic properties from an optimal pumping test set up and duration.

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.

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.

Laser-induced breakdown spectroscopy of bulk aqueous solutions at oceanic pressures: evaluation of key measurement parameters

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

Michel, Anna P. M.; Lawrence-Snyder, Marion; Angel, S. Michael

The development of in situ chemical sensors is critical for present-day expeditionary oceanography and the new mode of ocean observing systems that we are entering. New sensors take a significant amount of time to develop; therefore, validation of techniques in the laboratory for use in the ocean environment is necessary. Laser-induced breakdown spectroscopy (LIBS) is a promising in situ technique for oceanography. Laboratory investigations on the feasibility of using LIBS to detect analytes in bulk liquids at oceanic pressures were carried out. LIBS was successfully used to detect dissolved Na, Mn, Ca, K, and Li at pressures up to 2.76x107more » Pa. The effects of pressure, laser-pulse energy, interpulse delay, gate delay, temperature, and NaCl concentration on the LIBS signal were examined. An optimal range of laser-pulse energies was found to exist for analyte detection in bulk aqueous solutions at both low and high pressures. No pressure effect was seen on the emission intensity for Ca and Na, and an increase in emission intensity with increased pressure was seen for Mn. Using the dual-pulse technique for several analytes, a very short interpulse delay resulted in the greatest emission intensity. The presence of NaCl enhanced the emission intensity for Ca, but had no effect on peak intensity of Mn or K. Overall, increased pressure, the addition of NaCl to a solution, and temperature did not inhibit detection of analytes in solution and sometimes even enhanced the ability to detect the analytes. The results suggest that LIBS is a viable chemical sensing method for in situ analyte detection in high-pressure environments such as the deep ocean.« less

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.

A lower bound on the solutions of Kapustin-Witten equations

NASA Astrophysics Data System (ADS)

Huang, Teng

2016-11-01

In this article, we consider the Kapustin-Witten equations on a closed four-manifold. We study certain analytic properties of solutions to the equations on a closed manifold. The main result is that there exists an L2 -lower bound on the extra fields over a closed four-manifold satisfying certain conditions if the connections are not ASD connections. Furthermore, we also obtain a similar result about the Vafa-Witten equations.

Closed-form solution of the Ogden-Hill's compressible hyperelastic model for ramp loading

NASA Astrophysics Data System (ADS)

Berezvai, Szabolcs; Kossa, Attila

2017-05-01

This article deals with the visco-hyperelastic modelling approach for compressible polymer foam materials. Polymer foams can exhibit large elastic strains and displacements in case of volumetric compression. In addition, they often show significant rate-dependent properties. This material behaviour can be accurately modelled using the visco-hyperelastic approach, in which the large strain viscoelastic description is combined with the rate-independent hyperelastic material model. In case of polymer foams, the most widely used compressible hyperelastic material model, the so-called Ogden-Hill's model, was applied, which is implemented in the commercial finite element (FE) software Abaqus. The visco-hyperelastic model is defined in hereditary integral form, therefore, obtaining a closed-form solution for the stress is not a trivial task. However, the parameter-fitting procedure could be much faster and accurate if closed-form solution exists. In this contribution, exact stress solutions are derived in case of uniaxial, biaxial and volumetric compression loading cases using ramp-loading history. The analytical stress solutions are compared with the stress results in Abaqus using FE analysis. In order to highlight the benefits of the analytical closed-form solution during the parameter-fitting process experimental work has been carried out on a particular open-cell memory foam material. The results of the material identification process shows significant accuracy improvement in the fitting procedure by applying the derived analytical solutions compared to the so-called separated approach applied in the engineering practice.

Discrete breathers in an array of self-excited oscillators: Exact solutions and stability

NASA Astrophysics Data System (ADS)

Shiroky, I. B.; Gendelman, O. V.

2016-10-01

We consider dynamics of array of coupled self-excited oscillators. The model of Franklin bell is adopted as a mechanism for the self-excitation. The model allows derivation of exact analytic solutions for discrete breathers (DBs) and exploration of their stability in the space of parameters. The DB solutions exist for all frequencies in the attenuation zone but lose stability via Neimark-Sacker bifurcation in the vicinity of the bandgap boundary. Besides the well-known DBs with exponential localization, the considered system possesses novel type of solutions—discrete breathers with main frequency in the propagation zone of the chain. In these regimes, the energy irradiation into the chain is balanced by the self-excitation. The amplitude of oscillations is maximal at the localization site and then exponentially approaches constant value at infinity. We also derive these solutions in the closed analytic form. They are stable in a narrow region of system parameters bounded by Neimark-Sacker and pitchfork bifurcations.

Transient well flow in leaky multiple-aquifer systems

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1985-10-01

A previously developed eigenvalue analysis approach to groundwater flow in leaky multiple aquifers is used to derive exact solutions for transient well flow problems in leaky and confined systems comprising any number of aquifers. Equations are presented for the drawdown distribution in systems of infinite extent, caused by wells penetrating one or more of the aquifers completely and discharging each layer at a constant rate. Since the solution obtained may be regarded as a combined analytical-numerical technique, a type of one-dimensional modelling can be applied to find approximate solutions for several complicating conditions. Numerical evaluations are presented as time-drawdown curves and include effects of storage in the aquitard, unconfined conditions, partially penetrating wells and stratified aquifers. The outcome of calculations for relatively simple systems compares very well with published corresponding results. The proposed multilayer solution can be a valuable tool in aquifer test evaluation, as it provides the analytical expression required to enable the application of existing computer methods to the determination of aquifer characteristics.

Matter rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates.

PubMed

Sun, Wen-Rong; Wang, Lei

2018-01-01

To show the existence and properties of matter rogue waves in an F =1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F =1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

Matter rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Sun, Wen-Rong; Wang, Lei

2018-01-01

To show the existence and properties of matter rogue waves in an F=1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F=1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

Immuno Nanosensor for the Ultrasensitive Naked Eye Detection of Tuberculosis.

PubMed

Mohd Bakhori, Noremylia; Yusof, Nor Azah; Abdullah, Jaafar; Wasoh, Helmi; Md Noor, Siti Suraiya; Ahmad Raston, Nurul Hanun; Mohammad, Faruq

2018-06-14

In the present study, a beneficial approach for the ultrasensitive and affordable naked eye detection and diagnosis of tuberculosis (TB) by utilizing plasmonic enzyme-linked immunosorbent assay (ELISA) via antibody-antigen interaction was studied. Here, the biocatalytic cycle of the intracellular enzymes links to the formation and successive growth of the gold nanoparticles (GNPs) for ultrasensitive detection. The formation of different colored solutions by the plasmonic nanoparticles in the presence of enzyme labels links directly to the existence or non-existence of the TB analytes in the sample solutions. For disease detection, the adapted protocol is based mainly on the conventional ELISA procedure that involves catalase-labeled antibodies, i.e., the enzymes consume hydrogen peroxide and further produce GNPs with the addition of gold (III) chloride. The amount of hydrogen peroxide remaining in the solution determines whether the GNPs solution is to be formed in the color blue or the color red, as it serves as a confirmation for the naked eye detection of TB analytes. However, the conventional ELISA method only shows tonal colors that need a high concentration of analyte to achieve high confidence levels for naked eye detection. Also, in this research, we proposed the incorporation of protein biomarker, Mycobacterium tuberculosis ESAT-6-like protein esxB (CFP-10), as a means of TB detection using plasmonic ELISA. With the use of this technique, the CFP-10 detection limit can be lowered to 0.01 µg/mL by the naked eye. Further, our developed technique was successfully tested and confirmed with sputum samples from patients diagnosed with positive TB, thereby providing enough evidence for the utilization of our technique in the early diagnosis of TB disease.

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

Use of multivariable asymptotic expansions in a satellite theory

NASA Technical Reports Server (NTRS)

Dallas, S. S.

1973-01-01

Initial conditions and perturbative force of satellite are restricted to yield motion of equatorial satellite about oblate body. In this manner, exact analytic solution exists and can be used as standard of comparison in numerical accuracy comparisons. Detailed numerical accuracy studies of uniformly valid asymptotic expansions were made.

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.

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

Dall-Anese, Emiliano; Simonetto, Andrea

This paper focuses on the design of online algorithms based on prediction-correction steps to track the optimal solution of a time-varying constrained problem. Existing prediction-correction methods have been shown to work well for unconstrained convex problems and for settings where obtaining the inverse of the Hessian of the cost function can be computationally affordable. The prediction-correction algorithm proposed in this paper addresses the limitations of existing methods by tackling constrained problems and by designing a first-order prediction step that relies on the Hessian of the cost function (and do not require the computation of its inverse). Analytical results are establishedmore » to quantify the tracking error. Numerical simulations corroborate the analytical results and showcase performance and benefits of the algorithms.« 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.

Magnetization-induced dynamics of a Josephson junction coupled to a nanomagnet

NASA Astrophysics Data System (ADS)

Ghosh, Roopayan; Maiti, Moitri; Shukrinov, Yury M.; Sengupta, K.

2017-11-01

We study the superconducting current of a Josephson junction (JJ) coupled to an external nanomagnet driven by a time-dependent magnetic field both without and in the presence of an external ac drive. We provide an analytic, albeit perturbative, solution for the Landau-Lifshitz (LL) equations governing the coupled JJ-nanomagnet system in the presence of a magnetic field with arbitrary time dependence oriented along the easy axis of the nanomagnet's magnetization and in the limit of weak dimensionless coupling ɛ0 between the JJ and the nanomagnet. We show the existence of Shapiro-type steps in the I -V characteristics of the JJ subjected to a voltage bias for a constant or periodically varying magnetic field and explore the effect of rotation of the magnetic field and the presence of an external ac drive on these steps. We support our analytic results with exact numerical solution of the LL equations. We also extend our results to dissipative nanomagnets by providing a perturbative solution to the Landau-Lifshitz-Gilbert (LLG) equations for weak dissipation. We study the fate of magnetization-induced Shapiro steps in the presence of dissipation both from our analytical results and via numerical solution of the coupled LLG equations. We discuss experiments which can test our theory.

Periodic waves in fiber Bragg gratings

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

Chow, K. W.; Merhasin, Ilya M.; Malomed, Boris A.

2008-02-15

We construct two families of exact periodic solutions to the standard model of fiber Bragg grating (FBG) with Kerr nonlinearity. The solutions are named ''sn'' and ''cn'' waves, according to the elliptic functions used in their analytical representation. The sn wave exists only inside the FBG's spectral bandgap, while waves of the cn type may only exist at negative frequencies ({omega}<0), both inside and outside the bandgap. In the long-wave limit, the sn and cn families recover, respectively, the ordinary gap solitons, and (unstable) antidark and dark solitons. Stability of the periodic solutions is checked by direct numerical simulations and,more » in the case of the sn family, also through the calculation of instability growth rates for small perturbations. Although, rigorously speaking, all periodic solutions are unstable, a subfamily of practically stable sn waves, with a sufficiently large spatial period and {omega}>0, is identified. However, the sn waves with {omega}<0, as well as all cn solutions, are strongly unstable.« less

Universal consistent truncation for 6d/7d gauge/gravity duals

NASA Astrophysics Data System (ADS)

Passias, Achilleas; Rota, Andrea; Tomasiello, Alessandro

2015-10-01

Recently, AdS7 solutions of IIA supergravity have been classified; there are infinitely many of them, whose expression is known analytically, and with internal space of S 3 topology. Their field theory duals are six-dimensional (1,0) SCFT's. In this paper we show that for each of these AdS7 solutions there exists a consistent truncation from massive IIA supergravity to minimal gauged supergravity in seven dimensions. This theory has an SU(2) gauge group, and a single scalar, whose value is related to a certain distortion of the internal S 3. This explains the universality observed in recent work on AdS5 and AdS4 solutions dual to compactifications of the (1, 0) SCFT6's. Thanks to previous work on the minimal gauged supergravity, the truncation also implies the existence of holographic RG-flows connecting those solutions to the AdS7 vacuum, as well as new classes of IIA AdS3 solutions.

Localized solutions of Lugiato-Lefever equations with focused pump.

PubMed

Cardoso, Wesley B; Salasnich, Luca; Malomed, Boris A

2017-12-04

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too-in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.

Nonlinear analysis for dual-frequency concurrent energy harvesting

NASA Astrophysics Data System (ADS)

Yan, Zhimiao; Lei, Hong; Tan, Ting; Sun, Weipeng; Huang, Wenhu

2018-05-01

The dual-frequency responses of the hybrid energy harvester undergoing the base excitation and galloping were analyzed numerically. In this work, an approximate dual-frequency analytical method is proposed for the nonlinear analysis of such a system. To obtain the approximate analytical solutions of the full coupled distributed-parameter model, the forcing interactions is first neglected. Then, the electromechanical decoupled governing equation is developed using the equivalent structure method. The hybrid mechanical response is finally separated to be the self-excited and forced responses for deriving the analytical solutions, which are confirmed by the numerical simulations of the full coupled model. The forced response has great impacts on the self-excited response. The boundary of Hopf bifurcation is analytically determined by the onset wind speed to galloping, which is linearly increased by the electrical damping. Quenching phenomenon appears when the increasing base excitation suppresses the galloping. The theoretical quenching boundary depends on the forced mode velocity. The quenching region increases with the base acceleration and electrical damping, but decreases with the wind speed. Superior to the base-excitation-alone case, the existence of the aerodynamic force protects the hybrid energy harvester at resonance from damages caused by the excessive large displacement. From the view of the harvested power, the hybrid system surpasses the base-excitation-alone system or the galloping-alone system. This study advances our knowledge on intrinsic nonlinear dynamics of the dual-frequency energy harvesting system by taking advantage of the analytical solutions.

Calculation of the second term of the exact Green's function of the diffusion equation for diffusion-controlled chemical reactions

NASA Astrophysics Data System (ADS)

Plante, Ianik

2016-01-01

The exact Green's function of the diffusion equation (GFDE) is often considered to be the gold standard for the simulation of partially diffusion-controlled reactions. As the GFDE with angular dependency is quite complex, the radial GFDE is more often used. Indeed, the exact GFDE is expressed as a Legendre expansion, the coefficients of which are given in terms of an integral comprising Bessel functions. This integral does not seem to have been evaluated analytically in existing literature. While the integral can be evaluated numerically, the Bessel functions make the integral oscillate and convergence is difficult to obtain. Therefore it would be of great interest to evaluate the integral analytically. The first term was evaluated previously, and was found to be equal to the radial GFDE. In this work, the second term of this expansion was evaluated. As this work has shown that the first two terms of the Legendre polynomial expansion can be calculated analytically, it raises the question of the possibility that an analytical solution exists for the other terms.

Smart Hydrogel Particles: Biomarker Harvesting: One-step affinity purification, size exclusion, and protection against degradation

PubMed Central

Luchini, Alessandra; Geho, David H.; Bishop, Barney; Tran, Duy; Xia, Cassandra; Dufour, Robert; Jones, Clint; Espina, Virginia; Patanarut, Alexis; Zhu, Weidong; Ross, Mark; Tessitore, Alessandra; Petricoin, Emanuel; Liotta, Lance A.

2010-01-01

Disease-associated blood biomarkers exist in exceedingly low concentrations within complex mixtures of high-abundance proteins such as albumin. We have introduced an affinity bait molecule into N-isopropylacrylamide to produce a particle that will perform three independent functions within minutes, in one step, in solution: a) molecular size sieving b) affinity capture of all solution phase target molecules, and c) complete protection of harvested proteins from enzymatic degradation. The captured analytes can be readily electroeluted for analysis. PMID:18076201

Complex large-scale convection of a viscous incompressible fluid with heat exchange according to Newton's law

NASA Astrophysics Data System (ADS)

Gorshkov, A. V.; Prosviryakov, E. Yu.

2017-12-01

The paper considers the construction of analytical solutions to the Oberbeck-Boussinesq system. This system describes layered Bénard-Marangoni convective flows of an incompressible viscous fluid. The third-kind boundary condition, i. e. Newton's heat transfer law, is used on the boundaries of a fluid layer. The obtained solution is analyzed. It is demonstrated that there is a fluid layer thickness with tangential stresses vanishing simultaneously, this being equivalent to the existence of tensile and compressive stresses.

Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem.

PubMed

Altürk, Ahmet

2016-01-01

Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.

Nonlocal dark solitons under competing cubic-quintic nonlinearities.

PubMed

Chen, L; Wang, Q; Shen, M; Zhao, H; Lin, Y-Y; Jeng, C-C; Lee, R-K; Krolikowski, W

2013-01-01

We investigate properties of dark solitons under competing nonlocal cubic-local quintic nonlinearities. Analytical results, based on a variational approach and confirmed by direct numerical simulations, reveal the existence of a unique dark soliton solutions with their width being independent of the degree of nonlocality, due to the competing cubic-quintic nonlinearities.

An Analytical Solution for Yaw Maneuver Optimization on the International Space Station and Other Orbiting Space Vehicles

NASA Technical Reports Server (NTRS)

Dobrinskaya, Tatiana

2015-01-01

This paper suggests a new method for optimizing yaw maneuvers on the International Space Station (ISS). Yaw rotations are the most common large maneuvers on the ISS often used for docking and undocking operations, as well as for other activities. When maneuver optimization is used, large maneuvers, which were performed on thrusters, could be performed either using control moment gyroscopes (CMG), or with significantly reduced thruster firings. Maneuver optimization helps to save expensive propellant and reduce structural loads - an important factor for the ISS service life. In addition, optimized maneuvers reduce contamination of the critical elements of the vehicle structure, such as solar arrays. This paper presents an analytical solution for optimizing yaw attitude maneuvers. Equations describing pitch and roll motion needed to counteract the major torques during a yaw maneuver are obtained. A yaw rate profile is proposed. Also the paper describes the physical basis of the suggested optimization approach. In the obtained optimized case, the torques are significantly reduced. This torque reduction was compared to the existing optimization method which utilizes the computational solution. It was shown that the attitude profiles and the torque reduction have a good match for these two methods of optimization. The simulations using the ISS flight software showed similar propellant consumption for both methods. The analytical solution proposed in this paper has major benefits with respect to computational approach. In contrast to the current computational solution, which only can be calculated on the ground, the analytical solution does not require extensive computational resources, and can be implemented in the onboard software, thus, making the maneuver execution automatic. The automatic maneuver significantly simplifies the operations and, if necessary, allows to perform a maneuver without communication with the ground. It also reduces the probability of command errors. The suggested analytical solution provides a new method of maneuver optimization which is less complicated, automatic and more universal. A maneuver optimization approach, presented in this paper, can be used not only for the ISS, but for other orbiting space vehicles.

Disassortativity of random critical branching trees

NASA Astrophysics Data System (ADS)

Kim, J. S.; Kahng, B.; Kim, D.

2009-06-01

Random critical branching trees (CBTs) are generated by the multiplicative branching process, where the branching number is determined stochastically, independent of the degree of their ancestor. Here we show analytically that despite this stochastic independence, there exists the degree-degree correlation (DDC) in the CBT and it is disassortative. Moreover, the skeletons of fractal networks, the maximum spanning trees formed by the edge betweenness centrality, behave similarly to the CBT in the DDC. This analytic solution and observation support the argument that the fractal scaling in complex networks originates from the disassortativity in the DDC.

Elastic properties of rigid fiber-reinforced composites

NASA Astrophysics Data System (ADS)

Chen, J.; Thorpe, M. F.; Davis, L. C.

1995-05-01

We study the elastic properties of rigid fiber-reinforced composites with perfect bonding between fibers and matrix, and also with sliding boundary conditions. In the dilute region, there exists an exact analytical solution. Around the rigidity threshold we find the elastic moduli and Poisson's ratio by decomposing the deformation into a compression mode and a rotation mode. For perfect bonding, both modes are important, whereas only the compression mode is operative for sliding boundary conditions. We employ the digital-image-based method and a finite element analysis to perform computer simulations which confirm our analytical predictions.

Chameleon scalar fields in relativistic gravitational backgrounds

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

Tsujikawa, Shinji; Tamaki, Takashi; Tavakol, Reza, E-mail: shinji@rs.kagu.tus.ac.jp, E-mail: tamaki@gravity.phys.waseda.ac.jp, E-mail: r.tavakol@qmul.ac.uk

2009-05-15

We study the field profile of a scalar field {phi} that couples to a matter fluid (dubbed a chameleon field) in the relativistic gravitational background of a spherically symmetric spacetime. Employing a linear expansion in terms of the gravitational potential {Phi}{sub c} at the surface of a compact object with a constant density, we derive the thin-shell field profile both inside and outside the object, as well as the resulting effective coupling with matter, analytically. We also carry out numerical simulations for the class of inverse power-law potentials V({phi}) = M{sup 4+n}{phi}{sup -n} by employing the information provided by ourmore » analytical solutions to set the boundary conditions around the centre of the object and show that thin-shell solutions in fact exist if the gravitational potential {Phi}{sub c} is smaller than 0.3, which marginally covers the case of neutron stars. Thus the chameleon mechanism is present in the relativistic gravitational backgrounds, capable of reducing the effective coupling. Since thin-shell solutions are sensitive to the choice of boundary conditions, our analytic field profile is very helpful to provide appropriate boundary conditions for {Phi}{sub c}{approx}« less

Well test mathematical model for fractures network in tight oil reservoirs

NASA Astrophysics Data System (ADS)

Diwu, Pengxiang; Liu, Tongjing; Jiang, Baoyi; Wang, Rui; Yang, Peidie; Yang, Jiping; Wang, Zhaoming

2018-02-01

Well test, especially build-up test, has been applied widely in the development of tight oil reservoirs, since it is the only available low cost way to directly quantify flow ability and formation heterogeneity parameters. However, because of the fractures network near wellbore, generated from artificial fracturing linking up natural factures, traditional infinite and finite conductivity fracture models usually result in significantly deviation in field application. In this work, considering the random distribution of natural fractures, physical model of fractures network is proposed, and it shows a composite model feature in the large scale. Consequently, a nonhomogeneous composite mathematical model is established with threshold pressure gradient. To solve this model semi-analytically, we proposed a solution approach including Laplace transform and virtual argument Bessel function, and this method is verified by comparing with existing analytical solution. The matching data of typical type curves generated from semi-analytical solution indicates that the proposed physical and mathematical model can describe the type curves characteristic in typical tight oil reservoirs, which have up warping in late-term rather than parallel lines with slope 1/2 or 1/4. It means the composite model could be used into pressure interpretation of artificial fracturing wells in tight oil reservoir.

Role of partial miscibility on pressure buildup due to constant rate injection of CO2 into closed and open brine aquifers

NASA Astrophysics Data System (ADS)

Mathias, Simon A.; Gluyas, Jon G.; GonzáLez MartíNez de Miguel, Gerardo J.; Hosseini, Seyyed A.

2011-12-01

This work extends an existing analytical solution for pressure buildup because of CO2 injection in brine aquifers by incorporating effects associated with partial miscibility. These include evaporation of water into the CO2 rich phase and dissolution of CO2 into brine and salt precipitation. The resulting equations are closed-form, including the locations of the associated leading and trailing shock fronts. Derivation of the analytical solution involves making a number of simplifying assumptions including: vertical pressure equilibrium, negligible capillary pressure, and constant fluid properties. The analytical solution is compared to results from TOUGH2 and found to accurately approximate the extent of the dry-out zone around the well, the resulting permeability enhancement due to residual brine evaporation, the volumetric saturation of precipitated salt, and the vertically averaged pressure distribution in both space and time for the four scenarios studied. While brine evaporation is found to have a considerable effect on pressure, the effect of CO2 dissolution is found to be small. The resulting equations remain simple to evaluate in spreadsheet software and represent a significant improvement on current methods for estimating pressure-limited CO2 storage capacity.

Exact solutions for the static bending of Euler-Bernoulli beams using Eringen's two-phase local/nonlocal model

NASA Astrophysics Data System (ADS)

Wang, Y. B.; Zhu, X. W.; Dai, H. H.

2016-08-01

Though widely used in modelling nano- and micro- structures, Eringen's differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen's two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.

The effect of intra-wellbore head losses in a vertical well

NASA Astrophysics Data System (ADS)

Wang, Quanrong; Zhan, Hongbin

2017-05-01

Flow to a partially penetrating vertical well is made more complex by intra-wellbore losses. These are caused not only by the frictional effect, but also by the kinematic effect, which consists of the accelerational and fluid inflow effects inside a wellbore. Existing models of flow to a partially penetrating vertical well assume either a uniform-flux boundary condition (UFBC) or a uniform-head boundary condition (UHBC) for treating the flow into the wellbore. Neither approach considers intra-wellbore losses. In this study a new general solution, named the mixed-type boundary condition (MTBC) solution, is introduced to include intra-wellbore losses. It is developed from the existing solutions using a hybrid analytical-numerical method. The MTBC solution is capable of modeling various types of aquifer tests (constant-head tests, constant-rate tests, and slug tests) for partially or fully penetrating vertical wells in confined aquifers. Results show that intra-wellbore losses (both frictional and kinematic) can be significant in the early pumping stage. At later pumping times the UHBC solution is adequate because the difference between the MTBC and UHBC solutions becomes negligible.

Semianalytical solutions for contaminant transport under variable velocity field in a coastal aquifer

NASA Astrophysics Data System (ADS)

Koohbor, Behshad; Fahs, Marwan; Ataie-Ashtiani, Behzad; Simmons, Craig T.; Younes, Anis

2018-05-01

Existing closed-form solutions of contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. These solutions cannot be used to investigate contaminant transport in coastal aquifers where seawater intrusion induces a variable velocity field. An adaptation of the Fourier-Galerkin method is introduced to obtain semi-analytical solutions for contaminant transport in a confined coastal aquifer in which the saltwater wedge is in equilibrium with a freshwater discharge flow. Two scenarios dealing with contaminant leakage from the aquifer top surface and contaminant migration from a source at the landward boundary are considered. Robust implementation of the Fourier-Galerkin method is developed to efficiently solve the coupled flow, salt and contaminant transport equations. Various illustrative examples are generated and the semi-analytical solutions are compared against an in-house numerical code. The Fourier series are used to evaluate relevant metrics characterizing contaminant transport such as the discharge flux to the sea, amount of contaminant persisting in the groundwater and solute flux from the source. These metrics represent quantitative data for numerical code validation and are relevant to understand the effect of seawater intrusion on contaminant transport. It is observed that, for the surface contamination scenario, seawater intrusion limits the spread of the contaminant but intensifies the contaminant discharge to the sea. For the landward contamination scenario, moderate seawater intrusion affects only the spatial distribution of the contaminant plume while extreme seawater intrusion can increase the contaminant discharge to the sea. The developed semi-analytical solution presents an efficient tool for the verification of numerical models. It provides a clear interpretation of the contaminant transport processes in coastal aquifers subject to seawater intrusion. For practical usage in further studies, the full open source semi-analytical codes are made available at the website https://lhyges.unistra.fr/FAHS-Marwan.

Effects of the horizontal component of the Earth's rotation on wave propagation on an f-plane

NASA Astrophysics Data System (ADS)

Beckmann, Aike; Diebels, Stefan

Scaling arguments are used to show that effects due to the horizontal component of the Coriolis force should be taken into account as a first correction to the traditional hydrostatic theory, before frequency dispersion due to vertical acceleration and nonlinearity are included. It is shown analytically that wave propagation of the f--plane becomes anisotropic and that amphidromic systems do not exist in their usual definition. Another important consequence is the existence of free wave solutions at subinertial frequencies.

Global existence and energy decay rates for a Kirchhoff-type wave equation with nonlinear dissipation.

PubMed

Kim, Daewook; Kim, Dojin; Hong, Keum-Shik; Jung, Il Hyo

2014-01-01

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku'' + M(|A (1/2) u|(2))Au + g(u') = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.

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.

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)].

On behavior peculiarity of electron plasma

NASA Astrophysics Data System (ADS)

Gordeeva, N. M.; Yushkanov, A. A.

2018-03-01

The analysis of the analytical solution of the problem of the behavior of electron plasma in the AC electric field is fulfilled. Debye mode describes shielding of the external electric field in the plasma. The analysis of the region of existence of Debye mode, depending on the plasma parameters has been realized. A non-trivial dependence of the region of existence of Debye mode on the degree of degeneracy of the electron gas are revealed. For the case of nearly degenerate electron gas Debye mode has several areas of existence, depending on the frequency of the electric field.

Stability of equilibrium solutions of Hamiltonian systems with n-degrees of freedom and single resonance in the critical case

NASA Astrophysics Data System (ADS)

dos Santos, Fabio; Vidal, Claudio

2018-04-01

In this paper we give new results for the stability of one equilibrium solution of an autonomous analytic Hamiltonian system in a neighborhood of the equilibrium point with n-degrees of freedom. Our Main Theorem generalizes several results existing in the literature and mainly we give information in the critical cases (i.e., the condition of stability and instability is not fulfilled). In particular, our Main Theorem provides necessary and sufficient conditions for stability of the equilibrium solutions under the existence of a single resonance. Using analogous tools used in the Main Theorem for the critical case, we study the stability or instability of degenerate equilibrium points in Hamiltonian systems with one degree of freedom. We apply our results to the stability of Hamiltonians of the type of cosmological models as in planar as in the spatial case.

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

Corridor of existence of thermodynamically consistent solution of the Ornstein-Zernike equation.

PubMed

Vorob'ev, V S; Martynov, G A

2007-07-14

We obtain the exact equation for a correction to the Ornstein-Zernike (OZ) equation based on the assumption of the uniqueness of thermodynamical functions. We show that this equation is reduced to a differential equation with one arbitrary parameter for the hard sphere model. The compressibility factor within narrow limits of this parameter variation can either coincide with one of the formulas obtained on the basis of analytical solutions of the OZ equation or assume all intermediate values lying in a corridor between these solutions. In particular, we find the value of this parameter when the thermodynamically consistent compressibility factor corresponds to the Carnahan-Stirling formula.

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.

Methods for geochemical analysis

USGS Publications Warehouse

Baedecker, Philip A.

1987-01-01

The laboratories for analytical chemistry within the Geologic Division of the U.S. Geological Survey are administered by the Office of Mineral Resources. The laboratory analysts provide analytical support to those programs of the Geologic Division that require chemical information and conduct basic research in analytical and geochemical areas vital to the furtherance of Division program goals. Laboratories for research and geochemical analysis are maintained at the three major centers in Reston, Virginia, Denver, Colorado, and Menlo Park, California. The Division has an expertise in a broad spectrum of analytical techniques, and the analytical research is designed to advance the state of the art of existing techniques and to develop new methods of analysis in response to special problems in geochemical analysis. The geochemical research and analytical results are applied to the solution of fundamental geochemical problems relating to the origin of mineral deposits and fossil fuels, as well as to studies relating to the distribution of elements in varied geologic systems, the mechanisms by which they are transported, and their impact on the environment.

