An analytical solution for predicting the transient seepage from a subsurface drainage system

NASA Astrophysics Data System (ADS)

Xin, Pei; Dan, Han-Cheng; Zhou, Tingzhang; Lu, Chunhui; Kong, Jun; Li, Ling

2016-05-01

Subsurface drainage systems have been widely used to deal with soil salinization and waterlogging problems around the world. In this paper, a mathematical model was introduced to quantify the transient behavior of the groundwater table and the seepage from a subsurface drainage system. Based on the assumption of a hydrostatic pressure distribution, the model considered the pore-water flow in both the phreatic and vadose soil zones. An approximate analytical solution for the model was derived to quantify the drainage of soils which were initially water-saturated. The analytical solution was validated against laboratory experiments and a 2-D Richards equation-based model, and found to predict well the transient water seepage from the subsurface drainage system. A saturated flow-based model was also tested and found to over-predict the time required for drainage and the total water seepage by nearly one order of magnitude, in comparison with the experimental results and the present analytical solution. During drainage, a vadose zone with a significant water storage capacity developed above the phreatic surface. A considerable amount of water still remained in the vadose zone at the steady state with the water table situated at the drain bottom. Sensitivity analyses demonstrated that effects of the vadose zone were intensified with an increased thickness of capillary fringe, capillary rise and/or burying depth of drains, in terms of the required drainage time and total water seepage. The analytical solution provides guidance for assessing the capillary effects on the effectiveness and efficiency of subsurface drainage systems for combating soil salinization and waterlogging problems.

Analytic theory of photoacoustic wave generation from a spheroidal droplet.

PubMed

Li, Yong; Fang, Hui; Min, Changjun; Yuan, Xiaocong

2014-08-25

In this paper, we develop an analytic theory for describing the photoacoustic wave generation from a spheroidal droplet and derive the first complete analytic solution. Our derivation is based on solving the photoacoustic Helmholtz equation in spheroidal coordinates with the separation-of-variables method. As the verification, besides carrying out the asymptotic analyses which recover the standard solutions for a sphere, an infinite cylinder and an infinite layer, we also confirm that the partial transmission and reflection model previously demonstrated for these three geometries still stands. We expect that this analytic solution will find broad practical uses in interpreting experiment results, considering that its building blocks, the spheroidal wave functions (SWFs), can be numerically calculated by the existing computer programs.

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.

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.

Microfluidic-Based Robotic Sampling System for Radioactive Solutions

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

Jack D. Law; Julia L. Tripp; Tara E. Smith

A novel microfluidic based robotic sampling system has been developed for sampling and analysis of liquid solutions in nuclear processes. This system couples the use of a microfluidic sample chip with a robotic system designed to allow remote, automated sampling of process solutions in-cell and facilitates direct coupling of the microfluidic sample chip with analytical instrumentation. This system provides the capability for near real time analysis, reduces analytical waste, and minimizes the potential for personnel exposure associated with traditional sampling methods. A prototype sampling system was designed, built and tested. System testing demonstrated operability of the microfluidic based sample systemmore » and identified system modifications to optimize performance.« less

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.

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.

Steering particles by breaking symmetries

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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.

Modeling of heat flow and effective thermal conductivity of fractured media: Analytical and numerical methods

NASA Astrophysics Data System (ADS)

Nguyen, S. T.; Vu, M.-H.; Vu, M. N.; Tang, A. M.

2017-05-01

The present work aims to modeling the thermal conductivity of fractured materials using homogenization-based analytical and pattern-based numerical methods. These materials are considered as a network of cracks distributed inside a solid matrix. Heat flow through such media is perturbed by the crack system. The problem of heat flow across a single crack is firstly investigated. The classical Eshelby's solution, extended to the thermal conduction problem of an ellipsoidal inclusion embedding in an infinite homogeneous matrix, gives an analytical solution of temperature discontinuity across a non-conducting penny-shaped crack. This solution is then validated by the numerical simulation based on the finite elements method. The numerical simulation allows analyzing the effect of crack conductivity. The problem of a single crack is then extended to a medium containing multiple cracks. Analytical estimations for effective thermal conductivity, that take into account the interaction between cracks and their spatial distribution, are developed for the case of non-conducting cracks. Pattern-based numerical method is then employed for both cases non-conducting and conducting cracks. In the case of non-conducting cracks, numerical and analytical methods, both account for the spatial distribution of the cracks, fit perfectly. In the case of conducting cracks, the numerical analyzing of crack conductivity effect shows that highly conducting cracks weakly affect heat flow and the effective thermal conductivity of fractured media.

Weakly nonlinear behavior of a plate thickness-mode piezoelectric transformer.

PubMed

Yang, Jiashi; Chen, Ziguang; Hu, Yuantai; Jiang, Shunong; Guo, Shaohua

2007-04-01

We analyzed the weakly nonlinear behavior of a plate thickness-shear mode piezoelectric transformer near resonance. An approximate analytical solution was obtained. Numerical results based on the analytical solution are presented. It is shown that on one side of the resonant frequency the input-output relation becomes nonlinear, and on the other side the output voltage experiences jumps.

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.

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.

Chemical analysis of bleach and hydroxide-based solutions after decontamination of the chemical warfare agent O-ethyl S-2-diisopropylaminoethyl methylphosphonothiolate (VX).

PubMed

Hopkins, F B; Gravett, M R; Self, A J; Wang, M; Chua, Hoe-Chee; Hoe-Chee, C; Lee, H S Nancy; Sim, N Lee Hoi; Jones, J T A; Timperley, C M; Riches, J R

2014-08-01

Detailed chemical analysis of solutions used to decontaminate chemical warfare agents can be used to support verification and forensic attribution. Decontamination solutions are amongst the most difficult matrices for chemical analysis because of their corrosive and potentially emulsion-based nature. Consequently, there are relatively few publications that report their detailed chemical analysis. This paper describes the application of modern analytical techniques to the analysis of decontamination solutions following decontamination of the chemical warfare agent O-ethyl S-2-diisopropylaminoethyl methylphosphonothiolate (VX). We confirm the formation of N,N-diisopropylformamide and N,N-diisopropylamine following decontamination of VX with hypochlorite-based solution, whereas they were not detected in extracts of hydroxide-based decontamination solutions by nuclear magnetic resonance (NMR) spectroscopy or gas chromatography-mass spectrometry. We report the electron ionisation and chemical ionisation mass spectroscopic details, retention indices, and NMR spectra of N,N-diisopropylformamide and N,N-diisopropylamine, as well as analytical methods suitable for their analysis and identification in solvent extracts and decontamination residues.

Analytical solutions for systems of partial differential-algebraic equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2014-01-01

This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.

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.

A note on the accuracy of spectral method applied to nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

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 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.

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.

A capillary electrophoresis chip for the analysis of print and film photographic developing agents in commercial processing solutions using indirect fluorescence detection.

PubMed

Sirichai, S; de Mello, A J

2001-01-01

The separation and detection of both print and film developing agents (CD-3 and CD-4) in photographic processing solutions using chip-based capillary electrophoresis is presented. For simultaneous detection of both analytes under identical experimental conditions a buffer pH of 11.9 is used to partially ionise the analytes. Detection is made possible by indirect fluorescence, where the ions of the analytes displace the anionic fluorescing buffer ion to create negative peaks. Under optimal conditions, both analytes can be analyzed within 30 s. The limits of detection for CD-3 and CD-4 are 0.17 mM and 0.39 mM, respectively. The applicability of the method for the analysis of seasoned photographic processing developer solutions is also examined.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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.

Magnet pole shape design for reduction of thrust ripple of slotless permanent magnet linear synchronous motor with arc-shaped magnets considering end-effect based on analytical method

NASA Astrophysics Data System (ADS)

Shin, Kyung-Hun; Park, Hyung-Il; Kim, Kwan-Ho; Jang, Seok-Myeong; Choi, Jang-Young

2017-05-01

The shape of the magnet is essential to the performance of a slotless permanent magnet linear synchronous machine (PMLSM) because it is directly related to desirable machine performance. This paper presents a reduction in the thrust ripple of a PMLSM through the use of arc-shaped magnets based on electromagnetic field theory. The magnetic field solutions were obtained by considering end effect using a magnetic vector potential and two-dimensional Cartesian coordinate system. The analytical solution of each subdomain (PM, air-gap, coil, and end region) is derived, and the field solution is obtained by applying the boundary and interface conditions between the subdomains. In particular, an analytical method was derived for the instantaneous thrust and thrust ripple reduction of a PMLSM with arc-shaped magnets. In order to demonstrate the validity of the analytical results, the back electromotive force results of a finite element analysis and experiment on the manufactured prototype model were compared. The optimal point for thrust ripple minimization is suggested.

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.

Interpretation of leaching data for cementitious waste forms using analytical solutions based on mass transport theory and empiricism

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

Spence, R.D.; Godbee, H.W.; Tallent, O.K.

1989-01-01

The analysis of leaching data using analytical solutions based on mass transport theory and empiricism is presented. The waste forms leached to generate the data used in this analysis were prepared with a simulated radioactive waste slurry with traces of potassium ion, manganese ions, carbonate ions, phosphate ions, and sulfate ions solidified with several blends of cementitious materials. Diffusion coefficients were estimated from the results of ANS - 16.1 tests. Data of fraction leached versus time is presented and discussed.

Analytical Solutions for the Surface States of Bi1-xSbx (0 ≤ x ≲ 0.1)

NASA Astrophysics Data System (ADS)

Fuseya, Yuki; Fukuyama, Hidetoshi

2018-04-01

Analytical solutions for the surface state (SS) of an extended Wolff Hamiltonian, which is a common Hamiltonian for strongly spin-orbit coupled systems, are obtained both for semi-infinite and finite-thickness boundary conditions. For the semi-infinite system, there are two types of SS solutions: (I-a) linearly crossing SSs in the direct bulk band gap, and (I-b) SSs with linear dispersions entering the bulk conduction or valence bands away from the band edge. For the finite-thickness system, a gap opens in the SS of solution I-a. Numerical solutions for the SS are also obtained based on the tight-binding model of Liu and Allen [Phys. Rev. B 52, 1566 (1995)] for Bi1-xSbx (0 ≤ x ≤ 0.1). A perfect correspondence between the analytic and numerical solutions is obtained around the \\bar{M} point including their thickness dependence. This is the first time that the character of the SS numerically obtained is identified with the help of analytical solutions. The size of the gap for I-a SS can be larger than that of bulk band gap even for a "thick" films ( ≲ 200 bilayers ≃ 80 nm) of pure bismuth. Consequently, in such a film of Bi1-xSbx, there is no apparent change in the SSs through the band inversion at x ≃ 0.04, even though the nature of the SS is changed from solution I-a to I-b. Based on our theoretical results, the experimental results on the SS of Bi1-xSbx (0 ≤ x ≲ 0.1) are discussed.

Analytical solutions of travel time to a pumping well with variable evapotranspiration.

PubMed

Chen, Tian-Fei; Wang, Xu-Sheng; Wan, Li; Li, Hailong

2014-01-01

Analytical solutions of groundwater travel time to a pumping well in an unconfined aquifer have been developed in previous studies, however, the change in evapotranspiration was not considered. Here, we develop a mathematical model of unconfined flow toward a discharge well with redistribution of groundwater evapotranspiration for travel time analysis. Dependency of groundwater evapotranspiration on the depth to water table is described using a linear formula with an extinction depth. Analytical solutions of groundwater level and travel time are obtained. For a typical hypothetical example, these solutions perfectly agree with the numerical simulation results based on MODFLOW and MODPATH. As indicated in a dimensionless framework, a lumped parameter which is proportional to the pumping rate controls the distributions of groundwater evapotranspiration rate and the travel time along the radial direction. © 2013, National Ground Water Association.

Kinematics and dynamics of robotic systems with multiple closed loops

NASA Astrophysics Data System (ADS)

Zhang, Chang-De

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

Analytic hierarchy process-based approach for selecting a Pareto-optimal solution of a multi-objective, multi-site supply-chain planning problem

NASA Astrophysics Data System (ADS)

Ayadi, Omar; Felfel, Houssem; Masmoudi, Faouzi

2017-07-01

The current manufacturing environment has changed from traditional single-plant to multi-site supply chain where multiple plants are serving customer demands. In this article, a tactical multi-objective, multi-period, multi-product, multi-site supply-chain planning problem is proposed. A corresponding optimization model aiming to simultaneously minimize the total cost, maximize product quality and maximize the customer satisfaction demand level is developed. The proposed solution approach yields to a front of Pareto-optimal solutions that represents the trade-offs among the different objectives. Subsequently, the analytic hierarchy process method is applied to select the best Pareto-optimal solution according to the preferences of the decision maker. The robustness of the solutions and the proposed approach are discussed based on a sensitivity analysis and an application to a real case from the textile and apparel industry.

Recursive analytical solution describing artificial satellite motion perturbed by an arbitrary number of zonal terms

NASA Technical Reports Server (NTRS)

Mueller, A. C.

1977-01-01

An analytical first order solution has been developed which describes the motion of an artificial satellite perturbed by an arbitrary number of zonal harmonics of the geopotential. A set of recursive relations for the solution, which was deduced from recursive relations of the geopotential, was derived. The method of solution is based on Von-Zeipel's technique applied to a canonical set of two-body elements in the extended phase space which incorporates the true anomaly as a canonical element. The elements are of Poincare type, that is, they are regular for vanishing eccentricities and inclinations. Numerical results show that this solution is accurate to within a few meters after 500 revolutions.

Interactions between butterfly-shaped pulses in the inhomogeneous media

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

Liu, Wen-Jun; Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190; Huang, Long-Gang

2014-10-15

Pulse interactions affect pulse qualities during the propagation. Interactions between butterfly-shaped pulses are investigated to improve pulse qualities in the inhomogeneous media. In order to describe the interactions between butterfly-shaped pulses, analytic two-soliton solutions are derived. Based on those solutions, influences of corresponding parameters on pulse interactions are discussed. Methods to control the pulse interactions are suggested. - Highlights: • Interactions between butterfly-shaped pulses are investigated. • Methods to control the pulse interactions are suggested. • Analytic two-soliton solutions for butterfly-shaped pulses are derived.

Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.

PubMed

Reck, Kasper; Thomsen, Erik V; Hansen, Ole

2011-01-31

The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.

Analytical torque calculation and experimental verification of synchronous permanent magnet couplings with Halbach arrays

NASA Astrophysics Data System (ADS)

Seo, Sung-Won; Kim, Young-Hyun; Lee, Jung-Ho; Choi, Jang-Young

2018-05-01

This paper presents analytical torque calculation and experimental verification of synchronous permanent magnet couplings (SPMCs) with Halbach arrays. A Halbach array is composed of various numbers of segments per pole; we calculate and compare the magnetic torques for 2, 3, and 4 segments. Firstly, based on the magnetic vector potential, and using a 2D polar coordinate system, we obtain analytical solutions for the magnetic field. Next, through a series of processes, we perform magnetic torque calculations using the derived solutions and a Maxwell stress tensor. Finally, the analytical results are verified by comparison with the results of 2D and 3D finite element analysis and the results of an experiment.

Closed-form solutions and scaling laws for Kerr frequency combs

PubMed Central

Renninger, William H.; Rakich, Peter T.

2016-01-01

A single closed-form analytical solution of the driven nonlinear Schrödinger equation is developed, reproducing a large class of the behaviors in Kerr-comb systems, including bright-solitons, dark-solitons, and a large class of periodic wavetrains. From this analytical framework, a Kerr-comb area theorem and a pump-detuning relation are developed, providing new insights into soliton- and wavetrain-based combs along with concrete design guidelines for both. This new area theorem reveals significant deviation from the conventional soliton area theorem, which is crucial to understanding cavity solitons in certain limits. Moreover, these closed-form solutions represent the first step towards an analytical framework for wavetrain formation, and reveal new parameter regimes for enhanced Kerr-comb performance. PMID:27108810

Analytical and numerical solution for wave reflection from a porous wave absorber

NASA Astrophysics Data System (ADS)

Magdalena, Ikha; Roque, Marian P.

2018-03-01

In this paper, wave reflection from a porous wave absorber is investigated theoretically and numerically. The equations that we used are based on shallow water type model. Modification of motion inside the absorber is by including linearized friction term in momentum equation and introducing a filtered velocity. Here, an analytical solution for wave reflection coefficient from a porous wave absorber over a flat bottom is derived. Numerically, we solve the equations using the finite volume method on a staggered grid. To validate our numerical model, comparison of the numerical reflection coefficient is made against the analytical solution. Further, we implement our numerical scheme to study the evolution of surface waves pass through a porous absorber over varied bottom topography.

An analytical solution of Richards' equation providing the physical basis of SCS curve number method and its proportionality relationship

NASA Astrophysics Data System (ADS)

Hooshyar, Milad; Wang, Dingbao

2016-08-01

The empirical proportionality relationship, which indicates that the ratio of cumulative surface runoff and infiltration to their corresponding potentials are equal, is the basis of the extensively used Soil Conservation Service Curve Number (SCS-CN) method. The objective of this paper is to provide the physical basis of the SCS-CN method and its proportionality hypothesis from the infiltration excess runoff generation perspective. To achieve this purpose, an analytical solution of Richards' equation is derived for ponded infiltration in shallow water table environment under the following boundary conditions: (1) the soil is saturated at the land surface; and (2) there is a no-flux boundary which moves downward. The solution is established based on the assumptions of negligible gravitational effect, constant soil water diffusivity, and hydrostatic soil moisture profile between the no-flux boundary and water table. Based on the derived analytical solution, the proportionality hypothesis is a reasonable approximation for rainfall partitioning at the early stage of ponded infiltration in areas with a shallow water table for coarse textured soils.

Nonlinear feedback control for high alpha flight

NASA Technical Reports Server (NTRS)

Stalford, Harold

1990-01-01

Analytical aerodynamic models are derived from a high alpha 6 DOF wind tunnel model. One detail model requires some interpolation between nonlinear functions of alpha. One analytical model requires no interpolation and as such is a completely continuous model. Flight path optimization is conducted on the basic maneuvers: half-loop, 90 degree pitch-up, and level turn. The optimal control analysis uses the derived analytical model in the equations of motion and is based on both moment and force equations. The maximum principle solution for the half-loop is poststall trajectory performing the half-loop in 13.6 seconds. The agility induced by thrust vectoring capability provided a minimum effect on reducing the maneuver time. By means of thrust vectoring control the 90 degrees pitch-up maneuver can be executed in a small place over a short time interval. The agility capability of thrust vectoring is quite beneficial for pitch-up maneuvers. The level turn results are based currently on only outer layer solutions of singular perturbation. Poststall solutions provide high turn rates but generate higher losses of energy than that of classical sustained solutions.

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

NASA Astrophysics Data System (ADS)

Huang, Junqi; Christ, John A.; Goltz, Mark N.

2010-08-01

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 describing the governing processes acting on a dissolved compound during a modified push-pull test (advection, longitudinal and transverse dispersion, first-order decay, and rate-limited sorption/partitioning in steady, divergent, and convergent flow fields) is developed. The coupling of this solution with inverse modeling to estimate aquifer parameters provides an efficient methodology for subsurface characterization. Synthetic data for single-well push-pull tests are employed to demonstrate the utility of the solution for determining (1) estimates of aquifer longitudinal and transverse dispersivities, (2) sorption distribution coefficients and rate constants, and (3) non-aqueous phase liquid (NAPL) saturations. Employment of the solution to estimate NAPL saturations based on partitioning and non-partitioning tracers is designed to overcome limitations of previous efforts by including rate-limited mass transfer. This solution provides a new tool for use by practitioners when interpreting single-well push-pull test results.

Multianalyte detection using a capillary-based flow immunosensor.

PubMed

Narang, U; Gauger, P R; Kusterbeck, A W; Ligler, F S

1998-01-01

A highly sensitive, dual-analyte detection system using capillary-based immunosensors has been designed for explosive detection. This model system consists of two capillaries, one coated with antibodies specific for 2,4,6-trinitrotoluene (TNT) and the other specific for hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) combined into a single device. The fused silica capillaries are prepared by coating anti-TNT and anti-RDX antibodies onto the silanized inner walls using a hetero-bifunctional crosslinker. After immobilization, the antibodies are saturated with a suitable fluorophorelabeled antigen. A "T" connector is used to continuously flow the buffer solution through the individual capillaries. To perform the assay, an aliquot of TNT or RDX or a mixture of the two analytes is injected into the continuous flow stream. In each capillary, the target analyte displaces the fluorophore-labeled antigen from the binding pocket of the antibody. The labeled antigen displaced from either capillary is detected downstream using two portable spectrofluorometers. The limits of detection for TNT and RDX in the multi-analyte formate are 44 fmol (100 microliters of 0.1 ng/ml TNT solution) and 224 fmol (100 microliters of 0.5 ng/ml RDX solution), respectively. The entire assay for both analytes can be performed in less than 3 min.

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.

Study of the exact analytical solution of the equation of longitudinal waves in a liquid with account of its relaxation properties

NASA Astrophysics Data System (ADS)

Kudinov, I. V.; Kudinov, V. A.

2013-09-01

A mathematical model of elastic vibrations of an incompressible liquid has been developed based on the hypothesis on the finite velocity of propagation of field potentials in this liquid. A hyperbolic equation of vibrations of such a liquid with account of its relaxation properties has been obtained. An exact analytical solution of this equation has been found and investigated in detail.

Analytical solution of Luedeking-Piret equation for a batch fermentation obeying Monod growth kinetics.

PubMed

Garnier, Alain; Gaillet, Bruno

2015-12-01

Not so many fermentation mathematical models allow analytical solutions of batch process dynamics. The most widely used is the combination of the logistic microbial growth kinetics with Luedeking-Piret bioproduct synthesis relation. However, the logistic equation is principally based on formalistic similarities and only fits a limited range of fermentation types. In this article, we have developed an analytical solution for the combination of Monod growth kinetics with Luedeking-Piret relation, which can be identified by linear regression and used to simulate batch fermentation evolution. Two classical examples are used to show the quality of fit and the simplicity of the method proposed. A solution for the combination of Haldane substrate-limited growth model combined with Luedeking-Piret relation is also provided. These models could prove useful for the analysis of fermentation data in industry as well as academia. © 2015 Wiley Periodicals, Inc.

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

Validation of the enthalpy method by means of analytical solution

NASA Astrophysics Data System (ADS)

Kleiner, Thomas; Rückamp, Martin; Bondzio, Johannes; Humbert, Angelika

2014-05-01

Numerical simulations moved in the recent year(s) from describing the cold-temperate transition surface (CTS) towards an enthalpy description, which allows avoiding incorporating a singular surface inside the model (Aschwanden et al., 2012). In Enthalpy methods the CTS is represented as a level set of the enthalpy state variable. This method has several numerical and practical advantages (e.g. representation of the full energy by one scalar field, no restriction to topology and shape of the CTS). The proposed method is rather new in glaciology and to our knowledge not verified and validated against analytical solutions. Unfortunately we are still lacking analytical solutions for sufficiently complex thermo-mechanically coupled polythermal ice flow. However, we present two experiments to test the implementation of the enthalpy equation and corresponding boundary conditions. The first experiment tests particularly the functionality of the boundary condition scheme and the corresponding basal melt rate calculation. Dependent on the different thermal situations that occur at the base, the numerical code may have to switch to another boundary type (from Neuman to Dirichlet or vice versa). The main idea of this set-up is to test the reversibility during transients. A former cold ice body that run through a warmer period with an associated built up of a liquid water layer at the base must be able to return to its initial steady state. Since we impose several assumptions on the experiment design analytical solutions can be formulated for different quantities during distinct stages of the simulation. The second experiment tests the positioning of the internal CTS in a parallel-sided polythermal slab. We compare our simulation results to the analytical solution proposed by Greve and Blatter (2009). Results from three different ice flow-models (COMIce, ISSM, TIMFD3) are presented.

Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion

NASA Astrophysics Data System (ADS)

Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

2017-10-01

Over the recent decades, a number of fast approximate solutions of Lippmann-Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown in seismology. This paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media. We evaluated the numerical merits of those methods and provide an estimation of their numerical complexity. In our numerical realization we use the matrix-free implementation of the corresponding integral operator. We study the accuracy of those approximate solutions and demonstrate, that the quasi-analytical approximation is more accurate, than the Born approximation. Further, we apply the quasi-analytical approximation to the solution of the inverse problem. It is demonstrated that, this approach improves the estimation of the data gradient, comparing to the Born approximation. The developed inversion algorithm is based on the conjugate-gradient type optimization. Numerical model study demonstrates that the quasi-analytical solution significantly reduces computation time of the seismic full-waveform inversion. We also show how the quasi-analytical approximation can be extended to the case of elastic wavefield.

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

BASEFLOW SEPARATION BASED ON ANALYTICAL SOLUTIONS OF THE BOUSSINESQ EQUATION. (R824995)

EPA Science Inventory

Abstract

A technique for baseflow separation is presented based on similarity solutions of the Boussinesq equation. The method makes use of the simplifying assumptions that a horizontal impermeable layer underlies a Dupuit aquifer which is drained by a fully penetratin...

Aerosol hygroscopic growth parameterization based on a solute specific coefficient

NASA Astrophysics Data System (ADS)

Metzger, S.; Steil, B.; Xu, L.; Penner, J. E.; Lelieveld, J.

2011-09-01

Water is a main component of atmospheric aerosols and its amount depends on the particle chemical composition. We introduce a new parameterization for the aerosol hygroscopic growth factor (HGF), based on an empirical relation between water activity (aw) and solute molality (μs) through a single solute specific coefficient νi. Three main advantages are: (1) wide applicability, (2) simplicity and (3) analytical nature. (1) Our approach considers the Kelvin effect and covers ideal solutions at large relative humidity (RH), including CCN activation, as well as concentrated solutions with high ionic strength at low RH such as the relative humidity of deliquescence (RHD). (2) A single νi coefficient suffices to parameterize the HGF for a wide range of particle sizes, from nanometer nucleation mode to micrometer coarse mode particles. (3) In contrast to previous methods, our analytical aw parameterization depends not only on a linear correction factor for the solute molality, instead νi also appears in the exponent in form x · ax. According to our findings, νi can be assumed constant for the entire aw range (0-1). Thus, the νi based method is computationally efficient. In this work we focus on single solute solutions, where νi is pre-determined with the bisection method from our analytical equations using RHD measurements and the saturation molality μssat. The computed aerosol HGF and supersaturation (Köhler-theory) compare well with the results of the thermodynamic reference model E-AIM for the key compounds NaCl and (NH4)2SO4 relevant for CCN modeling and calibration studies. The equations introduced here provide the basis of our revised gas-liquid-solid partitioning model, i.e. version 4 of the EQuilibrium Simplified Aerosol Model (EQSAM4), described in a companion paper.

Modeling of dispersed-drug delivery from planar polymeric systems: optimizing analytical solutions.

PubMed

Helbling, Ignacio M; Ibarra, Juan C D; Luna, Julio A; Cabrera, María I; Grau, Ricardo J A

2010-11-15

Analytical solutions for the case of controlled dispersed-drug release from planar non-erodible polymeric matrices, based on Refined Integral Method, are presented. A new adjusting equation is used for the dissolved drug concentration profile in the depletion zone. The set of equations match the available exact solution. In order to illustrate the usefulness of this model, comparisons with experimental profiles reported in the literature are presented. The obtained results show that the model can be employed in a broad range of applicability. Copyright © 2010 Elsevier B.V. All rights reserved.

Meromorphic solutions of recurrence relations and DRA method for multicomponent master integrals

NASA Astrophysics Data System (ADS)

Lee, Roman N.; Mingulov, Kirill T.

2018-04-01

We formulate a method to find the meromorphic solutions of higher-order recurrence relations in the form of the sum over poles with coefficients defined recursively. Several explicit examples of the application of this technique are given. The main advantage of the described approach is that the analytical properties of the solutions are very clear (the position of poles is explicit, the behavior at infinity can be easily determined). These are exactly the properties that are required for the application of the multiloop calculation method based on dimensional recurrence relations and analyticity (the DRA method).