The mean and variance of phylogenetic diversity under rarefaction

PubMed Central

Matsen, Frederick A.

2013-01-01

Summary Phylogenetic diversity (PD) depends on sampling depth, which complicates the comparison of PD between samples of different depth. One approach to dealing with differing sample depth for a given diversity statistic is to rarefy, which means to take a random subset of a given size of the original sample. Exact analytical formulae for the mean and variance of species richness under rarefaction have existed for some time but no such solution exists for PD.We have derived exact formulae for the mean and variance of PD under rarefaction. We confirm that these formulae are correct by comparing exact solution mean and variance to that calculated by repeated random (Monte Carlo) subsampling of a dataset of stem counts of woody shrubs of Toohey Forest, Queensland, Australia. We also demonstrate the application of the method using two examples: identifying hotspots of mammalian diversity in Australasian ecoregions, and characterising the human vaginal microbiome.There is a very high degree of correspondence between the analytical and random subsampling methods for calculating mean and variance of PD under rarefaction, although the Monte Carlo method requires a large number of random draws to converge on the exact solution for the variance.Rarefaction of mammalian PD of ecoregions in Australasia to a common standard of 25 species reveals very different rank orderings of ecoregions, indicating quite different hotspots of diversity than those obtained for unrarefied PD. The application of these methods to the vaginal microbiome shows that a classical score used to quantify bacterial vaginosis is correlated with the shape of the rarefaction curve.The analytical formulae for the mean and variance of PD under rarefaction are both exact and more efficient than repeated subsampling. Rarefaction of PD allows for many applications where comparisons of samples of different depth is required. PMID:23833701

The mean and variance of phylogenetic diversity under rarefaction.

PubMed

Nipperess, David A; Matsen, Frederick A

2013-06-01

Phylogenetic diversity (PD) depends on sampling depth, which complicates the comparison of PD between samples of different depth. One approach to dealing with differing sample depth for a given diversity statistic is to rarefy, which means to take a random subset of a given size of the original sample. Exact analytical formulae for the mean and variance of species richness under rarefaction have existed for some time but no such solution exists for PD.We have derived exact formulae for the mean and variance of PD under rarefaction. We confirm that these formulae are correct by comparing exact solution mean and variance to that calculated by repeated random (Monte Carlo) subsampling of a dataset of stem counts of woody shrubs of Toohey Forest, Queensland, Australia. We also demonstrate the application of the method using two examples: identifying hotspots of mammalian diversity in Australasian ecoregions, and characterising the human vaginal microbiome.There is a very high degree of correspondence between the analytical and random subsampling methods for calculating mean and variance of PD under rarefaction, although the Monte Carlo method requires a large number of random draws to converge on the exact solution for the variance.Rarefaction of mammalian PD of ecoregions in Australasia to a common standard of 25 species reveals very different rank orderings of ecoregions, indicating quite different hotspots of diversity than those obtained for unrarefied PD. The application of these methods to the vaginal microbiome shows that a classical score used to quantify bacterial vaginosis is correlated with the shape of the rarefaction curve.The analytical formulae for the mean and variance of PD under rarefaction are both exact and more efficient than repeated subsampling. Rarefaction of PD allows for many applications where comparisons of samples of different depth is required.

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.

An abstract approach to evaporation models in rarefied gas dynamics

NASA Astrophysics Data System (ADS)

Greenberg, W.; van der Mee, C. V. M.

1984-03-01

Strong evaporation models involving 1D stationary problems with linear self-adjoint collision operators and solutions in abstract Hilbert spaces are investigated analytically. An efficient algorithm for locating the transition from existence to nonexistence of solutions is developed and applied to the 1D and 3D BGK model equations and the 3D BGK model in moment form, demonstrating the nonexistence of stationary evaporation states with supersonic drift velocities. Applications to similar models in electron and phonon transport, radiative transfer, and neutron transport are suggested.

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.

On similarity solutions of a boundary layer problem with an upstream moving wall

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Lakin, W. D.; Nachman, A.

1986-01-01

The problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream is examined. It was previously shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream. In particular, it was proved that a solution exists only if this parameter does not exceed a certain critical value, and numerical evidence was adduced to show that this solution is nonunique. Using Crocco formulation the present work proves this nonuniqueness. Also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter.

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.

Enhancing Information Awareness Through Directed Qualification of Semantic Relevancy Scoring Operations

DTIC Science & Technology

2014-06-01

analytics to evaluate document relevancy and order query results. 4 Background • Information environment complexity • Relevancy solutions for big data ...027 Primary Topic: Data , Information and Knowledge Alternatives: Organizational Concepts and Approaches; Experimentation, Metrics, and Analysis...instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send

An implementation of an aeroacoustic prediction model for broadband noise from a vertical axis wind turbine using a CFD informed methodology

NASA Astrophysics Data System (ADS)

Botha, J. D. M.; Shahroki, A.; Rice, H.

2017-12-01

This paper presents an enhanced method for predicting aerodynamically generated broadband noise produced by a Vertical Axis Wind Turbine (VAWT). The method improves on existing work for VAWT noise prediction and incorporates recently developed airfoil noise prediction models. Inflow-turbulence and airfoil self-noise mechanisms are both considered. Airfoil noise predictions are dependent on aerodynamic input data and time dependent Computational Fluid Dynamics (CFD) calculations are carried out to solve for the aerodynamic solution. Analytical flow methods are also benchmarked against the CFD informed noise prediction results to quantify errors in the former approach. Comparisons to experimental noise measurements for an existing turbine are encouraging. A parameter study is performed and shows the sensitivity of overall noise levels to changes in inflow velocity and inflow turbulence. Noise sources are characterised and the location and mechanism of the primary sources is determined, inflow-turbulence noise is seen to be the dominant source. The use of CFD calculations is seen to improve the accuracy of noise predictions when compared to the analytic flow solution as well as showing that, for inflow-turbulence noise sources, blade generated turbulence dominates the atmospheric inflow turbulence.

Determination of Mechanical Properties of Spatially Heterogeneous Breast Tissue Specimens Using Contact Mode Atomic Force Microscopy (AFM)

PubMed Central

Roy, Rajarshi; Desai, Jaydev P.

2016-01-01

This paper outlines a comprehensive parametric approach for quantifying mechanical properties of spatially heterogeneous thin biological specimens such as human breast tissue using contact-mode Atomic Force Microscopy. Using inverse finite element (FE) analysis of spherical nanoindentation, the force response from hyperelastic material models is compared with the predicted force response from existing analytical contact models, and a sensitivity study is carried out to assess uniqueness of the inverse FE solution. Furthermore, an automation strategy is proposed to analyze AFM force curves with varying levels of material nonlinearity with minimal user intervention. Implementation of our approach on an elastic map acquired from raster AFM indentation of breast tissue specimens indicates that a judicious combination of analytical and numerical techniques allow more accurate interpretation of AFM indentation data compared to relying on purely analytical contact models, while keeping the computational cost associated an inverse FE solution with reasonable limits. The results reported in this study have several implications in performing unsupervised data analysis on AFM indentation measurements on a wide variety of heterogeneous biomaterials. PMID:25015130

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

Wang, Y. B.; Zhu, X. W., E-mail: xiaowuzhu1026@znufe.edu.cn; Dai, H. H.

Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings aremore » considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.« less

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

A simple closed-form solution for assessing concentration uncertainty

NASA Astrophysics Data System (ADS)

de Barros, F. P. J.; Fiori, Aldo; Bellin, Alberto

2011-12-01

We propose closed-form approximate solutions for the moments of a nonreactive tracer that can be used in applications, such as risk analysis. This is in line with the tenet that analytical solutions provide useful information, with minimum cost, during initial site characterization efforts and can serve as a preliminary screening tool when used with prior knowledge. We show that with the help of a few assumptions, the first-order solutions of the concentration moments proposed by Fiori and Dagan (2000) can be further simplified to assume a form similar to well-known deterministic solutions, therefore facilitating their use in applications. A highly anisotropic formation is assumed, and we neglect the transverse components of the two-particle correlation trajectory. The proposed solution compares well with the work of Fiori and Dagan while presenting the same simplicity of use of existing solutions for homogeneous porous media.

New envelope solitons for Gerdjikov-Ivanov model in nonlinear fiber optics

NASA Astrophysics Data System (ADS)

Triki, Houria; Alqahtani, Rubayyi T.; Zhou, Qin; Biswas, Anjan

2017-11-01

Exact soliton solutions in a class of derivative nonlinear Schrödinger equations including a pure quintic nonlinearity are investigated. By means of the coupled amplitude-phase formulation, we derive a nonlinear differential equation describing the evolution of the wave amplitude in the non-Kerr quintic media. The resulting amplitude equation is then solved to get exact analytical chirped bright, kink, antikink, and singular soliton solutions for the model. It is also shown that the nonlinear chirp associated with these solitons is crucially dependent on the wave intensity and related to self-steepening and group velocity dispersion parameters. Parametric conditions on physical parameters for the existence of chirped solitons are also presented. These localized structures exist due to a balance among quintic nonlinearity, group velocity dispersion, and self-steepening effects.

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.

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

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.

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.

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

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...

Nonindependence and sensitivity analyses in ecological and evolutionary meta-analyses.

PubMed

Noble, Daniel W A; Lagisz, Malgorzata; O'dea, Rose E; Nakagawa, Shinichi

2017-05-01

Meta-analysis is an important tool for synthesizing research on a variety of topics in ecology and evolution, including molecular ecology, but can be susceptible to nonindependence. Nonindependence can affect two major interrelated components of a meta-analysis: (i) the calculation of effect size statistics and (ii) the estimation of overall meta-analytic estimates and their uncertainty. While some solutions to nonindependence exist at the statistical analysis stages, there is little advice on what to do when complex analyses are not possible, or when studies with nonindependent experimental designs exist in the data. Here we argue that exploring the effects of procedural decisions in a meta-analysis (e.g. inclusion of different quality data, choice of effect size) and statistical assumptions (e.g. assuming no phylogenetic covariance) using sensitivity analyses are extremely important in assessing the impact of nonindependence. Sensitivity analyses can provide greater confidence in results and highlight important limitations of empirical work (e.g. impact of study design on overall effects). Despite their importance, sensitivity analyses are seldom applied to problems of nonindependence. To encourage better practice for dealing with nonindependence in meta-analytic studies, we present accessible examples demonstrating the impact that ignoring nonindependence can have on meta-analytic estimates. We also provide pragmatic solutions for dealing with nonindependent study designs, and for analysing dependent effect sizes. Additionally, we offer reporting guidelines that will facilitate disclosure of the sources of nonindependence in meta-analyses, leading to greater transparency and more robust conclusions. © 2017 John Wiley & Sons Ltd.

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

NASA Astrophysics Data System (ADS)

Casetti, Lapo; Clementi, Cecilia; Pettini, Marco

1996-12-01

A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.

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.

Generalized analytical solutions to sequentially coupled multi-species advective-dispersive transport equations in a finite domain subject to an arbitrary time-dependent source boundary condition

NASA Astrophysics Data System (ADS)

Chen, Jui-Sheng; Liu, Chen-Wuing; Liang, Ching-Ping; Lai, Keng-Hsin

2012-08-01

SummaryMulti-species advective-dispersive transport equations sequentially coupled with first-order decay reactions are widely used to describe the transport and fate of the decay chain contaminants such as radionuclide, chlorinated solvents, and nitrogen. Although researchers attempted to present various types of methods for analytically solving this transport equation system, the currently available solutions are mostly limited to an infinite or a semi-infinite domain. A generalized analytical solution for the coupled multi-species transport problem in a finite domain associated with an arbitrary time-dependent source boundary is not available in the published literature. In this study, we first derive generalized analytical solutions for this transport problem in a finite domain involving arbitrary number of species subject to an arbitrary time-dependent source boundary. Subsequently, we adopt these derived generalized analytical solutions to obtain explicit analytical solutions for a special-case transport scenario involving an exponentially decaying Bateman type time-dependent source boundary. We test the derived special-case solutions against the previously published coupled 4-species transport solution and the corresponding numerical solution with coupled 10-species transport to conduct the solution verification. Finally, we compare the new analytical solutions derived for a finite domain against the published analytical solutions derived for a semi-infinite domain to illustrate the effect of the exit boundary condition on coupled multi-species transport with an exponential decaying source boundary. The results show noticeable discrepancies between the breakthrough curves of all the species in the immediate vicinity of the exit boundary obtained from the analytical solutions for a finite domain and a semi-infinite domain for the dispersion-dominated condition.

Parametrization of local CR automorphisms by finite jets and applications

NASA Astrophysics Data System (ADS)

Lamel, Bernhard; Mir, Nordine

2007-04-01

For any real-analytic hypersurface Msubset {C}^N , which does not contain any complex-analytic subvariety of positive dimension, we show that for every point pin M the local real-analytic CR automorphisms of M fixing p can be parametrized real-analytically by their ell_p jets at p . As a direct application, we derive a Lie group structure for the topological group operatorname{Aut}(M,p) . Furthermore, we also show that the order ell_p of the jet space in which the group operatorname{Aut}(M,p) embeds can be chosen to depend upper-semicontinuously on p . As a first consequence, it follows that given any compact real-analytic hypersurface M in {C}^N , there exists an integer k depending only on M such that for every point pin M germs at p of CR diffeomorphisms mapping M into another real-analytic hypersurface in {C}^N are uniquely determined by their k -jet at that point. Another consequence is the following boundary version of H. Cartan's uniqueness theorem: given any bounded domain Ω with smooth real-analytic boundary, there exists an integer k depending only on partial Ω such that if H\\colon Ωto Ω is a proper holomorphic mapping extending smoothly up to partial Ω near some point pin partial Ω with the same k -jet at p with that of the identity mapping, then necessarily H=Id . Our parametrization theorem also holds for the stability group of any essentially finite minimal real-analytic CR manifold of arbitrary codimension. One of the new main tools developed in the paper, which may be of independent interest, is a parametrization theorem for invertible solutions of a certain kind of singular analytic equations, which roughly speaking consists of inverting certain families of parametrized maps with singularities.

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

A Colloidal Route to Detection of Organic Molecules Based on Surface-Enhanced Raman Spectroscopy Using Nanostructured Substrate Derived from Aerosols

NASA Astrophysics Data System (ADS)

Gen, Masao; Kakuta, Hideo; Kamimoto, Yoshihito; Wuled Lenggoro, I.

2011-06-01

A detection method based on the surface-enhanced Raman spectroscopy (SERS)-active substrate derived from aerosol nanoparticles and a colloidal suspension for detecting organic molecules of a model analyte (a pesticide) is proposed. This approach can detect the molecules of the derived from its solution with the concentration levels of ppb. For substrate fabrication, a gas-phase method is used to directly deposit Ag nanoparticles on to a silicon substrate having pyramidal structures. By mixing the target analyte with a suspension of Ag colloids purchased in advance, clotianidin analyte on Ag colloid can exist in junctions of co-aggregated Ag colloids. Using (i) a nanostructured substrate made from aerosol nanoparticles and (ii) colloidal suspension can increase the number of activity spots.

Scattering of In-Plane Waves by Elastic Wedges

NASA Astrophysics Data System (ADS)

Mohammadi, K.; Asimaki, D.; Fradkin, L.

2014-12-01

The scattering of seismic waves by elastic wedges has been a topic of interest in seismology and geophysics for many decades. Analytical, semi-analytical, experimental and numerical studies on idealized wedges have provided insight into the seismic behavior of continental margins, mountain roots and crustal discontinuities. Published results, however, have almost exclusively focused on incident Rayleigh waves and out-of-plane body (SH) waves. Complementing the existing body of work, we here present results from our study on the res­ponse of elastic wedges to incident P or SV waves, an idealized pro­blem that can provide valuable insight to the understanding and parameterization of topographic ampli­fication of seismic ground mo­tion. We first show our earlier work on explicit finite difference simulations of SV-wave scattering by elastic wedges over a wide range of internal angles. We next present a semi-analytical solution that we developed using the approach proposed by Gautesen, to describe the scattered wavefield in the immediate vicinity of the wedge's tip (near-field). We use the semi-analytical solution to validate the numerical analyses, and improve resolution of the amplification factor at the wedge vertex that spikes when the internal wedge angle approaches the critical angle of incidence.

Testing density-dependent groundwater models: Two-dimensional steady state unstable convection in infinite, finite and inclined porous layers

USGS Publications Warehouse

Weatherill, D.; Simmons, C.T.; Voss, C.I.; Robinson, N.I.

2004-01-01

This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA-A model for saturated-unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4??2 and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature. ?? 2004 Elsevier Ltd. All rights reserved.

Solution of the advection-dispersion equation: Continuous load of finite duration

USGS Publications Warehouse

Runkel, R.L.

1996-01-01

Field studies of solute fate and transport in streams and rivers often involve an. experimental release of solutes at an upstream boundary for a finite period of time. A review of several standard references on surface-water-quality modeling indicates that the analytical solution to the constant-parameter advection-dispersion equation for this type of boundary condition has been generally overlooked. Here an exact analytical solution that considers a continuous load of unite duration is compared to an approximate analytical solution presented elsewhere. Results indicate that the exact analytical solution should be used for verification of numerical solutions and other solute-transport problems wherein a high level of accuracy is required. ?? ASCE.

New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics

NASA Astrophysics Data System (ADS)

Xie, Dexuan

2014-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model in the calculation of electrostatic potential energy for biomolecules in ionic solvent, but its numerical solution remains a challenge due to its strong singularity and nonlinearity caused by its singular distribution source terms and exponential nonlinear terms. To effectively deal with such a challenge, in this paper, new solution decomposition and minimization schemes are proposed, together with a new PBE analysis on solution existence and uniqueness. Moreover, a PBE finite element program package is developed in Python based on the FEniCS program library and GAMer, a molecular surface and volumetric mesh generation program package. Numerical tests on proteins and a nonlinear Born ball model with an analytical solution validate the new solution decomposition and minimization schemes, and demonstrate the effectiveness and efficiency of the new PBE finite element program package.

Particle contamination effects in EUVL: enhanced theory for the analytical determination of critical particle sizes

NASA Astrophysics Data System (ADS)

Brandstetter, Gerd; Govindjee, Sanjay

2012-03-01

Existing analytical and numerical methodologies are discussed and then extended in order to calculate critical contamination-particle sizes, which will result in deleterious effects during EUVL E-chucking in the face of an error budget on the image-placement-error (IPE). The enhanced analytical models include a gap dependant clamping pressure formulation, the consideration of a general material law for realistic particle crushing and the influence of frictional contact. We present a discussion of the defects of the classical de-coupled modeling approach where particle crushing and mask/chuck indentation are separated from the global computation of mask bending. To repair this defect we present a new analytic approach based on an exact Hankel transform method which allows a fully coupled solution. This will capture the contribution of the mask indentation to the image-placement-error (estimated IPE increase of 20%). A fully coupled finite element model is used to validate the analytical models and to further investigate the impact of a mask back-side CrN-layer. The models are applied to existing experimental data with good agreement. For a standard material combination, a given IPE tolerance of 1 nm and a 15 kPa closing pressure, we derive bounds for single particles of cylindrical shape (radius × height < 44 μm) and spherical shape (diameter < 12 μm).

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

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

Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg; Zhou, Yu

2016-07-15

Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonantmore » frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.« less

A singularity free analytical solution of artificial satellite motion with drag

NASA Technical Reports Server (NTRS)

Scheifele, G.; Mueller, A. C.; Starke, S. E.

1977-01-01

The connection between the existing Delaunay-Similar and Poincare-Similar satellite theories in the true anomaly version is outlined for the J(2) perturbation and the new drag approach. An overall description of the concept of the approach is given while the necessary expansions and the procedure to arrive at the computer program for the canonical forces is delineated. The procedure for the analytical integration of these developed equations is described. In addition, some numerical results are given. The computer program for the algebraic multiplication of the Fourier series which creates the FORTRAN coding in an automatic manner is described and documented.

A simple formula for the effective complex conductivity of periodic fibrous composites with interfacial impedance and applications to biological tissues

NASA Astrophysics Data System (ADS)

Bisegna, Paolo; Caselli, Federica

2008-06-01

This paper presents a simple analytical expression for the effective complex conductivity of a periodic hexagonal arrangement of conductive circular cylinders embedded in a conductive matrix, with interfaces exhibiting a capacitive impedance. This composite material may be regarded as an idealized model of a biological tissue comprising tubular cells, such as skeletal muscle. The asymptotic homogenization method is adopted, and the corresponding local problem is solved by resorting to Weierstrass elliptic functions. The effectiveness of the present analytical result is proved by convergence analysis and comparison with finite-element solutions and existing models.

Dispersive models describing mosquitoes’ population dynamics

NASA Astrophysics Data System (ADS)

Yamashita, W. M. S.; Takahashi, L. T.; Chapiro, G.

2016-08-01

The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.

Solution of Einsteins Equation for Deformation of a Magnetized Neutron Star

NASA Astrophysics Data System (ADS)

Rizaldy, R.; Sulaksono, A.

2018-04-01

We studied the effect of very large and non-uniform magnetic field existed in the neutron star on the deformation of the neutron star. We used in our analytical calculation, multipole expansion of the tensor metric and the momentum-energy tensor in Legendre polynomial expansion up to the quadrupole order. In this way we obtain the solutions of Einstein’s equation with the correction factors due to the magnetic field are taken into account. We obtain from our numerical calculation that the degree of deformation (ellipticity) is increased when the the mass is decreased.

Vector rogue waves and baseband modulation instability in the defocusing regime.

PubMed

Baronio, Fabio; Conforti, Matteo; Degasperis, Antonio; Lombardo, Sara; Onorato, Miguel; Wabnitz, Stefan

2014-07-18

We report and discuss analytical solutions of the vector nonlinear Schrödinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between modulational instability (MI) and rogue waves is displayed by showing that only a peculiar kind of MI, namely baseband MI, can sustain rogue-wave formation. The existence of vector rogue waves in the defocusing regime is expected to be a crucial progress in explaining extreme waves in a variety of physical scenarios described by multicomponent systems, from oceanography to optics and plasma physics.

Geodesic motion around traversable wormholes supported by a massless conformally coupled scalar field

NASA Astrophysics Data System (ADS)

Willenborg, Felix; Grunau, Saskia; Kleihaus, Burkhard; Kunz, Jutta

2018-06-01

We consider a traversable wormhole solution of Einstein's gravity conformally coupled to a massless scalar field, a solution derived by Barcelo and Visser based on the Janis-Newman-Winicour-Wyman spacetime. We study the geodesic motion of timelike and spacelike particles in this spacetime. We solve the equations of motion analytically in terms of the Weierstraß functions and discuss all possible orbit types and their parameter dependence. Interestingly, bound orbits occur for timelike geodesics only in one of the two worlds. Moreover, under no conditions there exist timelike two world bound orbits.

Parallel solution of sparse one-dimensional dynamic programming problems

NASA Technical Reports Server (NTRS)

Nicol, David M.

1989-01-01

Parallel computation offers the potential for quickly solving large computational problems. However, it is often a non-trivial task to effectively use parallel computers. Solution methods must sometimes be reformulated to exploit parallelism; the reformulations are often more complex than their slower serial counterparts. We illustrate these points by studying the parallelization of sparse one-dimensional dynamic programming problems, those which do not obviously admit substantial parallelization. We propose a new method for parallelizing such problems, develop analytic models which help us to identify problems which parallelize well, and compare the performance of our algorithm with existing algorithms on a multiprocessor.

Verification of Modelica-Based Models with Analytical Solutions for Tritium Diffusion

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

Rader, Jordan D.; Greenwood, Michael Scott; Humrickhouse, Paul W.

Here, tritium transport in metal and molten salt fluids combined with diffusion through high-temperature structural materials is an important phenomenon in both magnetic confinement fusion (MCF) and molten salt reactor (MSR) applications. For MCF, tritium is desirable to capture for fusion fuel. For MSRs, uncaptured tritium potentially can be released to the environment. In either application, quantifying the time- and space-dependent tritium concentration in the working fluid(s) and structural components is necessary.Whereas capability exists specifically for calculating tritium transport in such systems (e.g., using TMAP for fusion reactors), it is desirable to unify the calculation of tritium transport with othermore » system variables such as dynamic fluid and structure temperature combined with control systems such as those that might be found in a system code. Some capability for radioactive trace substance transport exists in thermal-hydraulic systems codes (e.g., RELAP5-3D); however, this capability is not coupled to species diffusion through solids. Combined calculations of tritium transport and thermal-hydraulic solution have been demonstrated with TRIDENT but only for a specific type of MSR.Researchers at Oak Ridge National Laboratory have developed a set of Modelica-based dynamic system modeling tools called TRANsient Simulation Framework Of Reconfigurable Models (TRANSFORM) that were used previously to model advanced fission reactors and associated systems. In this system, the augmented TRANSFORM library includes dynamically coupled fluid and solid trace substance transport and diffusion. Results from simulations are compared against analytical solutions for verification.« less

Verification of Modelica-Based Models with Analytical Solutions for Tritium Diffusion

DOE PAGES

Rader, Jordan D.; Greenwood, Michael Scott; Humrickhouse, Paul W.

2018-03-20

Here, tritium transport in metal and molten salt fluids combined with diffusion through high-temperature structural materials is an important phenomenon in both magnetic confinement fusion (MCF) and molten salt reactor (MSR) applications. For MCF, tritium is desirable to capture for fusion fuel. For MSRs, uncaptured tritium potentially can be released to the environment. In either application, quantifying the time- and space-dependent tritium concentration in the working fluid(s) and structural components is necessary.Whereas capability exists specifically for calculating tritium transport in such systems (e.g., using TMAP for fusion reactors), it is desirable to unify the calculation of tritium transport with othermore » system variables such as dynamic fluid and structure temperature combined with control systems such as those that might be found in a system code. Some capability for radioactive trace substance transport exists in thermal-hydraulic systems codes (e.g., RELAP5-3D); however, this capability is not coupled to species diffusion through solids. Combined calculations of tritium transport and thermal-hydraulic solution have been demonstrated with TRIDENT but only for a specific type of MSR.Researchers at Oak Ridge National Laboratory have developed a set of Modelica-based dynamic system modeling tools called TRANsient Simulation Framework Of Reconfigurable Models (TRANSFORM) that were used previously to model advanced fission reactors and associated systems. In this system, the augmented TRANSFORM library includes dynamically coupled fluid and solid trace substance transport and diffusion. Results from simulations are compared against analytical solutions for verification.« less

Connectivity, interoperability and manageability challenges in internet of things

NASA Astrophysics Data System (ADS)

Haseeb, Shariq; Hashim, Aisha Hassan A.; Khalifa, Othman O.; Ismail, Ahmad Faris

2017-09-01

The vision of Internet of Things (IoT) is about interconnectivity between sensors, actuators, people and processes. IoT exploits connectivity between physical objects like fridges, cars, utilities, buildings and cities for enhancing the lives of people through automation and data analytics. However, this sudden increase in connected heterogeneous IoT devices takes a huge toll on the existing Internet infrastructure and introduces new challenges for researchers to embark upon. This paper highlights the effects of heterogeneity challenges on connectivity, interoperability, management in greater details. It also surveys some of the existing solutions adopted in the core network to solve the challenges of massive IoT deployment. The paper finally concludes that IoT architecture and network infrastructure needs to be reengineered ground-up, so that IoT solutions can be safely and efficiently deployed.

Applications of the MapReduce programming framework to clinical big data analysis: current landscape and future trends

PubMed Central

2014-01-01

The emergence of massive datasets in a clinical setting presents both challenges and opportunities in data storage and analysis. This so called “big data” challenges traditional analytic tools and will increasingly require novel solutions adapted from other fields. Advances in information and communication technology present the most viable solutions to big data analysis in terms of efficiency and scalability. It is vital those big data solutions are multithreaded and that data access approaches be precisely tailored to large volumes of semi-structured/unstructured data. The MapReduce programming framework uses two tasks common in functional programming: Map and Reduce. MapReduce is a new parallel processing framework and Hadoop is its open-source implementation on a single computing node or on clusters. Compared with existing parallel processing paradigms (e.g. grid computing and graphical processing unit (GPU)), MapReduce and Hadoop have two advantages: 1) fault-tolerant storage resulting in reliable data processing by replicating the computing tasks, and cloning the data chunks on different computing nodes across the computing cluster; 2) high-throughput data processing via a batch processing framework and the Hadoop distributed file system (HDFS). Data are stored in the HDFS and made available to the slave nodes for computation. In this paper, we review the existing applications of the MapReduce programming framework and its implementation platform Hadoop in clinical big data and related medical health informatics fields. The usage of MapReduce and Hadoop on a distributed system represents a significant advance in clinical big data processing and utilization, and opens up new opportunities in the emerging era of big data analytics. The objective of this paper is to summarize the state-of-the-art efforts in clinical big data analytics and highlight what might be needed to enhance the outcomes of clinical big data analytics tools. This paper is concluded by summarizing the potential usage of the MapReduce programming framework and Hadoop platform to process huge volumes of clinical data in medical health informatics related fields. PMID:25383096

Applications of the MapReduce programming framework to clinical big data analysis: current landscape and future trends.

PubMed

Mohammed, Emad A; Far, Behrouz H; Naugler, Christopher

2014-01-01

The emergence of massive datasets in a clinical setting presents both challenges and opportunities in data storage and analysis. This so called "big data" challenges traditional analytic tools and will increasingly require novel solutions adapted from other fields. Advances in information and communication technology present the most viable solutions to big data analysis in terms of efficiency and scalability. It is vital those big data solutions are multithreaded and that data access approaches be precisely tailored to large volumes of semi-structured/unstructured data. THE MAPREDUCE PROGRAMMING FRAMEWORK USES TWO TASKS COMMON IN FUNCTIONAL PROGRAMMING: Map and Reduce. MapReduce is a new parallel processing framework and Hadoop is its open-source implementation on a single computing node or on clusters. Compared with existing parallel processing paradigms (e.g. grid computing and graphical processing unit (GPU)), MapReduce and Hadoop have two advantages: 1) fault-tolerant storage resulting in reliable data processing by replicating the computing tasks, and cloning the data chunks on different computing nodes across the computing cluster; 2) high-throughput data processing via a batch processing framework and the Hadoop distributed file system (HDFS). Data are stored in the HDFS and made available to the slave nodes for computation. In this paper, we review the existing applications of the MapReduce programming framework and its implementation platform Hadoop in clinical big data and related medical health informatics fields. The usage of MapReduce and Hadoop on a distributed system represents a significant advance in clinical big data processing and utilization, and opens up new opportunities in the emerging era of big data analytics. The objective of this paper is to summarize the state-of-the-art efforts in clinical big data analytics and highlight what might be needed to enhance the outcomes of clinical big data analytics tools. This paper is concluded by summarizing the potential usage of the MapReduce programming framework and Hadoop platform to process huge volumes of clinical data in medical health informatics related fields.

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.

Divergent expansion, Borel summability and three-dimensional Navier-Stokes equation.

PubMed

Costin, Ovidiu; Luo, Guo; Tanveer, Saleh

2008-08-13

We describe how the Borel summability of a divergent asymptotic expansion can be expanded and applied to nonlinear partial differential equations (PDEs). While Borel summation does not apply for non-analytic initial data, the present approach generates an integral equation (IE) applicable to much more general data. We apply these concepts to the three-dimensional Navier-Stokes (NS) system and show how the IE approach can give rise to local existence proofs. In this approach, the global existence problem in three-dimensional NS systems, for specific initial condition and viscosity, becomes a problem of asymptotics in the variable p (dual to 1/t or some positive power of 1/t). Furthermore, the errors in numerical computations in the associated IE can be controlled rigorously, which is very important for nonlinear PDEs such as NS when solutions are not known to exist globally.Moreover, computation of the solution of the IE over an interval [0,p0] provides sharper control of its p-->infinity behaviour. Preliminary numerical computations give encouraging results.

Prediction-Correction Algorithms for Time-Varying Constrained Optimization

DOE PAGES

Simonetto, Andrea; Dall'Anese, Emiliano

2017-07-26

This article develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do notmore » require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.« less

Extending BPM Environments of Your Choice with Performance Related Decision Support

NASA Astrophysics Data System (ADS)

Fritzsche, Mathias; Picht, Michael; Gilani, Wasif; Spence, Ivor; Brown, John; Kilpatrick, Peter

What-if Simulations have been identified as one solution for business performance related decision support. Such support is especially useful in cases where it can be automatically generated out of Business Process Management (BPM) Environments from the existing business process models and performance parameters monitored from the executed business process instances. Currently, some of the available BPM Environments offer basic-level performance prediction capabilities. However, these functionalities are normally too limited to be generally useful for performance related decision support at business process level. In this paper, an approach is presented which allows the non-intrusive integration of sophisticated tooling for what-if simulations, analytic performance prediction tools, process optimizations or a combination of such solutions into already existing BPM environments. The approach abstracts from process modelling techniques which enable automatic decision support spanning processes across numerous BPM Environments. For instance, this enables end-to-end decision support for composite processes modelled with the Business Process Modelling Notation (BPMN) on top of existing Enterprise Resource Planning (ERP) processes modelled with proprietary languages.

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

Simonetto, Andrea; Dall'Anese, Emiliano

This article develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do notmore » require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.« less

Reactive silica transport in fractured porous media: Analytical solutions for a system of parallel fractures

NASA Astrophysics Data System (ADS)

Yang, Jianwen

2012-04-01

A general analytical solution is derived by using the Laplace transformation to describe transient reactive silica transport in a conceptualized 2-D system involving a set of parallel fractures embedded in an impermeable host rock matrix, taking into account of hydrodynamic dispersion and advection of silica transport along the fractures, molecular diffusion from each fracture to the intervening rock matrix, and dissolution of quartz. A special analytical solution is also developed by ignoring the longitudinal hydrodynamic dispersion term but remaining other conditions the same. The general and special solutions are in the form of a double infinite integral and a single infinite integral, respectively, and can be evaluated using Gauss-Legendre quadrature technique. A simple criterion is developed to determine under what conditions the general analytical solution can be approximated by the special analytical solution. It is proved analytically that the general solution always lags behind the special solution, unless a dimensionless parameter is less than a critical value. Several illustrative calculations are undertaken to demonstrate the effect of fracture spacing, fracture aperture and fluid flow rate on silica transport. The analytical solutions developed here can serve as a benchmark to validate numerical models that simulate reactive mass transport in fractured porous media.

The possible equilibrium shapes of static pendant drops

NASA Astrophysics Data System (ADS)

Sumesh, P. T.; Govindarajan, Rama

2010-10-01

Analytical and numerical studies are carried out on the shapes of two-dimensional and axisymmetric pendant drops hanging under gravity from a solid surface. Drop shapes with both pinned and equilibrium contact angles are obtained naturally from a single boundary condition in the analytical energy optimization procedure. The numerical procedure also yields optimum energy shapes, satisfying Young's equation without the explicit imposition of a boundary condition at the plate. It is shown analytically that a static pendant two-dimensional drop can never be longer than 3.42 times the capillary length. A related finding is that a range of existing solutions for long two-dimensional drops correspond to unphysical drop shapes. Therefore, two-dimensional drops of small volume display only one static solution. In contrast, it is known that axisymmetric drops can display multiple solutions for a given volume. We demonstrate numerically that there is no limit to the height of multiple-lobed Kelvin drops, but the total volume is finite, with the volume of successive lobes forming a convergent series. The stability of such drops is in question, though. Drops of small volume can attain large heights. A bifurcation is found within the one-parameter space of Laplacian shapes, with a range of longer drops displaying a minimum in energy in the investigated space. Axisymmetric Kelvin drops exhibit an infinite number of bifurcations.

A two-dimensional transient analytical solution for a ponded ditch drainage system under the influence of source/sink

NASA Astrophysics Data System (ADS)

Sarmah, Ratan; Tiwari, Shubham

2018-03-01

An analytical solution is developed for predicting two-dimensional transient seepage into ditch drainage network receiving water from a non-uniform steady ponding field from the surface of the soil under the influence of source/sink in the flow domain. The flow domain is assumed to be saturated, homogeneous and anisotropic in nature and have finite extends in horizontal and vertical directions. The drains are assumed to be standing vertical and penetrating up to impervious layer. The water levels in the drains are unequal and invariant with time. The flow field is also assumed to be under the continuous influence of time-space dependent arbitrary source/sink term. The correctness of the proposed model is checked by developing a numerical code and also with the existing analytical solution for the simplified case. The study highlights the significance of source/sink influence in the subsurface flow. With the imposition of the source and sink term in the flow domain, the pathline and travel time of water particles started deviating from their original position and above that the side and top discharge to the drains were also observed to have a strong influence of the source/sink terms. The travel time and pathline of water particles are also observed to have a dependency on the height of water in the ditches and on the location of source/sink activation area.

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

NASA Astrophysics Data System (ADS)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

Coexistence of collapse and stable spatiotemporal solitons in multimode fibers

NASA Astrophysics Data System (ADS)

Shtyrina, Olga V.; Fedoruk, Mikhail P.; Kivshar, Yuri S.; Turitsyn, Sergei K.

2018-01-01

We analyze spatiotemporal solitons in multimode optical fibers and demonstrate the existence of stable solitons, in a sharp contrast to earlier predictions of collapse of multidimensional solitons in three-dimensional media. We discuss the coexistence of blow-up solutions and collapse stabilization by a low-dimensional external potential in graded-index media, and also predict the existence of stable higher-order nonlinear waves such as dipole-mode spatiotemporal solitons. To support the main conclusions of our numerical studies we employ a variational approach and derive analytically the stability criterion for input powers for the collapse stabilization.

Existence, uniqueness and regularity of a time-periodic probability density distribution arising in a sedimentation-diffusion problem

NASA Technical Reports Server (NTRS)

Nitsche, Ludwig C.; Nitsche, Johannes M.; Brenner, Howard

1988-01-01

The sedimentation and diffusion of a nonneutrally buoyant Brownian particle in vertical fluid-filled cylinder of finite length which is instantaneously inverted at regular intervals are investigated analytically. A one-dimensional convective-diffusive equation is derived to describe the temporal and spatial evolution of the probability density; a periodicity condition is formulated; the applicability of Fredholm theory is established; and the parameter-space regions are determined within which the existence and uniqueness of solutions are guaranteed. Numerical results for sample problems are presented graphically and briefly characterized.

Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics

NASA Astrophysics Data System (ADS)

Marrochio, Hugo; Noronha, Jorge; Denicol, Gabriel S.; Luzum, Matthew; Jeon, Sangyong; Gale, Charles

2015-01-01

We use symmetry arguments developed by Gubser to construct the first radially expanding explicit solutions of the Israel-Stewart formulation of hydrodynamics. Along with a general semi-analytical solution, an exact analytical solution is given which is valid in the cold plasma limit where viscous effects from shear viscosity and the relaxation time coefficient are important. The radially expanding solutions presented in this paper can be used as nontrivial checks of numerical algorithms employed in hydrodynamic simulations of the quark-gluon plasma formed in ultrarelativistic heavy ion collisions. We show this explicitly by comparing such analytic and semi-analytic solutions with the corresponding numerical solutions obtained using the music viscous hydrodynamics simulation code.

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.

Nonperturbative confinement in quantum chromodynamics. I. Study of an approximate equation of Mandelstam

NASA Astrophysics Data System (ADS)

Atkinson, D.; Drohm, J. K.; Johnson, P. W.; Stam, K.

1981-11-01

An approximated form of the Dyson-Schwinger equation for the gluon propagator in quarkless QCD is subjected to nonlinear functional and numerical analysis. It is found that solutions exist, and that these have a double pole at the origin of the square of the propagator momentum, together with an accumulation of soft branch points. This analytic structure is strongly suggestive of confinement by infrared slavery.

Solutions for the diurnally forced advection-diffusion equation to estimate bulk fluid velocity and diffusivity in streambeds from temperature time series

Treesearch

Charles H. Luce; Daniele Tonina; Frank Gariglio; Ralph Applebee

2013-01-01

Work over the last decade has documented methods for estimating fluxes between streams and streambeds from time series of temperature at two depths in the streambed. We present substantial extension to the existing theory and practice of using temperature time series to estimate streambed water fluxes and thermal properties, including (1) a new explicit analytical...

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

PubMed

Predoi, Mihai Valentin

2014-09-01

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

Higher order approximation to the Hill problem dynamics about the libration points

NASA Astrophysics Data System (ADS)

Lara, Martin; Pérez, Iván L.; López, Rosario

2018-06-01

An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture all the relevant periodic orbits originated from the libration points within a reasonable accuracy, the normalization is approached in complex variables. The validity of the solution extends to energy values considerably far away from that of the libration points and, therefore, can be used in the computation of Halo orbits as an alternative to the classical Lindstedt-Poincaré approach. Furthermore, the theory correctly predicts the existence of the two-lane bridge of periodic orbits linking the families of planar and vertical Lyapunov orbits.

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.

2009-07-01

In this paper, we restrict our attention to traveling wave solutions of a reaction-diffusion equation. Firstly we apply the Divisor Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to find a quasi-polynomial first integral of an explicit form to an equivalent autonomous system. Then through this first integral, we reduce the reaction-diffusion equation to a first-order integrable ordinary differential equation, and a class of traveling wave solutions is obtained accordingly. Comparisons with the existing results in the literature are also provided, which indicates that some analytical results in the literature contain errors. We clarify the errors and instead give a refined result in a simple and straightforward manner.

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.

Spinning BTZ black hole versus Kerr black hole: A closer look

NASA Astrophysics Data System (ADS)

Kim, Hongsu

1999-03-01

By applying Newman's algorithm, the AdS3 rotating black hole solution is ``derived'' from the nonrotating black hole solution of Bañados, Teitelboim, and Zanelli (BTZ). The rotating BTZ solution derived in this fashion is given in ``Boyer-Lindquist-type'' coordinates whereas the form of the solution originally given by BTZ is given in kind of ``unfamiliar'' coordinates which are related to each other by a transformation of time coordinate alone. The relative physical meaning between these two time coordinates is carefully studied. Since the Kerr-type and Boyer-Lindquist-type coordinates for rotating BTZ solution are newly found via Newman's algorithm, the transformation to Kerr-Schild-type coordinates is looked for. Indeed, such a transformation is found to exist. In these Kerr-Schild-type coordinates, a truly maximal extension of its global structure by analytically continuing to an ``antigravity universe'' region is carried out.

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.

Stability analysis of the Peregrine solution via squared eigenfunctions

NASA Astrophysics Data System (ADS)

Schober, C. M.; Strawn, M.

2017-10-01

A preliminary numerical investigation involving ensembles of perturbed initial data for the Peregrine soliton (the lowest order rational solution of the nonlinear Schrödinger equation) indicates that it is unstable [16]. In this paper we analytically investigate the linear stability of the Peregrine soliton, appealing to the fact that the Peregrine solution can be viewed as the singular limit of a single mode spatially periodic breathers (SPB). The "squared eigenfunction" connection between the Zakharov-Shabat (Z-S) system and the linearized NLS equation is employed in the stability analysis. Specifically, we determine the eigenfunctions of the Z-S system associated with the Peregrine soliton and construct a family of solutions of the associated linearized NLS (about the Peregrine) in terms of quadratic products of components of the eigenfunctions (i.e., the squared eigenfunction). We find there exist solutions of the linearization that grow exponentially in time, thus showing the Peregrine soliton is linearly unstable.

Hydration of nonelectrolytes in binary aqueous solutions

NASA Astrophysics Data System (ADS)

Rudakov, A. M.; Sergievskii, V. V.

2010-10-01

Literature data on the thermodynamic properties of binary aqueous solutions of nonelectrolytes that show negative deviations from Raoult's law due largely to the contribution of the hydration of the solute are briefly surveyed. Attention is focused on simulating the thermodynamic properties of solutions using equations of the cluster model. It is shown that the model is based on the assumption that there exists a distribution of stoichiometric hydrates over hydration numbers. In terms of the theory of ideal associated solutions, the equations for activity coefficients, osmotic coefficients, vapor pressure, and excess thermodynamic functions (volume, Gibbs energy, enthalpy, entropy) are obtained in analytical form. Basic parameters in the equations are the hydration numbers of the nonelectrolyte (the mathematical expectation of the distribution of hydrates) and the dispersions of the distribution. It is concluded that the model equations adequately describe the thermodynamic properties of a wide range of nonelectrolytes partly or completely soluble in water.

Analytical model for advective-dispersive transport involving flexible boundary inputs, initial distributions and zero-order productions

NASA Astrophysics Data System (ADS)

Chen, Jui-Sheng; Li, Loretta Y.; Lai, Keng-Hsin; Liang, Ching-Ping

2017-11-01

A novel solution method is presented which leads to an analytical model for the advective-dispersive transport in a semi-infinite domain involving a wide spectrum of boundary inputs, initial distributions, and zero-order productions. The novel solution method applies the Laplace transform in combination with the generalized integral transform technique (GITT) to obtain the generalized analytical solution. Based on this generalized analytical expression, we derive a comprehensive set of special-case solutions for some time-dependent boundary distributions and zero-order productions, described by the Dirac delta, constant, Heaviside, exponentially-decaying, or periodically sinusoidal functions as well as some position-dependent initial conditions and zero-order productions specified by the Dirac delta, constant, Heaviside, or exponentially-decaying functions. The developed solutions are tested against an analytical solution from the literature. The excellent agreement between the analytical solutions confirms that the new model can serve as an effective tool for investigating transport behaviors under different scenarios. Several examples of applications, are given to explore transport behaviors which are rarely noted in the literature. The results show that the concentration waves resulting from the periodically sinusoidal input are sensitive to dispersion coefficient. The implication of this new finding is that a tracer test with a periodic input may provide additional information when for identifying the dispersion coefficients. Moreover, the solution strategy presented in this study can be extended to derive analytical models for handling more complicated problems of solute transport in multi-dimensional media subjected to sequential decay chain reactions, for which analytical solutions are not currently available.

Low Mach-number collisionless electrostatic shocks and associated ion acceleration

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

Pusztai, Istvan; TenBarge, Jason; Csapó, Aletta N.

The existence and properties of low Mach-number (M >~ 1) electrostatic collisionless shocks are investigated with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations, where the shock is generated by the decay of an initial density discontinuity. By using this semi-analytical model, we also study the effect of electron-to-ion temperature ratio and presence of impurities on both the maximum shock potential and Mach number. We find that even a small amount of impurities can influence the shock propertiesmore » significantly, including the reflected light ion fraction, which can change several orders of magnitude. Electrostatic shocks in heavy ion plasmas reflect most of the hydrogen impurity ions.« less

Low Mach-number collisionless electrostatic shocks and associated ion acceleration

DOE PAGES

Pusztai, Istvan; TenBarge, Jason; Csapó, Aletta N.; ...

2017-12-19

The existence and properties of low Mach-number (M >~ 1) electrostatic collisionless shocks are investigated with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations, where the shock is generated by the decay of an initial density discontinuity. By using this semi-analytical model, we also study the effect of electron-to-ion temperature ratio and presence of impurities on both the maximum shock potential and Mach number. We find that even a small amount of impurities can influence the shock propertiesmore » significantly, including the reflected light ion fraction, which can change several orders of magnitude. Electrostatic shocks in heavy ion plasmas reflect most of the hydrogen impurity ions.« less

Development of a defect stream function, law of the wall/wake method for compressible turbulent boundary layers. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Wahls, Richard A.

1990-01-01

The method presented is designed to improve the accuracy and computational efficiency of existing numerical methods for the solution of flows with compressible turbulent boundary layers. A compressible defect stream function formulation of the governing equations assuming an arbitrary turbulence model is derived. This formulation is advantageous because it has a constrained zero-order approximation with respect to the wall shear stress and the tangential momentum equation has a first integral. Previous problems with this type of formulation near the wall are eliminated by using empirically based analytic expressions to define the flow near the wall. The van Driest law of the wall for velocity and the modified Crocco temperature-velocity relationship are used. The associated compressible law of the wake is determined and it extends the valid range of the analytical expressions beyond the logarithmic region of the boundary layer. The need for an inner-region eddy viscosity model is completely avoided. The near-wall analytic expressions are patched to numerically computed outer region solutions at a point determined during the computation. A new boundary condition on the normal derivative of the tangential velocity at the surface is presented; this condition replaces the no-slip condition and enables numerical integration to the surface with a relatively coarse grid using only an outer region turbulence model. The method was evaluated for incompressible and compressible equilibrium flows and was implemented into an existing Navier-Stokes code using the assumption of local equilibrium flow with respect to the patching. The method has proven to be accurate and efficient.

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.

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.

Analytical approaches to image orientation and stereo digitization applied in the Budnlab software. (Polish Title: Rozwiazania analityczne zwiazane z obsluga procesu orientacji zdjec oraz wykonywaniem opracowan wektorowych w programie Bundlab)

NASA Astrophysics Data System (ADS)

Kolecki, J.

2015-12-01

The Bundlab software has been developed mainly for academic and research application. This work can be treated as a kind of a report describing the current state of the development of this computer program, focusing especially on the analytical solutions. Firstly, the overall characteristics of the software are provided. Then the description of the image orientation procedure starting from the relative orientation is addressed. The applied solution is based on the coplanarity equation parametrized with the essential matrix. The problem is reformulated in order to solve it using methods of algebraic geometry. The solution is followed by the optimization involving the least square criterion. The formation of the image block from the oriented models as well as the absolute orientation procedure were implemented using the Horn approach as a base algorithm. The second part of the paper is devoted to the tools and methods applied in the stereo digitization module. The solutions that support the user and improve the accuracy are given. Within the paper a few exemplary applications and products are mentioned. The work finishes with the concepts of development and improvements of existing functions.

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

Lyra, Wladimir; Lin, Min-Kai, E-mail: wlyra@caltech.edu, E-mail: mklin924@cita.utoronto.ca

The Atacama Large Millimeter Array has returned images of transitional disks in which large asymmetries are seen in the distribution of millimeter sized dust in the outer disk. The explanation in vogue borrows from the vortex literature and suggests that these asymmetries are the result of dust trapping in giant vortices, excited via Rossby wave instabilities at planetary gap edges. Due to the drag force, dust trapped in vortices will accumulate in the center and diffusion is needed to maintain a steady state over the lifetime of the disk. While previous work derived semi-analytical models of the process, in thismore » paper we provide analytical steady-steady solutions. Exact solutions exist for certain vortex models. The solution is determined by the vortex rotation profile, the gas scale height, the vortex aspect ratio, and the ratio of dust diffusion to gas-dust friction. In principle, all of these quantities can be derived from observations, which would validate the model and also provide constrains on the strength of the turbulence inside the vortex core. Based on our solution, we derive quantities such as the gas-dust contrast, the trapped dust mass, and the dust contrast at the same orbital location. We apply our model to the recently imaged Oph IRS 48 system, finding values within the range of the observational uncertainties.« less

Protostellar Collapse with a Shock

NASA Technical Reports Server (NTRS)

Tsai, John C.; Hsu, Juliana J.

1995-01-01

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(exp -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Protostellar Collapse with a Shock

NASA Technical Reports Server (NTRS)

Tsai, John C.; Hsu, Juliana J. L.

1995-01-01

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(sup -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Stability properties of solitary waves for fractional KdV and BBM equations

NASA Astrophysics Data System (ADS)

Angulo Pava, Jaime

2018-03-01

This paper sheds new light on the stability properties of solitary wave solutions associated with Korteweg-de Vries-type models when the dispersion is very low. Using a compact, analytic approach and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so a criterium of spectral instability of solitary waves is obtained for both models. Moreover, the nonlinear stability and spectral instability of the ground state solutions for both models is obtained for some specific regimen of parameters. Via a Lyapunov strategy and a variational analysis, we obtain the stability of the blow-up of solitary waves for the critical fractional KdV equation. The arguments presented in this investigation show promise for use in the study of the instability of traveling wave solutions of other nonlinear evolution equations.

A review on the solution of Grad-Shafranov equation in the cylindrical coordinates based on the Chebyshev collocation technique

NASA Astrophysics Data System (ADS)

Amerian, Z.; Salem, M. K.; Salar Elahi, A.; Ghoranneviss, M.

2017-03-01

Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad-Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad-Shafranov equation (an axisymmetric, magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular cross-section of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.

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.

Numerical studies of the Bethe-Salpeter equation for a two-fermion bound state

NASA Astrophysics Data System (ADS)

de Paula, W.; Frederico, T.; Salmè, G.; Viviani, M.

2018-03-01

Some recent advances on the solution of the Bethe-Salpeter equation (BSE) for a two-fermion bound system directly in Minkowski space are presented. The calculations are based on the expression of the Bethe-Salpeter amplitude in terms of the so-called Nakanishi integral representation and on the light-front projection (i.e. the integration of the light-front variable k - = k 0 - k 3). The latter technique allows for the analytically exact treatment of the singularities plaguing the two-fermion BSE in Minkowski space. The good agreement observed between our results and those obtained using other existing numerical methods, based on both Minkowski and Euclidean space techniques, fully corroborate our analytical treatment.

Steady State Transportation Cooling in Porous Media Under Local, Non-Thermal Equilibrium Fluid Flow

NASA Technical Reports Server (NTRS)

Rodriquez, Alvaro Che

2002-01-01

An analytical solution to the steady-state fluid temperature for 1-D (one dimensional) transpiration cooling has been derived. Transpiration cooling has potential use in the aerospace industry for protection against high heating environments for re-entry vehicles. Literature for analytical treatments of transpiration cooling has been largely confined to the assumption of thermal equilibrium between the porous matrix and fluid. In the present analysis, the fundamental fluid and matrix equations are coupled through a volumetric heat transfer coefficient and investigated in non-thermal equilibrium. The effects of varying the thermal conductivity of the solid matrix and the heat transfer coefficient are investigated. The results are also compared to existing experimental data.

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...

Integrated pest management models and their dynamical behaviour.

PubMed

Tang, Sanyi; Xiao, Yanni; Chen, Lansun; Cheke, Robert A

2005-01-01

Two impulsive models of integrated pest management (IPM) strategies are proposed, one with fixed intervention times and the other with these unfixed. The first model allows natural enemies to survive but under some conditions may lead to extinction of the pest. We use a simple prey-dependent consumption model with fixed impulsive effects and show that there exists a globally stable pest-eradication periodic solution when the impulsive period is less than certain critical values. The effects of pest resistance to pesticides are also studied. The second model is constructed in the light of IPM practice such that when the pest population reaches the economic injury level (EIL), a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is invoked. Using analytical methods, we show that there exists an orbitally asymptotically stable periodic solution with a maximum value no larger than the given Economic Threshold (ET). The complete expression for this periodic solution is given and the ET is evaluated for given parameters. We also show that in some cases control costs can be reduced by replacing IPM interventions at unfixed times with periodic interventions. Further, we show that small perturbations of the system do not affect the existence and stability of the periodic solution. Thus, we provide the first demonstration using mathematical models that an IPM strategy is more effective than classical control methods.

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.

Approximation solution of Schrodinger equation for Q-deformed Rosen-Morse using supersymmetry quantum mechanics (SUSY QM)

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

Alemgadmi, Khaled I. K., E-mail: azozkied@yahoo.com; Suparmi; Cari

2015-09-30

The approximate analytical solution of Schrodinger equation for Q-Deformed Rosen-Morse potential was investigated using Supersymmetry Quantum Mechanics (SUSY QM) method. The approximate bound state energy is given in the closed form and the corresponding approximate wave function for arbitrary l-state given for ground state wave function. The first excited state obtained using upper operator and ground state wave function. The special case is given for the ground state in various number of q. The existence of Rosen-Morse potential reduce energy spectra of system. The larger value of q, the smaller energy spectra of system.

Self-sustained peristaltic waves: Explicit asymptotic solutions

NASA Astrophysics Data System (ADS)

Dudchenko, O. A.; Guria, G. Th.

2012-02-01

A simple nonlinear model for the coupled problem of fluid flow and contractile wall deformation is proposed to describe peristalsis. In the context of the model the ability of a transporting system to perform autonomous peristaltic pumping is interpreted as the ability to propagate sustained waves of wall deformation. Piecewise-linear approximations of nonlinear functions are used to analytically demonstrate the existence of traveling-wave solutions. Explicit formulas are derived which relate the speed of self-sustained peristaltic waves to the rheological properties of the transporting vessel and the transported fluid. The results may contribute to the development of diagnostic and therapeutic procedures for cases of peristaltic motility disorders.

Weibel instability for a streaming electron, counterstreaming e-e, and e-p plasmas with intrinsic temperature anisotropy

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

Ghorbanalilu, M.; Physics Department, Azarbaijan Shahid Madani University, Tabriz; Sadegzadeh, S.

2014-05-15

The existence of Weibel instability for a streaming electron, counterstreaming electron-electron (e-e), and electron-positron (e-p) plasmas with intrinsic temperature anisotropy is investigated. The temperature anisotropy is included in the directions perpendicular and parallel to the streaming direction. It is shown that the beam mean speed changes the instability mode, for a streaming electron beam, from the classic Weibel to the Weibel-like mode. The analytical and numerical solutions approved that Weibel-like modes are excited for both counterstreaming e-e and e-p plasmas. The growth rates of the instabilities in e-e and e-p plasmas are compared. The growth rate is larger for e-pmore » plasmas if the thermal anisotropy is small and the opposite is true for large thermal anisotropies. The analytical and numerical solutions are in good agreement only in the small parallel temperature and wave number limits, when the instability growth rate increases linearly with normalized wave number kc∕ω{sub p}.« less

Effect of slip on existence, uniqueness, and behavior of similarity solutions for steady incompressible laminar flow in porous tubes and channels

NASA Astrophysics Data System (ADS)

Chellam, Shankararaman; Liu, Mei

2006-08-01

The existence and multiplicity of similarity solutions for steady, fully developed, incompressible laminar flow in uniformly porous tubes and channels with one or two permeable walls is investigated from first principles. A fourth-order ordinary differential equation obtained by simplifying the Navier-Stokes equations by introducing Berman's stream function [A. S. Berman, J. Appl. Phys. 24, 1232 (1953)] and Terrill's transformation [R. M. Terrill, Aeronaut. Q. 15, 299 (1964)] is probed analytically. In this work that considers only symmetric flows for symmetric ducts; the no-slip boundary condition at porous walls is relaxed to account for momentum transfer within the porous walls. By employing the Saffman [P. G. Saffman, Stud. Appl. Math. 50, 93 (1971)] form of the slip boundary condition, the uniqueness of similarity solutions is investigated theoretically in terms of the signs of the guesses for the missing initial conditions. Solutions were obtained for all wall Reynolds numbers for channel flows whereas no solutions existed for intermediate values for tube flows. Introducing slip did not fundamentally change the number or the character of solutions corresponding to different sections. However, the range of wall Reynolds numbers for which similarity solutions are theoretically impossible in tube flows was found to be a weak function of the slip coefficient. Slip also weakly influenced the transition wall Reynolds number corresponding to flow in the direction of a favorable axial pressure gradient to one in the direction of an adverse pressure gradient. Momentum transfer from the longitudinal axis to the walls appears to occur more efficiently in porous channels compared to porous tubes even in the presence of slip.

Magnetized, mass-loaded, rotating accretion flows

NASA Astrophysics Data System (ADS)

Toniazzo, T.; Hartquist, T. W.; Durisen, R. H.

2001-03-01

We present a semi-analytical investigation of a simple one-dimensional, steady-state model for a mass-loaded, rotating, magnetized, hydrodynamical flow. Our approach is analogous to one used in early studies of magnetized winds. The model represents the infall towards a central point mass of the gas generated in a cluster of stars surrounding it, as is likely to occur in some active nuclei and starburst galaxies. We describe the properties of the different classes of infall solutions. We find that the flow becomes faster than the fast-mode speed, and hence decoupled from the centre, only for a limited range of parameter values, and when magnetic stresses are ineffective. Such flow is slowed as it approaches a centrifugal barrier, implying the existence of an accretion disc. When the flow does not become super-fast and the magnetic torque is insufficient, no steady solution extending inward to the centre exists. Finally, with a larger magnetic torque, solutions representing steady sub-Alfvénic flows are found, which can resemble spherical hydrodynamical infall. Such solutions, if applicable, would imply that rotation is not important and that any accretion disc formed would be of very limited size.