Analytic solution of field distribution and demagnetization function of ideal hollow cylindrical field source

NASA Astrophysics Data System (ADS)

Xu, Xiaonong; Lu, Dingwei; Xu, Xibin; Yu, Yang; Gu, Min

2017-09-01

The Halbach type hollow cylindrical permanent magnet array (HCPMA) is a volume compact and energy conserved field source, which have attracted intense interests in many practical applications. Here, using the complex variable integration method based on the Biot-Savart Law (including current distributions inside the body and on the surfaces of magnet), we derive analytical field solutions to an ideal multipole HCPMA in entire space including the interior of magnet. The analytic field expression inside the array material is used to construct an analytic demagnetization function, with which we can explain the origin of demagnetization phenomena in HCPMA by taking into account an ideal magnetic hysteresis loop with finite coercivity. These analytical field expressions and demagnetization functions provide deeper insight into the nature of such permanent magnet array systems and offer guidance in designing optimized array system.

Analytically-derived sensitivities in one-dimensional models of solute transport in porous media

USGS Publications Warehouse

Knopman, D.S.

1987-01-01

Analytically-derived sensitivities are presented for parameters in one-dimensional models of solute transport in porous media. Sensitivities were derived by direct differentiation of closed form solutions for each of the odel, and by a time integral method for two of the models. Models are based on the advection-dispersion equation and include adsorption and first-order chemical decay. Boundary conditions considered are: a constant step input of solute, constant flux input of solute, and exponentially decaying input of solute at the upstream boundary. A zero flux is assumed at the downstream boundary. Initial conditions include a constant and spatially varying distribution of solute. One model simulates the mixing of solute in an observation well from individual layers in a multilayer aquifer system. Computer programs produce output files compatible with graphics software in which sensitivities are plotted as a function of either time or space. (USGS)

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

PubMed

Imamura, Hiroshi; Honda, Shinya

2017-01-01

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

Analytical approximation and numerical simulations for periodic travelling water waves

NASA Astrophysics Data System (ADS)

Kalimeris, Konstantinos

2017-12-01

We present recent analytical and numerical results for two-dimensional periodic travelling water waves with constant vorticity. The analytical approach is based on novel asymptotic expansions. We obtain numerical results in two different ways: the first is based on the solution of a constrained optimization problem, and the second is realized as a numerical continuation algorithm. Both methods are applied on some examples of non-constant vorticity. This article is part of the theme issue 'Nonlinear water waves'.

Semi-analytical integration of the Earth's precession-nutation based on the GCRS coordinates of the CIP unit vector

NASA Astrophysics Data System (ADS)

Capitaine, N.; Folgueira, M.

2012-12-01

In a previous paper (Capitaine et al. 2006), referred here as Paper I, we demonstrated the possibility of integrating the Earth's rotational motion in terms of the coordinates (X, Y ) of the celestial intermediate pole (CIP) unit vector in the Geocentric celestial reference system (GCRS). Here, we report on the approach that has been followed for solving the equations in the case of an axially symmetric rigid Earth and the semi-analytical (X, Y ) solution obtained from the expression of the external torque acting on the Earth derived from the most complete semi-analytical solutions for the Earth, Moon and planets.

Sample distribution in peak mode isotachophoresis

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

Rubin, Shimon; Schwartz, Ortal; Bercovici, Moran, E-mail: mberco@technion.ac.il

We present an analytical study of peak mode isotachophoresis (ITP), and provide closed form solutions for sample distribution and electric field, as well as for leading-, trailing-, and counter-ion concentration profiles. Importantly, the solution we present is valid not only for the case of fully ionized species, but also for systems of weak electrolytes which better represent real buffer systems and for multivalent analytes such as proteins and DNA. The model reveals two major scales which govern the electric field and buffer distributions, and an additional length scale governing analyte distribution. Using well-controlled experiments, and numerical simulations, we verify andmore » validate the model and highlight its key merits as well as its limitations. We demonstrate the use of the model for determining the peak concentration of focused sample based on known buffer and analyte properties, and show it differs significantly from commonly used approximations based on the interface width alone. We further apply our model for studying reactions between multiple species having different effective mobilities yet co-focused at a single ITP interface. We find a closed form expression for an effective-on rate which depends on reactants distributions, and derive the conditions for optimizing such reactions. Interestingly, the model reveals that maximum reaction rate is not necessarily obtained when the concentration profiles of the reacting species perfectly overlap. In addition to the exact solutions, we derive throughout several closed form engineering approximations which are based on elementary functions and are simple to implement, yet maintain the interplay between the important scales. Both the exact and approximate solutions provide insight into sample focusing and can be used to design and optimize ITP-based assays.« less

Analytical and numerical solutions of the potential and electric field generated by different electrode arrays in a tumor tissue under electrotherapy.

PubMed

Bergues Pupo, Ana E; Reyes, Juan Bory; Bergues Cabrales, Luis E; Bergues Cabrales, Jesús M

2011-09-24

Electrotherapy is a relatively well established and efficient method of tumor treatment. In this paper we focus on analytical and numerical calculations of the potential and electric field distributions inside a tumor tissue in a two-dimensional model (2D-model) generated by means of electrode arrays with shapes of different conic sections (ellipse, parabola and hyperbola). Analytical calculations of the potential and electric field distributions based on 2D-models for different electrode arrays are performed by solving the Laplace equation, meanwhile the numerical solution is solved by means of finite element method in two dimensions. Both analytical and numerical solutions reveal significant differences between the electric field distributions generated by electrode arrays with shapes of circle and different conic sections (elliptic, parabolic and hyperbolic). Electrode arrays with circular, elliptical and hyperbolic shapes have the advantage of concentrating the electric field lines in the tumor. The mathematical approach presented in this study provides a useful tool for the design of electrode arrays with different shapes of conic sections by means of the use of the unifying principle. At the same time, we verify the good correspondence between the analytical and numerical solutions for the potential and electric field distributions generated by the electrode array with different conic sections.

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

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.

Closed-form analytical solutions of high-temperature heat pipe startup and frozen startup limitation

NASA Technical Reports Server (NTRS)

Cao, Y.; Faghri, A.

1992-01-01

Previous numerical and experimental studies indicate that the high-temperature heat pipe startup process is characterized by a moving hot zone with relatively sharp fronts. Based on the above observation, a flat-front model for an approximate analytical solution is proposed. A closed-form solution related to the temperature distribution in the hot zone and the hot zone length as a function of time are obtained. The analytical results agree well with the corresponding experimental data, and provide a quick prediction method for the heat pipe startup performance. Finally, a heat pipe limitation related to the frozen startup process is identified, and an explicit criterion for the high-temperature heat pipe startup is derived. The frozen startup limit identified in this paper provides a fundamental guidance for high-temperature heat pipe design.

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

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

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...

Demonstration/Validation of the Snap Sampler Passive Ground Water Sampling Device for Sampling Inorganic Analytes at the Former Pease Air Force Base

DTIC Science & Technology

2009-07-01

viii Unit Conversion Factors...sampler is also an economic alternative for sampling for inorganic analytes. ERDC/CRREL TR-09-12 xii Unit Conversion Factors Multiply By To Obtain...head- space and then covered with two layers of tightly fitting aluminum foil. To dissolve the analytes, the solutions were stirred for approximately

SmartAdP: Visual Analytics of Large-scale Taxi Trajectories for Selecting Billboard Locations.

PubMed

Liu, Dongyu; Weng, Di; Li, Yuhong; Bao, Jie; Zheng, Yu; Qu, Huamin; Wu, Yingcai

2017-01-01

The problem of formulating solutions immediately and comparing them rapidly for billboard placements has plagued advertising planners for a long time, owing to the lack of efficient tools for in-depth analyses to make informed decisions. In this study, we attempt to employ visual analytics that combines the state-of-the-art mining and visualization techniques to tackle this problem using large-scale GPS trajectory data. In particular, we present SmartAdP, an interactive visual analytics system that deals with the two major challenges including finding good solutions in a huge solution space and comparing the solutions in a visual and intuitive manner. An interactive framework that integrates a novel visualization-driven data mining model enables advertising planners to effectively and efficiently formulate good candidate solutions. In addition, we propose a set of coupled visualizations: a solution view with metaphor-based glyphs to visualize the correlation between different solutions; a location view to display billboard locations in a compact manner; and a ranking view to present multi-typed rankings of the solutions. This system has been demonstrated using case studies with a real-world dataset and domain-expert interviews. Our approach can be adapted for other location selection problems such as selecting locations of retail stores or restaurants using trajectory data.

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.

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

NASA Astrophysics Data System (ADS)

Mobarakeh, Pouyan Shakeri; Grinchenko, Victor T.

2015-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

A paper-based analytical device for the determination of hydrogen sulfide in fuel oils based on headspace liquid-phase microextraction and cyclic voltammetry.

PubMed

Nechaeva, Daria; Shishov, Andrey; Ermakov, Sergey; Bulatov, Andrey

2018-06-01

An easily performed miniaturized, cheap, selective and sensitive procedure for the determination of H 2 S in fuel oil samples based on a headspace liquid-phase microextraction followed by a cyclic voltammetry detection using a paper-based analytical device (PAD) was developed. A modified wax dipping method was applied to fabricate the PAD. The PAD included hydrophobic zones of sample and supporting electrolyte connecting by hydrophilic channel. The zones of sample and supporting electrolyte were connected with nickel working, platinum auxiliary and Ag/AgCl reference electrodes. The analytical procedure included separation of H 2 S from fuel oil sample based on the headspace liquid-phase microextraction in alkaline solution. Then, sulfide ions solution obtained and supporting electrolyte were dropped on the zones followed by analyte detection at + 0.45 V. Under the optimized conditions, H 2 S concentration in the range from 2 to 20 mg kg -1 had a good linear relation with the peak current. The limit of detection (3σ) was 0.6 mg kg -1 . The procedure was successfully applied to the analysis of fuel oil samples. Copyright © 2018 Elsevier B.V. All rights reserved.

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

Analytical method for dissolved-organic carbon fractionation

USGS Publications Warehouse

Leenheer, Jerry A.; Huffman, Edward W. D.

1979-01-01

A standard procedure for analytical-scale dissolved organic carbon fractionation is presented, whereby dissolved organic carbon in water is first fractionated by a nonionic macroreticular resin into acid, base, and neutral hydrophobic organic solute fractions, and next fractionated by ion-exchange resins into acid, base, and neutral hydrophilic solute fractions. The hydrophobic solutes are defined as those sorbed on a nonionic, acrylic-ester macroreticular resin and are differentiated into acid, base, and nautral fractions by sorption/desorption controlled by pH adjustment. The hydrophilic bases are next sorbed on strong-acid ion-exchange resin, followed by sorption of hydrophilic acids on a strong-base ion-exchange resin. Hydrophilic neutrals are not sorbed and remain dissolved in the deionized water at the end of the fractionation procedure. The complete fractionation can be performed on a 200-milliliter filtered water sample, whose dissolved organic carbon content is 5-25 mg/L and whose specific conductance is less than 2,000 μmhos/cm at 25°C. The applications of dissolved organic carbon fractionation analysis range from field studies of changes of organic solute composition with synthetic fossil fuel production, to fundamental studies of the nature of sorption processes.

Internet-based interface for STRMDEPL08

USGS Publications Warehouse

Reeves, Howard W.; Asher, A. Jeremiah

2010-01-01

The core of the computer program STRMDEPL08 that estimates streamflow depletion by a pumping well with one of four analytical solutions was re-written in the Javascript software language and made available through an internet-based interface (web page). In the internet-based interface, the user enters data for one of the four analytical solutions, Glover and Balmer (1954), Hantush (1965), Hunt (1999), and Hunt (2003), and the solution is run for constant pumping for a desired number of simulation days. Results are returned in tabular form to the user. For intermittent pumping, the interface allows the user to request that the header information for an input file for the stand-alone executable STRMDEPL08 be created. The user would add the pumping information to this header information and run the STRMDEPL08 executable that is available for download through the U.S. Geological Survey. Results for the internet-based and stand-alone versions of STRMDEPL08 are shown to match.

Numerical Problems and Agent-Based Models for a Mass Transfer Course

ERIC Educational Resources Information Center

Murthi, Manohar; Shea, Lonnie D.; Snurr, Randall Q.

2009-01-01

Problems requiring numerical solutions of differential equations or the use of agent-based modeling are presented for use in a course on mass transfer. These problems were solved using the popular technical computing language MATLABTM. Students were introduced to MATLAB via a problem with an analytical solution. A more complex problem to which no…

Experimental testing and modeling analysis of solute mixing at water distribution pipe junctions.

PubMed

Shao, Yu; Jeffrey Yang, Y; Jiang, Lijie; Yu, Tingchao; Shen, Cheng

2014-06-01

Flow dynamics at a pipe junction controls particle trajectories, solute mixing and concentrations in downstream pipes. The effect can lead to different outcomes of water quality modeling and, hence, drinking water management in a distribution network. Here we have investigated solute mixing behavior in pipe junctions of five hydraulic types, for which flow distribution factors and analytical equations for network modeling are proposed. First, based on experiments, the degree of mixing at a cross is found to be a function of flow momentum ratio that defines a junction flow distribution pattern and the degree of departure from complete mixing. Corresponding analytical solutions are also validated using computational-fluid-dynamics (CFD) simulations. Second, the analytical mixing model is further extended to double-Tee junctions. Correspondingly the flow distribution factor is modified to account for hydraulic departure from a cross configuration. For a double-Tee(A) junction, CFD simulations show that the solute mixing depends on flow momentum ratio and connection pipe length, whereas the mixing at double-Tee(B) is well represented by two independent single-Tee junctions with a potential water stagnation zone in between. Notably, double-Tee junctions differ significantly from a cross in solute mixing and transport. However, it is noted that these pipe connections are widely, but incorrectly, simplified as cross junctions of assumed complete solute mixing in network skeletonization and water quality modeling. For the studied pipe junction types, analytical solutions are proposed to characterize the incomplete mixing and hence may allow better water quality simulation in a distribution network. Published by Elsevier Ltd.

Physics-based and human-derived information fusion for analysts

NASA Astrophysics Data System (ADS)

Blasch, Erik; Nagy, James; Scott, Steve; Okoth, Joshua; Hinman, Michael

2017-05-01

Recent trends in physics-based and human-derived information fusion (PHIF) have amplified the capabilities of analysts; however with the big data opportunities there is a need for open architecture designs, methods of distributed team collaboration, and visualizations. In this paper, we explore recent trends in the information fusion to support user interaction and machine analytics. Challenging scenarios requiring PHIF include combing physics-based video data with human-derived text data for enhanced simultaneous tracking and identification. A driving effort would be to provide analysts with applications, tools, and interfaces that afford effective and affordable solutions for timely decision making. Fusion at scale should be developed to allow analysts to access data, call analytics routines, enter solutions, update models, and store results for distributed decision making.

GENERAL: The Analytic Solution of Schrödinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

NASA Astrophysics Data System (ADS)

Hu, Xian-Quan; Luo, Guang; Cui, Li-Peng; Li, Fang-Yu; Niu, Lian-Bin

2009-03-01

The analytic solution of the radial Schrödinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrödinger equation is V(r) = α1r8 + α2r3 + α3r2 + β3r-1 + β2r-3 + β1r-4. Generally speaking, there is only an approximate solution, but not analytic solution for Schrödinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrödinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → and r → 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schrödinger equation; and lastly, they discuss the solutions and make conclusions.

Approximate analytical solutions in the analysis of elastic structures of complex geometry

NASA Astrophysics Data System (ADS)

Goloskokov, Dmitriy P.; Matrosov, Alexander V.

2018-05-01

A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method.

Analytically solvable chaotic oscillator based on a first-order filter.

PubMed

Corron, Ned J; Cooper, Roy M; Blakely, Jonathan N

2016-02-01

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.

Analytically solvable chaotic oscillator based on a first-order filter

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

Corron, Ned J.; Cooper, Roy M.; Blakely, Jonathan N.

2016-02-15

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform formore » any stable infinite-impulse response filter is chaotic.« less

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.

Complexometric Determination of Mercury Based on a Selective Masking Reaction

ERIC Educational Resources Information Center

Romero, Mercedes; Guidi, Veronica; Ibarrolaza, Agustin; Castells, Cecilia

2009-01-01

In the first analytical chemistry course, students are introduced to the concepts of equilibrium in water solutions and classical (non-instrumental) analytical methods. Our teaching experience shows that "real samples" stimulate students' enthusiasm for the laboratory work. From this diagnostic, we implemented an optional activity at the end of…

A singularity free analytical solution of artificial satellite motion with drag

NASA Technical Reports Server (NTRS)

Mueller, A.

1978-01-01

An analytical satellite theory based on the regular, canonical Poincare-Similar (PS phi) elements is described along with an accurate density model which can be implemented into the drag theory. A computationally efficient manner in which to expand the equations of motion into a fourier series is discussed.

Simulation of flux during electro-membrane extraction based on the Nernst-Planck equation.

PubMed

Gjelstad, Astrid; Rasmussen, Knut Einar; Pedersen-Bjergaard, Stig

2007-12-07

The present work has for the first time described and verified a theoretical model of the analytical extraction process electro-membrane extraction (EME), where target analytes are extracted from an aqueous sample, through a thin layer of 2-nitrophenyl octylether immobilized as a supported liquid membrane (SLM) in the pores in the wall of a porous hollow fibre, and into an acceptor solution present inside the lumen of the hollow fibre by the application of an electrical potential difference. The mathematical model was based on the Nernst-Planck equation, and described the flux over the SLM. The model demonstrated that the magnitude of the electrical potential difference, the ion balance of the system, and the absolute temperature influenced the flux of analyte across the SLM. These conclusions were verified by experimental data with five basic drugs. The flux was strongly dependent of the potential difference over the SLM, and increased potential difference resulted in an increase in the flux. The ion balance, defined as the sum of ions in the donor solution divided by the sum of ions in the acceptor solution, was shown to influence the flux, and high ionic concentration in the acceptor solution relative to the sample solution was advantageous for high flux. Different temperatures also led to changes in the flux in the EME system.

Dynamic Beam Solutions for Real-Time Simulation and Control Development of Flexible Rockets

NASA Technical Reports Server (NTRS)

Su, Weihua; King, Cecilia K.; Clark, Scott R.; Griffin, Edwin D.; Suhey, Jeffrey D.; Wolf, Michael G.

2016-01-01

In this study, flexible rockets are structurally represented by linear beams. Both direct and indirect solutions of beam dynamic equations are sought to facilitate real-time simulation and control development for flexible rockets. The direct solution is completed by numerically integrate the beam structural dynamic equation using an explicit Newmark-based scheme, which allows for stable and fast transient solutions to the dynamics of flexile rockets. Furthermore, in the real-time operation, the bending strain of the beam is measured by fiber optical sensors (FOS) at intermittent locations along the span, while both angular velocity and translational acceleration are measured at a single point by the inertial measurement unit (IMU). Another study in this paper is to find the analytical and numerical solutions of the beam dynamics based on the limited measurement data to facilitate the real-time control development. Numerical studies demonstrate the accuracy of these real-time solutions to the beam dynamics. Such analytical and numerical solutions, when integrated with data processing and control algorithms and mechanisms, have the potential to increase launch availability by processing flight data into the flexible launch vehicle's control system.

Analytical Solution for Optimum Design of Furrow Irrigation Systems

NASA Astrophysics Data System (ADS)

Kiwan, M. E.

1996-05-01

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

Recent developments and future trends in solid phase microextraction techniques towards green analytical chemistry.

PubMed

Spietelun, Agata; Marcinkowski, Łukasz; de la Guardia, Miguel; Namieśnik, Jacek

2013-12-20

Solid phase microextraction find increasing applications in the sample preparation step before chromatographic determination of analytes in samples with a complex composition. These techniques allow for integrating several operations, such as sample collection, extraction, analyte enrichment above the detection limit of a given measuring instrument and the isolation of analytes from sample matrix. In this work the information about novel methodological and instrumental solutions in relation to different variants of solid phase extraction techniques, solid-phase microextraction (SPME), stir bar sorptive extraction (SBSE) and magnetic solid phase extraction (MSPE) is presented, including practical applications of these techniques and a critical discussion about their advantages and disadvantages. The proposed solutions fulfill the requirements resulting from the concept of sustainable development, and specifically from the implementation of green chemistry principles in analytical laboratories. Therefore, particular attention was paid to the description of possible uses of novel, selective stationary phases in extraction techniques, inter alia, polymeric ionic liquids, carbon nanotubes, and silica- and carbon-based sorbents. The methodological solutions, together with properly matched sampling devices for collecting analytes from samples with varying matrix composition, enable us to reduce the number of errors during the sample preparation prior to chromatographic analysis as well as to limit the negative impact of this analytical step on the natural environment and the health of laboratory employees. Copyright © 2013 Elsevier B.V. All rights reserved.

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

Zhou, Quanlin; Oldenburg, Curtis M.; Spangler, Lee H.

Analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form approximate solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined analytically for isotropic blocks (e.g., spheresmore » and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative approximation error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO 2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These approximate solutions are building blocks for development of analytical and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.« less

Analytical Expressions for Thermo-Osmotic Permeability of Clays

NASA Astrophysics Data System (ADS)

Gonçalvès, J.; Ji Yu, C.; Matray, J.-M.; Tremosa, J.

2018-01-01

In this study, a new formulation for the thermo-osmotic permeability of natural pore solutions containing monovalent and divalent cations is proposed. The mathematical formulation proposed here is based on the theoretical framework supporting thermo-osmosis which relies on water structure alteration in the pore space of surface-charged materials caused by solid-fluid electrochemical interactions. The ionic content balancing the surface charge of clay minerals causes a disruption in the hydrogen bond network when more structured water is present at the clay surface. Analytical expressions based on our heuristic model are proposed and compared to the available data for NaCl solutions. It is shown that the introduction of divalent cations reduces the thermo-osmotic permeability by one third compared to the monovalent case. The analytical expressions provided here can be used to advantage for safety calculations in deep underground nuclear waste repositories.

The exact solution of the monoenergetic transport equation for critical cylinders

NASA Technical Reports Server (NTRS)

Westfall, R. M.; Metcalf, D. R.

1972-01-01

An analytic solution for the critical, monoenergetic, bare, infinite cylinder is presented. The solution is obtained by modifying a previous development based on a neutron density transform and Case's singular eigenfunction method. Numerical results for critical radii and the neutron density as a function of position are included and compared with the results of other methods.

Effects of Thermal Resistance on One-Dimensional Thermal Analysis of the Epidermal Flexible Electronic Devices Integrated with Human Skin

NASA Astrophysics Data System (ADS)

Li, He; Cui, Yun

2017-12-01

Nowadays, flexible electronic devices are increasingly used in direct contact with human skin to monitor the real-time health of human body. Based on the Fourier heat conduction equation and Pennes bio-heat transfer equation, this paper deduces the analytical solutions of one - dimensional heat transfer for flexible electronic devices integrated with human skin under the condition of a constant power. The influence of contact thermal resistance between devices and skin is considered as well. The corresponding finite element model is established to verify the correctness of analytical solutions. The results show that the finite element analysis agrees well with the analytical solution. With bigger thermal resistance, temperature increase of skin surface will decrease. This result can provide guidance for the design of flexible electronic devices to reduce the negative impact that exceeding temperature leave on human skin.

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.

Electromagnetic field analysis and modeling of a relative position detection sensor for high speed maglev trains.

PubMed

Xue, Song; He, Ning; Long, Zhiqiang

2012-01-01

The long stator track for high speed maglev trains has a tooth-slot structure. The sensor obtains precise relative position information for the traction system by detecting the long stator tooth-slot structure based on nondestructive detection technology. The magnetic field modeling of the sensor is a typical three-dimensional (3-D) electromagnetic problem with complex boundary conditions, and is studied semi-analytically in this paper. A second-order vector potential (SOVP) is introduced to simplify the vector field problem to a scalar field one, the solution of which can be expressed in terms of series expansions according to Multipole Theory (MT) and the New Equivalent Source (NES) method. The coefficients of the expansions are determined by the least squares method based on the boundary conditions. Then, the solution is compared to the simulation result through Finite Element Analysis (FEA). The comparison results show that the semi-analytical solution agrees approximately with the numerical solution. Finally, based on electromagnetic modeling, a difference coil structure is designed to improve the sensitivity and accuracy of the sensor.

Electromagnetic Field Analysis and Modeling of a Relative Position Detection Sensor for High Speed Maglev Trains

PubMed Central

Xue, Song; He, Ning; Long, Zhiqiang

2012-01-01

The long stator track for high speed maglev trains has a tooth-slot structure. The sensor obtains precise relative position information for the traction system by detecting the long stator tooth-slot structure based on nondestructive detection technology. The magnetic field modeling of the sensor is a typical three-dimensional (3-D) electromagnetic problem with complex boundary conditions, and is studied semi-analytically in this paper. A second-order vector potential (SOVP) is introduced to simplify the vector field problem to a scalar field one, the solution of which can be expressed in terms of series expansions according to Multipole Theory (MT) and the New Equivalent Source (NES) method. The coefficients of the expansions are determined by the least squares method based on the boundary conditions. Then, the solution is compared to the simulation result through Finite Element Analysis (FEA). The comparison results show that the semi-analytical solution agrees approximately with the numerical solution. Finally, based on electromagnetic modeling, a difference coil structure is designed to improve the sensitivity and accuracy of the sensor. PMID:22778652

Polar decomposition for attitude determination from vector observations

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.

1993-01-01

This work treats the problem of weighted least squares fitting of a 3D Euclidean-coordinate transformation matrix to a set of unit vectors measured in the reference and transformed coordinates. A closed-form analytic solution to the problem is re-derived. The fact that the solution is the closest orthogonal matrix to some matrix defined on the measured vectors and their weights is clearly demonstrated. Several known algorithms for computing the analytic closed form solution are considered. An algorithm is discussed which is based on the polar decomposition of matrices into the closest unitary matrix to the decomposed matrix and a Hermitian matrix. A somewhat longer improved algorithm is suggested too. A comparison of several algorithms is carried out using simulated data as well as real data from the Upper Atmosphere Research Satellite. The comparison is based on accuracy and time consumption. It is concluded that the algorithms based on polar decomposition yield a simple although somewhat less accurate solution. The precision of the latter algorithms increase with the number of the measured vectors and with the accuracy of their measurement.

Analytical and numerical solutions of the potential and electric field generated by different electrode arrays in a tumor tissue under electrotherapy

PubMed Central

2011-01-01

Background Electrotherapy is a relatively well established and efficient method of tumor treatment. In this paper we focus on analytical and numerical calculations of the potential and electric field distributions inside a tumor tissue in a two-dimensional model (2D-model) generated by means of electrode arrays with shapes of different conic sections (ellipse, parabola and hyperbola). Methods Analytical calculations of the potential and electric field distributions based on 2D-models for different electrode arrays are performed by solving the Laplace equation, meanwhile the numerical solution is solved by means of finite element method in two dimensions. Results Both analytical and numerical solutions reveal significant differences between the electric field distributions generated by electrode arrays with shapes of circle and different conic sections (elliptic, parabolic and hyperbolic). Electrode arrays with circular, elliptical and hyperbolic shapes have the advantage of concentrating the electric field lines in the tumor. Conclusion The mathematical approach presented in this study provides a useful tool for the design of electrode arrays with different shapes of conic sections by means of the use of the unifying principle. At the same time, we verify the good correspondence between the analytical and numerical solutions for the potential and electric field distributions generated by the electrode array with different conic sections. PMID:21943385

Electrodialytic in-line preconcentration for ionic solute analysis.