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.

Utilizing HDF4 File Content Maps for the Cloud

NASA Technical Reports Server (NTRS)

Lee, Hyokyung Joe

2016-01-01

We demonstrate a prototype study that HDF4 file content map can be used for efficiently organizing data in cloud object storage system to facilitate cloud computing. This approach can be extended to any binary data formats and to any existing big data analytics solution powered by cloud computing because HDF4 file content map project started as long term preservation of NASA data that doesn't require HDF4 APIs to access data.

An Evaluation of the NEKTON Program

DTIC Science & Technology

1990-09-01

features could be studied. Test cases were chosen for which experimental data or analytic solutions exist. These test cases verify NEKTON’s unsteady flow ...including steady and unsteady incompressible flow problems in two or three spatial dimensions. NEKTON version 2.6, which was evaluated for this... unsteady flow decay of a free surface moderate [7] 2-D laminar flow flow past a cylinder 100 [7] 3-D Stokes flow spiral groove thrust bearing < 1 [8

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.

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.

Quantification of Water Flux in Vesicular Systems.

PubMed

Hannesschläger, Christof; Barta, Thomas; Siligan, Christine; Horner, Andreas

2018-06-04

Water transport across lipid membranes is fundamental to all forms of life and plays a major role in health and disease. However, not only typical water facilitators like aquaporins facilitate water flux, but also transporters, ion channels or receptors represent potent water pathways. The efforts directed towards a mechanistic understanding of water conductivity determinants in transmembrane proteins, the development of water flow inhibitors, and the creation of biomimetic membranes with incorporated membrane proteins or artificial water channels depend on reliable and accurate ways of quantifying water permeabilities P f . A conventional method is to subject vesicles to an osmotic gradient in a stopped-flow device: Fast recordings of scattered light intensity are converted into the time course of vesicle volume change. Even though an analytical solution accurately acquiring P f from scattered light intensities exists, approximations potentially misjudging P f by orders of magnitude are used. By means of computational and experimental data we point out that erroneous results such as that the single channel water permeability p f depends on the osmotic gradient are direct results of such approximations. Finally, we propose an empirical solution of which calculated permeability values closely match those calculated with the analytical solution in the relevant range of parameters.

Reference interaction site model with hydrophobicity induced density inhomogeneity: An analytical theory to compute solvation properties of large hydrophobic solutes in the mixture of polyatomic solvent molecules.

PubMed

Cao, Siqin; Sheong, Fu Kit; Huang, Xuhui

2015-08-07

Reference interaction site model (RISM) has recently become a popular approach in the study of thermodynamical and structural properties of the solvent around macromolecules. On the other hand, it was widely suggested that there exists water density depletion around large hydrophobic solutes (>1 nm), and this may pose a great challenge to the RISM theory. In this paper, we develop a new analytical theory, the Reference Interaction Site Model with Hydrophobicity induced density Inhomogeneity (RISM-HI), to compute solvent radial distribution function (RDF) around large hydrophobic solute in water as well as its mixture with other polyatomic organic solvents. To achieve this, we have explicitly considered the density inhomogeneity at the solute-solvent interface using the framework of the Yvon-Born-Green hierarchy, and the RISM theory is used to obtain the solute-solvent pair correlation. In order to efficiently solve the relevant equations while maintaining reasonable accuracy, we have also developed a new closure called the D2 closure. With this new theory, the solvent RDFs around a large hydrophobic particle in water and different water-acetonitrile mixtures could be computed, which agree well with the results of the molecular dynamics simulations. Furthermore, we show that our RISM-HI theory can also efficiently compute the solvation free energy of solute with a wide range of hydrophobicity in various water-acetonitrile solvent mixtures with a reasonable accuracy. We anticipate that our theory could be widely applied to compute the thermodynamic and structural properties for the solvation of hydrophobic solute.

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

Root finding in the complex plane for seismo-acoustic propagation scenarios with Green's function solutions.

PubMed

McCollom, Brittany A; Collis, Jon M

2014-09-01

A normal mode solution to the ocean acoustic problem of the Pekeris waveguide with an elastic bottom using a Green's function formulation for a compressional wave point source is considered. Analytic solutions to these types of waveguide propagation problems are strongly dependent on the eigenvalues of the problem; these eigenvalues represent horizontal wavenumbers, corresponding to propagating modes of energy. The eigenvalues arise as singularities in the inverse Hankel transform integral and are specified by roots to a characteristic equation. These roots manifest themselves as poles in the inverse transform integral and can be both subtle and difficult to determine. Following methods previously developed [S. Ivansson et al., J. Sound Vib. 161 (1993)], a root finding routine has been implemented using the argument principle. Using the roots to the characteristic equation in the Green's function formulation, full-field solutions are calculated for scenarios where an acoustic source lies in either the water column or elastic half space. Solutions are benchmarked against laboratory data and existing numerical solutions.

Review: visual analytics of climate networks

NASA Astrophysics Data System (ADS)

Nocke, T.; Buschmann, S.; Donges, J. F.; Marwan, N.; Schulz, H.-J.; Tominski, C.

2015-09-01

Network analysis has become an important approach in studying complex spatiotemporal behaviour within geophysical observation and simulation data. This new field produces increasing numbers of large geo-referenced networks to be analysed. Particular focus lies currently on the network analysis of the complex statistical interrelationship structure within climatological fields. The standard procedure for such network analyses is the extraction of network measures in combination with static standard visualisation methods. Existing interactive visualisation methods and tools for geo-referenced network exploration are often either not known to the analyst or their potential is not fully exploited. To fill this gap, we illustrate how interactive visual analytics methods in combination with geovisualisation can be tailored for visual climate network investigation. Therefore, the paper provides a problem analysis relating the multiple visualisation challenges to a survey undertaken with network analysts from the research fields of climate and complex systems science. Then, as an overview for the interested practitioner, we review the state-of-the-art in climate network visualisation and provide an overview of existing tools. As a further contribution, we introduce the visual network analytics tools CGV and GTX, providing tailored solutions for climate network analysis, including alternative geographic projections, edge bundling, and 3-D network support. Using these tools, the paper illustrates the application potentials of visual analytics for climate networks based on several use cases including examples from global, regional, and multi-layered climate networks.

Review: visual analytics of climate networks

NASA Astrophysics Data System (ADS)

Nocke, T.; Buschmann, S.; Donges, J. F.; Marwan, N.; Schulz, H.-J.; Tominski, C.

2015-04-01

Network analysis has become an important approach in studying complex spatiotemporal behaviour within geophysical observation and simulation data. This new field produces increasing amounts of large geo-referenced networks to be analysed. Particular focus lies currently on the network analysis of the complex statistical interrelationship structure within climatological fields. The standard procedure for such network analyses is the extraction of network measures in combination with static standard visualisation methods. Existing interactive visualisation methods and tools for geo-referenced network exploration are often either not known to the analyst or their potential is not fully exploited. To fill this gap, we illustrate how interactive visual analytics methods in combination with geovisualisation can be tailored for visual climate network investigation. Therefore, the paper provides a problem analysis, relating the multiple visualisation challenges with a survey undertaken with network analysts from the research fields of climate and complex systems science. Then, as an overview for the interested practitioner, we review the state-of-the-art in climate network visualisation and provide an overview of existing tools. As a further contribution, we introduce the visual network analytics tools CGV and GTX, providing tailored solutions for climate network analysis, including alternative geographic projections, edge bundling, and 3-D network support. Using these tools, the paper illustrates the application potentials of visual analytics for climate networks based on several use cases including examples from global, regional, and multi-layered climate networks.

Integrated Array/Metadata Analytics

NASA Astrophysics Data System (ADS)

Misev, Dimitar; Baumann, Peter

2015-04-01

Data comes in various forms and types, and integration usually presents a problem that is often simply ignored and solved with ad-hoc solutions. Multidimensional arrays are an ubiquitous data type, that we find at the core of virtually all science and engineering domains, as sensor, model, image, statistics data. Naturally, arrays are richly described by and intertwined with additional metadata (alphanumeric relational data, XML, JSON, etc). Database systems, however, a fundamental building block of what we call "Big Data", lack adequate support for modelling and expressing these array data/metadata relationships. Array analytics is hence quite primitive or non-existent at all in modern relational DBMS. Recognizing this, we extended SQL with a new SQL/MDA part seamlessly integrating multidimensional array analytics into the standard database query language. We demonstrate the benefits of SQL/MDA with real-world examples executed in ASQLDB, an open-source mediator system based on HSQLDB and rasdaman, that already implements SQL/MDA.

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.

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.

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.

An analytical solution to assess the SH seismoelectric response of the vadose zone

NASA Astrophysics Data System (ADS)

Monachesi, L. B.; Zyserman, F. I.; Jouniaux, L.

2018-03-01

We derive an analytical solution of the seismoelectric conversions generated in the vadose zone, when this region is crossed by a pure shear horizontal (SH) wave. Seismoelectric conversions are induced by electrokinetic effects linked to relative motions between fluid and porous media. The considered model assumes a one-dimensional soil constituted by a single layer on top of a half space in contact at the water table, and a shearing force located at the earth's surface as the wave source. The water table is an interface expected to induce a seismoelectric interfacial response (IR). The top layer represents a porous rock which porous space is partially saturated by water and air, while the half-space is completely saturated with water, representing the saturated zone. The analytical expressions for the coseismic fields and the interface responses, both electric and magnetic, are derived by solving Pride's equations with proper boundary conditions. An approximate analytical expression of the solution is also obtained, which is very simple and applicable in a fairly broad set of situations. Hypothetical scenarios are proposed to study and analyse the dependence of the electromagnetic fields on various parameters of the medium. An analysis of the approximate solution is also made together with a comparison to the exact solution. The main result of the present analysis is that the amplitude of the interface response generated at the water table is found to be proportional to the jump in the electric current density, which in turn depends on the saturation contrast, poro-mechanical and electrical properties of the medium and on the amplitude of the solid displacement produced by the source. This result is in agreement with the one numerically obtained by the authors, which has been published in a recent work. We also predict the existence of an interface response located at the surface, and that the electric interface response is several orders of magnitude bigger than the electric coseismic field, whereas it is the opposite using compressional waves as shown by theoretical and experimental results. This fact should encourage the performance of field and laboratory tests to check the viability of SHTE seismoelectrics as a near surface prospecting/monitoring tool.

An analytical solution to assess the SH seismoelectric response of the vadose zone

NASA Astrophysics Data System (ADS)

Monachesi, L. B.; Zyserman, F. I.; Jouniaux, L.

2018-06-01

We derive an analytical solution of the seismoelectric conversions generated in the vadose zone, when this region is crossed by a pure shear horizontal (SH) wave. Seismoelectric conversions are induced by electrokinetic effects linked to relative motions between fluid and porous media. The considered model assumes a 1D soil constituted by a single layer on top of a half-space in contact at the water table, and a shearing force located at the earth's surface as the wave source. The water table is an interface expected to induce a seismoelectric interfacial response (IR). The top layer represents a porous rock in which porous space is partially saturated by water and air, while the half-space is completely saturated with water, representing the saturated zone. The analytical expressions for the coseismic fields and the interface responses, both electric and magnetic, are derived by solving Pride's equations with proper boundary conditions. An approximate analytical expression of the solution is also obtained, which is very simple and applicable in a fairly broad set of situations. Hypothetical scenarios are proposed to study and analyse the dependence of the electromagnetic fields on various parameters of the medium. An analysis of the approximate solution is also made together with a comparison to the exact solution. The main result of the present analysis is that the amplitude of the interface response generated at the water table is found to be proportional to the jump in the electric current density, which in turn depends on the saturation contrast, poro-mechanical and electrical properties of the medium and on the amplitude of the solid displacement produced by the source. This result is in agreement with the one numerically obtained by the authors, which has been published in a recent work. We also predict the existence of an interface response located at the surface, and that the electric interface response is several orders of magnitude bigger than the electric coseismic field, whereas it is the opposite using compressional waves as shown by theoretical and experimental results. This fact should encourage the performance of field and laboratory tests to check the viability of SHTE seismoelectrics as a near surface prospecting/monitoring tool.

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...

Effect of injection screen slot geometry on hydraulic conductivity tests

NASA Astrophysics Data System (ADS)

Klammler, Harald; Nemer, Bassel; Hatfield, Kirk

2014-04-01

Hydraulic conductivity and its spatial variability are important hydrogeological parameters and are typically determined through injection tests at different scales. For injection test interpretation, shape factors are required to account for injection screen geometry. Shape factors act as proportionality constants between hydraulic conductivity and observed ratios of injection flow rate and injection head at steady-state. Existing results for such shape factors assume either an ideal screen (i.e., ignoring effects of screen slot geometry) or infinite screen length (i.e., ignoring effects of screen extremes). In the present work, we investigate the combined effects of circumferential screen slot geometry and finite screen length on injection shape factors. This is done in terms of a screen entrance resistance by solving a steady-state potential flow mixed type boundary value problem in a homogeneous axi-symmetric flow domain using a semi-analytical solution approach. Results are compared to existing analytical solutions for circumferential and longitudinal slots on infinite screens, which are found to be identical. Based on an existing approximation, an expression is developed for a dimensionless screen entrance resistance of infinite screens, which is a function of the relative slot area only. For anisotropic conditions, e.g., when conductivity is smaller in the vertical direction than in the horizontal, screen entrance losses for circumferential slots increase, while they remain unaffected for longitudinal slots. This work is not concerned with investigating the effects of (possibly turbulent) head losses inside the injection device including the passage through the injection slots prior to entering the porous aquifer.

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.

Estimating Aquifer Properties Using Sinusoidal Pumping Tests

NASA Astrophysics Data System (ADS)

Rasmussen, T. C.; Haborak, K. G.; Young, M. H.

2001-12-01

We develop the theoretical and applied framework for using sinusoidal pumping tests to estimate aquifer properties for confined, leaky, and partially penetrating conditions. The framework 1) derives analytical solutions for three boundary conditions suitable for many practical applications, 2) validates the analytical solutions against a finite element model, 3) establishes a protocol for conducting sinusoidal pumping tests, and 4) estimates aquifer hydraulic parameters based on the analytical solutions. The analytical solutions to sinusoidal stimuli in radial coordinates are derived for boundary value problems that are analogous to the Theis (1935) confined aquifer solution, the Hantush and Jacob (1955) leaky aquifer solution, and the Hantush (1964) partially penetrated confined aquifer solution. The analytical solutions compare favorably to a finite-element solution of a simulated flow domain, except in the region immediately adjacent to the pumping well where the implicit assumption of zero borehole radius is violated. The procedure is demonstrated in one unconfined and two confined aquifer units near the General Separations Area at the Savannah River Site, a federal nuclear facility located in South Carolina. Aquifer hydraulic parameters estimated using this framework provide independent confirmation of parameters obtained from conventional aquifer tests. The sinusoidal approach also resulted in the elimination of investigation-derived wastes.

Higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Wu, Xiao-Yu; Sun, Yan

2018-02-01

Under investigation in this paper is the higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials which can be applied in the nonlinear optics, hydrodynamics, plasma physics and Bose-Einstein condensation. Based on the Kadomtsev-Petviashvili hierarchy reduction, we construct the Nth order rogue wave-like solutions in terms of the Gramian under the integrable constraint. With the help of the analytic and graphic analysis, we exhibit the first-, second- and third-order rogue wave-like solutions through the different dispersion, nonlinearity and linear potential coefficients. We find that only if the dispersion and nonlinearity coefficients are proportional to each other, heights of the background of those rogue waves maintain unchanged with time increasing. Due to the existence of complex parameters, such nonautonomous rogue waves in the higher-order cases have more complex features than those in the lower.

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.

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...

Simultaneous Spectrophotometric Determination of Rifampicin, Isoniazid and Pyrazinamide in a Single Step

PubMed Central

Asadpour-Zeynali, Karim; Saeb, Elhameh

2016-01-01

Three antituberculosis medications are investigated in this work consist of rifampicin, isoniazid and pyrazinamide. The ultra violet (UV) spectra of these compounds are overlapped, thus use of suitable chemometric methods are helpful for simultaneous spectrophotometric determination of them. A generalized version of net analyte signal standard addition method (GNASSAM) was used for determination of three antituberculosis medications as a model system. In generalized net analyte signal standard addition method only one standard solution was prepared for all analytes. This standard solution contains a mixture of all analytes of interest, and the addition of such solution to sample, causes increases in net analyte signal of each analyte which are proportional to the concentrations of analytes in added standards solution. For determination of concentration of each analyte in some synthetic mixtures, the UV spectra of pure analytes and each sample were recorded in the range of 210 nm-550 nm. The standard addition procedure was performed for each sample and the UV spectrum was recorded after each addition and finally the results were analyzed by net analyte signal method. Obtained concentrations show acceptable performance of GNASSAM in these cases. PMID:28243267

Segmented strings and the McMillan map

DOE PAGES

Gubser, Steven S.; Parikh, Sarthak; Witaszczyk, Przemek

2016-07-25

We present new exact solutions describing motions of closed segmented strings in AdS 3 in terms of elliptic functions. The existence of analytic expressions is due to the integrability of the classical equations of motion, which in our examples reduce to instances of the McMillan map. Here, we also obtain a discrete evolution rule for the motion in AdS 3 of arbitrary bound states of fundamental strings and D1-branes in the test approximation.

Stability Analysis of Distributed Order Fractional Chen System

PubMed Central

Aminikhah, H.; Refahi Sheikhani, A.; Rezazadeh, H.

2013-01-01

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. PMID:24489508

Gaussian closure technique applied to the hysteretic Bouc model with non-zero mean white noise excitation

NASA Astrophysics Data System (ADS)

Waubke, Holger; Kasess, Christian H.

2016-11-01

Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit first-order vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.

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.

Permanence and asymptotic behaviors of stochastic predator-prey system with Markovian switching and Lévy noise

NASA Astrophysics Data System (ADS)

Wang, Sheng; Wang, Linshan; Wei, Tengda

2018-04-01

This paper concerns the dynamics of a stochastic predator-prey system with Markovian switching and Lévy noise. First, the existence and uniqueness of global positive solution to the system is proved. Then, by combining stochastic analytical techniques with M-matrix analysis, sufficient conditions of stochastic permanence and extinction are obtained. Furthermore, for the stochastic permanence case, by means of four constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems, both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated. Finally, our conclusions are illustrated through an example.

Low-frequency fluid waves in fractures and pipes

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

Korneev, Valeri

2010-09-01

Low-frequency analytical solutions have been obtained for phase velocities of symmetrical fluid waves within both an infinite fracture and a pipe filled with a viscous fluid. Three different fluid wave regimes can exist in such objects, depending on the various combinations of parameters, such as fluid density, fluid viscosity, walls shear modulus, channel thickness, and frequency. Equations for velocities of all these regimes have explicit forms and are verified by comparisons with the exact solutions. The dominant role of fractures in rock permeability at field scales and the strong amplitude and frequency effects of Stoneley guided waves suggest the importancemore » of including these wave effects into poroelastic theories.« less

Automated and Cooperative Vehicle Merging at Highway On-Ramps

DOE PAGES

Rios-Torres, Jackeline; Malikopoulos, Andreas A.

2016-08-05

Recognition of necessities of connected and automated vehicles (CAVs) is gaining momentum. CAVs can improve both transportation network efficiency and safety through control algorithms that can harmonically use all existing information to coordinate the vehicles. This paper addresses the problem of optimally coordinating CAVs at merging roadways to achieve smooth traffic flow without stop-and-go driving. Here we present an optimization framework and an analytical closed-form solution that allows online coordination of vehicles at merging zones. The effectiveness of the efficiency of the proposed solution is validated through a simulation, and it is shown that coordination of vehicles can significantly reducemore » both fuel consumption and travel time.« less

A spatially homogeneous and isotropic Einstein-Dirac cosmology

NASA Astrophysics Data System (ADS)

Finster, Felix; Hainzl, Christian

2011-04-01

We consider a spatially homogeneous and isotropic cosmological model where Dirac spinors are coupled to classical gravity. For the Dirac spinors we choose a Hartree-Fock ansatz where all one-particle wave functions are coherent and have the same momentum. If the scale function is large, the universe behaves like the classical Friedmann dust solution. If however the scale function is small, quantum effects lead to oscillations of the energy-momentum tensor. It is shown numerically and proven analytically that these quantum oscillations can prevent the formation of a big bang or big crunch singularity. The energy conditions are analyzed. We prove the existence of time-periodic solutions which go through an infinite number of expansion and contraction cycles.

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.

Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2013-12-01

The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.

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.

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

Curl forces and the nonlinear Fokker-Planck equation.

PubMed

Wedemann, R S; Plastino, A R; Tsallis, C

2016-12-01

Nonlinear Fokker-Planck equations endowed with curl drift forces are investigated. The conditions under which these evolution equations admit stationary solutions, which are q exponentials of an appropriate potential function, are determined. It is proved that when these stationary solutions exist, the nonlinear Fokker-Planck equations satisfy an H theorem in terms of a free-energy-like quantity involving the S_{q} entropy. A particular two-dimensional model admitting analytical, time-dependent q-Gaussian solutions is discussed in detail. This model describes a system of particles with short-range interactions, performing overdamped motion under drag effects due to a rotating resisting medium. It is related to models that have been recently applied to the study of type-II superconductors. The relevance of the present developments to the study of complex systems in physics, astronomy, and biology is discussed.

Accessible solitons of fractional dimension

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

Zhong, Wei-Ping, E-mail: zhongwp6@126.com; Texas A&M University at Qatar, P.O. Box 23874, Doha; Belić, Milivoj

We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential.more » •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.« less

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.

Expansion of a cold non-neutral plasma slab

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

Karimov, A. R.; Department of Electrophysical Facilities, National Research Nuclear University MEPhI, Kashirskoye shosse 31, Moscow 115409; Yu, M. Y., E-mail: myyu@zju.edu.cn

2014-12-15

Expansion of the ion and electron fronts of a cold non-neutral plasma slab with a quasi-neutral core bounded by layers containing only ions is investigated analytically and exact solutions are obtained. It is found that on average, the plasma expansion time scales linearly with the initial inverse ion plasma frequency as well as the degree of charge imbalance, and no expansion occurs if the cold plasma slab is stationary and overall neutral. However, in both cases, there can exist prominent oscillations on the electron front.

Integrable Time-Dependent Quantum Hamiltonians

NASA Astrophysics Data System (ADS)

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

2018-05-01

We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

On Chaotic Behavior of Temperature Distribution in a Heat Exchanger

NASA Astrophysics Data System (ADS)

Bagyalakshmi, Morachan; Gangadharan, Saisundarakrishnan; Ganesh, Madhu

The objective of this paper is to introduce the notion of fractional derivatives in the energy equations and to study the chaotic nature of the temperature distribution in a heat exchanger with variation of temperature dependent transport properties. The governing fractional partial differential equations are transformed to a set of recurrence relations using fractional differential transform method and solved using inverse transform. The approximate analytical solution obtained by the proposed method has good agreement with the existing results.

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.

The inverse Numerical Computer Program FLUX-BOT for estimating Vertical Water Fluxes from Temperature Time-Series.

NASA Astrophysics Data System (ADS)

Trauth, N.; Schmidt, C.; Munz, M.

2016-12-01

Heat as a natural tracer to quantify water fluxes between groundwater and surface water has evolved to a standard hydrological method. Typically, time series of temperatures in the surface water and in the sediment are observed and are subsequently evaluated by a vertical 1D representation of heat transport by advection and dispersion. Several analytical solutions as well as their implementation into user-friendly software exist in order to estimate water fluxes from the observed temperatures. Analytical solutions can be easily implemented but assumptions on the boundary conditions have to be made a priori, e.g. sinusoidal upper temperature boundary. Numerical models offer more flexibility and can handle temperature data which is characterized by irregular variations such as storm-event induced temperature changes and thus cannot readily be incorporated in analytical solutions. This also reduced the effort of data preprocessing such as the extraction of the diurnal temperature variation. We developed a software to estimate water FLUXes Based On Temperatures- FLUX-BOT. FLUX-BOT is a numerical code written in MATLAB which is intended to calculate vertical water fluxes in saturated sediments, based on the inversion of measured temperature time series observed at multiple depths. It applies a cell-centered Crank-Nicolson implicit finite difference scheme to solve the one-dimensional heat advection-conduction equation. Besides its core inverse numerical routines, FLUX-BOT includes functions visualizing the results and functions for performing uncertainty analysis. We provide applications of FLUX-BOT to generic as well as to measured temperature data to demonstrate its performance.

Providing solid angle formalism for skyshine calculations.

PubMed

Gossman, Michael S; Pahikkala, A Jussi; Rising, Mary B; McGinley, Patton H

2010-08-17

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.

Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

NASA Astrophysics Data System (ADS)

Heuzé, Thomas

2017-10-01

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.

Exact solutions for discrete breathers in a forced-damped chain.

PubMed

Gendelman, O V

2013-06-01

Exact solutions for symmetric on-site discrete breathers (DBs) are obtained in a forced-damped linear chain with on-site vibro-impact constraints. The damping in the system is caused by inelastic impacts; the forcing functions should satisfy conditions of periodicity and antisymmetry. Global conditions for existence and stability of the DBs are established by a combination of analytic and numeric methods. The DB can lose its stability through either pitchfork, or Neimark-Sacker bifurcations. The pitchfork bifurcation is related to the internal dynamics of each individual oscillator. It is revealed that the coupling can suppress this type of instability. To the contrary, the Neimark-Sacker bifurcation occurs for relatively large values of the coupling, presumably due to closeness of the excitation frequency to a boundary of the propagation zone of the chain. Both bifurcation mechanisms seem to be generic for the considered type of forced-damped lattices. Some unusual phenomena, like nonmonotonous dependence of the stability boundary on the forcing amplitude, are revealed analytically for the initial system and illustrated numerically for small periodic lattices.

Simplified model for determining local heat flux boundary conditions for slagging wall

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

Bingzhi Li; Anders Brink; Mikko Hupa

2009-07-15

In this work, two models for calculating heat transfer through a cooled vertical wall covered with a running slag layer are investigated. The first one relies on a discretization of the velocity equation, and the second one relies on an analytical solution. The aim is to find a model that can be used for calculating local heat flux boundary conditions in computational fluid dynamics (CFD) analysis of such processes. Two different cases where molten deposits exist are investigated: the black liquor recovery boiler and the coal gasifier. The results show that a model relying on discretization of the velocity equationmore » is more flexible in handling different temperature-viscosity relations. Nevertheless, a model relying on an analytical solution is the one fast enough for a potential use as a CFD submodel. Furthermore, the influence of simplifications to the heat balance in the model is investigated. It is found that simplification of the heat balance can be applied when the radiation heat flux is dominant in the balance. 9 refs., 7 figs., 10 tabs.« less

Analytical close-form solutions to the elastic fields of solids with dislocations and surface stress

NASA Astrophysics Data System (ADS)

Ye, Wei; Paliwal, Bhasker; Ougazzaden, Abdallah; Cherkaoui, Mohammed

2013-07-01

The concept of eigenstrain is adopted to derive a general analytical framework to solve the elastic field for 3D anisotropic solids with general defects by considering the surface stress. The formulation shows the elastic constants and geometrical features of the surface play an important role in determining the elastic fields of the solid. As an application, the analytical close-form solutions to the stress fields of an infinite isotropic circular nanowire are obtained. The stress fields are compared with the classical solutions and those of complex variable method. The stress fields from this work demonstrate the impact from the surface stress when the size of the nanowire shrinks but becomes negligible in macroscopic scale. Compared with the power series solutions of complex variable method, the analytical solutions in this work provide a better platform and they are more flexible in various applications. More importantly, the proposed analytical framework profoundly improves the studies of general 3D anisotropic materials with surface effects.

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.

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.

Conditions for critical effects in the mass action kinetics equations for water radiolysis

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

Wittman, Richard S.; Buck, Edgar C.; Mausolf, Edward J.

We report on a subtle global feature of the mass action kinetics equations for water radiolysis that results in predictions of a critical behavior in H2O2 and associated radical concentrations. While radiolysis kinetics has been studied extensively in the past, it is only in recent years that high speed computing has allowed the rapid exploration of the solution over widely varying dose and compositional conditions. We explore the radiolytic production of H2O2 under various externally fixed conditions of molecular H2 and O2 that have been regarded as problematic in the literature – specifically, “jumps” in predicted concentrations, and inconsistencies betweenmore » predictions and experiments have been reported for alpha radiolysis. We computationally map-out a critical concentration behavior for alpha radiolysis kinetics using a comprehensive set of reactions. We then show that all features of interest are accurately reproduced with 15 reactions. An analytical solution for steady-state concentrations of the 15 reactions reveals regions in [H2] and [O2] where the H2O2 concentration is not unique – both stable and unstable concentrations exist. The boundary of this region can be characterized analytically as a function of G-values and rate constants independent of dose rate. Physically, the boundary can be understood as separating a region where a steady-state H2O2 concentration exists, from one where it does not exist without a direct decomposition reaction. We show that this behavior is consistent with reported alpha radiolysis data and that no such behavior should occur for gamma radiolysis. We suggest experiments that could verify or discredit a critical concentration behavior for alpha radiolysis and could place more restrictive ranges on G-values from derived relationships between them.« less

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

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.

Maximal analytic extension and hidden symmetries of the dipole black ring

NASA Astrophysics Data System (ADS)

Armas, Jay

2011-12-01

We construct analytic extensions across the Killing horizons of non-extremal and extremal dipole black rings in Einstein-Maxwell’s theory using different methods. We show that these extensions are non-globally hyperbolic, have multiple asymptotically flat regions and, in the non-extremal case, are also maximal and timelike complete. Moreover, we find that in both cases, the causal structure of the maximally extended spacetime resembles that of the four-dimensional Reissner-Nordström black hole. Furthermore, motivated by the physical interpretation of one of these extensions, we find a separable solution to the Hamilton-Jacobi equation corresponding to zero energy null geodesics and relate it to the existence of a conformal Killing tensor and a conformal Killing-Yano tensor in a specific dimensionally reduced spacetime.

Solutions to an advanced functional partial differential equation of the pantograph type

PubMed Central

Zaidi, Ali A.; Van Brunt, B.; Wake, G. C.

2015-01-01

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained. PMID:26345391

Solutions to an advanced functional partial differential equation of the pantograph type.

PubMed

Zaidi, Ali A; Van Brunt, B; Wake, G C

2015-07-08

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.