PubMed

Ohira, Shin-Ichi; Yamasaki, Takayuki; Koda, Takumi; Kodama, Yuko; Toda, Kei

2018-04-01

Preconcentration is an effective way to improve analytical sensitivity. Many types of methods are used for enrichment of ionic solute analytes. However, current methods are batchwise and include procedures such as trapping and elution. In this manuscript, we propose in-line electrodialytic enrichment of ionic solutes. The method can enrich ionic solutes within seconds by quantitative transfer of analytes from the sample solution to the acceptor solution under an electric field. Because of quantitative ion transfer, the enrichment factor (the ratio of the concentration in the sample and to that in the obtained acceptor solution) only depends on the flow rate ratio of the sample solution to the acceptor solution. The ratios of the concentrations and flow rates are equal for ratios up to 70, 20, and 70 for the tested ionic solutes of inorganic cations, inorganic anions, and heavy metal ions, respectively. The sensitivity of ionic solute determinations is also improved based on the enrichment factor. The method can also simultaneously achieve matrix isolation and enrichment. The method was successively applied to determine the concentrations of trace amounts of chloroacetic acids in tap water. The regulated concentration levels cannot be determined by conventional high-performance liquid chromatography with ultraviolet detection (HPLC-UV) without enrichment. However, enrichment with the present method is effective for determination of tap water quality by improving the limits of detection of HPLC-UV. The standard addition test with real tap water samples shows good recoveries (94.9-109.6%). Copyright © 2017 Elsevier B.V. All rights reserved.

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

NASA Technical Reports Server (NTRS)

Turc, Catalin; Anand, Akash; Bruno, Oscar; Chaubell, Julian

2011-01-01

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.

A two-dimensional analytical model for groundwater flow in a leaky aquifer extending finite distance under the estuary

NASA Astrophysics Data System (ADS)

Chuang, Mo-Hsiung; Hung, Chi-Tung; -Yen Lin, Wen; Ma, Kuo-chen

2017-04-01

In recent years, cities and industries in the vicinity of the estuarine region have developed rapidly, resulting in a sharp increase in the population concerned. The increasing demand for human activities, agriculture irrigation, and aquaculture relies on massive pumping of water in estuarine area. Since the 1950s, numerous studies have focused on the effects of tidal fluctuations on groundwater flow in the estuarine area. Tide-induced head fluctuation in a two-dimensional estuarine aquifer system is complicated and rather important in dealing with many groundwater management or remediation problems. The conceptual model of the aquifer system considered is multi-layered with estuarine bank and the leaky aquifer extend finite distance under the estuary. The solution of the model describing the groundwater head distribution in such an estuarine aquifer system and subject to the tidal fluctuation effects from estuarine river is developed based on the method of separation of variables along with river boundary. The solutions by Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour. Res. 1997; 33:1429-35) as well as Tang and Jiao (Tang Z. and J. J. Jiao, A two-dimensional analytical solution for groundwater flow in a leaky confined aquifer system near open tidal water, Hydrological Processes, 2001; 15: 573-585) can be shown to be special cases of the present solution. On the basis of the analytical solution, the groundwater head distribution in response to estuarine boundary is examined and the influences of leakage, hydraulic parameters, and loading effect on the groundwater head fluctuation due to tide are investigated and discussed. KEYWORDS: analytical model, estuarine river, groundwater fluctuation, leaky aquifer.

A meshless method using radial basis functions for numerical solution of the two-dimensional KdV-Burgers equation

NASA Astrophysics Data System (ADS)

Zabihi, F.; Saffarian, M.

2016-07-01

The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.

Original analytic solution of a half-bridge modelled as a statically indeterminate system

NASA Astrophysics Data System (ADS)

Oanta, Emil M.; Panait, Cornel; Raicu, Alexandra; Barhalescu, Mihaela

2016-12-01

The paper presents an original computer based analytical model of a half-bridge belonging to a circular settling tank. The primary unknown is computed using the force method, the coefficients of the canonical equation being calculated using either the discretization of the bending moment diagram in trapezoids, or using the relations specific to the polygons. A second algorithm based on the method of initial parameters is also presented. Analyzing the new solution we came to the conclusion that most of the computer code developed for other model may be reused. The results are useful to evaluate the behavior of the structure and to compare with the results of the finite element models.

Semianalytical Solutions for Transport in Aquifer and Fractured Clay Matrix System

EPA Science Inventory

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 analytical solutions is derived based on specific initial and boundary conditions as well as ...

High Rayleigh number convection in rectangular enclosures with differentially heated vertical walls and aspect ratios between zero and unity

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

Kassemi, S.A.

1988-04-01

High Rayleigh number convection in a rectangular cavity with insulated horizontal surfaces and differentially heated vertical walls was analyzed for an arbitrary aspect ratio smaller than or equal to unity. Unlike previous analytical studies, a systematic method of solution based on linearization technique and analytical iteration procedure was developed to obtain approximate closed-form solutions for a wide range of aspect ratios. The predicted velocity and temperature fields are shown to be in excellent agreement with available experimental and numerical data.

High Rayleigh number convection in rectangular enclosures with differentially heated vertical walls and aspect ratios between zero and unity

NASA Technical Reports Server (NTRS)

Kassemi, Siavash A.

1988-01-01

High Rayleigh number convection in a rectangular cavity with insulated horizontal surfaces and differentially heated vertical walls was analyzed for an arbitrary aspect ratio smaller than or equal to unity. Unlike previous analytical studies, a systematic method of solution based on linearization technique and analytical iteration procedure was developed to obtain approximate closed-form solutions for a wide range of aspect ratios. The predicted velocity and temperature fields are shown to be in excellent agreement with available experimental and numerical data.

Satellite recovery - Attitude dynamics of the targets

NASA Technical Reports Server (NTRS)

Cochran, J. E., Jr.; Lahr, B. S.

1986-01-01

The problems of categorizing and modeling the attitude dynamics of uncontrolled artificial earth satellites which may be targets in recovery attempts are addressed. Methods of classification presented are based on satellite rotational kinetic energy, rotational angular momentum and orbit and on the type of control present prior to the benign failure of the control system. The use of approximate analytical solutions and 'exact' numerical solutions to the equations governing satellite attitude motions to predict uncontrolled attitude motion is considered. Analytical and numerical results are presented for the evolution of satellite attitude motions after active control termination.

Thermoelastic analysis of spent fuel and high level radioactive waste repositories in salt. A semi-analytical solution. [JUDITH

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

St. John, C.M.

1977-04-01

An underground repository containing heat generating, High Level Waste or Spent Unreprocessed Fuel may be approximated as a finite number of heat sources distributed across the plane of the repository. The resulting temperature, displacement and stress changes may be calculated using analytical solutions, providing linear thermoelasticity is assumed. This report documents a computer program based on this approach and gives results that form the basis for a comparison between the effects of disposing of High Level Waste and Spent Unreprocessed Fuel.

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

ERIC Educational Resources Information Center

Levesque, Luc

2012-01-01

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

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.

SAW-Based Phononic Crystal Microfluidic Sensor—Microscale Realization of Velocimetry Approaches for Integrated Analytical Platform Applications

PubMed Central

Lucklum, Ralf; Zubtsov, Mikhail; Schmidt, Marc-Peter; Mukhin, Nikolay V.; Hirsch, Soeren

2017-01-01

The current work demonstrates a novel surface acoustic wave (SAW) based phononic crystal sensor approach that allows the integration of a velocimetry-based sensor concept into single chip integrated solutions, such as Lab-on-a-Chip devices. The introduced sensor platform merges advantages of ultrasonic velocimetry analytic systems and a microacoustic sensor approach. It is based on the analysis of structural resonances in a periodic composite arrangement of microfluidic channels confined within a liquid analyte. Completed theoretical and experimental investigations show the ability to utilize periodic structure localized modes for the detection of volumetric properties of liquids and prove the efficacy of the proposed sensor concept. PMID:28946609

SAW-Based Phononic Crystal Microfluidic Sensor-Microscale Realization of Velocimetry Approaches for Integrated Analytical Platform Applications.

PubMed

Oseev, Aleksandr; Lucklum, Ralf; Zubtsov, Mikhail; Schmidt, Marc-Peter; Mukhin, Nikolay V; Hirsch, Soeren

2017-09-23

The current work demonstrates a novel surface acoustic wave (SAW) based phononic crystal sensor approach that allows the integration of a velocimetry-based sensor concept into single chip integrated solutions, such as Lab-on-a-Chip devices. The introduced sensor platform merges advantages of ultrasonic velocimetry analytic systems and a microacoustic sensor approach. It is based on the analysis of structural resonances in a periodic composite arrangement of microfluidic channels confined within a liquid analyte. Completed theoretical and experimental investigations show the ability to utilize periodic structure localized modes for the detection of volumetric properties of liquids and prove the efficacy of the proposed sensor concept.

DROMO formulation for planar motions: solution to the Tsien problem

NASA Astrophysics Data System (ADS)

Urrutxua, Hodei; Morante, David; Sanjurjo-Rivo, Manuel; Peláez, Jesús

2015-06-01

The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen's ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo-Stiefel methods.

Gravity discharge vessel revisited: An explicit Lambert W function solution

NASA Astrophysics Data System (ADS)

Digilov, Rafael M.

2017-07-01

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

Simplified multiple scattering model for radiative transfer in turbid water

NASA Technical Reports Server (NTRS)

Ghovanlou, A. H.; Gupta, G. N.

1978-01-01

Quantitative analytical procedures for relating selected water quality parameters to the characteristics of the backscattered signals, measured by remote sensors, require the solution of the radiative transport equation in turbid media. Presented is an approximate closed form solution of this equation and based on this solution, the remote sensing of sediments is discussed. The results are compared with other standard closed form solutions such as quasi-single scattering approximations.

Adsorption losses from urine-based cannabinoid calibrators during routine use.

PubMed

Blanc, J A; Manneh, V A; Ernst, R; Berger, D E; de Keczer, S A; Chase, C; Centofanti, J M; DeLizza, A J

1993-08-01

The major metabolite of cannabis found in urine, 11-nor-delta 9-tetrahydrocannabinol-9-carboxylic acid (delta 9-THC), is the compound most often used to calibrate cannabinoid immunoassays. The hydrophobic delta 9-THC molecule is known to adsorb to solid surfaces. This loss of analyte from calibrator solutions can lead to inaccuracy in the analytical system. Because the calibrators remain stable when not used, analyte loss is most probably caused by handling techniques. In an effort to develop an effective means of overcoming adsorption losses, we quantified cannabinoid loss from calibrators during the testing process. In studying handling of these solutions, we found noticeable, significant losses attributable to both the kind of pipette used for transfer and the contact surface-to-volume ratio of calibrator solution in the analyzer cup. Losses were quantified by immunoassay and by radioactive tracer. We suggest handling techniques that can minimize adsorption of delta 9-THC to surfaces. Using the appropriate pipette and maintaining a minimum surface-to-volume ratio in the analyzer cup effectively reduces analyte loss.

Robust analysis of the hydrophobic basic analytes loratadine and desloratadine in pharmaceutical preparations and biological fluids by sweeping-cyclodextrin-modified micellar electrokinetic chromatography.

PubMed

El-Awady, Mohamed; Belal, Fathalla; Pyell, Ute

2013-09-27

The analysis of hydrophobic basic analytes by micellar electrokinetic chromatography (MEKC) is usually challenging because of the tendency of these analytes to be adsorbed onto the inner capillary wall in addition to the difficulty to separate these compounds as they exhibit extremely high retention factors. A robust and reliable method for the simultaneous determination of loratadine (LOR) and its major metabolite desloratadine (DSL) is developed based on cyclodextrin-modified micellar electrokinetic chromatography (CD-MEKC) with acidic sample matrix and basic background electrolyte (BGE). The influence of the sample matrix on the reachable focusing efficiency is studied. It is shown that the application of a low pH sample solution mitigates problems associated with the low solubility of the hydrophobic basic analytes in aqueous solution while having advantages with regard to on-line focusing. Moreover, the use of a basic BGE reduces the adsorption of these analytes in the separation compartment. The separation of the studied analytes is achieved in less than 7min using a BGE consisting of 10mmolL(-1) disodium tetraborate buffer, pH 9.30 containing 40mmolL(-1) SDS and 20mmolL(-1) hydroxypropyl-β-CD while the sample solution is composed of 10mmolL(-1) phosphoric acid, pH 2.15. A full validation study of the developed method based on the pharmacopeial guidelines is performed. The method is successfully applied to the analysis of the studied drugs in tablets without interference of tablet additives as well as the analysis of spiked human urine without any sample pretreatment. Furthermore, DSL can be detected as an impurity in LOR bulk powder at the stated pharmacopeial limit (0.1%, w/w). The selectivity of the developed method allows the analysis of LOR and DSL in combination with the co-formulated drug pseudoephedrine. It is shown that in CD-MEKC with basic BGE, solute-wall interactions are effectively suppressed allowing the development of efficient and precise methods for the determination of hydrophobic basic analytes, whereas the use of a low pH sample solution has a positive impact on the attainable sweeping efficiency without compromising peak shape and resolution. Copyright © 2013 Elsevier B.V. All rights reserved.

Approximate solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO 2 in fractured rocks

DOE PAGES

Zhou, Quanlin; Oldenburg, Curtis M.; Spangler, Lee H.; ...

2017-01-05

Analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form approximate solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined analytically for isotropic blocks (e.g., spheresmore » and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative approximation error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO 2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These approximate solutions are building blocks for development of analytical and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.« less

Design and analysis of tubular permanent magnet linear generator for small-scale wave energy converter

NASA Astrophysics Data System (ADS)

Kim, Jeong-Man; Koo, Min-Mo; Jeong, Jae-Hoon; Hong, Keyyong; Cho, Il-Hyoung; Choi, Jang-Young

2017-05-01

This paper reports the design and analysis of a tubular permanent magnet linear generator (TPMLG) for a small-scale wave-energy converter. The analytical field computation is performed by applying a magnetic vector potential and a 2-D analytical model to determine design parameters. Based on analytical solutions, parametric analysis is performed to meet the design specifications of a wave-energy converter (WEC). Then, 2-D FEA is employed to validate the analytical method. Finally, the experimental result confirms the predictions of the analytical and finite element analysis (FEA) methods under regular and irregular wave conditions.

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.

Analytical solution of the nonlinear diffusion equation

NASA Astrophysics Data System (ADS)

Shanker Dubey, Ravi; Goswami, Pranay

2018-05-01

In the present paper, we derive the solution of the nonlinear fractional partial differential equations using an efficient approach based on the q -homotopy analysis transform method ( q -HATM). The fractional diffusion equations derivatives are considered in Caputo sense. The derived results are graphically demonstrated as well.

A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo of Natural Waters

EPA Science Inventory

Three numerical algorithms were compared to provide a solution of a radiative transfer equation (RTE) for plane albedo (hemispherical reflectance) in semi-infinite one-dimensional plane-parallel layer. Algorithms were based on the invariant imbedding method and two different var...

HYDRAULIC ANALYSIS OF BASE-FLOW AND BANK STORAGE IN ALLUVIAL STREAMS

EPA Science Inventory

This paper presents analytical solutions, which describe the effect of time-variable net recharge (net accretion to water table) and bank storage in alluvial aquifers on the sustenance of stream flows during storm and inter-storm events. The solutions relate the stream discharge,...

An algorithm for analytical solution of basic problems featuring elastostatic bodies with cavities and surface flaws

NASA Astrophysics Data System (ADS)

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

2018-03-01

Herein we propose a methodology for structuring a full parametric analytical solution to problems featuring elastostatic media based on state-of-the-art computing facilities that support computerized algebra. The methodology includes: direct and reverse application of P-Theorem; methods of accounting for physical properties of media; accounting for variable geometrical parameters of bodies, parameters of boundary states, independent parameters of volume forces, and remote stress factors. An efficient tool to address the task is the sustainable method of boundary states originally designed for the purposes of computerized algebra and based on the isomorphism of Hilbertian spaces of internal states and boundary states of bodies. We performed full parametric solutions of basic problems featuring a ball with a nonconcentric spherical cavity, a ball with a near-surface flaw, and an unlimited medium with two spherical cavities.

Reducing microwave absorption with fast frequency modulation.

PubMed

Qin, Juehang; Hubler, A

2017-05-01

We study the response of a two-level quantum system to a chirp signal, using both numerical and analytical methods. The numerical method is based on numerical solutions of the Schrödinger solution of the two-level system, while the analytical method is based on an approximate solution of the same equations. We find that when two-level systems are perturbed by a chirp signal, the peak population of the initially unpopulated state exhibits a high sensitivity to frequency modulation rate. We also find that the aforementioned sensitivity depends on the strength of the forcing, and weaker forcings result in a higher sensitivity, where the frequency modulation rate required to produce the same reduction in peak population would be lower. We discuss potential applications of this result in the field of microwave power transmission, as it shows applying fast frequency modulation to transmitted microwaves used for power transmission could decrease unintended absorption of microwaves by organic tissue.

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

NASA Astrophysics Data System (ADS)

Huang, Houxu; Li, Jie; Wei, Jiuqi

2017-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-07-01

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

Defining microchannels and valves on a hydrophobic paper by low-cost inkjet printing of aqueous or weak organic solutions.

PubMed

Cai, Longfei; Zhong, Minghua; Li, Huolin; Xu, Chunxiu; Yuan, Biyu

2015-07-01

We describe a simple and cost-effective strategy for rapid fabrication of microfluidic paper-based analytical devices and valves by inkjet printing. NaOH aqueous solution was printed onto a hydrophobic filter paper, which was previously obtained by soaking in a trimethoxyoctadecylsilane-heptane solution, allowing selective wet etching of hydrophobic cellulose to create hydrophilic-hydrophobic contrast with a relatively good resolution. Hexadecyltrimethylammonium bromide (CTMAB)-ethanol solution was printed onto hydrophobic paper to fabricate temperature-controlled valves. At low temperature, CTMAB deposited on the paper is insoluble in aqueous fluid, thus the paper remains hydrophobic. At high temperature, CTMAB becomes soluble so the CTMAB-deposited channel becomes hydrophilic, allowing the wicking of aqueous solution through the valve. We believe that this strategy will be very attractive for the development of simple micro analytical devices for point-of-care applications, including diagnostic testing, food safety control, and environmental monitoring.

Glycan characterization of the NIST RM monoclonal antibody using a total analytical solution: From sample preparation to data analysis.

PubMed

Hilliard, Mark; Alley, William R; McManus, Ciara A; Yu, Ying Qing; Hallinan, Sinead; Gebler, John; Rudd, Pauline M

Glycosylation is an important attribute of biopharmaceutical products to monitor from development through production. However, glycosylation analysis has traditionally been a time-consuming process with long sample preparation protocols and manual interpretation of the data. To address the challenges associated with glycan analysis, we developed a streamlined analytical solution that covers the entire process from sample preparation to data analysis. In this communication, we describe the complete analytical solution that begins with a simplified and fast N-linked glycan sample preparation protocol that can be completed in less than 1 hr. The sample preparation includes labelling with RapiFluor-MS tag to improve both fluorescence (FLR) and mass spectral (MS) sensitivities. Following HILIC-UPLC/FLR/MS analyses, the data are processed and a library search based on glucose units has been included to expedite the task of structural assignment. We then applied this total analytical solution to characterize the glycosylation of the NIST Reference Material mAb 8761. For this glycoprotein, we confidently identified 35 N-linked glycans and all three major classes, high mannose, complex, and hybrid, were present. The majority of the glycans were neutral and fucosylated; glycans featuring N-glycolylneuraminic acid and those with two galactoses connected via an α1,3-linkage were also identified.

Dry granular avalanche impact force on a rigid wall: Analytic shock solution versus discrete element simulations

NASA Astrophysics Data System (ADS)

Albaba, Adel; Lambert, Stéphane; Faug, Thierry

2018-05-01

The present paper investigates the mean impact force exerted by a granular mass flowing down an incline and impacting a rigid wall of semi-infinite height. First, this granular flow-wall interaction problem is modeled by numerical simulations based on the discrete element method (DEM). These DEM simulations allow computing the depth-averaged quantities—thickness, velocity, and density—of the incoming flow and the resulting mean force on the rigid wall. Second, that problem is described by a simple analytic solution based on a depth-averaged approach for a traveling compressible shock wave, whose volume is assumed to shrink into a singular surface, and which coexists with a dead zone. It is shown that the dead-zone dynamics and the mean force on the wall computed from DEM can be reproduced reasonably well by the analytic solution proposed over a wide range of slope angle of the incline. These results are obtained by feeding the analytic solution with the thickness, the depth-averaged velocity, and the density averaged over a certain distance along the incline rather than flow quantities taken at a singular section before the jump, thus showing that the assumption of a shock wave volume shrinking into a singular surface is questionable. The finite length of the traveling wave upstream of the grains piling against the wall must be considered. The sensitivity of the model prediction to that sampling length remains complicated, however, which highlights the need of further investigation about the properties and the internal structure of the propagating granular wave.

Eco-analytical Methodology in Environmental Problems Monitoring

NASA Astrophysics Data System (ADS)

Agienko, M. I.; Bondareva, E. P.; Chistyakova, G. V.; Zhironkina, O. V.; Kalinina, O. I.

2017-01-01

Among the problems common to all mankind, which solutions influence the prospects of civilization, the problem of ecological situation monitoring takes very important place. Solution of this problem requires specific methodology based on eco-analytical comprehension of global issues. Eco-analytical methodology should help searching for the optimum balance between environmental problems and accelerating scientific and technical progress. The fact that Governments, corporations, scientists and nations focus on the production and consumption of material goods cause great damage to environment. As a result, the activity of environmentalists is developing quite spontaneously, as a complement to productive activities. Therefore, the challenge posed by the environmental problems for the science is the formation of geo-analytical reasoning and the monitoring of global problems common for the whole humanity. So it is expected to find the optimal trajectory of industrial development to prevent irreversible problems in the biosphere that could stop progress of civilization.

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.

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.

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.

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

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

Qu Qixing; Sun Kun; Jiang Yan

2011-01-15

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

A new method for constructing analytic elements for groundwater flow.

NASA Astrophysics Data System (ADS)

Strack, O. D.

2007-12-01

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

Identification of Organic Colorants in Art Objects by Solution Spectrophotometry: Pigments.

ERIC Educational Resources Information Center

Billmeyer, Fred W., Jr.; And Others

1981-01-01

Describes solution spectrophotometry as a simple, rapid identification technique for organic paint pigments. Reports research which includes analytical schemes for the extraction and separation of organic pigments based on their solubilities, and the preparation of an extensive reference collection of spectral curves allowing their identification.…

Analytic Analysis of Convergent Shocks to Multi-Gigabar Conditions

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

PubMed

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

2011-01-01

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

New analytical solutions to the two-phase water faucet problem

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-06-17

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

Creep and stress relaxation induced by interface diffusion in metal matrix composites

NASA Astrophysics Data System (ADS)

Li, Yinfeng; Li, Zhonghua

2013-03-01

An analytical solution is developed to predict the creep rate induced by interface diffusion in unidirectional fiber-reinforced and particle reinforced composites. The driving force for the interface diffusion is the normal stress acting on the interface, which is obtained from rigorous Eshelby inclusion theory. The closed-form solution is an explicit function of the applied stress, volume fraction and radius of the fiber, as well as the modulus ratio between the fiber and the matrix. It is interesting that the solution is formally similar to that of Coble creep in polycrystalline materials. For the application of the present solution in the realistic composites, the scale effect is taken into account by finite element analysis based on a unit cell. Based on the solution, a closed-form solution is also given as a description of stress relaxation induced by interfacial diffusion under constant strain. In addition, the analytical solution for the interface stress presented in this study gives some insight into the relationship between the interface diffusion and interface slip. This work was supported by the financial support from the Nature Science Foundation of China (No. 10932007), the National Basic Research Program of China (No. 2010CB631003/5), and the Doctoral Program of Higher Education of China (No. 20100073110006).

Variable fidelity robust optimization of pulsed laser orbital debris removal under epistemic uncertainty

NASA Astrophysics Data System (ADS)

Hou, Liqiang; Cai, Yuanli; Liu, Jin; Hou, Chongyuan

2016-04-01

A variable fidelity robust optimization method for pulsed laser orbital debris removal (LODR) under uncertainty is proposed. Dempster-shafer theory of evidence (DST), which merges interval-based and probabilistic uncertainty modeling, is used in the robust optimization. The robust optimization method optimizes the performance while at the same time maximizing its belief value. A population based multi-objective optimization (MOO) algorithm based on a steepest descent like strategy with proper orthogonal decomposition (POD) is used to search robust Pareto solutions. Analytical and numerical lifetime predictors are used to evaluate the debris lifetime after the laser pulses. Trust region based fidelity management is designed to reduce the computational cost caused by the expensive model. When the solutions fall into the trust region, the analytical model is used to reduce the computational cost. The proposed robust optimization method is first tested on a set of standard problems and then applied to the removal of Iridium 33 with pulsed lasers. It will be shown that the proposed approach can identify the most robust solutions with minimum lifetime under uncertainty.

Lump-type solutions for the (4+1)-dimensional Fokas equation via symbolic computations

NASA Astrophysics Data System (ADS)

Cheng, Li; Zhang, Yi

2017-09-01

Based on the Hirota bilinear form, two classes of lump-type solutions of the (4+1)-dimensional nonlinear Fokas equation, rationally localized in almost all directions in the space are obtained through a direct symbolic computation with Maple. The resulting lump-type solutions contain free parameters. To guarantee the analyticity and rational localization of the solutions, the involved parameters need to satisfy certain constraints. A few particular lump-type solutions with special choices of the involved parameters are given.

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...

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

NASA Astrophysics Data System (ADS)

Heidmann, Pierre

2017-10-01

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

Satellite attitude motion models for capture and retrieval investigations

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

A hybrid approach to near-optimal launch vehicle guidance

NASA Technical Reports Server (NTRS)

Leung, Martin S. K.; Calise, Anthony J.

1992-01-01

This paper evaluates a proposed hybrid analytical/numerical approach to launch-vehicle guidance for ascent to orbit injection. The feedback-guidance approach is based on a piecewise nearly analytic zero-order solution evaluated using a collocation method. The zero-order solution is then improved through a regular perturbation analysis, wherein the neglected dynamics are corrected in the first-order term. For real-time implementation, the guidance approach requires solving a set of small dimension nonlinear algebraic equations and performing quadrature. Assessment of performance and reliability are carried out through closed-loop simulation for a vertically launched 2-stage heavy-lift capacity vehicle to a low earth orbit. The solutions are compared with optimal solutions generated from a multiple shooting code. In the example the guidance approach delivers over 99.9 percent of optimal performance and terminal constraint accuracy.

A new frequency domain analytical solution of a cascade of diffusive channels for flood routing

NASA Astrophysics Data System (ADS)

Cimorelli, Luigi; Cozzolino, Luca; Della Morte, Renata; Pianese, Domenico; Singh, Vijay P.

2015-04-01

Simplified flood propagation models are often employed in practical applications for hydraulic and hydrologic analyses. In this paper, we present a new numerical method for the solution of the Linear Parabolic Approximation (LPA) of the De Saint Venant equations (DSVEs), accounting for the space variation of model parameters and the imposition of appropriate downstream boundary conditions. The new model is based on the analytical solution of a cascade of linear diffusive channels in the Laplace Transform domain. The time domain solutions are obtained using a Fourier series approximation of the Laplace Inversion formula. The new Inverse Laplace Transform Diffusive Flood Routing model (ILTDFR) can be used as a building block for the construction of real-time flood forecasting models or in optimization models, because it is unconditionally stable and allows fast and fairly precise computation.

A semi-analytical solution for slug tests in an unconfined aquifer considering unsaturated flow

NASA Astrophysics Data System (ADS)

Sun, Hongbing

2016-01-01

A semi-analytical solution considering the vertical unsaturated flow is developed for groundwater flow in response to a slug test in an unconfined aquifer in Laplace space. The new solution incorporates the effects of partial penetrating, anisotropy, vertical unsaturated flow, and a moving water table boundary. Compared to the Kansas Geological Survey (KGS) model, the new solution can significantly improve the fittings of the modeled to the measured hydraulic heads at the late stage of slug tests in an unconfined aquifer, particularly when the slug well has a partially submerged screen and moisture drainage above the water table is significant. The radial hydraulic conductivities estimated with the new solution are comparable to those from the KGS, Bouwer and Rice, and Hvorslev methods. In addition, the new solution also can be used to examine the vertical conductivity, specific storage, specific yield, and the moisture retention parameters in an unconfined aquifer based on slug test data.

Approximate analytical solutions in the analysis of thin elastic plates

NASA Astrophysics Data System (ADS)

Goloskokov, Dmitriy P.; Matrosov, Alexander V.

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

Li, Can; Deng, Wei-Hua

2014-07-01

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

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

NASA Astrophysics Data System (ADS)

Phanikumar, Mantha S.; McGuire, Jennifer T.

2010-08-01

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

Lump and lump-soliton solutions to the (2+1) -dimensional Ito equation

NASA Astrophysics Data System (ADS)

Yang, Jin-Yun; Ma, Wen-Xiu; Qin, Zhenyun

2017-06-01

Based on the Hirota bilinear form of the (2+1) -dimensional Ito equation, one class of lump solutions and two classes of interaction solutions between lumps and line solitons are generated through analysis and symbolic computations with Maple. Analyticity is naturally guaranteed for the presented lump and interaction solutions, and the interaction solutions reduce to lumps (or line solitons) while the hyperbolic-cosine (or the quadratic function) disappears. Three-dimensional plots and contour plots are made for two specific examples of the resulting interaction solutions.

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

NASA Astrophysics Data System (ADS)

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

2009-12-01

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

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

NASA Technical Reports Server (NTRS)

Kia, T.; Longuski, J. M.

1984-01-01

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

Method and apparatus for simultaneous spectroelectrochemical analysis

DOEpatents

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

2013-11-19

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

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.

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.

Torsional vibration of a cracked rod by variational formulation and numerical analysis

NASA Astrophysics Data System (ADS)

Chondros, T. G.; Labeas, G. N.

2007-04-01

The torsional vibration of a circumferentially cracked cylindrical shaft is studied through an "exact" analytical solution and a numerical finite element (FE) analysis. The Hu-Washizu-Barr variational formulation is used to develop the differential equation and the boundary conditions of the cracked rod. The equations of motion for a uniform cracked rod in torsional vibration are derived and solved, and the Rayleigh quotient is used to further approximate the natural frequencies of the cracked rod. Results for the problem of the torsional vibration of a cylindrical shaft with a peripheral crack are provided through an analytical solution based on variational formulation to derive the equation of motion and a numerical analysis utilizing a parametric three-dimensional (3D) solid FE model of the cracked rod. The crack is modelled as a continuous flexibility based on fracture mechanics principles. The variational formulation results are compared with the FE alternative. The sensitivity of the FE discretization with respect to the analytical results is assessed.

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

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.

Analytical Solution for Time-drawdown Response to Constant Pumping from a Homogeneous, Confined Horizontal Aquifer with Unidirectional Flow

NASA Astrophysics Data System (ADS)

Parrish, K. E.; Zhang, J.; Teasdale, E.

2007-12-01

An exact analytical solution to the ordinary one-dimensional partial differential equation is derived for transient groundwater flow in a homogeneous, confined, horizontal aquifer using Laplace transformation. The theoretical analysis is based on the assumption that the aquifer is homogeneous and one-dimensional (horizontal); confined between impermeable formations on top and bottom; and of infinite horizontal extent and constant thickness. It is also assumed that there is only a single pumping well penetrating the entire aquifer; flow is everywhere horizontal within the aquifer to the well; the well is pumping with a constant discharge rate; the well diameter is infinitesimally small; and the hydraulic head is uniform throughout the aquifer before pumping. Similar to the Theis solution, this solution is suited to determine transmissivity and storativity for a two- dimensional, vertically confined aquifer, such as a long vertically fractured zone of high permeability within low permeable rocks or a long, high-permeability trench inside a low-permeability porous media. In addition, it can be used to analyze time-drawdown responses to pumping and injection in similar settings. The solution can also be used to approximate the groundwater flow for unconfined conditions if (1) the variation of transmissivity is negligible (groundwater table variation is small in comparison to the saturated thickness); and (2) the unsaturated flow is negligible. The errors associated with the use of the solution to unconfined conditions depend on the accuracies of the above two assumptions. The solution can also be used to assess the impacts of recharge from a seasonal river or irrigation canal on the groundwater system by assuming uniform, time- constant recharge along the river or canal. This paper presents the details for derivation of the analytical solution. The analytical solution is compared to numerical simulation results with example cases. Its accuracy is also assessed and discussed for confined and unconfined conditions.

The N+CPT resonance

NASA Astrophysics Data System (ADS)

Crescimanno, Michael; Hohensee, Michael; Hancox, Cindy; Phillips, David; Walsworth, Ron

2007-06-01

Of relevance to compact atomic frequency standards, we investigate a model of the N+CPT joint optical resonance. We compare analytical solutions of a 4-state theory, as well as numerical solutions of the optical Bloch equations, to experimental investigations of N+CPT resonances in 87Rb. Our results inform the optimization of N+CPT based frequency standards.

Mechanical properties of regular porous biomaterials made from truncated cube repeating unit cells: Analytical solutions and computational models.

PubMed

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

2016-03-01

Additive manufacturing (AM) has enabled fabrication of open-cell porous biomaterials based on repeating unit cells. The micro-architecture of the porous biomaterials and, thus, their physical properties could then be precisely controlled. Due to their many favorable properties, porous biomaterials manufactured using AM are considered as promising candidates for bone substitution as well as for several other applications in orthopedic surgery. The mechanical properties of such porous structures including static and fatigue properties are shown to be strongly dependent on the type of the repeating unit cell based on which the porous biomaterial is built. In this paper, we study the mechanical properties of porous biomaterials made from a relatively new unit cell, namely truncated cube. We present analytical solutions that relate the dimensions of the repeating unit cell to the elastic modulus, Poisson's ratio, yield stress, and buckling load of those porous structures. We also performed finite element modeling to predict the mechanical properties of the porous structures. The analytical solution and computational results were found to be in agreement with each other. The mechanical properties estimated using both the analytical and computational techniques were somewhat higher than the experimental data reported in one of our recent studies on selective laser melted Ti-6Al-4V porous biomaterials. In addition to porosity, the elastic modulus and Poisson's ratio of the porous structures were found to be strongly dependent on the ratio of the length of the inclined struts to that of the uninclined (i.e. vertical or horizontal) struts, α, in the truncated cube unit cell. The geometry of the truncated cube unit cell approaches the octahedral and cube unit cells when α respectively approaches zero and infinity. Consistent with those geometrical observations, the analytical solutions presented in this study approached those of the octahedral and cube unit cells when α approached respectively 0 and infinity. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

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.

Modeling Three-Dimensional Flow in Confined Aquifers by Superposition of Both Two- and Three-Dimensional Analytic Functions

NASA Astrophysics Data System (ADS)

Haitjema, Henk M.

1985-10-01

A technique is presented to incorporate three-dimensional flow in a Dupuit-Forchheimer model. The method is based on superposition of approximate analytic solutions to both two- and three-dimensional flow features in a confined aquifer of infinite extent. Three-dimensional solutions are used in the domain of interest, while farfield conditions are represented by two-dimensional solutions. Approximate three- dimensional solutions have been derived for a partially penetrating well and a shallow creek. Each of these solutions satisfies the condition that no flow occurs across the confining layers of the aquifer. Because of this condition, the flow at some distance of a three-dimensional feature becomes nearly horizontal. Consequently, remotely from a three-dimensional feature, its three-dimensional solution is replaced by a corresponding two-dimensional one. The latter solution is trivial as compared to its three-dimensional counterpart, and its use greatly enhances the computational efficiency of the model. As an example, the flow is modeled between a partially penetrating well and a shallow creek that occur in a regional aquifer system.

[Construction of NIRS-based process analytical system for production of salvianolic acid for injection and relative discussion].

PubMed

Zhang, Lei; Yue, Hong-Shui; Ju, Ai-Chun; Ye, Zheng-Liang

2016-10-01

Currently, near infrared spectroscopy (NIRS) has been considered as an efficient tool for achieving process analytical technology(PAT) in the manufacture of traditional Chinese medicine (TCM) products. In this article, the NIRS based process analytical system for the production of salvianolic acid for injection was introduced. The design of the process analytical system was described in detail, including the selection of monitored processes and testing mode, and potential risks that should be avoided. Moreover, the development of relative technologies was also presented, which contained the establishment of the monitoring methods for the elution of polyamide resin and macroporous resin chromatography processes, as well as the rapid analysis method for finished products. Based on author's experience of research and work, several issues in the application of NIRS to the process monitoring and control in TCM production were then raised, and some potential solutions were also discussed. The issues include building the technical team for process analytical system, the design of the process analytical system in the manufacture of TCM products, standardization of the NIRS-based analytical methods, and improving the management of process analytical system. Finally, the prospect for the application of NIRS in the TCM industry was put forward. Copyright© by the Chinese Pharmaceutical Association.

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...

An explicit closed-form analytical solution for European options under the CGMY model

NASA Astrophysics Data System (ADS)

Chen, Wenting; Du, Meiyu; Xu, Xiang

2017-01-01

In this paper, we consider the analytical pricing of European path-independent options under the CGMY model, which is a particular type of pure jump Le´vy process, and agrees well with many observed properties of the real market data by allowing the diffusions and jumps to have both finite and infinite activity and variation. It is shown that, under this model, the option price is governed by a fractional partial differential equation (FPDE) with both the left-side and right-side spatial-fractional derivatives. In comparison to derivatives of integer order, fractional derivatives at a point not only involve properties of the function at that particular point, but also the information of the function in a certain subset of the entire domain of definition. This ;globalness; of the fractional derivatives has added an additional degree of difficulty when either analytical methods or numerical solutions are attempted. Albeit difficult, we still have managed to derive an explicit closed-form analytical solution for European options under the CGMY model. Based on our solution, the asymptotic behaviors of the option price and the put-call parity under the CGMY model are further discussed. Practically, a reliable numerical evaluation technique for the current formula is proposed. With the numerical results, some analyses of impacts of four key parameters of the CGMY model on European option prices are also provided.

A Novel Consensus-Based Particle Swarm Optimization-Assisted Trust-Tech Methodology for Large-Scale Global Optimization.

PubMed

Zhang, Yong-Feng; Chiang, Hsiao-Dong

2017-09-01

A novel three-stage methodology, termed the "consensus-based particle swarm optimization (PSO)-assisted Trust-Tech methodology," to find global optimal solutions for nonlinear optimization problems is presented. It is composed of Trust-Tech methods, consensus-based PSO, and local optimization methods that are integrated to compute a set of high-quality local optimal solutions that can contain the global optimal solution. The proposed methodology compares very favorably with several recently developed PSO algorithms based on a set of small-dimension benchmark optimization problems and 20 large-dimension test functions from the CEC 2010 competition. The analytical basis for the proposed methodology is also provided. Experimental results demonstrate that the proposed methodology can rapidly obtain high-quality optimal solutions that can contain the global optimal solution. The scalability of the proposed methodology is promising.

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

Chemical Sensors Based on IR Spectroscopy and Surface-Modified Waveguides

NASA Technical Reports Server (NTRS)

Lopez, Gabriel P.; Niemczyk, Thomas

1999-01-01

Sol-gel processing techniques have been used to apply thin porous films to the surfaces of planar infrared (IR) waveguides to produce widely useful chemical sensors. The thin- film coating serves to diminish the concentration of water and increase the concentration of the analyte in the region probed by the evanescent IR wave. These porous films are composed of silica, and therefore, conventional silica surface modification techniques can be used to give the surface a specific functional character. The sol-gel film was surface-modified to make the film highly hydrophobic. These sensors were shown to be capable of detecting non-polar organic analytes, such as benzonitrile, in aqueous solution with detection limits in the ppb range. Further, these porous sol-gel structures allow the analytes to diffuse into and out of the films rapidly, thus reaching equilibrium in less than ten seconds. These sensors are unique because of the fact that their operation is based on the measurement of an IR absorption spectrum. Thus, these sensors are able to identify the analytes as well as measure concentration with high sensitivity. These developments have been documented in previous reports and publications. Recently, we have also targeted detection of the polar organic molecules acetone and isopropanol in aqueous solution. Polar organics are widely used in industrial and chemical processes, hence it is of interest to monitor their presence in effluents or decontamination process flows. Although large improvements in detection limits were expected with non-polar organic molecules in aqueous solutions using very hydrophobic porous sol-gel films on silicon attenuated total reflectance (Si ATR) waveguides, it was not as clear what the detection enhancements might be for polar organic molecules. This report describes the use of modified sol-gel-coated Si ATR sensors for trace detection and quantitation of small polar organic molecules in aqueous solutions. The detection of both acetone and isopropanol molecules in aqueous solution has been previously reported for chalcogenide fiber optic sensors. The sol-gel film was produced using a mixture of ethyltriethoxysilane and tetraethoxysilane and the surface modification was carried out using trimethylchlorosilane. We have demonstrated that this film concentrates the target polar analytes from aqueous solution in the region probed by the evanescent wave to improve detection limits by as much as a factor of 450.

On one solution of Volterra integral equations of second kind

NASA Astrophysics Data System (ADS)

Myrhorod, V.; Hvozdeva, I.

2016-10-01

A solution of Volterra integral equations of the second kind with separable and difference kernels based on solutions of corresponding equations linking the kernel and resolvent is suggested. On the basis of a discrete functions class, the equations linking the kernel and resolvent are obtained and the methods of their analytical solutions are proposed. A mathematical model of the gas-turbine engine state modification processes in the form of Volterra integral equation of the second kind with separable kernel is offered.

A sensor system based on a luminescent protein complex in a biopolymer matrix for detecting small concentrations of hydrogen sulfide in aqueous solutions

NASA Astrophysics Data System (ADS)

Sergeev, A. A.; Leonov, A. A.; Kamenev, D. G.; Voznesenskii, S. S.; Kul'chin, Yu. M.

2017-09-01

We have studied the properties of luminescent protein complexes based on myoglobin with covalently bound CY3 luminophore, which were incorporated into polysaccharide agarose films, as potential elements sensitive to hydrogen sulfide (H2S) in aqueous solutions. The presence of this analyte changes the absorption spectrum of myoglobin, which influences the efficiency of luminophore excitation while having almost no effect on its emission spectrum. This effect shows that a luminescent sensor system with the optical response determined by analyte-induced changes in the efficiency of luminescence excitation in the sensitive element can be created. For the system studied, the limit of detection of H2S dissolved in water amounted to 100 pM.

Novel three-stage kinetic model for aqueous benzene adsorption on activated carbon.

PubMed

Choi, Jae-Woo; Choi, Nag-Choul; Lee, Soon-Jae; Kim, Dong-Ju

2007-10-15

We propose a novel kinetic model for adsorption of aqueous benzene onto both granular activated carbon (GAC) and powdered activated carbon (PAC). The model is based on mass conservation of benzene coupled with three-stage adsorption: (1) the first portion for an instantaneous stage or external surface adsorption, (2) the second portion for a gradual stage with rate-limiting intraparticle diffusion, and (3) the third portion for a constant stage in which the aqueous phase no longer interacts with activated carbon. An analytical solution of the kinetic model was validated with the kinetic data obtained from aqueous benzene adsorption onto GAC and PAC in batch experiments with two different solution concentrations (C(0)=300 mg L(-1), 600 mg L(-1)). Experimental results revealed that benzene adsorption for the two concentrations followed three distinct stages for PAC but two stages for GAC. The analytical solution could successfully describe the kinetic adsorption of aqueous benzene in the batch reaction system, showing a fast instantaneous adsorption followed by a slow rate-limiting adsorption and a final long constant adsorption. Use of the two-stage model gave incorrect values of adsorption coefficients in the analytical solution due to inability to describe the third stage.

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

USGS Publications Warehouse

Kurylyk, Barret L.; McKenzie, Jeffrey M; MacQuarrie, Kerry T. B.; Voss, Clifford I.

2014-01-01

Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.

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

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1999-11-01

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

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

Strategic analytics: towards fully embedding evidence in healthcare decision-making.

PubMed

Garay, Jason; Cartagena, Rosario; Esensoy, Ali Vahit; Handa, Kiren; Kane, Eli; Kaw, Neal; Sadat, Somayeh

2015-01-01

Cancer Care Ontario (CCO) has implemented multiple information technology solutions and collected health-system data to support its programs. There is now an opportunity to leverage these data and perform advanced end-to-end analytics that inform decisions around improving health-system performance. In 2014, CCO engaged in an extensive assessment of its current data capacity and capability, with the intent to drive increased use of data for evidence-based decision-making. The breadth and volume of data at CCO uniquely places the organization to contribute to not only system-wide operational reporting, but more advanced modelling of current and future state system management and planning. In 2012, CCO established a strategic analytics practice to assist the agency's programs contextualize and inform key business decisions and to provide support through innovative predictive analytics solutions. This paper describes the organizational structure, services and supporting operations that have enabled progress to date, and discusses the next steps towards the vision of embedding evidence fully into healthcare decision-making. Copyright © 2014 Longwoods Publishing.

Analytical saturated domain orientation textures and electromechanical properties of ferroelectric ceramics due to electric/mechanical poling

NASA Astrophysics Data System (ADS)

Li, F. X.; Rajapakse, R. K. N. D.

2007-03-01

Saturated domain orientation textures of three types of pseudocubic (tetragonal, rhombohedral, and orthorhombic) ferroelectric ceramics after complete electric and uniaxial tension (compression) poling is studied analytically in this paper. A one-dimensional orientation distribution function (ODF) of the domain polar vectors is explicitly derived from the uniform inverse pole figures of the poling field axes on a stereographic projection with respect to the fixed crystallite coordinates. The analytical ODF is used to obtain the analytical solutions of saturated polarization and strain after electric/mechanical poling. Based on the closed form solution of the saturated domain orientation textures, the resultant intrinsic electromechanical properties of ferroelectric ceramics, which depend only on the ODF and properties of the corresponding single crystals, are obtained. The results show how the macroscopic symmetries of ferroelectric crystals change from 4mm (tetragonal), 3m (rhombohedral), and mm2 (orthorhombic) single crystals to a ∞mm (transversely isotropic) completely poled ceramic.

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.

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

NASA Technical Reports Server (NTRS)

Dorodnitsyn, A.; Kallman, T.

2017-01-01

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

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

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

Dorodnitsyn, A.; Kallman, T.

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

Analytical solutions to optimal underactuated spacecraft formation reconfiguration

NASA Astrophysics Data System (ADS)

Huang, Xu; Yan, Ye; Zhou, Yang

2015-11-01

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

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.

A finite-element method for large-amplitude, two-dimensional panel flutter at hypersonic speeds

NASA Technical Reports Server (NTRS)

Mei, Chuh; Gray, Carl E.

1989-01-01

The nonlinear flutter behavior of a two-dimensional panel in hypersonic flow is investigated analytically. An FEM formulation based unsteady third-order piston theory (Ashley and Zartarian, 1956; McIntosh, 1970) and taking nonlinear structural and aerodynamic phenomena into account is derived; the solution procedure is outlined; and typical results are presented in extensive tables and graphs. A 12-element finite-element solution obtained using an alternative method for linearizing the assumed limit-cycle time function is shown to give predictions in good agreement with classical analytical results for large-amplitude vibration in a vacuum and large-amplitude panel flutter, using linear aerodynamics.

Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application

NASA Astrophysics Data System (ADS)

Kundu, Anjan

2016-08-01

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

Analytical Characterization on Pulse Propagation in a Semiconductor Optical Amplifier Based on Homotopy Analysis Method

NASA Astrophysics Data System (ADS)

Jia, Xiaofei

2018-06-01

Starting from the basic equations describing the evolution of the carriers and photons inside a semiconductor optical amplifier (SOA), the equation governing pulse propagation in the SOA is derived. By employing homotopy analysis method (HAM), a series solution for the output pulse by the SOA is obtained, which can effectively characterize the temporal features of the nonlinear process during the pulse propagation inside the SOA. Moreover, the analytical solution is compared with numerical simulations with a good agreement. The theoretical results will benefit the future analysis of other problems related to the pulse propagation in the SOA.

Alternative formulations of the Laplace transform boundary element (LTBE) numerical method for the solution of diffusion-type equations

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

Moridis, G.

1992-03-01

The Laplace Transform Boundary Element (LTBE) method is a recently introduced numerical method, and has been used for the solution of diffusion-type PDEs. It completely eliminates the time dependency of the problem and the need for time discretization, yielding solutions numerical in space and semi-analytical in time. In LTBE solutions are obtained in the Laplace spare, and are then inverted numerically to yield the solution in time. The Stehfest and the DeHoog formulations of LTBE, based on two different inversion algorithms, are investigated. Both formulations produce comparable, extremely accurate solutions.

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.

A new unconditionally stable and consistent quasi-analytical in-stream water quality solution scheme for CSTR-based water quality simulators

NASA Astrophysics Data System (ADS)

Woldegiorgis, Befekadu Taddesse; van Griensven, Ann; Pereira, Fernando; Bauwens, Willy

2017-06-01

Most common numerical solutions used in CSTR-based in-stream water quality simulators are susceptible to instabilities and/or solution inconsistencies. Usually, they cope with instability problems by adopting computationally expensive small time steps. However, some simulators use fixed computation time steps and hence do not have the flexibility to do so. This paper presents a novel quasi-analytical solution for CSTR-based water quality simulators of an unsteady system. The robustness of the new method is compared with the commonly used fourth-order Runge-Kutta methods, the Euler method and three versions of the SWAT model (SWAT2012, SWAT-TCEQ, and ESWAT). The performance of each method is tested for different hypothetical experiments. Besides the hypothetical data, a real case study is used for comparison. The growth factors we derived as stability measures for the different methods and the R-factor—considered as a consistency measure—turned out to be very useful for determining the most robust method. The new method outperformed all the numerical methods used in the hypothetical comparisons. The application for the Zenne River (Belgium) shows that the new method provides stable and consistent BOD simulations whereas the SWAT2012 model is shown to be unstable for the standard daily computation time step. The new method unconditionally simulates robust solutions. Therefore, it is a reliable scheme for CSTR-based water quality simulators that use first-order reaction formulations.

Spatial correlations and exact solution of the problem of the boson peak profile in amorphous media

NASA Astrophysics Data System (ADS)

Kirillov, Sviatoslav A.; A. Voyiatzis, George; Kolomiyets, Tatiana M.; H. Anastasiadis, Spiros

1999-11-01

Based on a model correlation function which covers spatial correlations from Gaussian to exponential, we have arrived at an exact analytic solution of the problem of the Boson peak profile in amorphous media. Probe fits made for polyisoprene and triacetin prove the working ability of the formulae obtained.

An Analytical Chemistry Experiment in Simultaneous Spectrophotometric Determination of Fe(III) and Cu(II) with Hexacyanoruthenate(II) Reagent.

ERIC Educational Resources Information Center

Mehra, M. C.; Rioux, J.

1982-01-01

Experimental procedures, typical observations, and results for the simultaneous analysis of Fe(III) and Cu(II) in a solution are discussed. The method is based on selective interaction between the two ions and potassium hexacyanoruthenate(II) in acid solution involving no preliminary sample preparations. (Author/JN)

Analytic Closed-Form Solution of a Mixed Layer Model for Stratocumulus Clouds

NASA Astrophysics Data System (ADS)

Akyurek, Bengu Ozge

Stratocumulus clouds play an important role in climate cooling and are hard to predict using global climate and weather forecast models. Thus, previous studies in the literature use observations and numerical simulation tools, such as large-eddy simulation (LES), to solve the governing equations for the evolution of stratocumulus clouds. In contrast to the previous works, this work provides an analytic closed-form solution to the cloud thickness evolution of stratocumulus clouds in a mixed-layer model framework. With a focus on application over coastal lands, the diurnal cycle of cloud thickness and whether or not clouds dissipate are of particular interest. An analytic solution enables the sensitivity analysis of implicitly interdependent variables and extrema analysis of cloud variables that are hard to achieve using numerical solutions. In this work, the sensitivity of inversion height, cloud-base height, and cloud thickness with respect to initial and boundary conditions, such as Bowen ratio, subsidence, surface temperature, and initial inversion height, are studied. A critical initial cloud thickness value that can be dissipated pre- and post-sunrise is provided. Furthermore, an extrema analysis is provided to obtain the minima and maxima of the inversion height and cloud thickness within 24 h. The proposed solution is validated against LES results under the same initial and boundary conditions. Then, the proposed analytic framework is extended to incorporate multiple vertical columns that are coupled by advection through wind flow. This enables a bridge between the micro-scale and the mesoscale relations. The effect of advection on cloud evolution is studied and a sensitivity analysis is provided.

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

NASA Astrophysics Data System (ADS)

Luther, K.; Haitjema, H. M.

2000-04-01

We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.

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

NASA Astrophysics Data System (ADS)

Shan, Zhendong; Ling, Daosheng

2018-02-01

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

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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Exact analytical solution of a classical Josephson tunnel junction problem

NASA Astrophysics Data System (ADS)

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

2010-10-01

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

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

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

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

Problems and solutions of polyethylene glycol co-injection method in multiresidue pesticide analysis by gas chromatography-mass spectrometry: evaluation of instability phenomenon in type II pyrethroids and its suppression by novel analyte protectants.

PubMed

Akutsu, Kazuhiko; Kitagawa, Yoko; Yoshimitsu, Masato; Takatori, Satoshi; Fukui, Naoki; Osakada, Masakazu; Uchida, Kotaro; Azuma, Emiko; Kajimura, Keiji

2018-05-01

Polyethylene glycol 300 is commonly used as a base material for "analyte protection" in multiresidue pesticide analysis via gas chromatography-mass spectrometry. However, the disadvantage of the co-injection method using polyethylene glycol 300 is that it causes peak instability in α-cyano pyrethroids (type II pyrethroids) such as fluvalinate. In this study, we confirmed the instability phenomenon in type II pyrethroids and developed novel analyte protectants for acetone/n-hexane mixture solution to suppress the phenomenon. Our findings revealed that among the examined additive compounds, three lipophilic ascorbic acid derivatives, 3-O-ethyl-L-ascorbic acid, 6-O-palmitoyl-L-ascorbic acid, and 6-O-stearoyl-L-ascorbic acid, could effectively stabilize the type II pyrethroids in the presence of polyethylene glycol 300. A mixture of the three ascorbic acid derivatives and polyethylene glycol 300 proved to be an effective analyte protectant for multiresidue pesticide analysis. Further, we designed and evaluated a new combination of analyte protectant compounds without using polyethylene glycol or the troublesome hydrophilic compounds. Consequently, we obtained a set of 10 medium- and long-chain saturated fatty acids as an effective analyte protectant suitable for acetone/n-hexane solution that did not cause peak instability in type II pyrethroids. These analyte protectants will be useful in multiresidue pesticide analysis by gas chromatography-mass spectrometry in terms of ruggedness and reliable quantitativeness. Graphical abstract Comparison of effectiveness of the addition of lipophilic derivatives of ascorbic acid in controlling the instability phenomenon of fluvalinate with polyethylene glycol 300.

Modal analysis of graphene-based structures for large deformations, contact and material nonlinearities

NASA Astrophysics Data System (ADS)

Ghaffari, Reza; Sauer, Roger A.

2018-06-01

The nonlinear frequencies of pre-stressed graphene-based structures, such as flat graphene sheets and carbon nanotubes, are calculated. These structures are modeled with a nonlinear hyperelastic shell model. The model is calibrated with quantum mechanics data and is valid for high strains. Analytical solutions of the natural frequencies of various plates are obtained for the Canham bending model by assuming infinitesimal strains. These solutions are used for the verification of the numerical results. The performance of the model is illustrated by means of several examples. Modal analysis is performed for square plates under pure dilatation or uniaxial stretch, circular plates under pure dilatation or under the effects of an adhesive substrate, and carbon nanotubes under uniaxial compression or stretch. The adhesive substrate is modeled with van der Waals interaction (based on the Lennard-Jones potential) and a coarse grained contact model. It is shown that the analytical natural frequencies underestimate the real ones, and this should be considered in the design of devices based on graphene structures.