Dynamics of cholera epidemics with impulsive vaccination and disinfection.

PubMed

Sisodiya, Omprakash Singh; Misra, O P; Dhar, Joydip

2018-04-01

Waterborne diseases have a tremendous influence on human life. The contaminated drinking water causes water-borne disease like cholera. Pulse vaccination is an important and effective strategy for the elimination of infectious diseases. A waterborne disease like cholera can also be controlled by using impulse technique. In this paper, we have proposed a delayed SEIRB epidemic model with impulsive vaccination and disinfection. We have studied the pulse vaccination strategy and sanitation to control the cholera disease. The existence and stability of the disease-free and endemic periodic solution are investigated both analytically and numerically. It is shown that there exists an infection-free periodic solution, using the impulsive dynamical system defined by the stroboscopic map. It is observed that the infection-free periodic solution is globally attractive when the impulse period is less than some critical value. From the analysis of the model, we have obtained a sufficient condition for the permanence of the epidemic with pulse vaccination. The main highlight of this paper is to introduce impulse technique along with latent period into the SEIRB epidemic model to investigate the role of pulse vaccination and disinfection on the dynamics of the cholera epidemics. Copyright © 2018 Elsevier Inc. All rights reserved.

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.

Standards and Guidelines for Numerical Models for Tsunami Hazard Mitigation

NASA Astrophysics Data System (ADS)

Titov, V.; Gonzalez, F.; Kanoglu, U.; Yalciner, A.; Synolakis, C. E.

2006-12-01

An increased number of nations around the workd need to develop tsunami mitigation plans which invariably involve inundation maps for warning guidance and evacuation planning. There is the risk that inundation maps may be produced with older or untested methodology, as there are currently no standards for modeling tools. In the aftermath of the 2004 megatsunami, some models were used to model inundation for Cascadia events with results much larger than sediment records and existing state-of-the-art studies suggest leading to confusion among emergency management. Incorrectly assessing tsunami impact is hazardous, as recent events in 2006 in Tonga, Kythira, Greece and Central Java have suggested (Synolakis and Bernard, 2006). To calculate tsunami currents, forces and runup on coastal structures, and inundation of coastlines one must calculate the evolution of the tsunami wave from the deep ocean to its target site, numerically. No matter what the numerical model, validation (the process of ensuring that the model solves the parent equations of motion accurately) and verification (the process of ensuring that the model used represents geophysical reality appropriately) both are an essential. Validation ensures that the model performs well in a wide range of circumstances and is accomplished through comparison with analytical solutions. Verification ensures that the computational code performs well over a range of geophysical problems. A few analytic solutions have been validated themselves with laboratory data. Even fewer existing numerical models have been both validated with the analytical solutions and verified with both laboratory measurements and field measurements, thus establishing a gold standard for numerical codes for inundation mapping. While there is in principle no absolute certainty that a numerical code that has performed well in all the benchmark tests will also produce correct inundation predictions with any given source motions, validated codes reduce the level of uncertainty in their results to the uncertainty in the geophysical initial conditions. Further, when coupled with real--time free--field tsunami measurements from tsunameters, validated codes are the only choice for realistic forecasting of inundation; the consequences of failure are too ghastly to take chances with numerical procedures that have not been validated. We discuss a ten step process of benchmark tests for models used for inundation mapping. The associated methodology and algorithmes have to first be validated with analytical solutions, then verified with laboratory measurements and field data. The models need to be published in the scientific literature in peer-review journals indexed by ISI. While this process may appear onerous, it reflects our state of knowledge, and is the only defensible methodology when human lives are at stake. Synolakis, C.E., and Bernard, E.N, Tsunami science before and beyond Boxing Day 2004, Phil. Trans. R. Soc. A 364 1845, 2231--2263, 2005.

An analytical solution of groundwater level fluctuation in a U-shaped leaky coastal aquifer

NASA Astrophysics Data System (ADS)

Huang, Fu-Kuo; Chuang, Mo-Hsiung; Wang, Shu-chuan

2017-04-01

Tide-induced groundwater level fluctuations in coastal aquifers have attracted much attention in past years, especially for the issues associated with the impact of the coastline shape, multi-layered leaky aquifer system, and anisotropy of aquifers. In this study, a homogeneous but anisotropic multi-layered leaky aquifer system with U-shaped coastline is considered, where the subsurface system consisting of an unconfined aquifer, a leaky confined aquifer, and a semi-permeable layer between them. The analytical solution of the model obtained herein may be considered as an extended work of two solutions; one was developed by Huang et al. (Huang et al. Tide-induced groundwater level fluctuation in a U-shaped coastal aquifer, J. Hydrol. 2015; 530: 291-305) for two-dimensional interacting tidal waves bounded by three water-land boundaries while the other was by Li and Jiao (Li and Jiao. Tidal groundwater level fluctuations in L-shaped leaky coastal aquifer system, J. Hydrol. 2002; 268: 234-243) for two-dimensional interacting tidal waves of leaky coastal aquifer system adjacent to a cross-shore estuary. In this research, the effects of leakage and storativity of the semi-permeable layer on the amplitude and phase shift of the tidal head fluctuation, and the influence of anisotropy of the aquifer are all examined for the U-shaped leaky coastal aquifer. Some existing solutions in literatures can be regarded as the special cases of the present solution if the aquifer system is isotropic and non-leaky. The results obtained will be beneficial to coastal development and management for water resources.

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.

Topologically protected bound states in photonic parity-time-symmetric crystals.

PubMed

Weimann, S; Kremer, M; Plotnik, Y; Lumer, Y; Nolte, S; Makris, K G; Segev, M; Rechtsman, M C; Szameit, A

2017-04-01

Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.

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.

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.

Analytic quantum-interference conditions in Coulomb corrected photoelectron holography

NASA Astrophysics Data System (ADS)

Maxwell, A. S.; Al-Jawahiry, A.; Lai, X. Y.; Figueira de Morisson Faria, C.

2018-02-01

We provide approximate analytic expressions for above-threshold ionization (ATI) transition probabilities and photoelectron angular distributions. These analytic expressions are more general than those existing in the literature and include the residual binding potential in the electron continuum propagation. They successfully reproduce the ATI side lobes and specific holographic structures such as the near-threshold fan-shaped pattern and the spider-like structure that extends up to relatively high photoelectron energies. We compare such expressions with the Coulomb quantum orbit strong-field approximation (CQSFA) and the full solution of the time-dependent Schrödinger equation for different driving-field frequencies and intensities, and provide an in-depth analysis of the physical mechanisms behind specific holographic structures. Our results shed additional light on what aspects of the CQSFA must be prioritized in order to obtain the key holographic features, and highlight the importance of forward scattered trajectories. Furthermore, we find that the holographic patterns change considerably for different field parameters, even if the Keldysh parameter is kept roughly the same.

Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid.

PubMed

Xiao, Li; Luo, Ray

2017-12-07

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

A Green's function method for two-dimensional reactive solute transport in a parallel fracture-matrix system

NASA Astrophysics Data System (ADS)

Chen, Kewei; Zhan, Hongbin

2018-06-01

The reactive solute transport in a single fracture bounded by upper and lower matrixes is a classical problem that captures the dominant factors affecting transport behavior beyond pore scale. A parallel fracture-matrix system which considers the interaction among multiple paralleled fractures is an extension to a single fracture-matrix system. The existing analytical or semi-analytical solution for solute transport in a parallel fracture-matrix simplifies the problem to various degrees, such as neglecting the transverse dispersion in the fracture and/or the longitudinal diffusion in the matrix. The difficulty of solving the full two-dimensional (2-D) problem lies in the calculation of the mass exchange between the fracture and matrix. In this study, we propose an innovative Green's function approach to address the 2-D reactive solute transport in a parallel fracture-matrix system. The flux at the interface is calculated numerically. It is found that the transverse dispersion in the fracture can be safely neglected due to the small scale of fracture aperture. However, neglecting the longitudinal matrix diffusion would overestimate the concentration profile near the solute entrance face and underestimate the concentration profile at the far side. The error caused by neglecting the longitudinal matrix diffusion decreases with increasing Peclet number. The longitudinal matrix diffusion does not have obvious influence on the concentration profile in long-term. The developed model is applied to a non-aqueous-phase-liquid (DNAPL) contamination field case in New Haven Arkose of Connecticut in USA to estimate the Trichloroethylene (TCE) behavior over 40 years. The ratio of TCE mass stored in the matrix and the injected TCE mass increases above 90% in less than 10 years.

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...

NOTE: Solving the ECG forward problem by means of a meshless finite element method

NASA Astrophysics Data System (ADS)

Li, Z. S.; Zhu, S. A.; He, Bin

2007-07-01

The conventional numerical computational techniques such as the finite element method (FEM) and the boundary element method (BEM) require laborious and time-consuming model meshing. The new meshless FEM only uses the boundary description and the node distribution and no meshing of the model is required. This paper presents the fundamentals and implementation of meshless FEM and the meshless FEM method is adapted to solve the electrocardiography (ECG) forward problem. The method is evaluated on a single-layer torso model, in which the analytical solution exists, and tested in a realistic geometry homogeneous torso model, with satisfactory results being obtained. The present results suggest that the meshless FEM may provide an alternative for ECG forward solutions.

Novel conformal technique to reduce staircasing artifacts at material boundaries for FDTD modeling of the bioheat equation.

PubMed

Neufeld, E; Chavannes, N; Samaras, T; Kuster, N

2007-08-07

The modeling of thermal effects, often based on the Pennes Bioheat Equation, is becoming increasingly popular. The FDTD technique commonly used in this context suffers considerably from staircasing errors at boundaries. A new conformal technique is proposed that can easily be integrated into existing implementations without requiring a special update scheme. It scales fluxes at interfaces with factors derived from the local surface normal. The new scheme is validated using an analytical solution, and an error analysis is performed to understand its behavior. The new scheme behaves considerably better than the standard scheme. Furthermore, in contrast to the standard scheme, it is possible to obtain with it more accurate solutions by increasing the grid resolution.

Modulational instability and discrete breathers in a nonlinear helicoidal lattice model

NASA Astrophysics Data System (ADS)

Ding, Jinmin; Wu, Tianle; Chang, Xia; Tang, Bing

2018-06-01

We investigate the problem on the discrete modulation instability of plane waves and discrete breather modes in a nonlinear helicoidal lattice model, which is described by a discrete nonlinear Schrödinger equation with the first-, second-, and third-neighbor coupling. By means of the linear stability analysis, we present an analytical expression of the instability growth rate and identify the regions of modulational instability of plane waves. It is shown that the introduction of the third-neighbor coupling will affect the shape of the areas of modulational instability significantly. Based on the results obtained by the modulational instability analysis, we predict the existence conditions for the stationary breather modes. Otherwise, by making use of the semidiscrete multiple-scale method, we obtain analytical solutions of discrete breather modes and analyze their properties for different types of nonlinearities. Our results show that the discrete breathers obtained are stable for a long time only when the system exhibits the repulsive nonlinearity. In addition, it is found that the existence of the stable bright discrete breather closely relates to the presence of the third-neighbor coupling.

Computing the Evans function via solving a linear boundary value ODE

NASA Astrophysics Data System (ADS)

Wahl, Colin; Nguyen, Rose; Ventura, Nathaniel; Barker, Blake; Sandstede, Bjorn

2015-11-01

Determining the stability of traveling wave solutions to partial differential equations can oftentimes be computationally intensive but of great importance to understanding the effects of perturbations on the physical systems (chemical reactions, hydrodynamics, etc.) they model. For waves in one spatial dimension, one may linearize around the wave and form an Evans function - an analytic Wronskian-like function which has zeros that correspond in multiplicity to the eigenvalues of the linearized system. If eigenvalues with a positive real part do not exist, the traveling wave will be stable. Two methods exist for calculating the Evans function numerically: the exterior-product method and the method of continuous orthogonalization. The first is numerically expensive, and the second reformulates the originally linear system as a nonlinear system. We develop a new algorithm for computing the Evans function through appropriate linear boundary-value problems. This algorithm is cheaper than the previous methods, and we prove that it preserves analyticity of the Evans function. We also provide error estimates and implement it on some classical one- and two-dimensional systems, one being the Swift-Hohenberg equation in a channel, to show the advantages.

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.

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.

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.

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…

Drifting solutions with elliptic symmetry for the compressible Navier-Stokes equations with density-dependent viscosity

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

An, Hongli, E-mail: kaixinguoan@163.com; Yuen, Manwai, E-mail: nevetsyuen@hotmail.com

2014-05-15

In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic symmetry for the Navier-Stokes model wherein the velocity components are governed by a generalized Emden dynamical system. In particular, when the viscosity variables are taken the same as Yuen [M. W. Yuen, “Analytical solutions to the Navier-Stokes equations,” J. Math. Phys. 49, 113102 (2008)], our solutions constitute a generalization of that obtained by Yuen. Interestingly, numerical simulations show that the analytical solutions can be used to explain the driftingmore » phenomena of the propagation wave like Tsunamis in oceans.« less

Current Technical Approaches for the Early Detection of Foodborne Pathogens: Challenges and Opportunities.

PubMed

Cho, Il-Hoon; Ku, Seockmo

2017-09-30

The development of novel and high-tech solutions for rapid, accurate, and non-laborious microbial detection methods is imperative to improve the global food supply. Such solutions have begun to address the need for microbial detection that is faster and more sensitive than existing methodologies (e.g., classic culture enrichment methods). Multiple reviews report the technical functions and structures of conventional microbial detection tools. These tools, used to detect pathogens in food and food homogenates, were designed via qualitative analysis methods. The inherent disadvantage of these analytical methods is the necessity for specimen preparation, which is a time-consuming process. While some literature describes the challenges and opportunities to overcome the technical issues related to food industry legal guidelines, there is a lack of reviews of the current trials to overcome technological limitations related to sample preparation and microbial detection via nano and micro technologies. In this review, we primarily explore current analytical technologies, including metallic and magnetic nanomaterials, optics, electrochemistry, and spectroscopy. These techniques rely on the early detection of pathogens via enhanced analytical sensitivity and specificity. In order to introduce the potential combination and comparative analysis of various advanced methods, we also reference a novel sample preparation protocol that uses microbial concentration and recovery technologies. This technology has the potential to expedite the pre-enrichment step that precedes the detection process.

The effect of microscopic attractive interactions on piezoelectric coefficients of nanoscale DNA films and its resultant mirocantilever-based biosensor signals

NASA Astrophysics Data System (ADS)

Wu, Jun-Zheng; Zhou, Mei-Hong; Zhang, Neng-Hui

2017-10-01

The adsorption of charged biomolecules on a substrate will trigger a self-induced electric potential field that could deflect microcantilever biosensors in the nanometer regime. The paper is devoted to a multiscale characterization of the piezoelectric coefficient of double-stranded DNA (dsDNA) films with microscopic attractive interactions in multivalence salt solutions, which has a close relationship with biosensor signals. First, two different analytical models of cantilever deflections based on macroscopic piezoelectric theories or mesoscopic liquid crystal theories were combined in the sense of equivalent deformation in order to bridge the relation between the macroscopic piezoelectric coefficient of an adsorbate film and the sensitivity of its microstructure to surrounding conditions. Second, two interaction potentials of the free energy for repulsion-dominated DNA films in NaCl solution or attraction-repulsion-coexisted DNA films in multivalent salt solutions were used to compare the piezoelectric effect and the resultant cantilever deformation at various packing conditions, such as different packing density, various nucleotide numbers and two packing technologies, i.e. nano-grafting or self-assembling technology. The variational tendency of microcantilever deflections predicted by the present multiscale analytical model agrees well with the related DNA-mirocantilever experiments. Negative piezoelectric coefficient of dsDNA film exists in multivalent salt solutions, and its distinctive size effect with different packing densities and nucleotide numbers provides us with an opportunity to obtain a more sensitive microcantilever sensor by careful control of packing conditions.

Stiffness of frictional contact of dissimilar elastic solids

DOE PAGES

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.; ...

2017-12-22

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This study gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the frictionmore » coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations – adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. Finally, the correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.« less

Stiffness of frictional contact of dissimilar elastic solids

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

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This study gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the frictionmore » coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations – adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. Finally, the correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.« less

Stiffness of frictional contact of dissimilar elastic solids

NASA Astrophysics Data System (ADS)

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.; Xu, Haitao; Pharr, George M.

2018-03-01

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This paper gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the friction coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations - adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. The correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.

Development of an integrated BEM approach for hot fluid structure interaction: BEST-FSI: Boundary Element Solution Technique for Fluid Structure Interaction

NASA Technical Reports Server (NTRS)

Dargush, G. F.; Banerjee, P. K.; Shi, Y.

1992-01-01

As part of the continuing effort at NASA LeRC to improve both the durability and reliability of hot section Earth-to-orbit engine components, significant enhancements must be made in existing finite element and finite difference methods, and advanced techniques, such as the boundary element method (BEM), must be explored. The BEM was chosen as the basic analysis tool because the critical variables (temperature, flux, displacement, and traction) can be very precisely determined with a boundary-based discretization scheme. Additionally, model preparation is considerably simplified compared to the more familiar domain-based methods. Furthermore, the hyperbolic character of high speed flow is captured through the use of an analytical fundamental solution, eliminating the dependence of the solution on the discretization pattern. The price that must be paid in order to realize these advantages is that any BEM formulation requires a considerable amount of analytical work, which is typically absent in the other numerical methods. All of the research accomplishments of a multi-year program aimed toward the development of a boundary element formulation for the study of hot fluid-structure interaction in Earth-to-orbit engine hot section components are detailed. Most of the effort was directed toward the examination of fluid flow, since BEM's for fluids are at a much less developed state. However, significant strides were made, not only in the analysis of thermoviscous fluids, but also in the solution of the fluid-structure interaction problem.

Soliton stability in some knot soliton models

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

Adam, C.; Sanchez-Guillen, J.; Wereszczynski, A.

2007-02-15

We study the issue of stability of static solitonlike solutions in some nonlinear field theories which allow for knotted field configurations. Concretely, we investigate the Aratyn-Ferreira-Zimerman model [Phys. Lett. B 456, 162 (1999); Phys. Rev. Lett. 83, 1723 (1999)], based on a Lagrangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with different (integer) topological charges (Hopf index) are not separated by an infinite energy barrier. Further, if variations which change the topological charge are allowed, then the static solutions are not evenmore » critical points of the energy functional. We also explain why soliton solutions can exist at all, in spite of these facts. In addition, we briefly discuss the Nicole model [J. Phys. G 4, 1363 (1978)], which is based on a sigma-model-type Lagrangian. For the Nicole model we find that different topological sectors are separated by an infinite energy barrier.« less

Duality in left-right symmetric seesaw mechanism.

PubMed

Akhmedov, E Kh; Frigerio, M

2006-02-17

We consider type I + II seesaw mechanism, where the exchanges of both right-handed neutrinos and isotriplet Higgs bosons contribute to the neutrino mass. Working in the left-right symmetric framework and assuming the mass matrix of light neutrinos m(v) and the Dirac-type Yukawa couplings to be known, we find the triplet Yukawa coupling matrix f, which carries the information about the masses and mixing of the right-handed neutrinos. We show that in this case there exists a duality: for any solution f, there is a dual solution [symbol: see text] = m(v)/nu(L) - f, where nu(L) is the vacuum expectation value of the triplet Higgs boson. Thus, unlike in pure type I (II) seesaw, there is no unique allowed structure for the matrix f. For n lepton generations the number of solutions is 2(n). We develop an exact analytic method of solving the seesaw nonlinear matrix equation for f.

Analytical Phase Equilibrium Function for Mixtures Obeying Raoult's and Henry's Laws

NASA Astrophysics Data System (ADS)

Hayes, Robert

When a mixture of two substances exists in both the liquid and gas phase at equilibrium, Raoults and Henry's laws (ideal solution and ideal dilute solution approximations) can be used to estimate the gas and liquid mole fractions at the extremes of either very little solute or solvent. By assuming that a cubic polynomial can reasonably approximate the intermediate values to these extremes as a function of mole fraction, the cubic polynomial is solved and presented. A closed form equation approximating the pressure dependence on mole fraction of the constituents is thereby obtained. As a first approximation, this is a very simple and potentially useful means to estimate gas and liquid mole fractions of equilibrium mixtures. Mixtures with an azeotrope require additional attention if this type of approach is to be utilized. This work supported in part by federal Grant NRC-HQ-84-14-G-0059.

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

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.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation.

PubMed

Liu, Wei; Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation

PubMed Central

Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota’s bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides. PMID:29432495

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.

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.

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.

A family of heavenly metrics

NASA Astrophysics Data System (ADS)

Nutku, Y.; Sheftel, M. B.

2014-02-01

This is a corrected and essentially extended version of the unpublished manuscript by Y Nutku and M Sheftel which contains new results. It is proposed to be published in honour of Y Nutku’s memory. All corrections and new results in sections 1, 2 and 4 are due to M Sheftel. We present new anti-self-dual exact solutions of the Einstein field equations with Euclidean and neutral (ultra-hyperbolic) signatures that admit only one rotational Killing vector. Such solutions of the Einstein field equations are determined by non-invariant solutions of Boyer-Finley (BF) equation. For the case of Euclidean signature such a solution of the BF equation was first constructed by Calderbank and Tod. Two years later, Martina, Sheftel and Winternitz applied the method of group foliation to the BF equation and reproduced the Calderbank-Tod solution together with new solutions for the neutral signature. In the case of Euclidean signature we obtain new metrics which asymptotically locally look like a flat space and have a non-removable singular point at the origin. In the case of ultra-hyperbolic signature there exist three inequivalent forms of metric. Only one of these can be obtained by analytic continuation from the Calderbank-Tod solution whereas the other two are new.

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.

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.

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-01-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-06-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

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...

One-calibrant kinetic calibration for on-site water sampling with solid-phase microextraction.

PubMed

Ouyang, Gangfeng; Cui, Shufen; Qin, Zhipei; Pawliszyn, Janusz

2009-07-15

The existing solid-phase microextraction (SPME) kinetic calibration technique, using the desorption of the preloaded standards to calibrate the extraction of the analytes, requires that the physicochemical properties of the standard should be similar to those of the analyte, which limited the application of the technique. In this study, a new method, termed the one-calibrant kinetic calibration technique, which can use the desorption of a single standard to calibrate all extracted analytes, was proposed. The theoretical considerations were validated by passive water sampling in laboratory and rapid water sampling in the field. To mimic the variety of the environment, such as temperature, turbulence, and the concentration of the analytes, the flow-through system for the generation of standard aqueous polycyclic aromatic hydrocarbons (PAHs) solution was modified. The experimental results of the passive samplings in the flow-through system illustrated that the effect of the environmental variables was successfully compensated with the kinetic calibration technique, and all extracted analytes can be calibrated through the desorption of a single calibrant. On-site water sampling with rotated SPME fibers also illustrated the feasibility of the new technique for rapid on-site sampling of hydrophobic organic pollutants in water. This technique will accelerate the application of the kinetic calibration method and also will be useful for other microextraction techniques.

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.

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.

Equivalent circuit modeling of a piezo-patch energy harvester on a thin plate with AC-DC conversion

NASA Astrophysics Data System (ADS)

Bayik, B.; Aghakhani, A.; Basdogan, I.; Erturk, A.

2016-05-01

As an alternative to beam-like structures, piezoelectric patch-based energy harvesters attached to thin plates can be readily integrated to plate-like structures in automotive, marine, and aerospace applications, in order to directly exploit structural vibration modes of the host system without mass loading and volumetric occupancy of cantilever attachments. In this paper, a multi-mode equivalent circuit model of a piezo-patch energy harvester integrated to a thin plate is developed and coupled with a standard AC-DC conversion circuit. Equivalent circuit parameters are obtained in two different ways: (1) from the modal analysis solution of a distributed-parameter analytical model and (2) from the finite-element numerical model of the harvester by accounting for two-way coupling. After the analytical modeling effort, multi-mode equivalent circuit representation of the harvester is obtained via electronic circuit simulation software SPICE. Using the SPICE software, electromechanical response of the piezoelectric energy harvester connected to linear and nonlinear circuit elements are computed. Simulation results are validated for the standard AC-AC and AC-DC configurations. For the AC input-AC output problem, voltage frequency response functions are calculated for various resistive loads, and they show excellent agreement with modal analysis-based analytical closed-form solution and with the finite-element model. For the standard ideal AC input-DC output case, a full-wave rectifier and a smoothing capacitor are added to the harvester circuit for conversion of the AC voltage to a stable DC voltage, which is also validated against an existing solution by treating the single-mode plate dynamics as a single-degree-of-freedom system.

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.

Accretion onto a charged Kiselev black hole

NASA Astrophysics Data System (ADS)

Abbas, G.; Ditta, A.

2018-04-01

Accretion of matter onto a compact is one of the interesting astrophysical processes. Here, we study the accretion of matter onto a charged Kiselev black hole. The problem of static and spherically symmetric accretion of a polytropic fluid is explored for the analytic solution of equations of motion. We have investigated the necessary conditions for existence of the critical flow points and the mass accretion rate. Finally, we discuss the polytropic gas accretion in detail. It has been found that in the accretion process the quintessence and charge parameters play a dominant role.

Phase diagram for the Winfree model of coupled nonlinear oscillators.

PubMed

Ariaratnam, J T; Strogatz, S H

2001-05-07

In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.

Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators

NASA Astrophysics Data System (ADS)

Ariaratnam, Joel T.; Strogatz, Steven H.

2001-05-01

In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.

Thermocapillary convection in two immiscible liquid layers with free surface

NASA Technical Reports Server (NTRS)

Doi, Takao; Koster, Jean N.

1993-01-01

Thermocapillary convection is studied in two immiscible liquid layers with one free surface, one liquid/liquid interface, and differential heating applied parallel to the interfaces. An analytical solution is introduced for infinite horizontal layers. The defining parameter for the flow pattern is lambda, the ratio of the temperature coefficient of the interfacial tension to that of the surface tension. Four different flow patterns exist under zero gravity conditions. 'Halt' conditions which halt the fluid motion in the lower encapsulated liquid layer have been found. A numerical experiment is carried out to study effects of vertical end walls on the double layer convection in a 2D cavity. The halt condition obtained from the analytical study is found to be valid in the limit of small Reynolds numbers. The flow in the encapsulated liquid layer can be suppressed substantially.

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.

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.

Stress Transfer and Structural Failure of Bilayered Material Systems

NASA Astrophysics Data System (ADS)

Prieto-Munoz, Pablo Arthur

Bilayered material systems are common in naturally formed or artificially engineered structures. Understanding how loads transfer within these structural systems is necessary to predict failure and develop effective designs. Existing methods for evaluating the stress transfer in bilayered materials are limited to overly simplified models or require experimental calibration. As a result, these methods have failed to accurately account for such structural failures as the creep induced roofing panel collapse of Boston's I-90 connector tunnel, which was supported by adhesive anchors. The one-dimensional stress analyses currently used for adhesive anchor design cannot account for viscoelastic creep failure, and consequently results in dangerously under-designed structural systems. In this dissertation, a method for determining the two-dimensional stress and displacement fields for a generalized bilayered material system is developed, and proposes a closed-form analytical solution. A general linear-elastic solution is first proposed by decoupling the elastic governing equations from one another through the so-called plane assumption. Based on this general solution, an axisymmetric problem and a plane strain problem are formulated. These are applied to common bilayered material systems such as: (1) concrete adhesive anchors, (2) material coatings, (3) asphalt pavements, and (4) layered sedimentary rocks. The stress and displacement fields determined by this analytical analysis are validated through the use of finite element models. Through the correspondence principle, the linear-elastic solution is extended to consider time-dependent viscoelastic material properties, thus facilitating the analysis of adhesive anchors and asphalt pavements while incorporating their viscoelastic material behavior. Furthermore, the elastic stress analysis can explain the fracturing phenomenon of material coatings, pavements, and layered rocks, successfully predicting their fracture saturation ratio---which is the ratio of fracture spacing to the thickness of the weak layer where an increase in load will not cause any new fractures to form. Moreover, these specific material systems are looked at in the context of existing and novel experimental results, further demonstrating the advantage of the stress transfer analysis proposed. This research provides a closed-form stress solution for various structural systems that is applied to different failure analyses. The versatility of this method is in the flexibility and the ease upon which the stress and displacement field results can be applied to existing stress- or displacement-based structural failure criteria. As presented, this analysis can be directly used to: (1) design adhesive anchoring systems for long-term creep loading, (2) evaluate the fracture mechanics behind bilayered material coatings and pavement overlay systems, and (3) determine the fracture spacing to layer thickness ratio of layered sedimentary rocks. As is shown in the four material systems presented, this general solution has far reaching applications in facilitating design and analysis of typical bilayered structural systems.

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.

TRAC, a collaborative computer tool for tracer-test interpretation

NASA Astrophysics Data System (ADS)

Gutierrez, A.; Klinka, T.; Thiéry, D.; Buscarlet, E.; Binet, S.; Jozja, N.; Défarge, C.; Leclerc, B.; Fécamp, C.; Ahumada, Y.; Elsass, J.

2013-05-01

Artificial tracer tests are widely used by consulting engineers for demonstrating water circulation, proving the existence of leakage, or estimating groundwater velocity. However, the interpretation of such tests is often very basic, with the result that decision makers and professionals commonly face unreliable results through hasty and empirical interpretation. There is thus an increasing need for a reliable interpretation tool, compatible with the latest operating systems and available in several languages. BRGM, the French Geological Survey, has developed a project together with hydrogeologists from various other organizations to build software assembling several analytical solutions in order to comply with various field contexts. This computer program, called TRAC, is very light and simple, allowing the user to add his own analytical solution if the formula is not yet included. It aims at collaborative improvement by sharing the tool and the solutions. TRAC can be used for interpreting data recovered from a tracer test as well as for simulating the transport of a tracer in the saturated zone (for the time being). Calibration of a site operation is based on considering the hydrodynamic and hydrodispersive features of groundwater flow as well as the amount, nature and injection mode of the artificial tracer. The software is available in French, English and Spanish, and the latest version can be downloaded from the web site http://trac.brgm.fr">http://trac.brgm.fr.

Optimization of the Determination Method for Dissolved Cyanobacterial Toxin BMAA in Natural Water.