A Review of Interface Electronic Systems for AT-cut Quartz Crystal Microbalance Applications in Liquids

PubMed Central

Arnau, Antonio

2008-01-01

From the first applications of AT-cut quartz crystals as sensors in solutions more than 20 years ago, the so-called quartz crystal microbalance (QCM) sensor is becoming into a good alternative analytical method in a great deal of applications such as biosensors, analysis of biomolecular interactions, study of bacterial adhesion at specific interfaces, pathogen and microorganism detection, study of polymer film-biomolecule or cell-substrate interactions, immunosensors and an extensive use in fluids and polymer characterization and electrochemical applications among others. The appropriate evaluation of this analytical method requires recognizing the different steps involved and to be conscious of their importance and limitations. The first step involved in a QCM system is the accurate and appropriate characterization of the sensor in relation to the specific application. The use of the piezoelectric sensor in contact with solutions strongly affects its behavior and appropriate electronic interfaces must be used for an adequate sensor characterization. Systems based on different principles and techniques have been implemented during the last 25 years. The interface selection for the specific application is important and its limitations must be known to be conscious of its suitability, and for avoiding the possible error propagation in the interpretation of results. This article presents a comprehensive overview of the different techniques used for AT-cut quartz crystal microbalance in in-solution applications, which are based on the following principles: network or impedance analyzers, decay methods, oscillators and lock-in techniques. The electronic interfaces based on oscillators and phase-locked techniques are treated in detail, with the description of different configurations, since these techniques are the most used in applications for detection of analytes in solutions, and in those where a fast sensor response is necessary. PMID:27879713

Analytical evaluation of the trajectories of hypersonic projectiles launched into space

NASA Astrophysics Data System (ADS)

Stutz, John David

An equation of motion has been derived that may be solved using simple analytic functions which describes the motion of a projectile launched from the surface of the Earth into space accounting for both Newtonian gravity and aerodynamic drag. The equation of motion is based upon the Kepler equation of motion differential and variable transformations with the inclusion of a decaying angular momentum driving function and appropriate simplifying assumptions. The new equation of motion is first compared to various numerical and analytical trajectory approximations in a non-rotating Earth reference frame. The Modified Kepler solution is then corrected to include Earth rotation and compared to a rotating Earth simulation. Finally, the modified equation of motion is used to predict the apogee and trajectory of projectiles launched into space by the High Altitude Research Project from 1961 to 1967. The new equation of motion allows for the rapid equalization of projectile trajectories and intercept solutions that may be used to calculate firing solutions to enable ground launched projectiles to intercept or rendezvous with targets in low Earth orbit such as ballistic missiles.

Nuclear magnetic resonance signal dynamics of liquids in the presence of distant dipolar fields, revisited

PubMed Central

Barros, Wilson; Gochberg, Daniel F.; Gore, John C.

2009-01-01

The description of the nuclear magnetic resonance magnetization dynamics in the presence of long-range dipolar interactions, which is based upon approximate solutions of Bloch–Torrey equations including the effect of a distant dipolar field, has been revisited. New experiments show that approximate analytic solutions have a broader regime of validity as well as dependencies on pulse-sequence parameters that seem to have been overlooked. In order to explain these experimental results, we developed a new method consisting of calculating the magnetization via an iterative formalism where both diffusion and distant dipolar field contributions are treated as integral operators incorporated into the Bloch–Torrey equations. The solution can be organized as a perturbative series, whereby access to higher order terms allows one to set better boundaries on validity regimes for analytic first-order approximations. Finally, the method legitimizes the use of simple analytic first-order approximations under less demanding experimental conditions, it predicts new pulse-sequence parameter dependencies for the range of validity, and clarifies weak points in previous calculations. PMID:19425789

Derivation of a closed form analytical expression for fluorescence recovery after photo bleaching in the case of continuous bleaching during read out

NASA Astrophysics Data System (ADS)

Endress, E.; Weigelt, S.; Reents, G.; Bayerl, T. M.

2005-01-01

Measurements of very slow diffusive processes in membranes, like the diffusion of integral membrane proteins, by fluorescence recovery after photo bleaching (FRAP) are hampered by bleaching of the probe during the read out of the fluorescence recovery. In the limit of long observation time (very slow diffusion as in the case of large membrane proteins), this bleaching may cause errors to the recovery function and thus provides error-prone diffusion coefficients. In this work we present a new approach to a two-dimensional closed form analytical solution of the reaction-diffusion equation, based on the addition of a dissipative term to the conventional diffusion equation. The calculation was done assuming (i) a Gaussian laser beam profile for bleaching the spot and (ii) that the fluorescence intensity profile emerging from the spot can be approximated by a two-dimensional Gaussian. The detection scheme derived from the analytical solution allows for diffusion measurements without the constraint of observation bleaching. Recovery curves of experimental FRAP data obtained under non-negligible read-out bleaching for native membranes (rabbit endoplasmic reticulum) on a planar solid support showed excellent agreement with the analytical solution and allowed the calculation of the lipid diffusion coefficient.

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.

Analysis of THG modes for femtosecond laser pulse

NASA Astrophysics Data System (ADS)

Trofimov, Vyacheslav A.; Sidorov, Pavel S.

2017-05-01

THG is used nowadays in many practical applications such as a substance diagnostics, and biological objects imaging, and etc. With developing of new materials and technology (for example, photonic crystal) an attention to THG process analysis grow. Therefore, THG features understanding are a modern problem. Early we have developed new analytical approach based on using the problem invariant for analytical solution construction of the THG process. It should be stressed that we did not use a basic wave non-depletion approximation. Nevertheless, a long pulse duration approximation and plane wave approximation has applied. The analytical solution demonstrates, in particular, an optical bistability property (and may other regimes of frequency tripling) for the third harmonic generation process. But, obviously, this approach does not reflect an influence of a medium dispersion on the frequency tripling. Therefore, in this paper we analyze THG efficiency of a femtosecond laser pulse taking into account a second order dispersion affect as well as self- and crossmodulation of the interacting waves affect on the frequency conversion process. Analysis is made using a computer simulation on the base of Schrödinger equations describing the process under consideration.

User's manual for the one-dimensional hypersonic experimental aero-thermodynamic (1DHEAT) data reduction code

NASA Technical Reports Server (NTRS)

Hollis, Brian R.

1995-01-01

A FORTRAN computer code for the reduction and analysis of experimental heat transfer data has been developed. This code can be utilized to determine heat transfer rates from surface temperature measurements made using either thin-film resistance gages or coaxial surface thermocouples. Both an analytical and a numerical finite-volume heat transfer model are implemented in this code. The analytical solution is based on a one-dimensional, semi-infinite wall thickness model with the approximation of constant substrate thermal properties, which is empirically corrected for the effects of variable thermal properties. The finite-volume solution is based on a one-dimensional, implicit discretization. The finite-volume model directly incorporates the effects of variable substrate thermal properties and does not require the semi-finite wall thickness approximation used in the analytical model. This model also includes the option of a multiple-layer substrate. Fast, accurate results can be obtained using either method. This code has been used to reduce several sets of aerodynamic heating data, of which samples are included in this report.

A screening tool for delineating subregions of steady recharge within groundwater models

USGS Publications Warehouse

Dickinson, Jesse; Ferré, T.P.A.; Bakker, Mark; Crompton, Becky

2014-01-01

We have developed a screening method for simplifying groundwater models by delineating areas within the domain that can be represented using steady-state groundwater recharge. The screening method is based on an analytical solution for the damping of sinusoidal infiltration variations in homogeneous soils in the vadose zone. The damping depth is defined as the depth at which the flux variation damps to 5% of the variation at the land surface. Groundwater recharge may be considered steady where the damping depth is above the depth of the water table. The analytical solution approximates the vadose zone diffusivity as constant, and we evaluated when this approximation is reasonable. We evaluated the analytical solution through comparison of the damping depth computed by the analytic solution with the damping depth simulated by a numerical model that allows variable diffusivity. This comparison showed that the screening method conservatively identifies areas of steady recharge and is more accurate when water content and diffusivity are nearly constant. Nomograms of the damping factor (the ratio of the flux amplitude at any depth to the amplitude at the land surface) and the damping depth were constructed for clay and sand for periodic variations between 1 and 365 d and flux means and amplitudes from nearly 0 to 1 × 10−3 m d−1. We applied the screening tool to Central Valley, California, to identify areas of steady recharge. A MATLAB script was developed to compute the damping factor for any soil and any sinusoidal flux variation.

Exact Solution of Gas Dynamics Equations Through Reduced Differential Transform and Sumudu Transform Linked with Pades Approximants

NASA Astrophysics Data System (ADS)

Rao, T. R. Ramesh

2018-04-01

In this paper, we study the analytical method based on reduced differential transform method coupled with sumudu transform through Pades approximants. The proposed method may be considered as alternative approach for finding exact solution of Gas dynamics equation in an effective manner. This method does not require any discretization, linearization and perturbation.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Atmospheric guidance law for planar skip trajectories

NASA Technical Reports Server (NTRS)

Mease, K. D.; Mccreary, F. A.

1985-01-01

The applicability of an approximate, closed-form, analytical solution to the equations of motion, as a basis for a deterministic guidance law for controlling the in-plane motion during a skip trajectory, is investigated. The derivation of the solution by the method of matched asymptotic expansions is discussed. Specific issues that arise in the application of the solution to skip trajectories are addressed. Based on the solution, an explicit formula for the approximate energy loss due to an atmospheric pass is derived. A guidance strategy is proposed that illustrates the use of the approximate solution. A numerical example shows encouraging 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.

Acid-Base Properties of Azo Dyes in Solution Studied Using Spectrophotometry and Colorimetry

NASA Astrophysics Data System (ADS)

Snigur, D. V.; Chebotarev, A. N.; Bevziuk, K. V.

2018-03-01

Colorimetry and spectrophotometry with chemometric data processing were used to study the acid-base properties of azo dyes in aqueous solution. The capabilities of both methods were compared. Ionization constants of all the functional groups of the azo compounds studied could be determined relative to the change in the specific color difference depending on the acidity of the medium. The colorimetric functions of ion-molecular forms of azo compounds used as an analytical signal allow us to obtain complete information on the acid-base equilibrium in a wide acidity range.

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

NASA Astrophysics Data System (ADS)

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

2010-01-01

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

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2015-01-01

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

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.

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.

Lump Solutions for the (3+1)-Dimensional Kadomtsev-Petviashvili Equation

NASA Astrophysics Data System (ADS)

Liu, De-Yin; Tian, Bo; Xie, Xi-Yang

2016-12-01

In this article, we investigate the lump solutions for the Kadomtsev-Petviashvili equation in (3+1) dimensions that describe the dynamics of plasmas or fluids. Via the symbolic computation, lump solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation are derived based on the bilinear forms. The conditions to guarantee analyticity and rational localisation of the lump solutions are presented. The lump solutions contain eight parameters, two of which are totally free, and the other six of which need to satisfy the presented conditions. Plots with particular choices of the involved parameters are made to show the lump solutions and their energy distributions.

Towards wall functions for the prediction of solute segregation in plane front directional solidification

NASA Astrophysics Data System (ADS)

Chatelain, M.; Rhouzlane, S.; Botton, V.; Albaric, M.; Henry, D.; Millet, S.; Pelletier, D.; Garandet, J. P.

2017-10-01

The present paper focuses on solute segregation occurring in directional solidification processes with sharp solid/liquid interface, like silicon crystal growth. A major difficulty for the simulation of such processes is their inherently multi-scale nature: the impurity segregation problem is controlled at the solute boundary layer scale (micrometers) while the thermal problem is ruled at the crucible scale (meters). The thickness of the solute boundary layer is controlled by the convection regime and requires a specific refinement of the mesh of numerical models. In order to improve numerical simulations, wall functions describing solute boundary layers for convecto-diffusive regimes are derived from a scaling analysis. The aim of these wall functions is to obtain segregation profiles from purely thermo-hydrodynamic simulations, which do not require solute boundary layer refinement at the solid/liquid interface. Regarding industrial applications, various stirring techniques can be used to enhance segregation, leading to fully turbulent flows in the melt. In this context, the scaling analysis is further improved by taking into account the turbulent solute transport. The solute boundary layers predicted by the analytical model are compared to those obtained by transient segregation simulations in a canonical 2D lid driven cavity configuration for validation purposes. Convective regimes ranging from laminar to fully turbulent are considered. Growth rate and molecular diffusivity influences are also investigated. Then, a procedure to predict concentration fields in the solid phase from a hydrodynamic simulation of the solidification process is proposed. This procedure is based on the analytical wall functions and on solute mass conservation. It only uses wall shear-stress profiles at the solidification front as input data. The 2D analytical concentration fields are directly compared to the results of the complete simulation of segregation in the lid driven cavity configuration. Finally, an additional output from the analytical model is also presented. We put in light the correlation between different species convecto-diffusive behaviour; we use it to propose an estimation method for the segregation parameters of various chemical species knowing segregation parameters of one specific species.

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

An approximate analytical methodology for the concentration CDF and corresponding adverse health effects in 3D heterogeneous aquifers

NASA Astrophysics Data System (ADS)

Zarlenga, Antonio; de Barros, Felipe; Fiori, Aldo

2017-04-01

Predicting solutes displacement in ecosystems is a complex task because of heterogeneity of hydrogeological properties and limited financial resources for characterization. As a consequence, solute transport model predictions are subject to uncertainty and probabilistic methods are invoked. Despite the significant theoretical advances in subsurface hydrology, there is a compelling need to transfer those specialized know-hows into an easy-to-use practical tool. The deterministic approach is able to capture some features of the transport behavior but its adoption in practical applications (e.g. remediation strategies or health risk assessment) is often inadequate because of its inability to accurately model the phenomena triggered by the spatial heterogeneity. The rigorous evaluation of the local contaminant concentration in natural aquifers requires an accurate estimate of the domain properties and huge computational times; those aspects limit the adoption of fully 3D numerical models. In this presentation, we illustrate a physically-based methodology to analytically estimate of the statistics of the solute concentration in natural aquifers and the related health risk. Our methodology aims to provide a simple tool for a quick assessment of the contamination level in aquifers, as function of a few relevant, physically based parameters such as the log conductivity variance, the mean flow velocity, the Péclet number. Solutions of the 3D analytical model adopt the results of previous works: transport model is based on the solutions proposed by Zarlenga and Fiori (2013, 2014) where semi-analytical relations for the statics of local contaminant concentration are carry out through a Lagrangian first-order model. As suggested in de Barros and Fiori (2014), the Beta distribution is assumed for the concentration cumulative density function (CDF). We illustrate the use of the closed-form equations for the probability of local contaminant concentration and health risk in a series of problems of practical relevance. The basic scenario is constituted by a steady state plume in a 3D heterogeneous formation. In this case the non-reactive transport is ruled by interplay of the spreading (lateral and vertical) and dilution. The second scenario considers two different dynamics of degradation in aerobic and anaerobic conditions which allows the contaminant abatement. The final example links the environmental concentration with adverse health effects. For this case, additional information on toxicological and behavioral parameters are required. Despite the simplifying assumptions adopted, the proposed solutions are appealing in applications due to their simplicity and the fact that they allow to easily propagate the uncertainty from different sources in the final risk endpoint. de Barros, F.P., Fiori, A., 2014. First-order based cumulative distribution function for solute concentration in heterogeneous aquifers: theoretical analysis and implications for human health risk assessment. Water Resour. Res. 50, 4018-4037. Zarlenga, A., Fiori, A., 2013. Steady plumes in heterogeneous porous formations: a stochastic lagrangian approach. Water Resour. Res. 49, 864-873. Zarlenga, A., Fiori, A., 2014. Stochastic analytical modeling of the biodegradation of steady plumes. J. Contam. Hydrol. 157, 106-116.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-10-01

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

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-09-01

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

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev

2017-11-01

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

Hybrid-dual-fourier tomographic algorithm for a fast three-dimensionial optical image reconstruction in turbid media

NASA Technical Reports Server (NTRS)

Alfano, Robert R. (Inventor); Cai, Wei (Inventor)

2007-01-01

A reconstruction technique for reducing computation burden in the 3D image processes, wherein the reconstruction procedure comprises an inverse and a forward model. The inverse model uses a hybrid dual Fourier algorithm that combines a 2D Fourier inversion with a 1D matrix inversion to thereby provide high-speed inverse computations. The inverse algorithm uses a hybrid transfer to provide fast Fourier inversion for data of multiple sources and multiple detectors. The forward model is based on an analytical cumulant solution of a radiative transfer equation. The accurate analytical form of the solution to the radiative transfer equation provides an efficient formalism for fast computation of the forward model.

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.

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...

The Superior Lambert Algorithm

NASA Astrophysics Data System (ADS)

der, G.

2011-09-01

Lambert algorithms are used extensively for initial orbit determination, mission planning, space debris correlation, and missile targeting, just to name a few applications. Due to the significance of the Lambert problem in Astrodynamics, Gauss, Battin, Godal, Lancaster, Gooding, Sun and many others (References 1 to 15) have provided numerous formulations leading to various analytic solutions and iterative methods. Most Lambert algorithms and their computer programs can only work within one revolution, break down or converge slowly when the transfer angle is near zero or 180 degrees, and their multi-revolution limitations are either ignored or barely addressed. Despite claims of robustness, many Lambert algorithms fail without notice, and the users seldom have a clue why. The DerAstrodynamics lambert2 algorithm, which is based on the analytic solution formulated by Sun, works for any number of revolutions and converges rapidly at any transfer angle. It provides significant capability enhancements over every other Lambert algorithm in use today. These include improved speed, accuracy, robustness, and multirevolution capabilities as well as implementation simplicity. Additionally, the lambert2 algorithm provides a powerful tool for solving the angles-only problem without artificial singularities (pointed out by Gooding in Reference 16), which involves 3 lines of sight captured by optical sensors, or systems such as the Air Force Space Surveillance System (AFSSS). The analytic solution is derived from the extended Godal’s time equation by Sun, while the iterative method of solution is that of Laguerre, modified for robustness. The Keplerian solution of a Lambert algorithm can be extended to include the non-Keplerian terms of the Vinti algorithm via a simple targeting technique (References 17 to 19). Accurate analytic non-Keplerian trajectories can be predicted for satellites and ballistic missiles, while performing at least 100 times faster in speed than most numerical integration methods.

A noble refractive optical scanner with linear response

NASA Astrophysics Data System (ADS)

Mega, Yair J.; Lai, Zhenhua; DiMarzio, Charles A.

2013-03-01

Many applications in various fields of science and engineering use steered optical beam systems. Currently, many methods utilize mirrors in order to steer the beam. However, this approach is an off-axis solution, which normally increases the total size of the system as well as its error and complexity. Other methods use a "Risely Prisms" based solution, which is on-axis solution, however it poses some difficulties from an engineering standpoint, and therefore isn't widely used. We present here a novel technique for steering a beam on its optical axis with a linear deflection response. We derived the formulation for the profile required of the refractive optical component necessary for preforming the beam steering. The functionality of the device was simulated analytically using Matlab, as well as using a ray-tracing software, Zemax, and showed agreement with the analytical model. An optical element was manufactured based on the proposed design and the device was tested. The results show agreement with our hypothesis. We also present some proposed geometries of the several other devices, all based on the same concept, which can be used for higher performance applications such as two-dimensional scanner, video rate scanner etc.

A new sensitive method of dissociation constants determination based on the isohydric solutions principle.

PubMed

Michałowski, Tadeusz; Pilarski, Bogusław; Asuero, Agustin G; Dobkowska, Agnieszka

2010-10-15

The paper provides a new formulation and analytical proposals based on the isohydric solutions concept. It is particularly stated that a mixture formed, according to titrimetric mode, from a weak acid (HX, C(0)mol/L) and a strong acid (HB, Cmol/L) solutions, assumes constant pH, independently on the volumes of the solutions mixed, provided that the relation C(0)=C+C(2)·10(pK(1)) is valid, where pK(1)=-log K(1), K(1) the dissociation constant for HX. The generalized formulation, referred to the isohydric solutions thus obtained, was extended also to more complex acid-base systems. Particularly in the (HX, HB) system, the titration occurs at constant ionic strength (I) value, not resulting from presence of a basal electrolyte. This very advantageous conjunction of the properties provides, among others, a new, very sensitive method for verification of pK(1) value. The new method is particularly useful for weak acids HX characterized by low pK(1) values. The method was tested experimentally on four acid-base systems (HX, HB), in aqueous and mixed-solvent media and compared with the literature data. Some useful (linear and hyperbolic) correlations were stated and applied for validation of pK(1) values. Finally, some practical applications of analytical interest of the isohydricity (pH constancy) principle as one formulated in this paper were enumerated, proving the usefulness of such a property which has its remote roots in the Arrhenius concept. Copyright © 2010 Elsevier B.V. All rights reserved.

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

NASA Technical Reports Server (NTRS)

Bandyopadhyay, Alak; Majumdar, Alok

2007-01-01

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

Analytic derivation of the next-to-leading order proton structure function F2p(x ,Q2) based on the Laplace transformation

NASA Astrophysics Data System (ADS)

Khanpour, Hamzeh; Mirjalili, Abolfazl; Tehrani, S. Atashbar

2017-03-01

An analytical solution based on the Laplace transformation technique for the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations is presented at next-to-leading order accuracy in perturbative QCD. This technique is also applied to extract the analytical solution for the proton structure function, F2p(x ,Q2) , in the Laplace s space. We present the results for the separate parton distributions of all parton species, including valence quark densities, the antiquark and strange sea parton distribution functions (PDFs), and the gluon distribution. We successfully compare the obtained parton distribution functions and the proton structure function with the results from GJR08 [Gluck, Jimenez-Delgado, and Reya, Eur. Phys. J. C 53, 355 (2008)], 10.1140/epjc/s10052-007-0462-9 and KKT12 [Khanpour, Khorramian, and Tehrani, J. Phys. G 40, 045002 (2013)], 10.1088/0954-3899/40/4/045002 parametrization models as well as the x -space results using QCDnum code. Our calculations show a very good agreement with the available theoretical models as well as the deep inelastic scattering (DIS) experimental data throughout the small and large values of x . The use of our analytical solution to extract the parton densities and the proton structure function is discussed in detail to justify the analysis method, considering the accuracy and speed of calculations. Overall, the accuracy we obtain from the analytical solution using the inverse Laplace transform technique is found to be better than 1 part in 104 to 105. We also present a detailed QCD analysis of nonsinglet structure functions using all available DIS data to perform global QCD fits. In this regard we employ the Jacobi polynomial approach to convert the results from Laplace s space to Bjorken x space. The extracted valence quark densities are also presented and compared to the JR14, MMHT14, NNPDF, and CJ15 PDFs sets. We evaluate the numerical effects of target mass corrections (TMCs) and higher twist (HT) terms on various structure functions, and compare fits to data with and without these corrections.

One-dimensional model and solutions for creeping gas flows in the approximation of uniform pressure

NASA Astrophysics Data System (ADS)

Vedernikov, A.; Balapanov, D.

2016-11-01

A model, along with analytical and numerical solutions, is presented to describe a wide variety of one-dimensional slow flows of compressible heat-conductive fluids. The model is based on the approximation of uniform pressure valid for the flows, in which the sound propagation time is much shorter than the duration of any meaningful density variation in the system. The energy balance is described by the heat equation that is solved independently. This approach enables the explicit solution for the fluid velocity to be obtained. Interfacial and volumetric heat and mass sources as well as boundary motion are considered as possible sources of density variation in the fluid. A set of particular tasks is analyzed for different motion sources in planar, axial, and central symmetries in the quasistationary limit of heat conduction (i.e., for large Fourier number). The analytical solutions are in excellent agreement with corresponding numerical solutions of the whole system of the Navier-Stokes equations. This work deals with the ideal gas. The approach is also valid for other equations of state.

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.

Core-based intrinsic fiber-optic absorption sensor for the detection of volatile organic compounds

NASA Astrophysics Data System (ADS)

Klunder, Gregory L.; Russo, Richard E.

1995-03-01

A core-based intrinsic fiber-optic absorption sensor has been developed and tested for the detection of volatile organic compounds. The distal ends of transmitting and receiving fibers are connected by a small cylindrical section of an optically clear silicone rubber. The silicone rubber acts both as a light pipe and as a selective membrane into which the analyte molecules can diffuse. The sensor has been used to detect volatile organics (trichloroethylene, 1,1-dichloroethylene, and benzene) in both aqueous solutions and in the vapor phase or headspace. Absorption spectra obtained in the near-infrared (near-IR) provide qualitative and quantitative information about the analyte. Water, which has strong broad-band absorption in the near-IR, is excluded from the spectra because of the hydrophobic properties of the silicone rubber. The rate-limiting step is shown to be the diffusion through the Nernstian boundary layer surrounding the sensor and not the diffusion through the silicone polymer. The rate of analyte diffusion into the sensor, as measured by the t(sub 90) values (the time required for the sensor to reach 90% of the equilibrium value), is 30 min for measurements in aqueous solutions and approximately 3 min for measurements made in the headspace. The limit of detection obtained with this sensor is approximately 1.1 ppm for trichloroethylene in an aqueous solution.

Practical solution for control of the pre-analytical phase in decentralized clinical laboratories for meeting the requirements of the medical laboratory accreditation standard DIN EN ISO 15189.

PubMed

Vacata, Vladimir; Jahns-Streubel, Gerlinde; Baldus, Mirjana; Wood, William Graham

2007-01-01

This report was written in response to the article by Wood published recently in this journal. It describes a practical solution to the problems of controlling the pre-analytical phase in the clinical diagnostic laboratory. As an indicator of quality in the pre-analytical phase of sample processing, a target analyte was chosen which is sensitive to delay in centrifugation and/or analysis. The results of analyses of the samples sent by satellite medical practitioners were compared with those from an on-site hospital laboratory with a controllable optimized pre-analytical phase. The aim of the comparison was: (a) to identify those medical practices whose mean/median sample values significantly deviate from those of the control situation in the hospital laboratory due to the possible problems in the pre-analytical phase; (b) to aid these laboratories in the process of rectifying these problems. A Microsoft Excel-based Pre-Analytical Survey tool (PAS tool) has been developed which addresses the above mentioned problems. It has been tested on serum potassium which is known to be sensitive to delay and/or irregularities in sample treatment. The PAS tool has been shown to be one possibility for improving the quality of the analyses by identifying the sources of problems within the pre-analytical phase, thus allowing them to be rectified. Additionally, the PAS tool has an educational value and can also be adopted for use in other decentralized laboratories.

Rapid and high-precision measurement of sulfur isotope and sulfur concentration in sediment pore water by multi-collector inductively coupled plasma mass spectrometry.

PubMed

Bian, Xiao-Peng; Yang, Tao; Lin, An-Jun; Jiang, Shao-Yong

2015-01-01

We have developed a technique for the rapid, precise and accurate determination of sulfur isotopes (δ(34)S) by MC-ICP-MS applicable to a range of sulfur-bearing solutions of different sulfur content. The 10 ppm Alfa-S solution (ammonium sulfate solution, working standard of the lab of the authors) was used to bracket other Alfa-S solutions of different concentrations and the measured δ(34)SV-CDT values of Alfa-S solutions deviate from the reference value to varying degrees (concentration effect). The stability of concentration effect has been verified and a correction curve has been constructed based on Alfa-S solutions to correct measured δ(34)SV-CDT values. The curve has been applied to AS solutions (dissolved ammonium sulfate from the lab of the authors) and pore water samples successfully, validating the reliability of our analytical method. This method also enables us to measure the sulfur concentration simultaneously when analyzing the sulfur isotope composition. There is a strong linear correlation (R(2)>0.999) between the sulfur concentrations and the intensity ratios of samples and the standard. We have constructed a regression curve based on Alfa-S solutions and this curve has been successfully used to determine sulfur concentrations of AS solutions and pore water samples. The analytical technique presented here enable rapid, precise and accurate S isotope measurement for a wide range of sulfur-bearing solutions - in particular for pore water samples with complex matrix and varying sulfur concentrations. Also, simultaneous measurement of sulfur concentrations is available. Copyright © 2014 Elsevier B.V. All rights reserved.

Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams

PubMed Central

Abedi, Maryam

2014-01-01

This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. Natural frequencies and mode shapes of various Timoshenko beams are presented to demonstrate the efficiency of the methodology. PMID:24574879

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.

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.

Observability during planetary approach navigation

NASA Technical Reports Server (NTRS)

Bishop, Robert H.; Burkhart, P. Daniel; Thurman, Sam W.

1993-01-01

The objective of the research is to develop an analytic technique to predict the relative navigation capability of different Earth-based radio navigation measurements. In particular, the problem is to determine the relative ability of geocentric range and Doppler measurements to detect the effects of the target planet gravitational attraction on the spacecraft during the planetary approach and near-encounter mission phases. A complete solution to the two-dimensional problem has been developed. Relatively simple analytic formulas are obtained for range and Doppler measurements which describe the observability content of the measurement data along the approach trajectories. An observability measure is defined which is based on the observability matrix for nonlinear systems. The results show good agreement between the analytic observability analysis and the computational batch processing method.

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

NASA Astrophysics Data System (ADS)

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

2008-02-01

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

Determination of tannin in green tea infusion by flow-injection analysis based on quenching the fluorescence of 3-aminophthalate.

PubMed

Chen, Richie L C; Lin, Chun-Hsun; Chung, Chien-Yu; Cheng, Tzong-Jih

2005-11-02

A flow-injection analytical system was developed to determine tannin content in green tea infusions. The flow-injection system is based on measuring the quenching effect of tannin on the fluorescence of 3-aminophthalate. Fluorophore was obtained by auto-oxidation of luminol during solution preparation. System performance was satisfactory for routine analysis (sample throughput >20 h(-1); linear dynamic range for tannic acid, 0.005-0.3 mg/mL; linear dynamic range for green tea tannin, 0.02-1.0 mg/mL; CV < 3%). The flow-injection method is immune from interference by coexisting ascorbate in green tea infusion. Analytical results were verified by the ferrous tartrate method, the Japanese official analytical method.

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...

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.

Development of Amperometric Biosensors Based on Nanostructured Tyrosinase-Conducting Polymer Composite Electrodes

PubMed Central

Lupu, Stelian; Lete, Cecilia; Balaure, Paul Cătălin; Caval, Dan Ion; Mihailciuc, Constantin; Lakard, Boris; Hihn, Jean-Yves; del Campo, Francisco Javier

2013-01-01

Bio-composite coatings consisting of poly(3,4-ethylenedioxythiophene) (PEDOT) and tyrosinase (Ty) were successfully electrodeposited on conventional size gold (Au) disk electrodes and microelectrode arrays using sinusoidal voltages. Electrochemical polymerization of the corresponding monomer was carried out in the presence of various Ty amounts in aqueous buffered solutions. The bio-composite coatings prepared using sinusoidal voltages and potentiostatic electrodeposition methods were compared in terms of morphology, electrochemical properties, and biocatalytic activity towards various analytes. The amperometric biosensors were tested in dopamine (DA) and catechol (CT) electroanalysis in aqueous buffered solutions. The analytical performance of the developed biosensors was investigated in terms of linear response range, detection limit, sensitivity, and repeatability. A semi-quantitative multi-analyte procedure for simultaneous determination of DA and CT was developed. The amperometric biosensor prepared using sinusoidal voltages showed much better analytical performance. The Au disk biosensor obtained by 50 mV alternating voltage amplitude displayed a linear response for DA concentrations ranging from 10 to 300 μM, with a detection limit of 4.18 μM. PMID:23698270

Thermal modeling for pulsed radiofrequency ablation: analytical study based on hyperbolic heat conduction.

PubMed

López Molina, Juan A; Rivera, María J; Trujillo, Macarena; Berjano, Enrique J

2009-04-01

The objectives of this study were to model the temperature progress of a pulsed radiofrequency (RF) power during RF heating of biological tissue, and to employ the hyperbolic heat transfer equation (HHTE), which takes the thermal wave behavior into account, and compare the results to those obtained using the heat transfer equation based on Fourier theory (FHTE). A theoretical model was built based on an active spherical electrode completely embedded in the biological tissue, after which HHTE and FHTE were analytically solved. We found three typical waveforms for the temperature progress depending on the relations between the dimensionless duration of the RF pulse delta(a) and the expression square root of lambda(rho-1), with lambda as the dimensionless thermal relaxation time of the tissue and rho as the dimensionless position. In the case of a unique RF pulse, the temperature at any location was the result of the overlapping of two different heat sources delayed for a duration delta(a) (each heat source being produced by a RF pulse of limitless duration). The most remarkable feature in the HHTE analytical solution was the presence of temperature peaks traveling through the medium at a finite speed. These peaks not only occurred during the RF power switch-on period but also during switch off. Finally, a physical explanation for these temperature peaks is proposed based on the interaction of forward and reverse thermal waves. All-purpose analytical solutions for FHTE and HHTE were obtained during pulsed RF heating of biological tissues, which could be used for any value of pulsing frequency and duty cycle.

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.

Providing the physical basis of SCS curve number method and its proportionality relationship from Richards' equation

NASA Astrophysics Data System (ADS)

Hooshyar, M.; Wang, D.

2016-12-01

The empirical proportionality relationship, which indicates that the ratio of cumulative surface runoff and infiltration to their corresponding potentials are equal, is the basis of the extensively used Soil Conservation Service Curve Number (SCS-CN) method. The objective of this paper is to provide the physical basis of the SCS-CN method and its proportionality hypothesis from the infiltration excess runoff generation perspective. To achieve this purpose, an analytical solution of Richards' equation is derived for ponded infiltration in shallow water table environment under the following boundary conditions: 1) the soil is saturated at the land surface; and 2) there is a no-flux boundary which moves downward. The solution is established based on the assumptions of negligible gravitational effect, constant soil water diffusivity, and hydrostatic soil moisture profile between the no-flux boundary and water table. Based on the derived analytical solution, the proportionality hypothesis is a reasonable approximation for rainfall partitioning at the early stage of ponded infiltration in areas with a shallow water table for coarse textured soils.

Using sequential self-calibration method to identify conductivity distribution: Conditioning on tracer test data

USGS Publications Warehouse

Hu, B.X.; He, C.

2008-01-01

An iterative inverse method, the sequential self-calibration method, is developed for mapping spatial distribution of a hydraulic conductivity field by conditioning on nonreactive tracer breakthrough curves. A streamline-based, semi-analytical simulator is adopted to simulate solute transport in a heterogeneous aquifer. The simulation is used as the forward modeling step. In this study, the hydraulic conductivity is assumed to be a deterministic or random variable. Within the framework of the streamline-based simulator, the efficient semi-analytical method is used to calculate sensitivity coefficients of the solute concentration with respect to the hydraulic conductivity variation. The calculated sensitivities account for spatial correlations between the solute concentration and parameters. The performance of the inverse method is assessed by two synthetic tracer tests conducted in an aquifer with a distinct spatial pattern of heterogeneity. The study results indicate that the developed iterative inverse method is able to identify and reproduce the large-scale heterogeneity pattern of the aquifer given appropriate observation wells in these synthetic cases. ?? International Association for Mathematical Geology 2008.

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

Quantifying Seepage Flux using Sediment Temperatures

EPA Science Inventory

This report provides a demonstration of different modeling approaches that use sediment temperatures to estimate the magnitude and direction of water flux across the groundwater-surface water transition zone. Analytical models based on steady-state or transient temperature solut...

Comparing an analytical spacetime metric for a merging binary to a fully nonlinear numerical evolution using curvature scalars

NASA Astrophysics Data System (ADS)

Sadiq, Jam; Zlochower, Yosef; Nakano, Hiroyuki

2018-04-01

We introduce a new geometrically invariant prescription for comparing two different spacetimes based on geodesic deviation. We use this method to compare a family of recently introduced analytical spacetime representing inspiraling black-hole binaries to fully nonlinear numerical solutions to the Einstein equations. Our method can be used to improve analytical spacetime models by providing a local measure of the effects that violations of the Einstein equations will have on timelike geodesics, and indirectly, gas dynamics. We also discuss the advantages and limitations of this method.

Improvement of analytical dynamic models using modal test data

NASA Technical Reports Server (NTRS)

Berman, A.; Wei, F. S.; Rao, K. V.

1980-01-01

A method developed to determine maximum changes in analytical mass and stiffness matrices to make them consistent with a set of measured normal modes and natural frequencies is presented. The corrected model will be an improved base for studies of physical changes, boundary condition changes, and for prediction of forced responses. The method features efficient procedures not requiring solutions of the eigenvalue problem, and the ability to have more degrees of freedom than the test data. In addition, modal displacements are obtained for all analytical degrees of freedom, and the frequency dependence of the coordinate transformations is properly treated.

Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system.

PubMed

Bezekci, B; Biktashev, V N

2017-09-01

We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.

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.

Free vibration analysis of a robotic fish based on a continuous and non-uniform flexible backbone with distributed masses

NASA Astrophysics Data System (ADS)

Coral, W.; Rossi, C.; Curet, O. M.

2015-12-01

This paper presents a Differential Quadrature Element Method for free transverse vibration of a robotic fish based on a continuous and non-uniform flexible backbone with distributed masses (fish ribs). The proposed method is based on the theory of a Timoshenko cantilever beam. The effects of the masses (number, magnitude and position) on the value of natural frequencies are investigated. Governing equations, compatibility and boundary conditions are formulated according to the Differential Quadrature rules. The convergence, efficiency and accuracy are compared to other analytical solution proposed in the literature. Moreover, the proposed method has been validate against the physical prototype of a flexible fish backbone. The main advantages of this method, compared to the exact solutions available in the literature are twofold: first, smaller computational cost and second, it allows analysing the free vibration in beams whose section is an arbitrary function, which is normally difficult or even impossible with other analytical methods.

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.

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.

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.

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.

Fusion Analytics: A Data Integration System for Public Health and Medical Disaster Response Decision Support

PubMed Central

Passman, Dina B.

2013-01-01

Objective The objective of this demonstration is to show conference attendees how they can integrate, analyze, and visualize diverse data type data from across a variety of systems by leveraging an off-the-shelf enterprise business intelligence (EBI) solution to support decision-making in disasters. Introduction Fusion Analytics is the data integration system developed by the Fusion Cell at the U.S. Department of Health and Human Services (HHS), Office of the Assistant Secretary for Preparedness and Response (ASPR). Fusion Analytics meaningfully augments traditional public and population health surveillance reporting by providing web-based data analysis and visualization tools. Methods Fusion Analytics serves as a one-stop-shop for the web-based data visualizations of multiple real-time data sources within ASPR. The 24-7 web availability makes it an ideal analytic tool for situational awareness and response allowing stakeholders to access the portal from any internet-enabled device without installing any software. The Fusion Analytics data integration system was built using off-the-shelf EBI software. Fusion Analytics leverages the full power of statistical analysis software and delivers reports to users in a secure web-based environment. Fusion Analytics provides an example of how public health staff can develop and deploy a robust public health informatics solution using an off-the shelf product and with limited development funding. It also provides the unique example of a public health information system that combines patient data for traditional disease surveillance with manpower and resource data to provide overall decision support for federal public health and medical disaster response operations. Conclusions We are currently in a unique position within public health. One the one hand, we have been gaining greater and greater access to electronic data of all kinds over the last few years. On the other, we are working in a time of reduced government spending to support leveraging this data for decision support with robust analytics and visualizations. Fusion Analytics provides an opportunity for attendees to see how various types of data are integrated into a single application for population health decision support. It also can provide them with ideas of how they can use their own staff to create analyses and reports that support their public health activities.

Bending of an Infinite beam on a base with two parameters in the absence of a part of the base

NASA Astrophysics Data System (ADS)

Aleksandrovskiy, Maxim; Zaharova, Lidiya

2018-03-01

Currently, in connection with the rapid development of high-rise construction and the improvement of joint operation of high-rise structures and bases models, the questions connected with the use of various calculation methods become topical. The rigor of analytical methods is capable of more detailed and accurate characterization of the structures behavior, which will affect the reliability of objects and can lead to a reduction in their cost. In the article, a model with two parameters is used as a computational model of the base that can effectively take into account the distributive properties of the base by varying the coefficient reflecting the shift parameter. The paper constructs the effective analytical solution of the problem of a beam of infinite length interacting with a two-parameter voided base. Using the Fourier integral equations, the original differential equation is reduced to the Fredholm integral equation of the second kind with a degenerate kernel, and all the integrals are solved analytically and explicitly, which leads to an increase in the accuracy of the computations in comparison with the approximate methods. The paper consider the solution of the problem of a beam loaded with a concentrated force applied at the point of origin with a fixed value of the length of the dip section. The paper gives the analysis of the obtained results values for various parameters of coefficient taking into account cohesion of the ground.

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.

3-D Inhomogeous Radiative Transfer Model using a Planar-stratified Forward RT Model and Horizontal Perturbation Series

NASA Astrophysics Data System (ADS)

Zhang, K.; Gasiewski, A. J.

2017-12-01

A horizontally inhomogeneous unified microwave radiative transfer (HI-UMRT) model based upon a nonspherical hydrometeor scattering model is being developed at the University of Colorado at Boulder to facilitate forward radiative simulations for 3-dimensionally inhomogeneous clouds in severe weather. The HI-UMRT 3-D analytical solution is based on incorporating a planar-stratified 1-D UMRT algorithm within a horizontally inhomogeneous iterative perturbation scheme. Single-scattering parameters are computed using the Discrete Dipole Scattering (DDSCAT v7.3) program for hundreds of carefully selected nonspherical complex frozen hydrometeors from the NASA/GSFC DDSCAT database. The required analytic factorization symmetry of transition matrix in a normalized RT equation was analytically proved and validated numerically using the DDSCAT-based full Stokes matrix of randomly oriented hydrometeors. The HI-UMRT model thus inherits the properties of unconditional numerical stability, efficiency, and accuracy from the UMRT algorithm and provides a practical 3-D two-Stokes parameter radiance solution with Jacobian to be used within microwave retrievals and data assimilation schemes. In addition, a fast forward radar reflectivity operator with Jacobian based on DDSCAT backscatter efficiency computed for large hydrometeors is incorporated into the HI-UMRT model to provide applicability to active radar sensors. The HI-UMRT will be validated strategically at two levels: 1) intercomparison of brightness temperature (Tb) results with those of several 1-D and 3-D RT models, including UMRT, CRTM and Monte Carlo models, 2) intercomparison of Tb with observed data from combined passive and active spaceborne sensors (e.g. GPM GMI and DPR). The precise expression for determining the required number of 3-D iterations to achieve an error bound on the perturbation solution will be developed to facilitate the numerical verification of the HI-UMRT code complexity and computation performance.

Numerical solution of potential flow about arbitrary 2-dimensional multiple bodies

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Thames, F. C.

1982-01-01

A procedure for the finite-difference numerical solution of the lifting potential flow about any number of arbitrarily shaped bodies is given. The solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having coordinate lines coincident with the contours of all bodies in the field, regardless of their shapes and number. The effects of all numerical parameters involved are analyzed and appropriate values are recommended. Comparisons with analytic solutions for single Karman-Trefftz airfoils and a circular cylinder pair show excellent agreement. The technique of application of the boundary-fitted coordinate systems to the numerical solution of partial differential equations is illustrated.

On the first crossing distributions in fractional Brownian motion and the mass function of dark matter haloes

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

Hiotelis, Nicos; Popolo, Antonino Del, E-mail: adelpopolo@oact.inaf.it, E-mail: hiotelis@ipta.demokritos.gr

We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions derived by simulating paths from fractional Brownian motion. We compare the results of the analytical solutions with both those of simulations and those of some approximated solutions which have been used in the literature. Finally, we present multiplicity functions for dark matter structures resulting from our analytical approach and we compare with those resulting from N-body simulations. We show that the results of analytical solutions aremore » in good agreement with those of path simulations but differ significantly from those derived from approximated solutions. Additionally, multiplicity functions derived from fractional Brownian motion are poor fits of the those which result from N-body simulations. We also present comparisons with other models which are exist in the literature and we discuss different ways of improving the agreement between analytical results and N-body simulations.« less

An analytical solution for Dean flow in curved ducts with rectangular cross section

NASA Astrophysics Data System (ADS)

Norouzi, M.; Biglari, N.

2013-05-01

In this paper, a full analytical solution for incompressible flow inside the curved ducts with rectangular cross-section is presented for the first time. The perturbation method is applied to solve the governing equations and curvature ratio is considered as the perturbation parameter. The previous perturbation solutions are usually restricted to the flow in curved circular or annular pipes related to the overly complex form of solutions or singularity situation for flow in curved ducts with non-circular shapes of cross section. This issue specifies the importance of analytical studies in the field of Dean flow inside the non-circular ducts. In this study, the main flow velocity, stream function of lateral velocities (secondary flows), and flow resistance ratio in rectangular curved ducts are obtained analytically. The effect of duct curvature and aspect ratio on flow field is investigated as well. Moreover, it is important to mention that the current analytical solution is able to simulate the Taylor-Görtler and Dean vortices (vortices in stable and unstable situations) in curved channels.

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.

Analytical and numerical analysis of frictional damage in quasi brittle materials

NASA Astrophysics Data System (ADS)

Zhu, Q. Z.; Zhao, L. Y.; Shao, J. F.

2016-07-01

Frictional sliding and crack growth are two main dissipation processes in quasi brittle materials. The frictional sliding along closed cracks is the origin of macroscopic plastic deformation while the crack growth induces a material damage. The main difficulty of modeling is to consider the inherent coupling between these two processes. Various models and associated numerical algorithms have been proposed. But there are so far no analytical solutions even for simple loading paths for the validation of such algorithms. In this paper, we first present a micro-mechanical model taking into account the damage-friction coupling for a large class of quasi brittle materials. The model is formulated by combining a linear homogenization procedure with the Mori-Tanaka scheme and the irreversible thermodynamics framework. As an original contribution, a series of analytical solutions of stress-strain relations are developed for various loading paths. Based on the micro-mechanical model, two numerical integration algorithms are exploited. The first one involves a coupled friction/damage correction scheme, which is consistent with the coupling nature of the constitutive model. The second one contains a friction/damage decoupling scheme with two consecutive steps: the friction correction followed by the damage correction. With the analytical solutions as reference results, the two algorithms are assessed through a series of numerical tests. It is found that the decoupling correction scheme is efficient to guarantee a systematic numerical convergence.

Thermodynamic Studies of Levitated Microdroplets of Highly Supersaturated Electrolyte Solutions

NASA Technical Reports Server (NTRS)

Myerson, Allan S.; Izmailov, Alexander F.; Na, Han-Soo

1996-01-01

Highly supersaturated electrolyte solutions are studied by employing an electrodynamic levitator trap (ELT) technique. The ELT technique involves containerless suspension of a microdroplet thus eliminating dust, dirt, and container walls which normally cause heterogeneous nucleation. This allows very high supersaturations to be achieved. A theoretical study of the experimental results obtained for the water activity in microdroplets of various electrolyte solutions is based on the development of the Cahn-Hilliard formalism for electrolyte solutions. A correspondence of 96-99% between the theory and experiment for the all solutions studied was achieved and allowed the determination of an analytical expression for the spinodal concentration n(sub spin) and its calculation for various electrolyte solutions at 298 K.

Proportional reasoning as a heuristic-based process: time constraint and dual task considerations.

PubMed

Gillard, Ellen; Van Dooren, Wim; Schaeken, Walter; Verschaffel, Lieven

2009-01-01

The present study interprets the overuse of proportional solution methods from a dual process framework. Dual process theories claim that analytic operations involve time-consuming executive processing, whereas heuristic operations are fast and automatic. In two experiments to test whether proportional reasoning is heuristic-based, the participants solved "proportional" problems, for which proportional solution methods provide correct answers, and "nonproportional" problems known to elicit incorrect answers based on the assumption of proportionality. In Experiment 1, the available solution time was restricted. In Experiment 2, the executive resources were burdened with a secondary task. Both manipulations induced an increase in proportional answers and a decrease in correct answers to nonproportional problems. These results support the hypothesis that the choice for proportional methods is heuristic-based.

Analytical solutions for solute transport in groundwater and riverine flow using Green's Function Method and pertinent coordinate transformation method

NASA Astrophysics Data System (ADS)

Sanskrityayn, Abhishek; Suk, Heejun; Kumar, Naveen

2017-04-01

In this study, analytical solutions of one-dimensional pollutant transport originating from instantaneous and continuous point sources were developed in groundwater and riverine flow using both Green's Function Method (GFM) and pertinent coordinate transformation method. Dispersion coefficient and flow velocity are considered spatially and temporally dependent. The spatial dependence of the velocity is linear, non-homogeneous and that of dispersion coefficient is square of that of velocity, while the temporal dependence is considered linear, exponentially and asymptotically decelerating and accelerating. Our proposed analytical solutions are derived for three different situations depending on variations of dispersion coefficient and velocity, respectively which can represent real physical processes occurring in groundwater and riverine systems. First case refers to steady solute transport situation in steady flow in which dispersion coefficient and velocity are only spatially dependent. The second case represents transient solute transport in steady flow in which dispersion coefficient is spatially and temporally dependent while the velocity is spatially dependent. Finally, the third case indicates transient solute transport in unsteady flow in which both dispersion coefficient and velocity are spatially and temporally dependent. The present paper demonstrates the concentration distribution behavior from a point source in realistically occurring flow domains of hydrological systems including groundwater and riverine water in which the dispersivity of pollutant's mass is affected by heterogeneity of the medium as well as by other factors like velocity fluctuations, while velocity is influenced by water table slope and recharge rate. Such capabilities give the proposed method's superiority about application of various hydrological problems to be solved over other previously existing analytical solutions. Especially, to author's knowledge, any other solution doesn't exist for both spatially and temporally variations of dispersion coefficient and velocity. In this study, the existing analytical solutions from previous widely known studies are used for comparison as validation tools to verify the proposed analytical solution as well as the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) code and the developed 1D finite difference code (FDM). All such solutions show perfect match with the respective proposed solutions.

Sample injection and electrophoretic separation on a simple laminated paper based analytical device.

PubMed

Xu, Chunxiu; Zhong, Minghua; Cai, Longfei; Zheng, Qingyu; Zhang, Xiaojun

2016-02-01

We described a strategy to perform multistep operations on a simple laminated paper-based separation device by using electrokinetic flow to manipulate the fluids. A laminated crossed-channel paper-based separation device was fabricated by cutting a filter paper sheet followed by lamination. Multiple function units including sample loading, sample injection, and electrophoretic separation were integrated on a single paper based analytical device for the first time, by applying potential at different reservoirs for sample, sample waste, buffer, and buffer waste. As a proof-of-concept demonstration, mixed sample solution containing carmine and sunset yellow were loaded in the sampling channel, and then injected into separation channel followed by electrophoretic separation, by adjusting the potentials applied at the four terminals of sampling and separation channel. The effects of buffer pH, buffer concentration, channel width, and separation time on resolution of electrophoretic separation were studied. This strategy may be used to perform multistep operations such as reagent dilution, sample injection, mixing, reaction, and separation on a single microfluidic paper based analytical device, which is very attractive for building micro total analysis systems on microfluidic paper based analytical devices. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

From bead to rod: Comparison of theories by measuring translational drag coefficients of micron-sized magnetic bead-chains in Stokes flow

PubMed Central

Lu, Chen; Zhao, Xiaodan; Kawamura, Ryo

2017-01-01

Frictional drag force on an object in Stokes flow follows a linear relationship with the velocity of translation and a translational drag coefficient. This drag coefficient is related to the size, shape, and orientation of the object. For rod-like objects, analytical solutions of the drag coefficients have been proposed based on three rough approximations of the rod geometry, namely the bead model, ellipsoid model, and cylinder model. These theories all agree that translational drag coefficients of rod-like objects are functions of the rod length and aspect ratio, but differ among one another on the correction factor terms in the equations. By tracking the displacement of the particles through stationary fluids of calibrated viscosity in magnetic tweezers setup, we experimentally measured the drag coefficients of micron-sized beads and their bead-chain formations with chain length of 2 to 27. We verified our methodology with analytical solutions of dimers of two touching beads, and compared our measured drag coefficient values of rod-like objects with theoretical calculations. Our comparison reveals several analytical solutions that used more appropriate approximation and derived formulae that agree with our measurement better. PMID:29145447

Electronic Structure and Properties of Deformed Carbon Nanotubes

NASA Technical Reports Server (NTRS)

Yang, Liu; Arnold, Jim (Technical Monitor)

2001-01-01

A theoretical framework based on Huckel tight-binding model has been formulated to analyze the electronic structure of carbon nanotubes under uniform deformation. The model successfully quantifies the dispersion relation, density of states and bandgap change of nanotubes under uniform stretching, compression, torsion and bending. Our analysis shows that the shifting of the Fermi point away from the Brillouin zone vertices is the key reason for these changes. As a result of this shifting, the electronic structure of deformed carbon nanotubes varies dramatically depending on their chirality and deformation mode. Treating the Fermi point as a function of strain and tube chirality, the analytical solution preserves the concise form of undeformed carbon nanotubes. It predicts the shifting, merging and splitting of the Van Hove singularities in the density of states and the zigzag pattern of bandgap change under strains. Four orbital tight-binding simulations of carbon nanotubes under uniform stretching, compression, torsion and bending have been performed to verify the analytical solution. Extension to more complex systems are being performed to relate this analytical solution to the spectroscopic characterization, device performance and proposed quantum structures induced by the deformation. The limitations of this model will also be discussed.

Guidelines and Parameter Selection for the Simulation of Progressive Delamination

NASA Technical Reports Server (NTRS)

Song, Kyongchan; Davila, Carlos G.; Rose, Cheryl A.

2008-01-01

Turon s methodology for determining optimal analysis parameters for the simulation of progressive delamination is reviewed. Recommended procedures for determining analysis parameters for efficient delamination growth predictions using the Abaqus/Standard cohesive element and relatively coarse meshes are provided for single and mixed-mode loading. The Abaqus cohesive element, COH3D8, and a user-defined cohesive element are used to develop finite element models of the double cantilever beam specimen, the end-notched flexure specimen, and the mixed-mode bending specimen to simulate progressive delamination growth in Mode I, Mode II, and mixed-mode fracture, respectively. The predicted responses are compared with their analytical solutions. The results show that for single-mode fracture, the predicted responses obtained with the Abaqus cohesive element correlate well with the analytical solutions. For mixed-mode fracture, it was found that the response predicted using COH3D8 elements depends on the damage evolution criterion that is used. The energy-based criterion overpredicts the peak loads and load-deflection response. The results predicted using a tabulated form of the BK criterion correlate well with the analytical solution and with the results predicted with the user-written element.

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.

Improving sensitivity of gold nanoparticle based fluorescence quenching and colorimetric aptasensor by using water resuspended gold nanoparticle.