PubMed

Yan, Boyin; Liu, Zhiquan; Huang, Rui; Xu, Yongpeng; Liu, Dongmei; Lin, Tsair-Fuh; Cui, Fuyi

2017-10-17

There is a serious dispute on the existence of β-N-methylamino-l-alanine (BMAA) in water, which is a neurotoxin that may cause amyotrophic lateral sclerosis/Parkinson's disease (ALS/PDC) and Alzheimer' disease. It is believed that a reliable and sensitive analytical method for the determination of BMAA is urgently required to resolve this dispute. In the present study, the solid phase extraction (SPE) procedure and the analytical method for dissolved BMAA in water were investigated and optimized. The results showed both derivatized and underivatized methods were qualified for the measurement of BMAA and its isomer in natural water, and the limit of detection and the precision of the two methods were comparable. Cartridge characteristics and SPE conditions could greatly affect the SPE performance, and the competition of natural organic matter is the primary factor causing the low recovery of BMAA, which was reduced from approximately 90% in pure water to 38.11% in natural water. The optimized SPE method for BMAA was a combination of rinsed SPE cartridges, controlled loading/elution rates and elution solution, evaporation at 55 °C, reconstitution of a solution mixture, and filtration by polyvinylidene fluoride membrane. This optimized method achieved > 88% recovery of BMAA in both algal solution and river water. The developed method can provide an efficient way to evaluate the actual concentration levels of BMAA in actual water environments and drinking water systems.

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.

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

Mechanical Properties of Additively Manufactured Thick Honeycombs.

PubMed

Hedayati, Reza; Sadighi, Mojtaba; Mohammadi Aghdam, Mohammad; Zadpoor, Amir Abbas

2016-07-23

Honeycombs resemble the structure of a number of natural and biological materials such as cancellous bone, wood, and cork. Thick honeycomb could be also used for energy absorption applications. Moreover, studying the mechanical behavior of honeycombs under in-plane loading could help understanding the mechanical behavior of more complex 3D tessellated structures such as porous biomaterials. In this paper, we study the mechanical behavior of thick honeycombs made using additive manufacturing techniques that allow for fabrication of honeycombs with arbitrary and precisely controlled thickness. Thick honeycombs with different wall thicknesses were produced from polylactic acid (PLA) using fused deposition modelling, i.e., an additive manufacturing technique. The samples were mechanically tested in-plane under compression to determine their mechanical properties. We also obtained exact analytical solutions for the stiffness matrix of thick hexagonal honeycombs using both Euler-Bernoulli and Timoshenko beam theories. The stiffness matrix was then used to derive analytical relationships that describe the elastic modulus, yield stress, and Poisson's ratio of thick honeycombs. Finite element models were also built for computational analysis of the mechanical behavior of thick honeycombs under compression. The mechanical properties obtained using our analytical relationships were compared with experimental observations and computational results as well as with analytical solutions available in the literature. It was found that the analytical solutions presented here are in good agreement with experimental and computational results even for very thick honeycombs, whereas the analytical solutions available in the literature show a large deviation from experimental observation, computational results, and our analytical solutions.

Two-Dimensional Model for Reactive-Sorption Columns of Cylindrical Geometry: Analytical Solutions and Moment Analysis.

PubMed

Khan, Farman U; Qamar, Shamsul

2017-05-01

A set of analytical solutions are presented for a model describing the transport of a solute in a fixed-bed reactor of cylindrical geometry subjected to the first (Dirichlet) and third (Danckwerts) type inlet boundary conditions. Linear sorption kinetic process and first-order decay are considered. Cylindrical geometry allows the use of large columns to investigate dispersion, adsorption/desorption and reaction kinetic mechanisms. The finite Hankel and Laplace transform techniques are adopted to solve the model equations. For further analysis, statistical temporal moments are derived from the Laplace-transformed solutions. The developed analytical solutions are compared with the numerical solutions of high-resolution finite volume scheme. Different case studies are presented and discussed for a series of numerical values corresponding to a wide range of mass transfer and reaction kinetics. A good agreement was observed in the analytical and numerical concentration profiles and moments. The developed solutions are efficient tools for analyzing numerical algorithms, sensitivity analysis and simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

High temperature ion channels and pores

NASA Technical Reports Server (NTRS)

Cheley, Stephen (Inventor); Gu, Li Qun (Inventor); Bayley, Hagan (Inventor); Kang, Xiaofeng (Inventor)

2011-01-01

The present invention includes an apparatus, system and method for stochastic sensing of an analyte to a protein pore. The protein pore may be an engineer protein pore, such as an ion channel at temperatures above 55.degree. C. and even as high as near 100.degree. C. The analyte may be any reactive analyte, including chemical weapons, environmental toxins and pharmaceuticals. The analyte covalently bonds to the sensor element to produce a detectable electrical current signal. Possible signals include change in electrical current. Detection of the signal allows identification of the analyte and determination of its concentration in a sample solution. Multiple analytes present in the same solution may also be detected.

Optical Peregrine rogue waves of self-induced transparency in a resonant erbium-doped fiber.

PubMed

Chen, Shihua; Ye, Yanlin; Baronio, Fabio; Liu, Yi; Cai, Xian-Ming; Grelu, Philippe

2017-11-27

The resonant interaction of an optical field with two-level doping ions in a cryogenic optical fiber is investigated within the framework of nonlinear Schrödinger and Maxwell-Bloch equations. We present explicit fundamental rational rogue wave solutions in the context of self-induced transparency for the coupled optical and matter waves. It is exhibited that the optical wave component always features a typical Peregrine-like structure, while the matter waves involve more complicated yet spatiotemporally balanced amplitude distribution. The existence and stability of these rogue waves is then confirmed by numerical simulations, and they are shown to be excited amid the onset of modulation instability. These solutions can also be extended, using the same analytical framework, to include higher-order dispersive and nonlinear effects, highlighting their universality.

Analysis of the interaction of a weak normal shock wave with a turbulent boundary layer

NASA Technical Reports Server (NTRS)

Melnik, R. E.; Grossman, B.

1974-01-01

The method of matched asymptotic expansions is used to analyze the interaction of a normal shock wave with an unseparated turbulent boundary layer on a flat surface at transonic speeds. The theory leads to a three-layer description of the interaction in the double limit of Reynolds number approaching infinity and Mach number approaching unity. The interaction involves an outer, inviscid rotational layer, a constant shear-stress wall layer, and a blending region between them. The pressure distribution is obtained from a numerical solution of the outer-layer equations by a mixed-flow relaxation procedure. An analytic solution for the skin friction is determined from the inner-layer equations. The significance of the mathematical model is discussed with reference to existing experimental data.

A Numerical Study of Coupled Non-Linear Equations of Thermo-Viscous Fluid Flow in Cylindrical Geometry

NASA Astrophysics Data System (ADS)

Pothanna, N.; Aparna, P.; Gorla, R. S. R.

2017-12-01

In this paper we present numerical solutions to coupled non-linear governing equations of thermo-viscous fluid flow in cylindrical geometry using MATHEMATICA software solver. The numerical results are presented in terms of velocity, temperature and pressure distribution for various values of the material parameters such as the thermo-mechanical stress coefficient, thermal conductivity coefficient, Reiner Rivlin cross viscosity coefficient and the Prandtl number in the form of tables and graphs. Also, the solutions to governing equations for slow steady motion of a fluid have been obtained numerically and compared with the existing analytical results and are found to be in excellent agreement. The results of the present study will hopefully enable a better understanding applications of the flow under consideration.

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

Systems and methods for laser assisted sample transfer to solution for chemical analysis

DOEpatents

Van Berkel, Gary J.; Kertesz, Vilmos; Ovchinnikova, Olga S.

2014-06-03

Systems and methods are described for laser ablation of an analyte from a specimen and capturing of the analyte in a dispensed solvent to form a testing solution. A solvent dispensing and extraction system can form a liquid microjunction with the specimen. The solvent dispensing and extraction system can include a surface sampling probe. The laser beam can be directed through the surface sampling probe. The surface sampling probe can also serve as an atomic force microscopy probe. The surface sampling probe can form a seal with the specimen. The testing solution including the analyte can then be analyzed using an analytical instrument or undergo further processing.

Systems and methods for laser assisted sample transfer to solution for chemical analysis

DOEpatents

Van Berkel, Gary J.; Kertesz, Vilmos; Ovchinnikova, Olga S.

2015-09-29

Systems and methods are described for laser ablation of an analyte from a specimen and capturing of the analyte in a dispensed solvent to form a testing solution. A solvent dispensing and extraction system can form a liquid microjunction with the specimen. The solvent dispensing and extraction system can include a surface sampling probe. The laser beam can be directed through the surface sampling probe. The surface sampling probe can also serve as an atomic force microscopy probe. The surface sampling probe can form a seal with the specimen. The testing solution including the analyte can then be analyzed using an analytical instrument or undergo further processing.

Systems and methods for laser assisted sample transfer to solution for chemical analysis

DOEpatents

Van Berkel, Gary J; Kertesz, Vilmos; Ovchinnikova, Olga S

2013-08-27

Systems and methods are described for laser ablation of an analyte from a specimen and capturing of the analyte in a dispensed solvent to form a testing solution. A solvent dispensing and extraction system can form a liquid microjunction with the specimen. The solvent dispensing and extraction system can include a surface sampling probe. The laser beam can be directed through the surface sampling probe. The surface sampling probe can also serve as an atomic force microscopy probe. The surface sampling probe can form a seal with the specimen. The testing solution including the analyte can then be analyzed using an analytical instrument or undergo further processing.

Nonlinear core deflection in injection molding

NASA Astrophysics Data System (ADS)

Poungthong, P.; Giacomin, A. J.; Saengow, C.; Kolitawong, C.; Liao, H.-C.; Tseng, S.-C.

2018-05-01

Injection molding of thin slender parts is often complicated by core deflection. This deflection is caused by molten plastics race tracking through the slit between the core and the rigid cavity wall. The pressure of this liquid exerts a lateral force of the slender core causing the core to bend, and this bending is governed by a nonlinear fifth order ordinary differential equation for the deflection that is not directly in the position along the core. Here we subject this differential equation to 6 sets of boundary conditions, corresponding to 6 commercial core constraints. For each such set of boundary conditions, we develop an explicit approximate analytical solution, including both a linear term and a nonlinear term. By comparison with finite difference solutions, we find our new analytical solutions to be accurate. We then use these solutions to derive explicit analytical approximations for maximum deflections and for the core position of these maximum deflections. Our experiments on the base-gated free-tip boundary condition agree closely with our new explicit approximate analytical solution.

Numerical applications of the advective-diffusive codes for the inner magnetosphere

NASA Astrophysics Data System (ADS)

Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

2016-11-01

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

Analytical study of robustness of a negative feedback oscillator by multiparameter sensitivity

PubMed Central

2014-01-01

Background One of the distinctive features of biological oscillators such as circadian clocks and cell cycles is robustness which is the ability to resume reliable operation in the face of different types of perturbations. In the previous study, we proposed multiparameter sensitivity (MPS) as an intelligible measure for robustness to fluctuations in kinetic parameters. Analytical solutions directly connect the mechanisms and kinetic parameters to dynamic properties such as period, amplitude and their associated MPSs. Although negative feedback loops are known as common structures to biological oscillators, the analytical solutions have not been presented for a general model of negative feedback oscillators. Results We present the analytical expressions for the period, amplitude and their associated MPSs for a general model of negative feedback oscillators. The analytical solutions are validated by comparing them with numerical solutions. The analytical solutions explicitly show how the dynamic properties depend on the kinetic parameters. The ratio of a threshold to the amplitude has a strong impact on the period MPS. As the ratio approaches to one, the MPS increases, indicating that the period becomes more sensitive to changes in kinetic parameters. We present the first mathematical proof that the distributed time-delay mechanism contributes to making the oscillation period robust to parameter fluctuations. The MPS decreases with an increase in the feedback loop length (i.e., the number of molecular species constituting the feedback loop). Conclusions Since a general model of negative feedback oscillators was employed, the results shown in this paper are expected to be true for many of biological oscillators. This study strongly supports that the hypothesis that phosphorylations of clock proteins contribute to the robustness of circadian rhythms. The analytical solutions give synthetic biologists some clues to design gene oscillators with robust and desired period. PMID:25605374

A simple analytical method to estimate all exit parameters of a cross-flow air dehumidifier using liquid desiccant.

PubMed

Bassuoni, M M

2014-03-01

The dehumidifier is a key component in liquid desiccant air-conditioning systems. Analytical solutions have more advantages than numerical solutions in studying the dehumidifier performance parameters. This paper presents the performance results of exit parameters from an analytical model of an adiabatic cross-flow liquid desiccant air dehumidifier. Calcium chloride is used as desiccant material in this investigation. A program performing the analytical solution is developed using the engineering equation solver software. Good accuracy has been found between analytical solution and reliable experimental results with a maximum deviation of +6.63% and -5.65% in the moisture removal rate. The method developed here can be used in the quick prediction of the dehumidifier performance. The exit parameters from the dehumidifier are evaluated under the effects of variables such as air temperature and humidity, desiccant temperature and concentration, and air to desiccant flow rates. The results show that hot humid air and desiccant concentration have the greatest impact on the performance of the dehumidifier. The moisture removal rate is decreased with increasing both air inlet temperature and desiccant temperature while increases with increasing air to solution mass ratio, inlet desiccant concentration, and inlet air humidity ratio.

Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids

NASA Astrophysics Data System (ADS)

Boué, Laurent; Dasgupta, Ratul; Laurie, Jason; L'Vov, Victor; Nazarenko, Sergey; Procaccia, Itamar

2011-08-01

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett.JTPLA20021-364010.1134/S002136401008014X 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.

Analytical solutions of Landau (1+1)-dimensional hydrodynamics

DOE PAGES

Wong, Cheuk-Yin; Sen, Abhisek; Gerhard, Jochen; ...

2014-12-17

To help guide our intuition, summarize important features, and point out essential elements, we review the analytical solutions of Landau (1+1)-dimensional hydrodynamics and exhibit the full evolution of the dynamics from the very beginning to subsequent times. Special emphasis is placed on the matching and the interplay between the Khalatnikov solution and the Riemann simple wave solution at the earliest times and in the edge regions at later times.

Some exact solutions for maximally symmetric topological defects in Anti de Sitter space

NASA Astrophysics Data System (ADS)

Alvarez, Orlando; Haddad, Matthew

2018-03-01

We obtain exact analytical solutions for a class of SO( l) Higgs field theories in a non-dynamic background n-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric p-dimensional topological defects where n = ( p + 1) + l. The radius of curvature of anti de Sitter space provides an extra length scale that allows us to study the equations of motion in a limit where the masses of the Higgs field and the massive vector bosons are both vanishing. We call this the double BPS limit. In anti de Sitter space, the equations of motion depend on both p and l. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects ( p = 0 , 1 , 2 , . . . ; l = 1), vortex-like defects ( p = 1 , 2 , 3; l = 2), and the 't Hooft-Polyakov monopole ( p = 0; l = 3). A bonus is that the double BPS limit automatically gives a maximally symmetric classical glueball type solution. In certain cases where we did not find an analytic solution, we present numerical solutions to the equations of motion. The asymptotically exponentially increasing volume with distance of anti de Sitter space imposes different constraints than those found in the study of defects in Minkowski space.

Exact analytic solution for non-linear density fluctuation in a ΛCDM universe

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

Yoo, Jaiyul; Gong, Jinn-Ouk, E-mail: jyoo@physik.uzh.ch, E-mail: jinn-ouk.gong@apctp.org

We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a ΛCDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.

Regarding on the prototype solutions for the nonlinear fractional-order biological population model

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

Baskonus, Haci Mehmet, E-mail: hmbaskonus@gmail.com; Bulut, Hasan

2016-06-08

In this study, we have submitted to literature a method newly extended which is called as Improved Bernoulli sub-equation function method based on the Bernoulli Sub-ODE method. The proposed analytical scheme has been expressed with steps. We have obtained some new analytical solutions to the nonlinear fractional-order biological population model by using this technique. Two and three dimensional surfaces of analytical solutions have been drawn by wolfram Mathematica 9. Finally, a conclusion has been submitted by mentioning important acquisitions founded in this study.

Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material.

PubMed

Dalarsson, Mariana; Tassin, Philippe

2009-04-13

We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results obtained by accurate numerical simulations. Our model straightforwardly allows for arbitrary spectral dispersion.

AN ANALYTIC MODEL OF DUSTY, STRATIFIED, SPHERICAL H ii REGIONS

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

Rodríguez-Ramírez, J. C.; Raga, A. C.; Lora, V.

2016-12-20

We study analytically the effect of radiation pressure (associated with photoionization processes and with dust absorption) on spherical, hydrostatic H ii regions. We consider two basic equations, one for the hydrostatic balance between the radiation-pressure components and the gas pressure, and another for the balance among the recombination rate, the dust absorption, and the ionizing photon rate. Based on appropriate mathematical approximations, we find a simple analytic solution for the density stratification of the nebula, which is defined by specifying the radius of the external boundary, the cross section of dust absorption, and the luminosity of the central star. Wemore » compare the analytic solution with numerical integrations of the model equations of Draine, and find a wide range of the physical parameters for which the analytic solution is accurate.« less

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.

Analytical solution for boundary heat fluxes from a radiating rectangular medium

NASA Technical Reports Server (NTRS)

Siegel, R.

1991-01-01

Reference is made to the work of Shah (1979) which demonstrated the possibility of partially integrating the radiative equations analytically to obtain an 'exact' solution. Shah's solution was given as a double integration of the modified Bessel function of order zero. Here, it is shown that the 'exact' solution for a rectangular region radiating to cold black walls can be conveniently derived, and expressed in simple form, by using an integral function, Sn, analogous to the exponential integral function appearing in plane-layer solutions.

Performance evaluation soil samples utilizing encapsulation technology

DOEpatents

Dahlgran, J.R.

1999-08-17

Performance evaluation soil samples and method of their preparation uses encapsulation technology to encapsulate analytes which are introduced into a soil matrix for analysis and evaluation by analytical laboratories. Target analytes are mixed in an appropriate solvent at predetermined concentrations. The mixture is emulsified in a solution of polymeric film forming material. The emulsified solution is polymerized to form microcapsules. The microcapsules are recovered, quantitated and introduced into a soil matrix in a predetermined ratio to form soil samples with the desired analyte concentration. 1 fig.

Performance evaluation soil samples utilizing encapsulation technology

DOEpatents

Dahlgran, James R.

1999-01-01

Performance evaluation soil samples and method of their preparation using encapsulation technology to encapsulate analytes which are introduced into a soil matrix for analysis and evaluation by analytical laboratories. Target analytes are mixed in an appropriate solvent at predetermined concentrations. The mixture is emulsified in a solution of polymeric film forming material. The emulsified solution is polymerized to form microcapsules. The microcapsules are recovered, quantitated and introduced into a soil matrix in a predetermined ratio to form soil samples with the desired analyte concentration.

Analyte detection using an active assay

DOEpatents

Morozov, Victor; Bailey, Charles L.; Evanskey, Melissa R.

2010-11-02

Analytes using an active assay may be detected by introducing an analyte solution containing a plurality of analytes to a lacquered membrane. The lacquered membrane may be a membrane having at least one surface treated with a layer of polymers. The lacquered membrane may be semi-permeable to nonanalytes. The layer of polymers may include cross-linked polymers. A plurality of probe molecules may be arrayed and immobilized on the lacquered membrane. An external force may be applied to the analyte solution to move the analytes towards the lacquered membrane. Movement may cause some or all of the analytes to bind to the lacquered membrane. In cases where probe molecules are presented, some or all of the analytes may bind to probe molecules. The direction of the external force may be reversed to remove unbound or weakly bound analytes. Bound analytes may be detected using known detection types.

Analytical Solutions of the KDV-KZK Equation

NASA Astrophysics Data System (ADS)

Gan, W. S.

The KdV-KZK equation for fluids developed by me was presented at the ICSV 11 in St. Petersburg in July 2004. In this paper, I made an attempt on the analytical solutions of this equation using the perturbation method. Some physical interpretation of the solutions is given. A brief introduction to KdV-KZK equation for solids is given

New integrable models and analytical solutions in f (R ) cosmology with an ideal gas

NASA Astrophysics Data System (ADS)

Papagiannopoulos, G.; Basilakos, Spyros; Barrow, John D.; Paliathanasis, Andronikos

2018-01-01

In the context of f (R ) gravity with a spatially flat FLRW metric containing an ideal fluid, we use the method of invariant transformations to specify families of models which are integrable. We find three families of f (R ) theories for which new analytical solutions are given and closed-form solutions are provided.

An Analytical Solution for Transient Thermal Response of an Insulated Structure

NASA Technical Reports Server (NTRS)

Blosser, Max L.

2012-01-01

An analytical solution was derived for the transient response of an insulated aerospace vehicle structure subjected to a simplified heat pulse. This simplified problem approximates the thermal response of a thermal protection system of an atmospheric entry vehicle. The exact analytical solution is solely a function of two non-dimensional parameters. A simpler function of these two parameters was developed to approximate the maximum structural temperature over a wide range of parameter values. Techniques were developed to choose constant, effective properties to represent the relevant temperature and pressure-dependent properties for the insulator and structure. A technique was also developed to map a time-varying surface temperature history to an equivalent square heat pulse. Using these techniques, the maximum structural temperature rise was calculated using the analytical solutions and shown to typically agree with finite element simulations within 10 to 20 percent over the relevant range of parameters studied.

Finite analytic numerical solution of heat transfer and flow past a square channel cavity

NASA Technical Reports Server (NTRS)

Chen, C.-J.; Obasih, K.

1982-01-01

A numerical solution of flow and heat transfer characteristics is obtained by the finite analytic method for a two dimensional laminar channel flow over a two-dimensional square cavity. The finite analytic method utilizes the local analytic solution in a small element of the problem region to form the algebraic equation relating an interior nodal value with its surrounding nodal values. Stable and rapidly converged solutions were obtained for Reynolds numbers ranging to 1000 and Prandtl number to 10. Streamfunction, vorticity and temperature profiles are solved. Local and mean Nusselt number are given. It is found that the separation streamlines between the cavity and channel flow are concave into the cavity at low Reynolds number and convex at high Reynolds number (Re greater than 100) and for square cavity the mean Nusselt number may be approximately correlated with Peclet number as Nu(m) = 0.365 Pe exp 0.2.

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

An explicit analytical solution for sound propagation in a three-dimensional penetrable wedge with small apex angle.

PubMed

Petrov, Pavel S; Sturm, Frédéric

2016-03-01

A problem of sound propagation in a shallow-water waveguide with a weakly sloping penetrable bottom is considered. The adiabatic mode parabolic equations are used to approximate the solution of the three-dimensional (3D) Helmholtz equation by modal decomposition of the acoustic pressure field. The mode amplitudes satisfy parabolic equations that admit analytical solutions in the special case of the 3D wedge. Using the analytical formula for modal amplitudes, an explicit and remarkably simple expression for the acoustic pressure in the wedge is obtained. The proposed solution is validated by the comparison with a solution of the 3D penetrable wedge problem obtained using a fully 3D parabolic equation that includes a leading-order cross term correction.

Analytical solution for the transient response of a fluid/saturated porous medium halfspace system subjected to an impulsive line source

NASA Astrophysics Data System (ADS)

Shan, Zhendong; Ling, Daosheng; Jing, Liping; Li, Yongqiang

2018-05-01

In this paper, transient wave propagation is investigated within a fluid/saturated porous medium halfspace system with a planar interface that is subjected to a cylindrical P-wave line source. Assuming the permeability coefficient is sufficiently large, analytical solutions for the transient response of the fluid/saturated porous medium halfspace system are developed. Moreover, the analytical solutions are presented in simple closed forms wherein each term represents a transient physical wave, especially the expressions for head waves. The methodology utilised to determine where the head wave can emerge within the system is also given. The wave fields within the fluid and porous medium are first defined considering the behaviour of two compressional waves and one tangential wave in the saturated porous medium and one compressional wave in the fluid. Substituting these wave fields into the interface continuity conditions, the analytical solutions in the Laplace domain are then derived. To transform the solutions into the time domain, a suitable distortion of the contour is provided to change the integration path of the solution, after which the analytical solutions in the Laplace domain are transformed into the time domain by employing Cagniard's method. Numerical examples are provided to illustrate some interesting features of the fluid/saturated porous medium halfspace system. In particular, the interface wave and head waves that propagate along the interface between the fluid and saturated porous medium can be observed.

Hypergeometric Series Solution to a Class of Second-Order Boundary Value Problems via Laplace Transform with Applications to Nanofluids

NASA Astrophysics Data System (ADS)

Ebaid, Abdelhalim; Wazwaz, Abdul-Majid; Alali, Elham; Masaedeh, Basem S.

2017-03-01

Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.

Application of Hamilton's law of varying action

NASA Technical Reports Server (NTRS)

Bailey, C. D.

1975-01-01

The law of varying action enunciated by Hamilton in 1834-1835 permits the direct analytical solution of the problems of mechanics, both stationary and nonstationary, without consideration of force equilibrium and the theory of differential equations associated therewith. It has not been possible to obtain direct analytical solutions to nonstationary systems through the use of energy theory, which has been limited for 140 years to the principle of least action and to Hamilton's principle. It is shown here that Hamilton's law permits the direct analytical solution to nonstationary, initial value systems in the mechanics of solids without any knowledge or use of the theory of differential equations. Solutions are demonstrated for nonconservative, nonstationary particle motion, both linear and nonlinear.

Capillary Driven Flows Along Differentially Wetted Interior Corners

NASA Technical Reports Server (NTRS)

Golliher, Eric L. (Technical Monitor); Nardin, C. L.; Weislogel, M. M.

2005-01-01

Closed-form analytic solutions useful for the design of capillary flows in a variety of containers possessing interior corners were recently collected and reviewed. Low-g drop tower and aircraft experiments performed at NASA to date show excellent agreement between theory and experiment for perfectly wetting fluids. The analytical expressions are general in terms of contact angle, but do not account for variations in contact angle between the various surfaces within the system. Such conditions may be desirable for capillary containment or to compute the behavior of capillary corner flows in containers consisting of different materials with widely varying wetting characteristics. A simple coordinate rotation is employed to recast the governing system of equations for flows in containers with interior corners with differing contact angles on the faces of the corner. The result is that a large number of capillary driven corner flows may be predicted with only slightly modified geometric functions dependent on corner angle and the two (or more) contact angles of the system. A numerical solution is employed to verify the new problem formulation. The benchmarked computations support the use of the existing theoretical approach to geometries with variable wettability. Simple experiments to confirm the theoretical findings are recommended. Favorable agreement between such experiments and the present theory may argue well for the extension of the analytic results to predict fluid performance in future large length scale capillary fluid systems for spacecraft as well as for small scale capillary systems on Earth.

Thermal transport in dimerized harmonic lattices: Exact solution, crossover behavior, and extended reservoirs

NASA Astrophysics Data System (ADS)

Chien, Chih-Chun; Kouachi, Said; Velizhanin, Kirill A.; Dubi, Yonatan; Zwolak, Michael

2017-01-01

We present a method for calculating analytically the thermal conductance of a classical harmonic lattice with both alternating masses and nearest-neighbor couplings when placed between individual Langevin reservoirs at different temperatures. The method utilizes recent advances in analytic diagonalization techniques for certain classes of tridiagonal matrices. It recovers the results from a previous method that was applicable for alternating on-site parameters only, and extends the applicability to realistic systems in which masses and couplings alternate simultaneously. With this analytic result in hand, we show that the thermal conductance is highly sensitive to the modulation of the couplings. This is due to the existence of topologically induced edge modes at the lattice-reservoir interface and is also a reflection of the symmetries of the lattice. We make a connection to a recent work that demonstrates thermal transport is analogous to chemical reaction rates in solution given by Kramers' theory [Velizhanin et al., Sci. Rep. 5, 17506 (2015)], 10.1038/srep17506. In particular, we show that the turnover behavior in the presence of edge modes prevents calculations based on single-site reservoirs from coming close to the natural—or intrinsic—conductance of the lattice. Obtaining the correct value of the intrinsic conductance through simulation of even a small lattice where ballistic effects are important requires quite large extended reservoir regions. Our results thus offer a route for both the design and proper simulation of thermal conductance of nanoscale devices.

A Framework for Understanding Physics Students' Computational Modeling Practices

NASA Astrophysics Data System (ADS)

Lunk, Brandon Robert

With the growing push to include computational modeling in the physics classroom, we are faced with the need to better understand students' computational modeling practices. While existing research on programming comprehension explores how novices and experts generate programming algorithms, little of this discusses how domain content knowledge, and physics knowledge in particular, can influence students' programming practices. In an effort to better understand this issue, I have developed a framework for modeling these practices based on a resource stance towards student knowledge. A resource framework models knowledge as the activation of vast networks of elements called "resources." Much like neurons in the brain, resources that become active can trigger cascading events of activation throughout the broader network. This model emphasizes the connectivity between knowledge elements and provides a description of students' knowledge base. Together with resources resources, the concepts of "epistemic games" and "frames" provide a means for addressing the interaction between content knowledge and practices. Although this framework has generally been limited to describing conceptual and mathematical understanding, it also provides a means for addressing students' programming practices. In this dissertation, I will demonstrate this facet of a resource framework as well as fill in an important missing piece: a set of epistemic games that can describe students' computational modeling strategies. The development of this theoretical framework emerged from the analysis of video data of students generating computational models during the laboratory component of a Matter & Interactions: Modern Mechanics course. Student participants across two semesters were recorded as they worked in groups to fix pre-written computational models that were initially missing key lines of code. Analysis of this video data showed that the students' programming practices were highly influenced by their existing physics content knowledge, particularly their knowledge of analytic procedures. While this existing knowledge was often applied in inappropriate circumstances, the students were still able to display a considerable amount of understanding of the physics content and of analytic solution procedures. These observations could not be adequately accommodated by the existing literature of programming comprehension. In extending the resource framework to the task of computational modeling, I model students' practices in terms of three important elements. First, a knowledge base includes re- sources for understanding physics, math, and programming structures. Second, a mechanism for monitoring and control describes students' expectations as being directed towards numerical, analytic, qualitative or rote solution approaches and which can be influenced by the problem representation. Third, a set of solution approaches---many of which were identified in this study---describe what aspects of the knowledge base students use and how they use that knowledge to enact their expectations. This framework allows us as researchers to track student discussions and pinpoint the source of difficulties. This work opens up many avenues of potential research. First, this framework gives researchers a vocabulary for extending Resource Theory to other domains of instruction, such as modeling how physics students use graphs. Second, this framework can be used as the basis for modeling expert physicists' programming practices. Important instructional implications also follow from this research. Namely, as we broaden the use of computational modeling in the physics classroom, our instructional practices should focus on helping students understand the step-by-step nature of programming in contrast to the already salient analytic procedures.