PubMed

Liu, Jinchuan; Guan, Zheng; Lv, Zhenzhen; Jiang, Xiaoling; Yang, Shuming; Chen, Ailiang

2014-02-15

Gold nanoparticles (AuNPs) based fluorescence quenching or colorimetric aptasensor have been developed for many analytes recently largely because of the ease of detection, high sensitivity, and potential for high-throughput analysis. However, the effects of remnant non-AuNPs components in the colloid gold solution on these assays performance remain unclear. For the first time, we demonstrated that the remnant sodium citrate and the reaction products of three acids play counteractive roles in AuNPs based fluorescence quenching and colorimetric aptasensor in three ways in this study. First, the remnant sodium citrate in the colloid gold solution could increase the fluorescence intensity of FAM labeled on the aptamer that reduce the efficiency of AuNPs fluorescent quenching. Second, the reaction products of citric acid, HCl and ketoglutaric acid reduce the fluorescence recovery by quenching the fluorescence of FAM labeled on the aptamer dissociated from the surface of AuNPs upon addition of target. Lastly, the reaction products of three acids reduce the pH value of the colloid gold solution that reduce the sensitivity of AuNPs based colorimetric aptasensor by increasing the adsorption of aptamer to surface of AuNPs. With sulfadimethoxine and thrombin as model analytes, we found that water resuspended AuNPs can significantly increase the sensitivity by more than 10-fold for AuNPs based fluorescence quenching aptasensor. In the AuNPs based colorimetric aptasensor for sulfadimethoxine using the water resuspended AuNPs, the sensitivity also was increased by 10-fold compared with that of original AuNPs. The findings in this study provide theoretical guidance for further improving AuNPs based fluorescent quenching and colorimetric aptasensor by adjusting the composition of AuNPs solution. © 2013 Elsevier B.V. All rights reserved.

Reversible thrombin detection by aptamer functionalized STING sensors

PubMed Central

Actis, Paolo; Rogers, Adam; Nivala, Jeff; Vilozny, Boaz; Seger, R. Adam; Jejelowo, Olufisayo; Pourmand, Nader

2011-01-01

Signal Transduction by Ion NanoGating (STING) is a label-free technology based on functionalized quartz nanopipettes. The nanopipette pore can be decorated with a variety of recognition elements and the molecular interaction is transduced via a simple electrochemical system. A STING sensor can be easily and reproducibly fabricated and tailored at the bench starting from inexpensive quartz capillaries. The analytical application of this new biosensing platform, however, was limited due to the difficult correlation between the measured ionic current and the analyte concentration in solution. Here we show that STING sensors functionalized with aptamers allow the quantitative detection of thrombin. The binding of thrombin generates a signal that can be directly correlated to its concentration in the bulk solution. PMID:21636261

Comparing Anisotropic Output-Based Grid Adaptation Methods by Decomposition

NASA Technical Reports Server (NTRS)

Park, Michael A.; Loseille, Adrien; Krakos, Joshua A.; Michal, Todd

2015-01-01

Anisotropic grid adaptation is examined by decomposing the steps of flow solution, ad- joint solution, error estimation, metric construction, and simplex grid adaptation. Multiple implementations of each of these steps are evaluated by comparison to each other and expected analytic results when available. For example, grids are adapted to analytic metric fields and grid measures are computed to illustrate the properties of multiple independent implementations of grid adaptation mechanics. Different implementations of each step in the adaptation process can be evaluated in a system where the other components of the adaptive cycle are fixed. Detailed examination of these properties allows comparison of different methods to identify the current state of the art and where further development should be targeted.

On the wing behaviour of the overtones of self-localized modes

NASA Astrophysics Data System (ADS)

Dusi, R.; Wagner, M.

1998-08-01

In this paper the solutions for self-localized modes in a nonlinear chain are investigated. We present a converging iteration procedure, which is based on analytical information of the wings and which takes into account higher overtones of the solitonic oscillations. The accuracy is controlled in a step by step manner by means of a Gaussian error analysis. Our numerical procedure allows for highly accurate solutions, in all anharmonicity regimes, and beyond the rotating-wave approximation (RWA). It is found that the overtone wings change their analytical behaviour at certain critical values of the energy of the self-localized mode: there is a turnover in the exponent of descent. The results are shown for a Fermi-Pasta-Ulam (FPU) chain with quartic anharmonicity.

Exact solution of a linear molecular motor model driven by two-step fluctuations and subject to protein friction.

PubMed

Fogedby, Hans C; Metzler, Ralf; Svane, Axel

2004-08-01

We investigate by analytical means the stochastic equations of motion of a linear molecular motor model based on the concept of protein friction. Solving the coupled Langevin equations originally proposed by Mogilner et al. [Phys. Lett. A 237, 297 (1998)], and averaging over both the two-step internal conformational fluctuations and the thermal noise, we present explicit, analytical expressions for the average motion and the velocity-force relationship. Our results allow for a direct interpretation of details of this motor model which are not readily accessible from numerical solutions. In particular, we find that the model is able to predict physiologically reasonable values for the load-free motor velocity and the motor mobility.

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

PubMed

Hall, A J; Minchin, P E H

2013-12-01

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

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 ...

Calibration-free optical chemical sensors

DOEpatents

DeGrandpre, Michael D.

2006-04-11

An apparatus and method for taking absorbance-based chemical measurements are described. In a specific embodiment, an indicator-based pCO₂ (partial pressure of CO₂) sensor displays sensor-to-sensor reproducibility and measurement stability. These qualities are achieved by: 1) renewing the sensing solution, 2) allowing the sensing solution to reach equilibrium with the analyte, and 3) calculating the response from a ratio of the indicator solution absorbances which are determined relative to a blank solution. Careful solution preparation, wavelength calibration, and stray light rejection also contribute to this calibration-free system. Three pCO₂ sensors were calibrated and each had response curves which were essentially identical within the uncertainty of the calibration. Long-term laboratory and field studies showed the response had no drift over extended periods (months). The theoretical response, determined from thermodynamic characterization of the indicator solution, also predicted the observed calibration-free performance.

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.

The Relationship Between Partial Contaminant Source Zone Remediation and Groundwater Plume Attenuation

NASA Astrophysics Data System (ADS)

Falta, R. W.

2004-05-01

Analytical solutions are developed that relate changes in the contaminant mass in a source area to the behavior of biologically reactive dissolved contaminant groundwater plumes. Based on data from field experiments, laboratory experiments, numerical streamtube models, and numerical multiphase flow models, the chemical discharge from a source region is assumed to be a nonlinear power function of the fraction of contaminant mass removed from the source zone. This function can approximately represent source zone mass discharge behavior over a wide range of site conditions ranging from simple homogeneous systems, to complex heterogeneous systems. A mass balance on the source zone with advective transport and first order decay leads to a nonlinear differential equation that is solved analytically to provide a prediction of the time-dependent contaminant mass discharge leaving the source zone. The solution for source zone mass discharge is coupled semi-analytically with a modified version of the Domenico (1987) analytical solution for three-dimensional reactive advective and dispersive transport in groundwater. The semi-analytical model then employs the BIOCHLOR (Aziz et al., 2000; Sun et al., 1999) transformations to model sequential first order parent-daughter biological decay reactions of chlorinated ethenes and ethanes in the groundwater plume. The resulting semi-analytic model thus allows for transient simulation of complex source zone behavior that is fully coupled to a dissolved contaminant plume undergoing sequential biological reactions. Analyses of several realistic scenarios show that substantial changes in the ground water plume can result from the partial removal of contaminant mass from the source zone. These results, however, are sensitive to the nature of the source mass reduction-source discharge reduction curve, and to the rates of degradation of the primary contaminant and its daughter products in the ground water plume. Aziz, C.E., C.J. Newell, J.R. Gonzales, P. Haas, T.P. Clement, and Y. Sun, 2000, BIOCHLOR Natural Attenuation Decision Support System User's Manual Version 1.0, US EPA Report EPA/600/R-00/008 Domenico, P.A., 1987, An analytical model for multidimensional transport of a decaying contaminant species, J. Hydrol., 91: 49-58. Sun, Y., J.N. Petersen, T.P. Clement, and R.S. Skeen, 1999, A new analytical solution for multi-species transport equations with serial and parallel reactions, Water Resour. Res., 35(1): 185-190.

Analytical Method Used to Calculate Pile Foundations with the Widening Up on a Horizontal Static Impact

NASA Astrophysics Data System (ADS)

Kupchikova, N. V.; Kurbatskiy, E. N.

2017-11-01

This paper presents a methodology for the analytical research solutions for the work pile foundations with surface broadening and inclined side faces in the ground array, based on the properties of Fourier transform of finite functions. The comparative analysis of the calculation results using the suggested method for prismatic piles, piles with surface broadening prismatic with precast piles and end walls with precast wedges on the surface is described.

PAUSE: Predictive Analytics Using SPARQL-Endpoints

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

Sukumar, Sreenivas R; Ainsworth, Keela; Bond, Nathaniel

2014-07-11

This invention relates to the medical industry and more specifically to methods of predicting risks. With the impetus towards personalized and evidence-based medicine, the need for a framework to analyze/interpret quantitative measurements (blood work, toxicology, etc.) with qualitative descriptions (specialist reports after reading images, bio-medical knowledgebase, etc.) to predict diagnostic risks is fast emerging. We describe a software solution that leverages hardware for scalable in-memory analytics and applies next-generation semantic query tools on medical data.

Granular material flow in two-dimensional hoppers

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

Brennen, C.; Pearce, J.C.

To aid in improving the transport of granular media for industrial purposes, the California Institute of Technology presents a comparison of experimental data with analytical results for the flow of dry granular media (such as coal) through a two-dimensional or wedge-shaped hopper. The analytical solution, which is based on the constitutive postulates (suggested by A.W. Jenike and R.T. Shield) of intergrain Coulomb friction and isotropy, produces results that are in good agreement with the experimental measurements.

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.

Parameter identification of partially covered piezoelectric cantilever power scavenger based on the coupled distributed parameter solution

NASA Astrophysics Data System (ADS)

Hosseini; Hamedi; Ebrahimi Mamaghani; Kim; Kim; Dayou

2017-07-01

Among the various techniques of power scavenging, piezoelectric energy harvesting usually has more power density. Although piezoceramics are usually more efficient than other piezoelectric materials, since they are very brittle and fragile, researchers are looking for alternative materials. Recently Cellulose Electro-active paper (EAPap) has been recognized as a smart material with piezoelectric behavior that can be used in energy scavenging systems. The majority of researches in energy harvesting area, use unimorph piezoelectric cantilever beams. This paper presents an analytical solution based on distributed parameter model for partially covered pieoelectric cantilever energy harvester. The purpose of the paper is to describe the changes in generated power with damping and the load resistance using analytical calculations. The analytical data are verified using experiment on a vibrating cantilever substrate that is partially covered by EAPap films. The results are very close to each other. Also asymptotic trends of the voltage, current and power outputs are investigated and expressions are obtained for the extreme conditions of the load resistance. These new findings provide guidelines for identification and manipulation of effective parameters in order to achieve the efficient performance in different ambient source conditions.

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

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Baumeister, Joseph F.

1994-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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.

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.

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.

Advances in analytical chemistry

NASA Technical Reports Server (NTRS)

Arendale, W. F.; Congo, Richard T.; Nielsen, Bruce J.

1991-01-01

Implementation of computer programs based on multivariate statistical algorithms makes possible obtaining reliable information from long data vectors that contain large amounts of extraneous information, for example, noise and/or analytes that we do not wish to control. Three examples are described. Each of these applications requires the use of techniques characteristic of modern analytical chemistry. The first example, using a quantitative or analytical model, describes the determination of the acid dissociation constant for 2,2'-pyridyl thiophene using archived data. The second example describes an investigation to determine the active biocidal species of iodine in aqueous solutions. The third example is taken from a research program directed toward advanced fiber-optic chemical sensors. The second and third examples require heuristic or empirical models.

Design of analytical systems based on functionality of doped ice.

PubMed

Okada, Tetsuo

2014-01-01

Ice plays an important role for the circulations of some compounds in the global environment. Both the ice surface and the liquid phase developed in a frozen solution are involved in such reactions of the molecules of environmental importance. This leads to the idea that ice can be used to design novel analytical reaction systems. We devised ice chromatography, in which ice particles are used as the liquid chromatographic stationary phase, and have subsequently developed various analytical systems utilizing the functionality of ice. This review focuses our attention on the analytical facets of ice containing impurities such as salts; hereinafter, we call this "doped ice". The design of novel separation systems and use as microreactors with doped ice are mainly discussed.

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.

Photophysics of detection of explosive vapours via luminescence quenching of thin films: impact of inter-molecular interactions.

PubMed

Shoaee, Safa; Fan, Shengqiang; Burn, Paul L; Shaw, Paul E

2016-09-21

Fluorescence-based detection of explosive analytes requires an understanding of the nature of the excited state responsible for the luminescence response of a sensing material. Many measurements are carried out to elucidate the fundamental photophysical properties of an emissive material in solution. However, simple transfer of the understanding gained from the solution measurements to the solid-state can lead to errors. This is in part due to the absence of inter-molecular interactions of the chromophores in solution, which are present in the solid-state. To understand the role of inter-molecular interactions on the detection of explosive analytes we have chosen dendrimers from two different families, D1 and D2, which allow facile control of the inter-molecular interactions through the choice of dendrons and emissive chromophores. Using ultrafast transient absorption spectroscopy we find that the solution photoinduced absorption (PA) for both materials can be explained in terms of the generation of singlet excitons, which decay to the ground state, or intersystem cross (ISC) to form a triplet exciton. In neat films however, we observe different photophysical behaviours; first, ISC to the triplet state does not occur, and second, depending on the chromophore, charge transfer and charge separated states are formed. Furthermore, we find that when either dendrimer is interfaced with analyte vapour, the singlet state is strongly quenched, generating a charge transfer state that undergoes geminate recombination.

Automatically assessing properties of dynamic cameras for camera selection and rapid deployment of video content analysis tasks in large-scale ad-hoc networks

NASA Astrophysics Data System (ADS)

den Hollander, Richard J. M.; Bouma, Henri; van Rest, Jeroen H. C.; ten Hove, Johan-Martijn; ter Haar, Frank B.; Burghouts, Gertjan J.

2017-10-01

Video analytics is essential for managing large quantities of raw data that are produced by video surveillance systems (VSS) for the prevention, repression and investigation of crime and terrorism. Analytics is highly sensitive to changes in the scene, and for changes in the optical chain so a VSS with analytics needs careful configuration and prompt maintenance to avoid false alarms. However, there is a trend from static VSS consisting of fixed CCTV cameras towards more dynamic VSS deployments over public/private multi-organization networks, consisting of a wider variety of visual sensors, including pan-tilt-zoom (PTZ) cameras, body-worn cameras and cameras on moving platforms. This trend will lead to more dynamic scenes and more frequent changes in the optical chain, creating structural problems for analytics. If these problems are not adequately addressed, analytics will not be able to continue to meet end users' developing needs. In this paper, we present a three-part solution for managing the performance of complex analytics deployments. The first part is a register containing meta data describing relevant properties of the optical chain, such as intrinsic and extrinsic calibration, and parameters of the scene such as lighting conditions or measures for scene complexity (e.g. number of people). A second part frequently assesses these parameters in the deployed VSS, stores changes in the register, and signals relevant changes in the setup to the VSS administrator. A third part uses the information in the register to dynamically configure analytics tasks based on VSS operator input. In order to support the feasibility of this solution, we give an overview of related state-of-the-art technologies for autocalibration (self-calibration), scene recognition and lighting estimation in relation to person detection. The presented solution allows for rapid and robust deployment of Video Content Analysis (VCA) tasks in large scale ad-hoc networks.

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.

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.

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.

Analytical and experimental study of axisymmetric truncated plug nozzle flow fields

NASA Technical Reports Server (NTRS)

Muller, T. J.; Sule, W. P.; Fanning, A. E.; Giel, T. V.; Galanga, F. L.

1972-01-01

Experimental and analytical investigation of the flow field and base pressure of internal-external-expansion truncated plug nozzles are discussed. Experimental results for two axisymmetric, conical plug-cylindrical shroud, truncated plug nozzles are presented for both open and closed wake operations. These results include extensive optical and pressure data covering nozzle flow field and base pressure characteristics, diffuser effects, lip shock strength, Mach disc behaviour, and the recompression and reverse flow regions. Transonic experiments for a special planar transonic section are presented. An extension of the analytical method of Hall and Mueller to include the internal shock wave from the shroud exit is presented for closed wake operation. Results of this analysis include effects on the flow field and base pressure of ambient pressure ratio, nozzle geometry, and the ratio of specific heats. Static thrust is presented as a function of ambient pressure ratio and nozzle geometry. A new transonic solution method is also presented.

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

Amendment to "Analytical Solution for the Convectively-Mixed Atmospheric Boundary Layer": Inclusion of Subsidence

NASA Astrophysics Data System (ADS)

Ouwersloot, H. G.; de Arellano, J. Vilà-Guerau

2013-09-01

In Ouwersloot and Vilà-Guerau de Arellano (Boundary-Layer Meteorol. doi: 10.1007/s10546-013-9816-z , 2013, this issue), the analytical solutions for the boundary-layer height and scalar evolutions are derived for the convective boundary layer, based on the prognostic equations of mixed-layer slab models without taking subsidence into account. Here, we include and quantify the added effect of subsidence if the subsidence velocity scales linearly with height throughout the atmosphere. This enables analytical analyses for a wider range of observational cases. As a demonstration, the sensitivity of the boundary-layer height and the potential temperature jump to subsidence and the free tropospheric stability is graphically presented. The new relations show the importance of the temporal distribution of the surface buoyancy flux in determining the evolution if there is subsidence.

Load sharing in distributed real-time systems with state-change broadcasts

NASA Technical Reports Server (NTRS)

Shin, Kang G.; Chang, Yi-Chieh

1989-01-01

A decentralized dynamic load-sharing (LS) method based on state-change broadcasts is proposed for a distributed real-time system. Whenever the state of a node changes from underloaded to fully loaded and vice versa, the node broadcasts this change to a set of nodes, called a buddy set, in the system. The performance of the method is evaluated with both analytic modeling and simulation. It is modeled first by an embedded Markov chain for which numerical solutions are derived. The model solutions are then used to calculate the distribution of queue lengths at the nodes and the probability of meeting task deadlines. The analytical results show that buddy sets of 10 nodes outperform those of less than 10 nodes, and the incremental benefit gained from increasing the buddy set size beyond 15 nodes is insignificant. These and other analytical results are verified by simulation. The proposed LS method is shown to meet task deadlines with a very high probability.

Matrix-enhanced secondary ion mass spectrometry: The Alchemist's solution?

NASA Astrophysics Data System (ADS)

Delcorte, Arnaud

2006-07-01

Because of the requirements of large molecule characterization and high-lateral resolution SIMS imaging, the possibility of improving molecular ion yields by the use of specific sample preparation procedures has recently generated a renewed interest in the static SIMS community. In comparison with polyatomic projectiles, however, signal enhancement by a matrix might appear to some as the alchemist's versus the scientist's solution to the current problems of organic SIMS. In this contribution, I would like to discuss critically the pros and cons of matrix-enhanced SIMS procedures, in the new framework that includes polyatomic ion bombardment. This discussion is based on a short review of the experimental and theoretical developments achieved in the last decade with respect to the three following approaches: (i) blending the analyte with a low-molecular weight organic matrix (MALDI-type preparation procedure); (ii) mixing alkali/noble metal salts with the analyte; (iii) evaporating a noble metal layer on the analyte sample surface (organic molecules, polymers).

Wetting boundary condition for the color-gradient lattice Boltzmann method: Validation with analytical and experimental data

NASA Astrophysics Data System (ADS)

Akai, Takashi; Bijeljic, Branko; Blunt, Martin J.

2018-06-01

In the color gradient lattice Boltzmann model (CG-LBM), a fictitious-density wetting boundary condition has been widely used because of its ease of implementation. However, as we show, this may lead to inaccurate results in some cases. In this paper, a new scheme for the wetting boundary condition is proposed which can handle complicated 3D geometries. The validity of our method for static problems is demonstrated by comparing the simulated results to analytical solutions in 2D and 3D geometries with curved boundaries. Then, capillary rise simulations are performed to study dynamic problems where the three-phase contact line moves. The results are compared to experimental results in the literature (Heshmati and Piri, 2014). If a constant contact angle is assumed, the simulations agree with the analytical solution based on the Lucas-Washburn equation. However, to match the experiments, we need to implement a dynamic contact angle that varies with the flow rate.

Solvent microextraction-flame atomic absorption spectrometry (SME-FAAS) for determination of ultratrace amounts of cadmium in meat and fish samples.

PubMed

Goudarzi, Nasser

2009-02-11

A simple, low cost and highly sensitive method based on solvent microextraction (SME) for separation/preconcentration and flame atomic absorption spectrometry (FAAS) was proposed for the determination of ultratrace amounts of cadmium in meat and fish samples. The analytical procedure involved the formation of a hydrophobic complex by mixing the analyte solution with an ammonium pyrrolidinedithiocarbamate (APDC) solution. In suitable conditions, the complex of cadmium-APDC entered the micro organic phase, and thus, separation of the analyte from the matrix was achieved. Under optimal chemical and instrumental conditions, a detection limit (3 sigma) of 0.8 ng L(-1) and an enrichment factor of 93 were achieved. The relative standard deviation for the method was found to be 2.2% for Cd. The interference effects of some anions and cations were also investigated. The developed method has been applied to the determination of trace Cd in meat and fish samples.

Applications of computer algebra to distributed parameter systems

NASA Technical Reports Server (NTRS)

Storch, Joel A.

1993-01-01

In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.

Removal of emerging micropollutants from water using cyclodextrin.

PubMed

Nagy, Zsuzsanna Magdolna; Molnár, Mónika; Fekete-Kertész, Ildikó; Molnár-Perl, Ibolya; Fenyvesi, Éva; Gruiz, Katalin

2014-07-01

Small scale laboratory experiment series were performed to study the suitability of a cyclodextrin-based sorbent (ß-cyclodextrin bead polymer, BCDP) for modelling the removal of micropollutants from drinking water and purified waste water using simulated inflow test solutions containing target analytes (ibuprofen, naproxen, ketoprofen, bisphenol-A, diclofenac, β-estradiol, ethinylestradiol, estriol, cholesterol at 2-6 μg/L level). This work was focused on the preliminary evaluation of BCDP as a sorbent in two different model systems (filtration and fluidization) applied for risk reduction of emerging micropollutants. For comparison different filter systems combined with various sorbents (commercial filter and activated carbon) were applied and evaluated in the filtration experiment series. The spiked test solution (inflow) and the treated outflows were characterized by an integrated methodology including chemical analytical methods gas chromatography-tandem mass spectrometry (GC-MS/MS) and various environmental toxicity tests to determine the efficiency and selectivity of the applied sorbents. Under experimental conditions the cyclodextrin-based filters used for purification of drinking water in most cases were able to absorb more than 90% of the bisphenol-A and of the estrogenic compounds. Both the analytical chemistry and toxicity results showed efficient elimination of these pollutants. Especially the toxicity of the filtrate decreased considerably. Laboratory experiment modelling post-purification of waste water was also performed applying fluidization technology by ß-cyclodextrin bead polymer. The BCDP removed efficiently from the spiked test solution most of the micropollutants, especially the bisphenol-A (94%) and the hormones (87-99%) The results confirmed that the BCDP-containing sorbents provide a good solution to water quality problems and they are able to decrease the load and risk posed by micropollutants to the water systems. Copyright © 2014 Elsevier B.V. All rights reserved.

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.

Portable sample preparation and analysis system for micron and sub-micron particle characterization using light scattering and absorption spectroscopy

DOEpatents

Stark, Peter C [Los Alamos, NM; Zurek, Eduardo [Barranquilla, CO; Wheat, Jeffrey V [Fort Walton Beach, FL; Dunbar, John M [Santa Fe, NM; Olivares, Jose A [Los Alamos, NM; Garcia-Rubio, Luis H [Temple Terrace, FL; Ward, Michael D [Los Alamos, NM

2011-07-26

There is provided a method and device for remote sampling, preparation and optical interrogation of a sample using light scattering and light absorption methods. The portable device is a filtration-based device that removes interfering background particle material from the sample matrix by segregating or filtering the chosen analyte from the sample solution or matrix while allowing the interfering background particles to be pumped out of the device. The segregated analyte is then suspended in a diluent for analysis. The device is capable of calculating an initial concentration of the analyte, as well as diluting the analyte such that reliable optical measurements can be made. Suitable analytes include cells, microorganisms, bioparticles, pathogens and diseases. Sample matrixes include biological fluids such as blood and urine, as well as environmental samples including waste water.

Shape anomaly detection under strong measurement noise: An analytical approach to adaptive thresholding

NASA Astrophysics Data System (ADS)

Krasichkov, Alexander S.; Grigoriev, Eugene B.; Bogachev, Mikhail I.; Nifontov, Eugene M.

2015-10-01

We suggest an analytical approach to the adaptive thresholding in a shape anomaly detection problem. We find an analytical expression for the distribution of the cosine similarity score between a reference shape and an observational shape hindered by strong measurement noise that depends solely on the noise level and is independent of the particular shape analyzed. The analytical treatment is also confirmed by computer simulations and shows nearly perfect agreement. Using this analytical solution, we suggest an improved shape anomaly detection approach based on adaptive thresholding. We validate the noise robustness of our approach using typical shapes of normal and pathological electrocardiogram cycles hindered by additive white noise. We show explicitly that under high noise levels our approach considerably outperforms the conventional tactic that does not take into account variations in the noise level.

Prediction of unsaturated flow and water backfill during infiltration in layered soils

NASA Astrophysics Data System (ADS)

Cui, Guotao; Zhu, Jianting

2018-02-01

We develop a new analytical infiltration model to determine water flow dynamics around layer interfaces during infiltration process in layered soils. The model mainly involves the analytical solutions to quadratic equations to determine the flux rates around the interfaces. Active water content profile behind the wetting front is developed based on the solution of steady state flow to dynamically update active parameters in sharp wetting front infiltration equations and to predict unsaturated flow in coarse layers before the front reaches an impeding fine layer. The effect of water backfill to saturate the coarse layers after the wetting front encounters the impeding fine layer is analytically expressed based on the active water content profiles. Comparison to the numerical solutions of the Richards equation shows that the new model can well capture water dynamics in relation to the arrangement of soil layers. The steady state active water content profile can be used to predict the saturation state of all layers when the wetting front first passes through these layers during the unsteady infiltration process. Water backfill effect may occur when the unsaturated wetting front encounters a fine layer underlying a coarse layer. Sensitivity analysis shows that saturated hydraulic conductivity is the parameter dictating the occurrence of unsaturated flow and water backfill and can be used to represent the coarseness of soil layers. Water backfill effect occurs in coarse layers between upper and lower fine layers when the lower layer is not significantly coarser than the upper layer.

Solution of second order quasi-linear boundary value problems by a wavelet method

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

Zhang, Lei; Zhou, Youhe; Wang, Jizeng, E-mail: jzwang@lzu.edu.cn

2015-03-10

A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can evenmore » reach orders of 5.8.« less

Data visualisation in surveillance for injury prevention and control: conceptual bases and case studies

PubMed Central

Martinez, Ramon; Ordunez, Pedro; Soliz, Patricia N; Ballesteros, Michael F

2016-01-01

Background The complexity of current injury-related health issues demands the usage of diverse and massive data sets for comprehensive analyses, and application of novel methods to communicate data effectively to the public health community, decision-makers and the public. Recent advances in information visualisation, availability of new visual analytic methods and tools, and progress on information technology provide an opportunity for shaping the next generation of injury surveillance. Objective To introduce data visualisation conceptual bases, and propose a visual analytic and visualisation platform in public health surveillance for injury prevention and control. Methods The paper introduces data visualisation conceptual bases, describes a visual analytic and visualisation platform, and presents two real-world case studies illustrating their application in public health surveillance for injury prevention and control. Results Application of visual analytic and visualisation platform is presented as solution for improved access to heterogeneous data sources, enhance data exploration and analysis, communicate data effectively, and support decision-making. Conclusions Applications of data visualisation concepts and visual analytic platform could play a key role to shape the next generation of injury surveillance. Visual analytic and visualisation platform could improve data use, the analytic capacity, and ability to effectively communicate findings and key messages. The public health surveillance community is encouraged to identify opportunities to develop and expand its use in injury prevention and control. PMID:26728006

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.

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.

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.