Analytical approximate solutions for a general class of nonlinear delay differential equations.

PubMed

Căruntu, Bogdan; Bota, Constantin

2014-01-01

We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

Analytic, High-beta Solutions of the Helical Grad-Shafranov Equation

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

D.R. Smith; A.H. Reiman

We present analytic, high-beta ({beta} {approx} O(1)), helical equilibrium solutions for a class of helical axis configurations having large helical aspect ratio, with the helix assumed to be tightly wound. The solutions develop a narrow boundary layer of strongly compressed flux, similar to that previously found in high beta tokamak equilibrium solutions. The boundary layer is associated with a strong localized current which prevents the equilibrium from having zero net current.

An analytically iterative method for solving problems of cosmic-ray modulation

NASA Astrophysics Data System (ADS)

Kolesnyk, Yuriy L.; Bobik, Pavol; Shakhov, Boris A.; Putis, Marian

2017-09-01

The development of an analytically iterative method for solving steady-state as well as unsteady-state problems of cosmic-ray (CR) modulation is proposed. Iterations for obtaining the solutions are constructed for the spherically symmetric form of the CR propagation equation. The main solution of the considered problem consists of the zero-order solution that is obtained during the initial iteration and amendments that may be obtained by subsequent iterations. The finding of the zero-order solution is based on the CR isotropy during propagation in the space, whereas the anisotropy is taken into account when finding the next amendments. To begin with, the method is applied to solve the problem of CR modulation where the diffusion coefficient κ and the solar wind speed u are constants with an Local Interstellar Spectra (LIS) spectrum. The solution obtained with two iterations was compared with an analytical solution and with numerical solutions. Finally, solutions that have only one iteration for two problems of CR modulation with u = constant and the same form of LIS spectrum were obtained and tested against numerical solutions. For the first problem, κ is proportional to the momentum of the particle p, so it has the form κ = k0η, where η =p/m_0c. For the second problem, the diffusion coefficient is given in the form κ = k0βη, where β =v/c is the particle speed relative to the speed of light. There was a good matching of the obtained solutions with the numerical solutions as well as with the analytical solution for the problem where κ = constant.

Stochastic modeling of macrodispersion in unsaturated heterogeneous porous media. Final report

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

Yeh, T.C.J.

1995-02-01

Spatial heterogeneity of geologic media leads to uncertainty in predicting both flow and transport in the vadose zone. In this work an efficient and flexible, combined analytical-numerical Monte Carlo approach is developed for the analysis of steady-state flow and transient transport processes in highly heterogeneous, variably saturated porous media. The approach is also used for the investigation of the validity of linear, first order analytical stochastic models. With the Monte Carlo analysis accurate estimates of the ensemble conductivity, head, velocity, and concentration mean and covariance are obtained; the statistical moments describing displacement of solute plumes, solute breakthrough at a compliancemore » surface, and time of first exceedance of a given solute flux level are analyzed; and the cumulative probability density functions for solute flux across a compliance surface are investigated. The results of the Monte Carlo analysis show that for very heterogeneous flow fields, and particularly in anisotropic soils, the linearized, analytical predictions of soil water tension and soil moisture flux become erroneous. Analytical, linearized Lagrangian transport models also overestimate both the longitudinal and the transverse spreading of the mean solute plume in very heterogeneous soils and in dry soils. A combined analytical-numerical conditional simulation algorithm is also developed to estimate the impact of in-situ soil hydraulic measurements on reducing the uncertainty of concentration and solute flux predictions.« less

Things that go bump in the light - On the optical specification of contact severity

NASA Technical Reports Server (NTRS)

Kaiser, Mary K.; Phatak, Anil V.

1993-01-01

Psychologists are intrigued with the idea that optical variables can specify not only the time until an object impacts an observer but also the severity of the impact. However, the mapping between the optical variables and the kinematic variables has been misstated, erroneously implying that there exist critical values of the optical variables used for locomotion and control. In this commentary, the mathematical relationship between the optical and kinematic variables is reexamined and the erroneous assumptions that have led to the proposal of critical values are shown. Also examined are the empirical data on deceleration to approach to assess whether the proposed optical variables are likely candidates for control strategies. Finally, problems associated with numerical approximations to dynamic systems, particularly when analytic solutions exist, are discussed.

Semi-analytical study of the tokamak pedestal density profile in a single-null diverted plasma with puffing-recycling gas sources

NASA Astrophysics Data System (ADS)

Shi, Bingren

2010-10-01

The tokamak pedestal density structure is generally studied using a diffusion-dominant model. Recent investigations (Stacey and Groebner 2009 Phys. Plasmas 16 102504) from first principle based physics have shown a plausible existence of large inward convection in the pedestal region. The diffusion-convection equation with rapidly varying convection and diffusion coefficients in the near edge region and model puffing-recycling neutral particles is studied in this paper. A peculiar property of its solution for the existence of the large convection case is that the pedestal width of the density profile, qualitatively different from the diffusion-dominant case, depends mainly on the width of the inward convection and only weakly on the neutral penetration length and its injection position.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves.

PubMed

Tsitoura, F; Gietz, U; Chabchoub, A; Hoffmann, N

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

NASA Astrophysics Data System (ADS)

Tsitoura, F.; Gietz, U.; Chabchoub, A.; Hoffmann, N.

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

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.

A structured population model with diffusion in structure space.

PubMed

Pugliese, Andrea; Milner, Fabio

2018-05-09

A structured population model is described and analyzed, in which individual dynamics is stochastic. The model consists of a PDE of advection-diffusion type in the structure variable. The population may represent, for example, the density of infected individuals structured by pathogen density x, [Formula: see text]. The individuals with density [Formula: see text] are not infected, but rather susceptible or recovered. Their dynamics is described by an ODE with a source term that is the exact flux from the diffusion and advection as [Formula: see text]. Infection/reinfection is then modeled moving a fraction of these individuals into the infected class by distributing them in the structure variable through a probability density function. Existence of a global-in-time solution is proven, as well as a classical bifurcation result about equilibrium solutions: a net reproduction number [Formula: see text] is defined that separates the case of only the trivial equilibrium existing when [Formula: see text] from the existence of another-nontrivial-equilibrium when [Formula: see text]. Numerical simulation results are provided to show the stabilization towards the positive equilibrium when [Formula: see text] and towards the trivial one when [Formula: see text], result that is not proven analytically. Simulations are also provided to show the Allee effect that helps boost population sizes at low densities.

Revisitation of the dipole tracer test for heterogeneous porous formations

NASA Astrophysics Data System (ADS)

Zech, Alraune; D'Angelo, Claudia; Attinger, Sabine; Fiori, Aldo

2018-05-01

In this paper, a new analytical solution for interpreting dipole tests in heterogeneous media is derived by associating the shape of the tracer breakthrough curve with the log-conductivity variance. It is presented how the solution can be used for interpretation of dipole field test in view of geostatistical aquifer characterization on three illustrative examples. The analytical solution for the tracer breakthrough curve at the pumping well in a dipole tracer test is developed by considering a perfectly stratified formation. The analysis is carried out making use of the travel time of a generic solute particle, from the injection to the pumping well. Injection conditions are adapted to different possible field setting. Solutions are presented for resident and flux proportional injection mode as well as for an instantaneous pulse of solute and continuous solute injections. The analytical form of the solution allows a detailed investigation on the impact of heterogeneity, the tracer input conditions and ergodicity conditions at the well. The impact of heterogeneity manifests in a significant spreading of solute particles that increases the natural tendency to spreading induced by the dipole setup. Furthermore, with increasing heterogeneity the number of layers needed to reach ergodic conditions become larger. Thus, dipole test in highly heterogeneous aquifers might take place under non-ergodic conditions giving that the log-conductivity variance is underestimated. The method is a promising geostatistical analyzing tool being the first analytical solution for dipole tracer test analysis taking heterogeneity of hydraulic conductivity into account.

Mechanical Properties of Additively Manufactured Thick Honeycombs

PubMed Central

Hedayati, Reza; Sadighi, Mojtaba; Mohammadi Aghdam, Mohammad; Zadpoor, Amir Abbas

2016-01-01

Honeycombs resemble the structure of a number of natural and biological materials such as cancellous bone, wood, and cork. Thick honeycomb could be also used for energy absorption applications. Moreover, studying the mechanical behavior of honeycombs under in-plane loading could help understanding the mechanical behavior of more complex 3D tessellated structures such as porous biomaterials. In this paper, we study the mechanical behavior of thick honeycombs made using additive manufacturing techniques that allow for fabrication of honeycombs with arbitrary and precisely controlled thickness. Thick honeycombs with different wall thicknesses were produced from polylactic acid (PLA) using fused deposition modelling, i.e., an additive manufacturing technique. The samples were mechanically tested in-plane under compression to determine their mechanical properties. We also obtained exact analytical solutions for the stiffness matrix of thick hexagonal honeycombs using both Euler-Bernoulli and Timoshenko beam theories. The stiffness matrix was then used to derive analytical relationships that describe the elastic modulus, yield stress, and Poisson’s ratio of thick honeycombs. Finite element models were also built for computational analysis of the mechanical behavior of thick honeycombs under compression. The mechanical properties obtained using our analytical relationships were compared with experimental observations and computational results as well as with analytical solutions available in the literature. It was found that the analytical solutions presented here are in good agreement with experimental and computational results even for very thick honeycombs, whereas the analytical solutions available in the literature show a large deviation from experimental observation, computational results, and our analytical solutions. PMID:28773735

Functionalized magnetic nanoparticle analyte sensor

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

Yantasee, Wassana; Warner, Maryin G; Warner, Cynthia L

2014-03-25

A method and system for simply and efficiently determining quantities of a preselected material in a particular solution by the placement of at least one superparamagnetic nanoparticle having a specified functionalized organic material connected thereto into a particular sample solution, wherein preselected analytes attach to the functionalized organic groups, these superparamagnetic nanoparticles are then collected at a collection site and analyzed for the presence of a particular analyte.

Approximate Solution to the Angular Speeds of a Nearly-Symmetric Mass-Varying Cylindrical Body

NASA Astrophysics Data System (ADS)

Nanjangud, Angadh; Eke, Fidelis

2017-06-01

This paper examines the rotational motion of a nearly axisymmetric rocket type system with uniform burn of its propellant. The asymmetry comes from a slight difference in the transverse principal moments of inertia of the system, which then results in a set of nonlinear equations of motion even when no external torque is applied to the system. It is often difficult, or even impossible, to generate analytic solutions for such equations; closed form solutions are even more difficult to obtain. In this paper, a perturbation-based approach is employed to linearize the equations of motion and generate analytic solutions. The solutions for the variables of transverse motion are analytic and a closed-form solution to the spin rate is suggested. The solutions are presented in a compact form that permits rapid computation. The approximate solutions are then applied to the torque-free motion of a typical solid rocket system and the results are found to agree with those obtained from the numerical solution of the full non-linear equations of motion of the mass varying system.

Dielectric elastomer peristaltic pump module with finite deformation

NASA Astrophysics Data System (ADS)

Mao, Guoyong; Huang, Xiaoqiang; Liu, Junjie; Li, Tiefeng; Qu, Shaoxing; Yang, Wei

2015-07-01

Inspired by various peristaltic structures existing in nature, several bionic peristaltic actuators have been developed. In this study, we propose a novel dielectric elastomer peristaltic pump consisting of short tubular modules, with the saline solution as the electrodes. We investigate the performance of this soft pump module under hydraulic pressure and voltage via experiments and an analytical model based on nonlinear field theory. It is observed that the individual pump module undergoes finite deformation and may experience electromechanical instability during operations. The driving pressure and displaced volume of the peristaltic pump module can be modulated by applied voltage. The efficiency of the pump module is enhanced by alternating current voltage, which can suppress the electromechanical pull-in instability. An analytical model is developed within the framework of the nonlinear field theory, and its predictive capacity is checked by experimental observations. The effects of the prestretch, aspect ratio, and voltage on the performance of the pump modules are characterized by the analytical model. This work can guide the designs of soft active peristaltic pumps in the field of artificial organs and industrial conveying systems.

Analytically optimal parameters of dynamic vibration absorber with negative stiffness

NASA Astrophysics Data System (ADS)

Shen, Yongjun; Peng, Haibo; Li, Xianghong; Yang, Shaopu

2017-02-01

In this paper the optimal parameters of a dynamic vibration absorber (DVA) with negative stiffness is analytically studied. The analytical solution is obtained by Laplace transform method when the primary system is subjected to harmonic excitation. The research shows there are still two fixed points independent of the absorber damping in the amplitude-frequency curve of the primary system when the system contains negative stiffness. Then the optimum frequency ratio and optimum damping ratio are respectively obtained based on the fixed-point theory. A new strategy is proposed to obtain the optimum negative stiffness ratio and make the system remain stable at the same time. At last the control performance of the presented DVA is compared with those of three existing typical DVAs, which were presented by Den Hartog, Ren and Sims respectively. The comparison results in harmonic and random excitation show that the presented DVA in this paper could not only reduce the peak value of the amplitude-frequency curve of the primary system significantly, but also broaden the efficient frequency range of vibration mitigation.

Photoemission studies of fluorine functionalized porous graphitic carbon

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

Ganegoda, Hasitha; Olive, Daniel; Cheng, Lidens

2012-03-01

Porous graphitic carbon (PGC) has unique properties desirable for liquid chromatography applications when used as a stationary phase. The polar retention effect on graphite (PREG) allows efficient separation of polar and non-polar solutes. Perfluorinated hydrocarbons however lack polarizabilty and display strong lipo- and hydrophobicity, hence common lipophilic and hydrophilic analytes have low partition coefficiency in fluorinated stationary phases. Attractive interaction between fluorinated stationary phase and fluorinated analytes results in strong retention compared to non-fluorinated analytes. In order to change the selectivities of PGC, it is necessary to develop a bonded PGC stationary phase. In this study, we have synthesized perfluorinated,more » PGC using hepatadecafluoro-1-iodooctane, under different temperature conditions. Surface functionalization of the raw material was studied using photoelectron spectroscopy (PES). Results indicate the existence of fluorine containing functional groups, -CF, -CF{sub 2} along with an intercalated electron donor species. Multiple oxygen functional groups were also observed, likely due to the presence of oxygen in the starting material. These oxygen species may be responsible for significant modifications to planer and tetrahedral carbon ratios.« less

Modeling photoacoustic spectral features of micron-sized particles

NASA Astrophysics Data System (ADS)

Strohm, Eric M.; Gorelikov, Ivan; Matsuura, Naomi; Kolios, Michael C.

2014-10-01

The photoacoustic signal generated from particles when irradiated by light is determined by attributes of the particle such as the size, speed of sound, morphology and the optical absorption coefficient. Unique features such as periodically varying minima and maxima are observed throughout the photoacoustic signal power spectrum, where the periodicity depends on these physical attributes. The frequency content of the photoacoustic signals can be used to obtain the physical attributes of unknown particles by comparison to analytical solutions of homogeneous symmetric geometric structures, such as spheres. However, analytical solutions do not exist for irregularly shaped particles, inhomogeneous particles or particles near structures. A finite element model (FEM) was used to simulate photoacoustic wave propagation from four different particle configurations: a homogeneous particle suspended in water, a homogeneous particle on a reflecting boundary, an inhomogeneous particle with an absorbing shell and non-absorbing core, and an irregularly shaped particle such as a red blood cell. Biocompatible perfluorocarbon droplets, 3-5 μm in diameter containing optically absorbing nanoparticles were used as the representative ideal particles, as they are spherical, homogeneous, optically translucent, and have known physical properties. The photoacoustic spectrum of micron-sized single droplets in suspension and on a reflecting boundary were measured over the frequency range of 100-500 MHz and compared directly to analytical models and the FEM. Good agreement between the analytical model, FEM and measured values were observed for a droplet in suspension, where the spectral minima agreed to within a 3.3 MHz standard deviation. For a droplet on a reflecting boundary, spectral features were correctly reproduced using the FEM but not the analytical model. The photoacoustic spectra from other common particle configurations such as particle with an absorbing shell and a biconcave-shaped red blood cell were also investigated, where unique features in the power spectrum could be used to identify them.

Cloud point extraction thermospray flame quartz furnace atomic absorption spectrometry for determination of ultratrace cadmium in water and urine

NASA Astrophysics Data System (ADS)

Wu, Peng; Zhang, Yunchang; Lv, Yi; Hou, Xiandeng

2006-12-01

A simple, low cost and highly sensitive method based on cloud point extraction (CPE) for separation/preconcentration and thermospray flame quartz furnace atomic absorption spectrometry was proposed for the determination of ultratrace cadmium in water and urine samples. The analytical procedure involved the formation of analyte-entrapped surfactant micelles by mixing the analyte solution with an ammonium pyrrolidinedithiocarbamate (APDC) solution and a Triton X-114 solution. When the temperature of the system was higher than the cloud point of Triton X-114, the complex of cadmium-PDC entered the surfactant-rich phase and thus separation of the analyte from the matrix was achieved. Under optimal chemical and instrumental conditions, the limit of detection was 0.04 μg/L for cadmium with a sample volume of 10 mL. The analytical results of cadmium in water and urine samples agreed well with those by ICP-MS.

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

Karakaya, Mahmut; Qi, Hairong

This paper addresses the communication and energy efficiency in collaborative visual sensor networks (VSNs) for people localization, a challenging computer vision problem of its own. We focus on the design of a light-weight and energy efficient solution where people are localized based on distributed camera nodes integrating the so-called certainty map generated at each node, that records the target non-existence information within the camera s field of view. We first present a dynamic itinerary for certainty map integration where not only each sensor node transmits a very limited amount of data but that a limited number of camera nodes ismore » involved. Then, we perform a comprehensive analytical study to evaluate communication and energy efficiency between different integration schemes, i.e., centralized and distributed integration. Based on results obtained from analytical study and real experiments, the distributed method shows effectiveness in detection accuracy as well as energy and bandwidth efficiency.« less

Predicting Upscaled Behavior of Aqueous Reactants in Heterogeneous Porous Media

NASA Astrophysics Data System (ADS)

Wright, E. E.; Hansen, S. K.; Bolster, D.; Richter, D. H.; Vesselinov, V. V.

2017-12-01

When modeling reactive transport, reaction rates are often overestimated due to the improper assumption of perfect mixing at the support scale of the transport model. In reality, fronts tend to form between participants in thermodynamically favorable reactions, leading to segregation of reactants into islands or fingers. When such a configuration arises, reactions are limited to the interface between the reactive solutes. Closure methods for estimating control-volume-effective reaction rates in terms of quantities defined at the control volume scale do not presently exist, but their development is crucial for effective field-scale modeling. We attack this problem through a combination of analytical and numerical means. Specifically, we numerically study reactive transport through an ensemble of realizations of two-dimensional heterogeneous porous media. We then employ regression analysis to calibrate an analytically-derived relationship between reaction rate and various dimensionless quantities representing conductivity-field heterogeneity and the respective strengths of diffusion, reaction and advection.

Probability theory versus simulation of petroleum potential in play analysis

USGS Publications Warehouse

Crovelli, R.A.

1987-01-01

An analytic probabilistic methodology for resource appraisal of undiscovered oil and gas resources in play analysis is presented. This play-analysis methodology is a geostochastic system for petroleum resource appraisal in explored as well as frontier areas. An objective was to replace an existing Monte Carlo simulation method in order to increase the efficiency of the appraisal process. Underlying the two methods is a single geologic model which considers both the uncertainty of the presence of the assessed hydrocarbon and its amount if present. The results of the model are resource estimates of crude oil, nonassociated gas, dissolved gas, and gas for a geologic play in terms of probability distributions. The analytic method is based upon conditional probability theory and a closed form solution of all means and standard deviations, along with the probabilities of occurrence. ?? 1987 J.C. Baltzer A.G., Scientific Publishing Company.

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.

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 and numerical solutions for heat transfer and effective thermal conductivity of cracked media

NASA Astrophysics Data System (ADS)

Tran, A. B.; Vu, M. N.; Nguyen, S. T.; Dong, T. Q.; Le-Nguyen, K.

2018-02-01

This paper presents analytical solutions to heat transfer problems around a crack and derive an adaptive model for effective thermal conductivity of cracked materials based on singular integral equation approach. Potential solution of heat diffusion through two-dimensional cracked media, where crack filled by air behaves as insulator to heat flow, is obtained in a singular integral equation form. It is demonstrated that the temperature field can be described as a function of temperature and rate of heat flow on the boundary and the temperature jump across the cracks. Numerical resolution of this boundary integral equation allows determining heat conduction and effective thermal conductivity of cracked media. Moreover, writing this boundary integral equation for an infinite medium embedding a single crack under a far-field condition allows deriving the closed-form solution of temperature discontinuity on the crack and particularly the closed-form solution of temperature field around the crack. These formulas are then used to establish analytical effective medium estimates. Finally, the comparison between the developed numerical and analytical solutions allows developing an adaptive model for effective thermal conductivity of cracked media. This model takes into account both the interaction between cracks and the percolation threshold.

Flow through three-dimensional arrangements of cylinders with alternating streamwise planar tilt

NASA Astrophysics Data System (ADS)

Sahraoui, M.; Marshall, H.; Kaviany, M.

1993-09-01

In this report, fluid flow through a three-dimensional model for the fibrous filters is examined. In this model, the three-dimensional Stokes equation with the appropriate periodic boundary conditions is solved using the finite volume method. In addition to the numerical solution, we attempt to model this flow analytically by using the two-dimensional extended analytic solution in each of the unit cells of the three-dimensional structure. Particle trajectories computed using the superimposed analytic solution of the flow field are closed to those computed using the numerical solution of the flow field. The numerical results show that the pressure drop is not affected significantly by the relative angle of rotation of the cylinders for the high porosity used in this study (epsilon = 0.8 and epsilon = 0.95). The numerical solution and the superimposed analytic solution are also compared in terms of the particle capture efficiency. The results show that the efficiency predictions using the two methods are within 10% for St = 0.01 and 5% for St = 100. As the the porosity decreases, the three-dimensional effect becomes more significant and a difference of 35% is obtained for epsilon = 0.8.

Liouvillian integrability of gravitating static isothermal fluid spheres

NASA Astrophysics Data System (ADS)

Iacono, Roberto; Llibre, Jaume

2014-10-01

We examine the integrability properties of the Einstein field equations for static, spherically symmetric fluid spheres, complemented with an isothermal equation of state, ρ = np. In this case, Einstein's equations can be reduced to a nonlinear, autonomous second order ordinary differential equation (ODE) for m/R (m is the mass inside the radius R) that has been solved analytically only for n = -1 and n = -3, yielding the cosmological solutions by De Sitter and Einstein, respectively, and for n = -5, case for which the solution can be derived from the De Sitter's one using a symmetry of Einstein's equations. The solutions for these three cases are of Liouvillian type, since they can be expressed in terms of elementary functions. Here, we address the question of whether Liouvillian solutions can be obtained for other values of n. To do so, we transform the second order equation into an equivalent autonomous Lotka-Volterra quadratic polynomial differential system in {R}^2, and characterize the Liouvillian integrability of this system using Darboux theory. We find that the Lotka-Volterra system possesses Liouvillian first integrals for n = -1, -3, -5, which descend from the existence of invariant algebraic curves of degree one, and for n = -6, a new solvable case, associated to an invariant algebraic curve of higher degree (second). For any other value of n, eventual first integrals of the Lotka-Volterra system, and consequently of the second order ODE for the mass function must be non-Liouvillian. This makes the existence of other solutions of the isothermal fluid sphere problem with a Liouvillian metric quite unlikely.

Global Resolution of the Physical Vacuum Singularity for Three-Dimensional Isentropic Inviscid Flows with Damping in Spherically Symmetric Motions

NASA Astrophysics Data System (ADS)

Zeng, Huihui

2017-10-01

For the gas-vacuum interface problem with physical singularity and the sound speed being {C^{{1}/{2}}}-Hölder continuous near vacuum boundaries of the isentropic compressible Euler equations with damping, the global existence of smooth solutions and the convergence to Barenblatt self-similar solutions of the corresponding porous media equation are proved in this paper for spherically symmetric motions in three dimensions; this is done by overcoming the analytical difficulties caused by the coordinate's singularity near the center of symmetry, and the physical vacuum singularity to which standard methods of symmetric hyperbolic systems do not apply. Various weights are identified to resolve the singularity near the vacuum boundary and the center of symmetry globally in time. The results obtained here contribute to the theory of global solutions to vacuum boundary problems of compressible inviscid fluids, for which the currently available results are mainly for the local-in-time well-posedness theory, and also to the theory of global smooth solutions of dissipative hyperbolic systems which fail to be strictly hyperbolic.

Nonlocal electron transport: direct and Greens function solution and comparison of our model with the SNB model

NASA Astrophysics Data System (ADS)

Colombant, Denis; Manheimer, Wallace; Schmitt, Andrew J.

2013-10-01

At least two models, ours and SNB (Schurtz-Nicolai-Busquet), and two methods of solution, direct numerical solution (DS) and Greens function (GF) are being used in multi-dimensional radiation hydrodynamics codes. We present results of a laser target implosion using both methods of solution. Although our model and SNB differ in some physical content, direct comparisons have been non-existent up to now. However a paper by Marocchino et al. has recently presented the results of two nanosecond-time-scale test problems, showing that the preheat calculated by the two models are different by about three orders of magnitude. We have rerun these problems and we find much less difference between the two than they do. One can show analytically that the results should be quite similar and are about an order of magnitude less than the maximum, and two orders of magnitude more than the minimum preheating in. We have been able to trace the somewhat different results back to the different physical assumptions made in each model. Work supported by DoE-NNSA and ONR.

A new time domain random walk method for solute transport in 1-D heterogeneous media

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

Banton, O.; Delay, F.; Porel, G.

A new method to simulate solute transport in 1-D heterogeneous media is presented. This time domain random walk method (TDRW), similar in concept to the classical random walk method, calculates the arrival time of a particle cloud at a given location (directly providing the solute breakthrough curve). The main advantage of the method is that the restrictions on the space increments and the time steps which exist with the finite differences and random walk methods are avoided. In a homogeneous zone, the breakthrough curve (BTC) can be calculated directly at a given distance using a few hundred particles or directlymore » at the boundary of the zone. Comparisons with analytical solutions and with the classical random walk method show the reliability of this method. The velocity and dispersivity calculated from the simulated results agree within two percent with the values used as input in the model. For contrasted heterogeneous media, the random walk can generate high numerical dispersion, while the time domain approach does not.« less

Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave.

PubMed

Frisvad, Jeppe Revall

2018-04-01

In absorbing media, electromagnetic plane waves are most often inhomogeneous. Existing solutions for the scattering of an inhomogeneous plane wave by a spherical particle provide no explicit expressions for the scattering components. In addition, current analytical solutions require evaluation of the complex hypergeometric function F 1 2 for every term of a series expansion. In this work, I develop a simpler solution based on associated Legendre functions with argument zero. It is similar to the solution for homogeneous plane waves but with new explicit expressions for the angular dependency of the far-field scattering components, that is, the phase function. I include recurrence formulas for practical evaluation and provide numerical examples to evaluate how well the new expressions match previous work in some limiting cases. The predicted difference in the scattering phase function due to inhomogeneity is not negligible for light entering an absorbing medium at an oblique angle. The presented theory could thus be useful for predicting scattering behavior in dye-based random lasing and in solar cell absorption enhancement.

Analytical and numerical solutions of the equation for the beam propagation in a photovoltaic-photorefractive media

NASA Astrophysics Data System (ADS)

Lin, Ji; Wang, Hou

2013-07-01

We use the classical Lie-group method to study the evolution equation describing a photovoltaic-photorefractive media with the effects of diffusion process and the external electric field. We reduce it to some similarity equations firstly, and then obtain some analytically exact solutions including the soliton solution, the exponential solution and the oscillatory solution. We also obtain the numeric solitons from these similarity equations. Moreover, We show theoretically that these solutions have two types of trajectories. One type is a straight line. The other is a parabolic curve, which indicates these solitons have self-deflection.

A simple analytical method to estimate all exit parameters of a cross-flow air dehumidifier using liquid desiccant

PubMed Central

Bassuoni, M.M.

2013-01-01

The dehumidifier is a key component in liquid desiccant air-conditioning systems. Analytical solutions have more advantages than numerical solutions in studying the dehumidifier performance parameters. This paper presents the performance results of exit parameters from an analytical model of an adiabatic cross-flow liquid desiccant air dehumidifier. Calcium chloride is used as desiccant material in this investigation. A program performing the analytical solution is developed using the engineering equation solver software. Good accuracy has been found between analytical solution and reliable experimental results with a maximum deviation of +6.63% and −5.65% in the moisture removal rate. The method developed here can be used in the quick prediction of the dehumidifier performance. The exit parameters from the dehumidifier are evaluated under the effects of variables such as air temperature and humidity, desiccant temperature and concentration, and air to desiccant flow rates. The results show that hot humid air and desiccant concentration have the greatest impact on the performance of the dehumidifier. The moisture removal rate is decreased with increasing both air inlet temperature and desiccant temperature while increases with increasing air to solution mass ratio, inlet desiccant concentration, and inlet air humidity ratio. PMID:25685485

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.

Analytical solution of groundwater flow in a sloping aquifer with stream-aquifer interaction.

NASA Astrophysics Data System (ADS)

Liu, X.; Zhan, H.

2017-12-01

This poster presents a new analytical solution to study water exchange, hydraulic head distribution and water flow in a stream-unconfined aquifer interaction system with a sloping bed and stream of varying heads in presence of two thin vertical sedimentary layers. The formation of a clogging bed of fine-grained sediments allows the interfaces among a sloping aquifer and two rivers as the third kind and Cauchy boundary conditions. The numerical solution of the corresponding nonlinear Boussinesq equation is also developed to compare the performance of the analytical solution. The effects of precipitation recharge, bed slope and stage variation rate of two rivers for water flow in the sloping aquifer are discussed in the results.

An analytical solution for two-dimensional vacuum preloading combined with electro-osmosis consolidation using EKG electrodes

PubMed Central

Qiu, Chenchen; Li, Yande

2017-01-01

China is a country with vast territory, but economic development and population growth have reduced the usable land resources in recent years. Therefore, reclamation by pumping and filling is carried out in eastern coastal regions of China in order to meet the needs of urbanization. However, large areas of reclaimed land need rapid drainage consolidation treatment. Based on past researches on how to improve the treatment efficiency of soft clay using vacuum preloading combined with electro-osmosis, a two-dimensional drainage plane model was proposed according to the Terzaghi and Esrig consolidation theory. However, the analytical solution using two-dimensional plane model was never involved. Current analytical solutions can’t have a thorough theoretical analysis of practical engineering and give relevant guidance. Considering the smearing effect and the rectangle arrangement pattern, an analytical solution is derived to describe the behavior of pore-water and the consolidation process by using EKG (electro-kinetic geo synthetics) materials. The functions of EKG materials include drainage, electric conduction and corrosion resistance. Comparison with test results is carried out to verify the analytical solution. It is found that the measured value is larger than the applied vacuum degree because of the stacking effect of the vacuum preloading and electro-osmosis. The trends of the mean measured value and the mean analytical value processes are comparable. Therefore, the consolidation model can accurately assess the change in pore-water pressure and the consolidation process during vacuum preloading combined with electro-osmosis. PMID:28771496

Synchronization properties of network motifs: Influence of coupling delay and symmetry

NASA Astrophysics Data System (ADS)

D'Huys, O.; Vicente, R.; Erneux, T.; Danckaert, J.; Fischer, I.

2008-09-01

We investigate the effect of coupling delays on the synchronization properties of several network motifs. In particular, we analyze the synchronization patterns of unidirectionally coupled rings, bidirectionally coupled rings, and open chains of Kuramoto oscillators. Our approach includes an analytical and semianalytical study of the existence and stability of different in-phase and out-of-phase periodic solutions, complemented by numerical simulations. The delay is found to act differently on networks possessing different symmetries. While for the unidirectionally coupled ring the coupling delay is mainly observed to induce multistability, its effect on bidirectionally coupled rings is to enhance the most symmetric solution. We also study the influence of feedback and conclude that it also promotes the in-phase solution of the coupled oscillators. We finally discuss the relation between our theoretical results on delay-coupled Kuramoto oscillators and the synchronization properties of networks consisting of real-world delay-coupled oscillators, such as semiconductor laser arrays and neuronal circuits.

Self-Synchronized Phenomena Generated in Rotor-Type Oscillators: On the Influence of Coupling Condition between Oscillators

NASA Astrophysics Data System (ADS)

Bonkobara, Yasuhiro; Mori, Hiroki; Kondou, Takahiro; Ayabe, Takashi

Self-synchronized phenomena generated in rotor-type oscillators mounted on a straight-line spring-mass system are investigated experimentally and analytically. In the present study, we examine the occurrence region and pattern of self-synchronization in two types of coupled oscillators: rigidly coupled oscillators and elastically coupled oscillators. It is clarified that the existence regions of stable solutions are governed mainly by the linear natural frequency of each spring-mass system. The results of numerical analysis confirm that the self-synchronized solutions of the elastically coupled oscillators correspond to those of the rigidly coupled oscillators. In addition, the results obtained in the present study are compared with the previously reported results for a metronome system and a moving apparatus and the different properties of the phenomena generated in the rotor-type oscillators and the pendulum-type oscillators are shown in terms of the construction of branches of self-synchronized solution and the stability.

Nonlocal Symmetries and Interaction Solutions for Potential Kadomtsev-Petviashvili Equation

NASA Astrophysics Data System (ADS)

Ren, Bo; Yu, Jun; Liu, Xi-Zhong

2016-03-01

The nonlocal symmetry for the potential Kadomtsev-Petviashvili (pKP) equation is derived by the truncated Painlevé analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing the auxiliary dependent variable. Thanks to localization process, the finite symmetry transformations related with the nonlocal symmetry are obtained by solving the prolonged systems. The inelastic interactions among the multiple-front waves of the pKP equation are generated from the finite symmetry transformations. Based on the consistent tanh expansion method, a nonauto-Bäcklund transformation (BT) theorem of the pKP equation is constructed. We can get many new types of interaction solutions because of the existence of an arbitrary function in the nonauto-BT theorem. Some special interaction solutions are investigated both in analytical and graphical ways. Supported by the National Natural Science Foundation of China under Grant Nos. 11305106, 11275129 and 11405110, the Natural Science Foundation of Zhejiang Province of China under Grant No. LQ13A050001

The effect of topography on the evolution of unstable disturbances in a baroclinic atmosphere

NASA Technical Reports Server (NTRS)

Clark, J. H. E.

1985-01-01

A two layer spectral quasi-geostrophic model is used to simulate the effects of topography on the equilibria, their stability, and the long term evolution of incipient unstable waves. The flow is forced by latitudinally dependent radiative heating. Dissipation is in the form of Rayleigh friction. An analytical solution is found for the propagating finite amplitude waves which result from baroclinic instability of the zonal winds when topography is absent. The appearance of this solution for wavelengths just longer than the Rossby radius of deformation and disappearance of ultra-long wavelengths is interpreted in terms of the Hopf bifurcation theory. Simple dynamic and thermodynamic criteria for the existence of periodic Rossby solutions are presented. A Floquet stability analysis shows that the waves are neutral. The nature of the form drag instability of high index equilibria is investigated. The proximity of the equilibrium shear to a resonant value is essential for the instability, provided the equilibrium occurs at a slightly stronger shear than resonance.

On the membrane approximation in isothermal film casting

NASA Astrophysics Data System (ADS)

Hagen, Thomas

2014-08-01

In this work, a one-dimensional model for isothermal film casting is studied. Film casting is an important engineering process to manufacture thin films and sheets from a highly viscous polymer melt. The model equations account for variations in film width and film thickness, and arise from thinness and kinematic assumptions for the free liquid film. The first aspect of our study is a rigorous discussion of the existence and uniqueness of stationary solutions. This objective is approached via the argument principle, exploiting the homotopy invariance of a family of analytic functions. As our second objective, we analyze the linearization of the governing equations about stationary solutions. It is shown that solutions for the associated boundary-initial value problem are given by a strongly continuous semigroup of bounded linear operators. To reach this result, we cast the relevant Cauchy problem in a more accessible form. These transformed equations allow us insight into the regularity of the semigroup, thus yielding the validity of the spectral mapping theorem for the semigroup and the spectrally determined growth property.

Small-x asymptotics of the quark helicity distribution: Analytic results

DOE PAGES

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

2017-06-15

In this Letter, we analytically solve the evolution equations for the small-x asymptotic behavior of the (flavor singlet) quark helicity distribution in the large- N c limit. Here, these evolution equations form a set of coupled integro-differential equations, which previously could only be solved numerically. This approximate numerical solution, however, revealed simplifying properties of the small-x asymptotics, which we exploit here to obtain an analytic solution.

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.

Strongly localized dark modes in binary discrete media with cubic-quintic nonlinearity within the anti-continuum limit

NASA Astrophysics Data System (ADS)

Taib, L. Abdul; Hadi, M. S. Abdul; Umarov, B. A.

2017-12-01

The existence of dark strongly localized modes of binary discrete media with cubic-quintic nonlinearity is numerically demonstrated by solving the relevant discrete nonlinear Schrödinger equations. In the model, the coupling coefficients between adjacent sites are set to be relatively small representing the anti-continuum limit. In addition, approximated analytical solutions for vectorial solitons with various topologies are derived. Stability analysis of the localized states was performed using the standard linearized eigenfrequency problem. The prediction from the stability analysis are furthermore verified by direct numerical integrations.

Determination of vertical pressures on running wheels of freight trolleys of bridge type cranes

NASA Astrophysics Data System (ADS)

Goncharov, K. A.; Denisov, I. A.

2018-03-01

The problematic issues of the design of the bridge-type trolley crane, connected with ensuring uniform load distribution between the running wheels, are considered. The shortcomings of the existing methods of calculation of reference pressures are described. The results of the analytical calculation of the pressure of the support wheels are compared with the results of the numerical solution of this problem for various schemes of trolley supporting frames. Conclusions are given on the applicability of various methods for calculating vertical pressures, depending on the type of metal structures used in the trolley.

Dynamical behavior of a stochastic SVIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Zhang, Xinhong; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir

2017-10-01

In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s < 1, the disease of stochastic autonomous SVIR model will die out exponentially; if R˜0s > 1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R˜0s > 1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Chen, Lin-Jie; Ma, Chang-Feng

2010-01-01

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form ut + αuux + βunux + γuxx + δuxxx + ζuxxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions.

The flight of Newton's cannonball

NASA Astrophysics Data System (ADS)

Pesnell, W. Dean

2018-05-01

Newton's Cannon is a thought experiment used to motivate orbital motion. Cannonballs were fired from a high mountain at increasing muzzle velocity until they orbit the Earth. We will use the trajectories of these cannonballs to describe the shape of orbital tunnels that allow a cannonball fired from a high mountain to pass through the Earth. A sphere of constant density is used as the model of the Earth to take advantage of the analytic solutions for the interior trajectories that exist for that model. For the example shown, the cannonball trajectories that pass through the Earth intersect near the antipodal point of the cannon.

Soliton polarization rotation in fiber lasers

NASA Astrophysics Data System (ADS)

Afanasjev, V. V.

1995-02-01

I have found the approximate analytical solution in explicit form for a vector soliton with an arbitrary component ratio. My solution describes the dependence of soliton intensity on polarization angle and also nonlinear polarization rotation. The analytical results agree well with the numerical simulations.

CTEPP STANDARD OPERATING PROCEDURE FOR PREPARATION OF SURROGATE RECOVERY STANDARD AND INTERNAL STANDARD SOLUTIONS FOR NEUTRAL TARGET ANALYTES (SOP-5.25)

EPA Science Inventory

This standard operating procedure describes the method used for preparing internal standard, surrogate recovery standard and calibration standard solutions for neutral analytes used for gas chromatography/mass spectrometry analysis.

Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow

NASA Astrophysics Data System (ADS)

Saengow, C.; Giacomin, A. J.

2017-12-01

The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we use part of our exact solution for shear stress to arrive at unique exact analytical solutions for the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. We find the new exact analytical solutions to be compact and intrinsically beautiful. These solutions reduce to those of our previous work on the special case of the corotational Maxwell fluid. Our solutions also agree with our new truncated Goddard integral expansion for the special case of the corotational Jeffreys fluid. The limiting behaviors of these exact solutions also yield new explicit expressions. Finally, we use our exact solutions to see how η∞ affects the normal stress differences in LAOS.

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.

Three dimensional cylindrical Kadomtsev-Petviashvili equation in a very dense electron-positron-ion plasma

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

Moslem, W. M.; Sabry, R.; Shukla, P. K.

2010-03-15

By using the hydrodynamic equations of ions, Thomas-Fermi electron/positron density distribution, and Poisson equation, a three-dimensional cylindrical Kadomtsev-Petviashvili (CKP) equation is derived for small but finite amplitude ion-acoustic waves. The generalized expansion method is used to analytically solve the CKP equation. New class of solutions admits a train of well-separated bell-shaped periodic pulses is obtained. At certain condition, the latter degenerates to solitary wave solution. The effects of physical parameters on the solitary pulse structures are examined. Furthermore, the energy integral equation is used to study the existence regions of the localized pulses. The present study might be helpful tomore » understand the excitation of nonlinear ion-acoustic waves in a very dense astrophysical objects such as white dwarfs.« less

Stability of nonlinear waves and patterns and related topics

NASA Astrophysics Data System (ADS)

Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn

2018-04-01

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Elementary solutions of coupled model equations in the kinetic theory of gases

NASA Technical Reports Server (NTRS)

Kriese, J. T.; Siewert, C. E.; Chang, T. S.

1974-01-01

The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases. Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism. The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically, and a highly accurate value of the temperature-slip coefficient is reported.

Stochastic sensing through covalent interactions

DOEpatents

Bayley, Hagan; Shin, Seong-Ho; Luchian, Tudor; Cheley, Stephen

2013-03-26

A system and method for stochastic sensing in which the analyte covalently bonds to the sensor element or an adaptor element. If such bonding is irreversible, the bond may be broken by a chemical reagent. The sensor element may be a protein, such as the engineered P.sub.SH type or .alpha.HL protein pore. The analyte may be any reactive analyte, including chemical weapons, environmental toxins and pharmaceuticals. The analyte covalently bonds to the sensor element to produce a detectable signal. Possible signals include change in electrical current, change in force, and change in fluorescence. Detection of the signal allows identification of the analyte and determination of its concentration in a sample solution. Multiple analytes present in the same solution may be detected.

Finite Element Modeling of a Cylindrical Contact Using Hertzian Assumptions

NASA Technical Reports Server (NTRS)

Knudsen, Erik

2003-01-01

The turbine blades in the high-pressure fuel turbopump/alternate turbopump (HPFTP/AT) are subjected to hot gases rapidly flowing around them. This flow excites vibrations in the blades. Naturally, one has to worry about resonance, so a damping device was added to dissipate some energy from the system. The foundation is now laid for a very complex problem. The damper is in contact with the blade, so now there are contact stresses (both normal and tangential) to contend with. Since these stresses can be very high, it is not all that difficult to yield the material. Friction is another non-linearity and the blade is made out of a Nickel-based single-crystal superalloy that is orthotropic. A few approaches exist to solve such a problem and computer models, using contact elements, have been built with friction, plasticity, etc. These models are quite cumbersome and require many hours to solve just one load case and material orientation. A simpler approach is required. Ideally, the model should be simplified so the analysis can be conducted faster. When working with contact problems determining the contact patch and the stresses in the material are the main concerns. Closed-form solutions for non-conforming bodies, developed by Hertz, made out of isotropic materials are readily available. More involved solutions for 3-D cases using different materials are also available. The question is this: can Hertzian1 solutions be applied, or superimposed, to more complicated problems-like those involving anisotropic materials? That is the point of the investigation here. If these results agree with the more complicated computer models, then the analytical solutions can be used in lieu of the numerical solutions that take a very long time to process. As time goes on, the analytical solution will eventually have to include things like friction and plasticity. The models in this report use no contact elements and are essentially an applied load problem using Hertzian assumptions to determine the contact patch dimensions.

Characterization of highly concentrated antibody solution - A toolbox for the description of protein long-term solution stability

PubMed Central

Schermeyer, Marie-Therese; Wöll, Anna K.; Eppink, Michel; Hubbuch, Jürgen

2017-01-01

ABSTRACT High protein titers are gaining importance in biopharmaceutical industry. A major challenge in the development of highly concentrated mAb solutions is their long-term stability and often incalculable viscosity. The complexity of the molecule itself, as well as the various molecular interactions, make it difficult to describe their solution behavior. To study the formulation stability, long- and short-range interactions and the formation of complex network structures have to be taken into account. For a better understanding of highly concentrated solutions, we combined established and novel analytical tools to characterize the effect of solution properties on the stability of highly concentrated mAb formulations. In this study, monoclonal antibody solutions in a concentration range of 50–200 mg/ml at pH 5–9 with and without glycine, PEG4000, and Na2SO4 were analyzed. To determine the monomer content, analytical size-exclusion chromatography runs were performed. ζ-potential measurements were conducted to analyze the electrophoretic properties in different solutions. The melting and aggregation temperatures were determined with the help of fluorescence and static light scattering measurements. Additionally, rheological measurements were conducted to study the solution viscosity and viscoelastic behavior of the mAb solutions. The so-determined analytical parameters were scored and merged in an analytical toolbox. The resulting scoring was then successfully correlated with long-term storage (40 d of incubation) experiments. Our results indicate that the sensitivity of complex rheological measurements, in combination with the applied techniques, allows reliable statements to be made with respect to the effect of solution properties, such as protein concentration, ionic strength, and pH shift, on the strength of protein-protein interaction and solution colloidal stability. PMID:28617076

Ion concentration in micro and nanoscale electrospray emitters.

PubMed

Yuill, Elizabeth M; Baker, Lane A

2018-06-01

Solution-phase ion transport during electrospray has been characterized for nanopipettes, or glass capillaries pulled to nanoscale tip dimensions, and micron-sized electrospray ionization emitters. Direct visualization of charged fluorophores during the electrospray process is used to evaluate impacts of emitter size, ionic strength, analyte size, and pressure-driven flow on heterogeneous ion transport during electrospray. Mass spectrometric measurements of positively- and negatively-charged proteins were taken for micron-sized and nanopipette emitters under low ionic strength conditions to further illustrate a discrepancy in solution-driven transport of charged analytes. A fundamental understanding of analyte electromigration during electrospray, which is not always considered, is expected to provide control over selective analyte depletion and enrichment, and can be harnessed for sample cleanup. Graphical abstract Fluorescence micrographs of ion migration in nanoscale pipettes while solution is electrosprayed.

Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies

NASA Technical Reports Server (NTRS)

Mirels, Harold

1959-01-01

Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.

Dynamic response of gold nanoparticle chemiresistors to organic analytes in aqueous solution.

PubMed

Müller, Karl-Heinz; Chow, Edith; Wieczorek, Lech; Raguse, Burkhard; Cooper, James S; Hubble, Lee J

2011-10-28

We investigate the response dynamics of 1-hexanethiol-functionalized gold nanoparticle chemiresistors exposed to the analyte octane in aqueous solution. The dynamic response is studied as a function of the analyte-water flow velocity, the thickness of the gold nanoparticle film and the analyte concentration. A theoretical model for analyte limited mass-transport is used to model the analyte diffusion into the film, the partitioning of the analyte into the 1-hexanethiol capping layers and the subsequent swelling of the film. The degree of swelling is then used to calculate the increase of the electron tunnel resistance between adjacent nanoparticles which determines the resistance change of the film. In particular, the effect of the nonlinear relationship between resistance and swelling on the dynamic response is investigated at high analyte concentration. Good agreement between experiment and the theoretical model is achieved. This journal is © the Owner Societies 2011

Propagation of solutes and pressure into aquifers following river stage rise

NASA Astrophysics Data System (ADS)

Welch, Chani; Cook, Peter G.; Harrington, Glenn A.; Robinson, Neville I.

2013-09-01

Water level rises associated with river flow events induce both pressure and solute movement into adjacent aquifers at vastly different rates. We present a simple analytical solution that relates the travel time and travel distance of solutes into an aquifer following river stage rise to aquifer properties. Combination with an existing solution for pressure propagation indicates that the ratio of solute to pressure travel times is proportional to the ratio of the volume of water stored in the aquifer before the river stage rise and the volume added by the stage rise and is independent of hydraulic conductivity. Two-dimensional numerical simulations of an aquifer slice perpendicular to a river demonstrate that the solutions are broadly applicable to variably saturated aquifers and partially penetrating rivers. The solutions remain applicable where river stage rise and fall occur, provided that regional hydraulic gradients are low and the duration of the river stage rise is less than pressure and solute travel times to the observation point in the aquifer. Consequently, the solutions provide new insight into the relationships between aquifer properties and distance and time of solute propagation and, in some cases, may be used to estimate system characteristics. Travel time metrics obtained for a flood event in the Cockburn River in eastern Australia using electrical conductivity measurements enabled estimates of aquifer properties and a lateral extent of river-aquifer mixing of 25 m. A detailed time series of any soluble tracer with distinctly different concentrations in river water and groundwater may be used.

Force-Free Magnetic Fields Calculated from Automated Tracing of Coronal Loops with AIA/SDO

NASA Astrophysics Data System (ADS)

Aschwanden, M. J.

2013-12-01

One of the most realistic magnetic field models of the solar corona is a nonlinear force-free field (NLFFF) solution. There exist about a dozen numeric codes that compute NLFFF solutions based on extrapolations of photospheric vector magnetograph data. However, since the photosphere and lower chromosphere is not force-free, a suitable correction has to be applied to the lower boundary condition. Despite of such "pre-processing" corrections, the resulting theoretical magnetic field lines deviate substantially from observed coronal loop geometries. - Here we developed an alternative method that fits an analytical NLFFF approximation to the observed geometry of coronal loops. The 2D coordinates of the geometry of coronal loop structures observed with AIA/SDO are traced with the "Oriented Coronal CUrved Loop Tracing" (OCCULT-2) code, an automated pattern recognition algorithm that has demonstrated the fidelity in loop tracing matching visual perception. A potential magnetic field solution is then derived from a line-of-sight magnetogram observed with HMI/SDO, and an analytical NLFFF approximation is then forward-fitted to the twisted geometry of coronal loops. We demonstrate the performance of this magnetic field modeling method for a number of solar active regions, before and after major flares observed with SDO. The difference of the NLFFF and the potential field energies allows us then to compute the free magnetic energy, which is an upper limit of the energy that is released during a solar flare.

New trends in astrodynamics and applications: optimal trajectories for space guidance.

PubMed

Azimov, Dilmurat; Bishop, Robert

2005-12-01

This paper represents recent results on the development of optimal analytic solutions to the variation problem of trajectory optimization and their application in the construction of on-board guidance laws. The importance of employing the analytically integrated trajectories in a mission design is discussed. It is assumed that the spacecraft is equipped with a power-limited propulsion and moving in a central Newtonian field. Satisfaction of the necessary and sufficient conditions for optimality of trajectories is analyzed. All possible thrust arcs and corresponding classes of the analytical solutions are classified based on the propulsion system parameters and performance index of the problem. The solutions are presented in a form convenient for applications in escape, capture, and interorbital transfer problems. Optimal guidance and neighboring optimal guidance problems are considered. It is shown that the analytic solutions can be used as reference trajectories in constructing the guidance algorithms for the maneuver problems mentioned above. An illustrative example of a spiral trajectory that terminates on a given elliptical parking orbit is discussed.

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.

Substrate mass transfer: analytical approach for immobilized enzyme reactions

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Saibavani, T. N.

2018-04-01

In this paper, the boundary value problem in immobilized enzyme reactions is formulated and approximate expression for substrate concentration without external mass transfer resistance is presented. He’s variational iteration method is used to give approximate and analytical solutions of non-linear differential equation containing a non linear term related to enzymatic reaction. The relevant analytical solution for the dimensionless substrate concentration profile is discussed in terms of dimensionless reaction parameters α and β.

Quality control analytical methods: refractive index.

PubMed

Allen, Loyd V

2015-01-01

There are numerous analytical methods that can be utilized in a compounding pharmacy for a quality-assurance program. Since the index of refraction of a liquid/solution is a physical constant, it can be used to assist in identification of a substance, establish its purity, and, in some instances, to determine the concentration of an analyte in solution. This article serves as an introduction to refractive index and some applications of its use in a compounding program.

New solutions for steady bubbles in a Hele-Shaw cell

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

Tanveer, S.

1987-03-01

Exact solutions are presented for steadily moving bubbles in a Hele--Shaw cell when the effect of surface tension is neglected. These solutions form a three-parameter family. For specified area, both the speed of the bubble and the distance of its centroid from the channel centerline remain arbitrary when surface tension is ignored. However, numerical evidence suggests that this twofold arbitrariness is removed by the effect of surface tension, i.e., for given bubble area and surface tension, solutions exist only when the bubble velocity and the centroid distance from the channel centerline attain one or more isolated values. From a limitedmore » numerical search, no nonsymmetric solutions could be found; however, a branch of symmetric bubble solutions that was not found in earlier work was found. This branch corresponds to one of the Romero-Vanden-Broeck branch of finger solutions when the bubble size is large. A new procedure for numerical calculations of bubble solutions in the presence of surface tension is presented and is found to work very well for reasonably large bubbles, unlike the previous method of Tanveer (Phys. Fluids 29, 3537 (1986)). The precise power law dependence of bubble velocity on surface tension for small surface tension is explored for bubbles of different area. Agreement is noted with recent analytical results for a finger.« less

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.

The analytical solution for drug delivery system with nonhomogeneous moving boundary condition

NASA Astrophysics Data System (ADS)

Saudi, Muhamad Hakimi; Mahali, Shalela Mohd; Harun, Fatimah Noor

2017-08-01

This paper discusses the development and the analytical solution of a mathematical model based on drug release system from a swelling delivery device. The mathematical model is represented by a one-dimensional advection-diffusion equation with nonhomogeneous moving boundary condition. The solution procedures consist of three major steps. Firstly, the application of steady state solution method, which is used to transform the nonhomogeneous moving boundary condition to homogeneous boundary condition. Secondly, the application of the Landau transformation technique that gives a significant impact in removing the advection term in the system of equation and transforming the moving boundary condition to a fixed boundary condition. Thirdly, the used of separation of variables method to find the analytical solution for the resulted initial boundary value problem. The results show that the swelling rate of delivery device and drug release rate is influenced by value of growth factor r.

Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg-Landau equation in a nonlinear fiber

NASA Astrophysics Data System (ADS)

Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong

2017-10-01

In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.

An automated baseline correction protocol for infrared spectra of atmospheric aerosols collected on polytetrafluoroethylene (Teflon) filters

NASA Astrophysics Data System (ADS)

Kuzmiakova, Adele; Dillner, Ann M.; Takahama, Satoshi

2016-06-01

A growing body of research on statistical applications for characterization of atmospheric aerosol Fourier transform infrared (FT-IR) samples collected on polytetrafluoroethylene (PTFE) filters (e.g., Russell et al., 2011; Ruthenburg et al., 2014) and a rising interest in analyzing FT-IR samples collected by air quality monitoring networks call for an automated PTFE baseline correction solution. The existing polynomial technique (Takahama et al., 2013) is not scalable to a project with a large number of aerosol samples because it contains many parameters and requires expert intervention. Therefore, the question of how to develop an automated method for baseline correcting hundreds to thousands of ambient aerosol spectra given the variability in both environmental mixture composition and PTFE baselines remains. This study approaches the question by detailing the statistical protocol, which allows for the precise definition of analyte and background subregions, applies nonparametric smoothing splines to reproduce sample-specific PTFE variations, and integrates performance metrics from atmospheric aerosol and blank samples alike in the smoothing parameter selection. Referencing 794 atmospheric aerosol samples from seven Interagency Monitoring of PROtected Visual Environment (IMPROVE) sites collected during 2011, we start by identifying key FT-IR signal characteristics, such as non-negative absorbance or analyte segment transformation, to capture sample-specific transitions between background and analyte. While referring to qualitative properties of PTFE background, the goal of smoothing splines interpolation is to learn the baseline structure in the background region to predict the baseline structure in the analyte region. We then validate the model by comparing smoothing splines baseline-corrected spectra with uncorrected and polynomial baseline (PB)-corrected equivalents via three statistical applications: (1) clustering analysis, (2) functional group quantification, and (3) thermal optical reflectance (TOR) organic carbon (OC) and elemental carbon (EC) predictions. The discrepancy rate for a four-cluster solution is 10 %. For all functional groups but carboxylic COH the discrepancy is ≤ 10 %. Performance metrics obtained from TOR OC and EC predictions (R2 ≥ 0.94 %, bias ≤ 0.01 µg m-3, and error ≤ 0.04 µg m-3) are on a par with those obtained from uncorrected and PB-corrected spectra. The proposed protocol leads to visually and analytically similar estimates as those generated by the polynomial method. More importantly, the automated solution allows us and future users to evaluate its analytical reproducibility while minimizing reducible user bias. We anticipate the protocol will enable FT-IR researchers and data analysts to quickly and reliably analyze a large amount of data and connect them to a variety of available statistical learning methods to be applied to analyte absorbances isolated in atmospheric aerosol samples.

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.

Localization in finite vibroimpact chains: Discrete breathers and multibreathers.

PubMed

Grinberg, Itay; Gendelman, Oleg V

2016-09-01

We explore the dynamics of strongly localized periodic solutions (discrete solitons or discrete breathers) in a finite one-dimensional chain of oscillators. Localization patterns with both single and multiple localization sites (breathers and multibreathers) are considered. The model involves parabolic on-site potential with rigid constraints (the displacement domain of each particle is finite) and a linear nearest-neighbor coupling. When the particle approaches the constraint, it undergoes an inelastic impact according to Newton's impact model. The rigid nonideal impact constraints are the only source of nonlinearity and damping in the system. We demonstrate that this vibro-impact model allows derivation of exact analytic solutions for the breathers and multibreathers with an arbitrary set of localization sites, both in conservative and in forced-damped settings. Periodic boundary conditions are considered; exact solutions for other types of boundary conditions are also available. Local character of the nonlinearity permits explicit derivation of a monodromy matrix for the breather solutions. Consequently, the stability of the derived breather and multibreather solutions can be efficiently studied in the framework of simple methods of linear algebra, and with rather moderate computational efforts. One reveals that that the finiteness of the chain fragment and possible proximity of the localization sites strongly affect both the existence and the stability patterns of these localized solutions.

Exact solutions for rate and synchrony in recurrent networks of coincidence detectors.

PubMed

Mikula, Shawn; Niebur, Ernst

2008-11-01

We provide analytical solutions for mean firing rates and cross-correlations of coincidence detector neurons in recurrent networks with excitatory or inhibitory connectivity, with rate-modulated steady-state spiking inputs. We use discrete-time finite-state Markov chains to represent network state transition probabilities, which are subsequently used to derive exact analytical solutions for mean firing rates and cross-correlations. As illustrated in several examples, the method can be used for modeling cortical microcircuits and clarifying single-neuron and population coding mechanisms. We also demonstrate that increasing firing rates do not necessarily translate into increasing cross-correlations, though our results do support the contention that firing rates and cross-correlations are likely to be coupled. Our analytical solutions underscore the complexity of the relationship between firing rates and cross-correlations.

Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

NASA Astrophysics Data System (ADS)

Wu, Baisheng; Liu, Weijia; Lim, C. W.

2017-07-01

A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.

Analytical solution for the advection-dispersion transport equation in layered media

USDA-ARS?s Scientific Manuscript database

The advection-dispersion transport equation with first-order decay was solved analytically for multi-layered media using the classic integral transform technique (CITT). The solution procedure used an associated non-self-adjoint advection-diffusion eigenvalue problem that had the same form and coef...

Thermal Analysis of Antenna Structures. Part 2: Panel Temperature Distribution

NASA Technical Reports Server (NTRS)

Schonfeld, D.; Lansing, F. L.

1983-01-01

This article is the second in a series that analyzes the temperature distribution in microwave antennas. An analytical solution in a series form is obtained for the temperature distribution in a flat plate analogous to an antenna surface panel under arbitrary temperature and boundary conditions. The solution includes the effects of radiation and air convection from the plate. Good agreement is obtained between the numerical and analytical solutions.

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.