Analysis of Oblique Wave Interaction with a Comb-Type Caisson Breakwater

NASA Astrophysics Data System (ADS)

Wang, Xinyu; Liu, Yong; Liang, Bingchen

2018-04-01

This study develops an analytical solution for oblique wave interaction with a comb-type caisson breakwater based on linear potential theory. The fluid domain is divided into inner and outer regions according to the geometrical shape of breakwater. By using periodic boundary condition and separation of variables, series solutions of velocity potentials in inner and outer regions are developed. Unknown expansion coefficients in series solutions are determined by matching velocity and pressure of continuous conditions on the interface between two regions. Then, hydrodynamic quantities involving reflection coefficients and wave forces acting on breakwater are estimated. Analytical solution is validated by a multi-domain boundary element method solution for the present problem. Diffusion reflection due to periodic variations in breakwater shape and corresponding surface elevations around the breakwater are analyzed. Numerical examples are also presented to examine effects of caisson parameters on total wave forces acting on caissons and total wave forces acting on side plates. Compared with a traditional vertical wall breakwater, the wave force acting on a suitably designed comb-type caisson breakwater can be significantly reduced. This study can give a better understanding of the hydrodynamic performance of comb-type caisson breakwaters.

Closed-form analytical solutions for assessing the consequences of sea-level rise on unconfined sloping island aquifers

NASA Astrophysics Data System (ADS)

Chesnaux, R.

2016-04-01

Closed-form analytical solutions for assessing the consequences of sea-level rise on fresh groundwater oceanic island lenses are provided for the cases of both strip and circular islands. Solutions are proposed for directly calculating the change in the thickness of the lens, the changes in volume and the changes in travel time of fresh groundwater within island aquifers. The solutions apply for homogenous aquifers recharged by surface infiltration and discharged by a down-gradient, fixed-head boundary. They also take into account the inland shift of the ocean due to land surface inundation, this shift being determined by the coastal slope of inland aquifers. The solutions are given for two simple island geometries: circular islands and strip islands. Base case examples are presented to illustrate, on one hand, the amplitude of the change of the fresh groundwater lens thickness and the volume depletion of the lens in oceanic island with sea-level rise, and on the other hand, the shortening of time required for groundwater to discharge into the ocean. These consequences can now be quantified and may help decision-makers to anticipate the effects of sea-level rise on fresh groundwater availability in oceanic island aquifers.

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.

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.

Agent-based model for the h-index - exact solution

NASA Astrophysics Data System (ADS)

Żogała-Siudem, Barbara; Siudem, Grzegorz; Cena, Anna; Gagolewski, Marek

2016-01-01

Hirsch's h-index is perhaps the most popular citation-based measure of scientific excellence. In 2013, Ionescu and Chopard proposed an agent-based model describing a process for generating publications and citations in an abstract scientific community [G. Ionescu, B. Chopard, Eur. Phys. J. B 86, 426 (2013)]. Within such a framework, one may simulate a scientist's activity, and - by extension - investigate the whole community of researchers. Even though the Ionescu and Chopard model predicts the h-index quite well, the authors provided a solution based solely on simulations. In this paper, we complete their results with exact, analytic formulas. What is more, by considering a simplified version of the Ionescu-Chopard model, we obtained a compact, easy to compute formula for the h-index. The derived approximate and exact solutions are investigated on a simulated and real-world data sets.

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.

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

NASA Astrophysics Data System (ADS)

Saberi, Elaheh; Reza Hejazi, S.

2018-02-01

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

Complete factorisation and analytic solutions of generalized Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Brenig, L.

1988-11-01

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

Pressure-coupled combustion response model for solid propellants based on Zeldovich-Novozhilov approach

NASA Technical Reports Server (NTRS)

Harstad, K. G.; Strand, L. D.

1987-01-01

An exact analytical solution is given to the problem of long-time propellant thermal response to a specified pressure oscillation. Coupling to the gas phase is made using the quasisteady Zeldovich-Novozhilov approximation. Explicit linear and lowest order (quadratic) nonlinear expressions for propellant response are obtained from the implicit nonlinear solutions. Using these expressions, response curves are presented for an ammonium perchlorate composite propellant and HMX monopropellant.

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.

On the nullspace of TLS multi-station adjustment

NASA Astrophysics Data System (ADS)

Sterle, Oskar; Kogoj, Dušan; Stopar, Bojan; Kregar, Klemen

2018-07-01

In the article we present an analytic aspect of TLS multi-station least-squares adjustment with the main focus on the datum problem. The datum problem is, compared to previously published researches, theoretically analyzed and solved, where the solution is based on nullspace derivation of the mathematical model. The importance of datum problem solution is seen in a complete description of TLS multi-station adjustment solutions from a set of all minimally constrained least-squares solutions. On a basis of known nullspace, estimable parameters are described and the geometric interpretation of all minimally constrained least squares solutions is presented. At the end a simulated example is used to analyze the results of TLS multi-station minimally constrained and inner constrained least-squares adjustment solutions.

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.

BIOCHLOR: NATURAL ATTENUATION DECISION SUPPORT SYSTEM, USER'S MANUAL, VERSION 1.0

EPA Science Inventory

BIOCHLOR is an easy-to-use screening model that simulates remediation by natural attenuation (RNA) of dissolved solvents at chlorinated solvent release sites. The software, programmed in the Microsoft Excel spreadsheet environment and based on the Domenico analytical solute tran...

A Semi-Analytical Model for Dispersion Modelling Studies in the Atmospheric Boundary Layer

NASA Astrophysics Data System (ADS)

Gupta, A.; Sharan, M.

2017-12-01

The severe impact of harmful air pollutants has always been a cause of concern for a wide variety of air quality analysis. The analytical models based on the solution of the advection-diffusion equation have been the first and remain the convenient way for modeling air pollutant dispersion as it is easy to handle the dispersion parameters and related physics in it. A mathematical model describing the crosswind integrated concentration is presented. The analytical solution to the resulting advection-diffusion equation is limited to a constant and simple profiles of eddy diffusivity and wind speed. In practice, the wind speed depends on the vertical height above the ground and eddy diffusivity profiles on the downwind distance from the source as well as the vertical height. In the present model, a method of eigen-function expansion is used to solve the resulting partial differential equation with the appropriate boundary conditions. This leads to a system of first order ordinary differential equations with a coefficient matrix depending on the downwind distance. The solution of this system, in general, can be expressed in terms of Peano-baker series which is not easy to compute, particularly when the coefficient matrix becomes non-commutative (Martin et al., 1967). An approach based on Taylor's series expansion is introduced to find the numerical solution of first order system. The method is applied to various profiles of wind speed and eddy diffusivities. The solution computed from the proposed methodology is found to be efficient and accurate in comparison to those available in the literature. The performance of the model is evaluated with the diffusion datasets from Copenhagen (Gryning et al., 1987) and Hanford (Doran et al., 1985). In addition, the proposed method is used to deduce three dimensional concentrations by considering the Gaussian distribution in crosswind direction, which is also evaluated with diffusion data corresponding to a continuous point source.

Analytical analysis of the temporal asymmetry between seawater intrusion and retreat

NASA Astrophysics Data System (ADS)

Rathore, Saubhagya Singh; Zhao, Yue; Lu, Chunhui; Luo, Jian

2018-01-01

The quantification of timescales associated with the movement of the seawater-freshwater interface is useful for developing effective management strategies for controlling seawater intrusion (SWI). In this study, for the first time, we derive an explicit analytical solution for the timescales of SWI and seawater retreat (SWR) in a confined, homogeneous coastal aquifer system under the quasi-steady assumption, based on a classical sharp-interface solution for approximating freshwater outflow rates into the sea. The flow continuity and hydrostatic equilibrium across the interface are identified as two primary mechanisms governing timescales of the interface movement driven by an abrupt change in discharge rates or hydraulic heads at the inland boundary. Through theoretical analysis, we quantified the dependence of interface-movement timescales on porosity, hydraulic conductivity, aquifer thickness, aquifer length, density ratio, and boundary conditions. Predictions from the analytical solution closely agreed with those from numerical simulations. In addition, we define a temporal asymmetry index (the ratio of the SWI timescale to the SWR timescale) to represent the resilience of the coastal aquifer in response to SWI. The developed analytical solutions provide a simple tool for the quick assessment of SWI and SWR timescales and reveal that the temporal asymmetry between SWI and SWR mainly relies on the initial and final values of the freshwater flux at the inland boundary, and is weakly affected by aquifer parameters. Furthermore, we theoretically examined the log-linearity relationship between the timescale and the freshwater flux at the inland boundary, and found that the relationship may be approximated by two linear functions with a slope of -2 and -1 for large changes at the boundary flux for SWI and SWR, respectively.

Randomization-Based Inference about Latent Variables from Complex Samples: The Case of Two-Stage Sampling

ERIC Educational Resources Information Center

Li, Tiandong

2012-01-01

In large-scale assessments, such as the National Assessment of Educational Progress (NAEP), plausible values based on Multiple Imputations (MI) have been used to estimate population characteristics for latent constructs under complex sample designs. Mislevy (1991) derived a closed-form analytic solution for a fixed-effect model in creating…

Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

DOE PAGES

Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; ...

2015-07-10

Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes themore » rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight into the shock structure afforded by the numerical methods.« less

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.

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.

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.

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.

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.

Reversible thrombin detection by aptamer functionalized STING sensors.

PubMed

Actis, Paolo; Rogers, Adam; Nivala, Jeff; Vilozny, Boaz; Seger, R Adam; Jejelowo, Olufisayo; Pourmand, Nader

2011-07-15

Signal Transduction by Ion NanoGating (STING) is a label-free technology based on functionalized quartz nanopipettes. The nanopipette pore can be decorated with a variety of recognition elements and the molecular interaction is transduced via a simple electrochemical system. A STING sensor can be easily and reproducibly fabricated and tailored at the bench starting from inexpensive quartz capillaries. The analytical application of this new biosensing platform, however, was limited due to the difficult correlation between the measured ionic current and the analyte concentration in solution. Here we show that STING sensors functionalized with aptamers allow the quantitative detection of thrombin. The binding of thrombin generates a signal that can be directly correlated to its concentration in the bulk solution. Copyright © 2011 Elsevier B.V. All rights reserved.

Development of computer-based analytical tool for assessing physical protection system

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

Mardhi, Alim, E-mail: alim-m@batan.go.id; Chulalongkorn University, Faculty of Engineering, Nuclear Engineering Department, 254 Phayathai Road, Pathumwan, Bangkok Thailand. 10330; Pengvanich, Phongphaeth, E-mail: ppengvan@gmail.com

Assessment of physical protection system effectiveness is the priority for ensuring the optimum protection caused by unlawful acts against a nuclear facility, such as unauthorized removal of nuclear materials and sabotage of the facility itself. Since an assessment based on real exercise scenarios is costly and time-consuming, the computer-based analytical tool can offer the solution for approaching the likelihood threat scenario. There are several currently available tools that can be used instantly such as EASI and SAPE, however for our research purpose it is more suitable to have the tool that can be customized and enhanced further. In this work,more » we have developed a computer–based analytical tool by utilizing the network methodological approach for modelling the adversary paths. The inputs are multi-elements in security used for evaluate the effectiveness of the system’s detection, delay, and response. The tool has capability to analyze the most critical path and quantify the probability of effectiveness of the system as performance measure.« less

Prediction of Time Response of Electrowetting

NASA Astrophysics Data System (ADS)

Lee, Seung Jun; Hong, Jiwoo; Kang, Kwan Hyoung

2009-11-01

It is very important to predict the time response of electrowetting-based devices, such as liquid lenses, reflective displays, and optical switches. We investigated the time response of electrowetting, based on an analytical and a numerical method, to find out characteristic scales and a scaling law for the switching time. For this, spreading process of a sessile droplet was analyzed based on the domain perturbation method. First, we considered the case of weakly viscous fluids. The analytical result for the spreading process was compared with experimental results, which showed very good agreement in overall time response. It was shown that the overall dynamics is governed by P2 shape mode. We derived characteristic scales combining the droplet volume, density, and surface tension. The overall dynamic process was scaled quite well by the scales. A scaling law was derived from the analytical solution and was verified experimentally. We also suggest a scaling law for highly viscous liquids, based on results of numerical analysis for the electrowetting-actuated spreading process.

Development of computer-based analytical tool for assessing physical protection system

NASA Astrophysics Data System (ADS)

Mardhi, Alim; Pengvanich, Phongphaeth

2016-01-01

Assessment of physical protection system effectiveness is the priority for ensuring the optimum protection caused by unlawful acts against a nuclear facility, such as unauthorized removal of nuclear materials and sabotage of the facility itself. Since an assessment based on real exercise scenarios is costly and time-consuming, the computer-based analytical tool can offer the solution for approaching the likelihood threat scenario. There are several currently available tools that can be used instantly such as EASI and SAPE, however for our research purpose it is more suitable to have the tool that can be customized and enhanced further. In this work, we have developed a computer-based analytical tool by utilizing the network methodological approach for modelling the adversary paths. The inputs are multi-elements in security used for evaluate the effectiveness of the system's detection, delay, and response. The tool has capability to analyze the most critical path and quantify the probability of effectiveness of the system as performance measure.

An accelerated photo-magnetic imaging reconstruction algorithm based on an analytical forward solution and a fast Jacobian assembly method

NASA Astrophysics Data System (ADS)

Nouizi, F.; Erkol, H.; Luk, A.; Marks, M.; Unlu, M. B.; Gulsen, G.

2016-10-01

We previously introduced photo-magnetic imaging (PMI), an imaging technique that illuminates the medium under investigation with near-infrared light and measures the induced temperature increase using magnetic resonance thermometry (MRT). Using a multiphysics solver combining photon migration and heat diffusion, PMI models the spatiotemporal distribution of temperature variation and recovers high resolution optical absorption images using these temperature maps. In this paper, we present a new fast non-iterative reconstruction algorithm for PMI. This new algorithm uses analytic methods during the resolution of the forward problem and the assembly of the sensitivity matrix. We validate our new analytic-based algorithm with the first generation finite element method (FEM) based reconstruction algorithm previously developed by our team. The validation is performed using, first synthetic data and afterwards, real MRT measured temperature maps. Our new method accelerates the reconstruction process 30-fold when compared to a single iteration of the FEM-based algorithm.

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.

The factor structure of the Alcohol Use Disorders Identification Test (AUDIT).

PubMed

Doyle, Suzanne R; Donovan, Dennis M; Kivlahan, Daniel R

2007-05-01

Past research assessing the factor structure of the Alcohol Use Disorders Identification Test (AUDIT) with various exploratory and confirmatory factor analytic techniques has identified one-, two-, and three-factor solutions. Because different factor analytic procedures may result in dissimilar findings, we examined the factor structure of the AUDIT using the same factor analytic technique on two new large clinical samples and on archival data from six samples studied in previous reports. Responses to the AUDIT were obtained from participants who met Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition (DSM-IV), criteria for alcohol dependence in two large randomized clinical trials: the COMBINE (Combining Medications and Behavioral Interventions) Study (N = 1,337; 69% men) and Project MATCH (Matching Alcoholism Treatments to Client Heterogeneity; N = 1,711; 76% men). Supplementary analyses involved six correlation matrices of AUDIT data obtained from five previously published articles. Confirmatory factor analyses based on one-, two-, and three-factor models were conducted on the eight correlation matrices to assess the factor structure of the AUDIT. Across samples, analyses supported a correlated, two-factor solution representing alcohol consumption and alcohol-related consequences. The three-factor solution fit the data equally well, but two factors (alcohol dependence and harmful alcohol use) were highly correlated. The one-factor solution did not provide a good fit to the data. These findings support a two-factor solution for the AUDIT (alcohol consumption and alcohol-related consequences). The results contradict the original three-factor design of the AUDIT and the prevalent use of the AUDIT as a one-factor screening instrument with a single cutoff score.

Cross-Disciplinary Consultancy to Bridge Public Health Technical Needs and Analytic Developers: Asyndromic Surveillance Use Case

PubMed Central

Faigen, Zachary; Deyneka, Lana; Ising, Amy; Neill, Daniel; Conway, Mike; Fairchild, Geoffrey; Gunn, Julia; Swenson, David; Painter, Ian; Johnson, Lauren; Kiley, Chris; Streichert, Laura

2015-01-01

Introduction: We document a funded effort to bridge the gap between constrained scientific challenges of public health surveillance and methodologies from academia and industry. Component tasks are the collection of epidemiologists’ use case problems, multidisciplinary consultancies to refine them, and dissemination of problem requirements and shareable datasets. We describe an initial use case and consultancy as a concrete example and challenge to developers. Materials and Methods: Supported by the Defense Threat Reduction Agency Biosurveillance Ecosystem project, the International Society for Disease Surveillance formed an advisory group to select tractable use case problems and convene inter-disciplinary consultancies to translate analytic needs into well-defined problems and to promote development of applicable solution methods. The initial consultancy’s focus was a problem originated by the North Carolina Department of Health and its NC DETECT surveillance system: Derive a method for detection of patient record clusters worthy of follow-up based on free-text chief complaints and without syndromic classification. Results: Direct communication between public health problem owners and analytic developers was informative to both groups and constructive for the solution development process. The consultancy achieved refinement of the asyndromic detection challenge and of solution requirements. Participants summarized and evaluated solution approaches and discussed dissemination and collaboration strategies. Practice Implications: A solution meeting the specification of the use case described above could improve human monitoring efficiency with expedited warning of events requiring follow-up, including otherwise overlooked events with no syndromic indicators. This approach can remove obstacles to collaboration with efficient, minimal data-sharing and without costly overhead. PMID:26834939

Cross-Disciplinary Consultancy to Bridge Public Health Technical Needs and Analytic Developers: Asyndromic Surveillance Use Case.

PubMed

Faigen, Zachary; Deyneka, Lana; Ising, Amy; Neill, Daniel; Conway, Mike; Fairchild, Geoffrey; Gunn, Julia; Swenson, David; Painter, Ian; Johnson, Lauren; Kiley, Chris; Streichert, Laura; Burkom, Howard

2015-01-01

We document a funded effort to bridge the gap between constrained scientific challenges of public health surveillance and methodologies from academia and industry. Component tasks are the collection of epidemiologists' use case problems, multidisciplinary consultancies to refine them, and dissemination of problem requirements and shareable datasets. We describe an initial use case and consultancy as a concrete example and challenge to developers. Supported by the Defense Threat Reduction Agency Biosurveillance Ecosystem project, the International Society for Disease Surveillance formed an advisory group to select tractable use case problems and convene inter-disciplinary consultancies to translate analytic needs into well-defined problems and to promote development of applicable solution methods. The initial consultancy's focus was a problem originated by the North Carolina Department of Health and its NC DETECT surveillance system: Derive a method for detection of patient record clusters worthy of follow-up based on free-text chief complaints and without syndromic classification. Direct communication between public health problem owners and analytic developers was informative to both groups and constructive for the solution development process. The consultancy achieved refinement of the asyndromic detection challenge and of solution requirements. Participants summarized and evaluated solution approaches and discussed dissemination and collaboration strategies. A solution meeting the specification of the use case described above could improve human monitoring efficiency with expedited warning of events requiring follow-up, including otherwise overlooked events with no syndromic indicators. This approach can remove obstacles to collaboration with efficient, minimal data-sharing and without costly overhead.

A highly reproducible solenoid micropump system for the analysis of total inorganic carbon and ammonium using gas-diffusion with conductimetric detection.

PubMed

Henríquez, Camelia; Horstkotte, Burkhard; Cerdà, Víctor

2014-01-01

In this work, a simple, economic, and miniaturized flow-based analyzer based on solenoid micropumps is presented. It was applied to determine two parameters of high environmental interest: ammonium and total inorganic carbon (TIC) in natural waters. The method is based on gas diffusion (GD) of CO₂ and NH3 through a hydrophobic gas permeable membrane from an acidic or alkaline donor stream, respectively. The analytes are trapped in an acceptor solution, being slightly alkaline for CO₂ and slightly acidic for NH₃. The analytes are quantified using a homemade stainless steel conductimetric cell. The proposed system required five solenoid micro-pumps, one for each reagent and sample. Two especially made air bubble traps were placed down-stream of the solendoid pumps, which provided the acceptor solutions, by this increasing the method's reproducibility. Values of RSD lower than 1% were obtained. Achieved limits of detection were 0.27 µmol L⁻¹ for NH₄⁺ and 50 µmol L⁻¹ for TIC. Add-recovery tests were used to prove the trueness of the method and recoveries of 99.5 ± 7.5% were obtained for both analytes. The proposed system proved to be adequate for monitoring purpose of TIC and NH₄⁺ due to its high sample throughput and repeatability. © 2013 Published by Elsevier B.V.

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.

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

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.

Analyticity in Time and Smoothing Effect of Solutions to Nonlinear Schrödinger Equations

NASA Astrophysics Data System (ADS)

Hayashi, Nakao; Kato, Keiichi

In this paper we consider analyticity in time and smoothing effect of solutions to nonlinear Schrödinger equations where . We prove that if φ satisfies then there exists a unique solution of (1) and positive constants T, C0, C1 such that is analytic in time and space variables for and and has an analytic continuation on and In the case the condition (2) can be relaxed as follows: where m= 0 if n= 1, p= 1, m= 1 if n= 2, and m= 1 if n= 3, p= 1.

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 octagonal honeycombs.

PubMed

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

2016-12-01

Honeycomb structures have found numerous applications as structural and biomedical materials due to their favourable properties such as low weight, high stiffness, and porosity. Application of additive manufacturing and 3D printing techniques allows for manufacturing of honeycombs with arbitrary shape and wall thickness, opening the way for optimizing the mechanical and physical properties for specific applications. In this study, the mechanical properties of honeycomb structures with a new geometry, called octagonal honeycomb, were investigated using analytical, numerical, and experimental approaches. An additive manufacturing technique, namely fused deposition modelling, was used to fabricate the honeycomb from polylactic acid (PLA). The honeycombs structures were then mechanically tested under compression and the mechanical properties of the structures were determined. In addition, the Euler-Bernoulli and Timoshenko beam theories were used for deriving analytical relationships for elastic modulus, yield stress, Poisson's ratio, and buckling stress of this new design of honeycomb structures. Finite element models were also created to analyse the mechanical behaviour of the honeycombs computationally. The analytical solutions obtained using Timoshenko beam theory were close to computational results in terms of elastic modulus, Poisson's ratio and yield stress, especially for relative densities smaller than 25%. The analytical solutions based on the Timoshenko analytical solution and the computational results were in good agreement with experimental observations. Finally, the elastic properties of the proposed honeycomb structure were compared to those of other honeycomb structures such as square, triangular, hexagonal, mixed, diamond, and Kagome. The octagonal honeycomb showed yield stress and elastic modulus values very close to those of regular hexagonal honeycombs and lower than the other considered honeycombs. Copyright © 2016 Elsevier B.V. All rights reserved.

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.

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.

Colorimetric and Fluorescent Biosensors Based on Directed Assembly of Nanomaterials with Functional DNA

NASA Astrophysics Data System (ADS)

Liu, Juewen; Lu, Yi

This chapter reviews recent progress in the interface between functional nucleic acids and nanoscale science and technology, and its analytical applications. In particular, the use of metallic nanoparticles as the color reporting groups for the action (binding, catalysis, or both) of aptamers, DNAzymes, and aptazymes is described in detail. Because metallic nanoparticles possess high extinction coefficients and distance-dependent optical properties, they allow highly sensitive detections with minimal consumption of materials. The combination of quantum dots (QDs) with functional nucleic acids as fluorescent sensors is also described. The chapter starts with the design of colorimetric and fluorescent sensors responsive to single analytes, followed by sensors responsive to multiple analytes with controllable cooperativity and multiplex detection using both colorimetric and fluorescent signals in one pot, and ends by transferring solution-based detections into litmus paper type of tests, making them generally applicable and usable for a wide range of on-site and real-time analytical applications such as household tests, environmental monitoring, and clinical diagnostics.

Electrochemical Enzyme Biosensors Revisited: Old Solutions for New Problems.

PubMed

Monteiro, Tiago; Almeida, Maria Gabriela

2018-05-14

Worldwide legislation is driving the development of novel and highly efficient analytical tools for assessing the composition of every material that interacts with Consumers or Nature. The biosensor technology is one of the most active R&D domains of Analytical Sciences focused on the challenge of taking analytical chemistry to the field. Electrochemical biosensors based on redox enzymes, in particular, are highly appealing due to their usual quick response, high selectivity and sensitivity, low cost and portable dimensions. This review paper aims to provide an overview of the most important advances made in the field since the proposal of the first biosensor, the well-known hand-held glucose meter. The first section addresses the current needs and challenges for novel analytical tools, followed by a brief description of the different components and configurations of biosensing devices, and the fundamentals of enzyme kinetics and amperometry. The following sections emphasize on enzyme-based amperometric biosensors and the different stages of their development.

Three-dimensional time-dependent computer modeling of the electrothermal atomizers for analytical spectrometry

NASA Astrophysics Data System (ADS)

Tsivilskiy, I. V.; Nagulin, K. Yu.; Gilmutdinov, A. Kh.

2016-02-01

A full three-dimensional nonstationary numerical model of graphite electrothermal atomizers of various types is developed. The model is based on solution of a heat equation within solid walls of the atomizer with a radiative heat transfer and numerical solution of a full set of Navier-Stokes equations with an energy equation for a gas. Governing equations for the behavior of a discrete phase, i.e., atomic particles suspended in a gas (including gas-phase processes of evaporation and condensation), are derived from the formal equations molecular kinetics by numerical solution of the Hertz-Langmuir equation. The following atomizers test the model: a Varian standard heated electrothermal vaporizer (ETV), a Perkin Elmer standard THGA transversely heated graphite tube with integrated platform (THGA), and the original double-stage tube-helix atomizer (DSTHA). The experimental verification of computer calculations is carried out by a method of shadow spectral visualization of the spatial distributions of atomic and molecular vapors in an analytical space of an atomizer.

Joule heating induced stream broadening in free-flow zone electrophoresis.

PubMed

Dutta, Debashis

2018-03-01

The use of an electric field in free-flow zone electrophoresis (FFZE) automatically leads to Joule heating yielding a higher temperature at the center of the separation chamber relative to that around the channel walls. For small amounts of heat generated, this thermal effect introduces a variation in the equilibrium position of the analyte molecules due to the dependence of liquid viscosity and analyte diffusivity on temperature leading to a modification in the position of the analyte stream as well as the zone width. In this article, an analytic theory is presented to quantitate such effects of Joule heating on FFZE assays in the limit of small temperature differentials across the channel gap yielding a closed form expression for the stream position and zone variance under equilibrium conditions. A method-of-moments approach is employed to develop this analytic theory, which is further validated with numerical solutions of the governing equations. Interestingly, the noted analyses predict that Joule heating can drift the location of the analyte stream either way of its equilibrium position realized in the absence of any temperature rise in the system, and also tends to reduce zone dispersion. The extent of these modifications, however, is governed by the electric field induced temperature rise and three Péclet numbers evaluated based on the axial pressure-driven flow, transverse electroosmotic and electrophoretic solute velocities in the separation chamber. Monte Carlo simulations of the FFZE system further establish a time and a length scale over which the results from the analytic theory are valid. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Class and Home Problems. The Lambert W Function in Ultrafiltration and Diafiltration

ERIC Educational Resources Information Center

Foley, Greg

2016-01-01

Novel analytical solutions based on the Lambert W function for two problems in ultrafiltration and diafiltration are described. Example problems, suitable for incorporation into an introductory module in unit operations, membrane processing, or numerical methods are provided in each case.

Optimal time-domain technique for pulse width modulation in power electronics

NASA Astrophysics Data System (ADS)

Mayergoyz, I.; Tyagi, S.

2018-05-01

Optimal time-domain technique for pulse width modulation is presented. It is based on exact and explicit analytical solutions for inverter circuits, obtained for any sequence of input voltage rectangular pulses. Two optimal criteria are discussed and illustrated by numerical examples.

Analytical method for predicting the pressure distribution about a nacelle at transonic speeds

NASA Technical Reports Server (NTRS)

Keith, J. S.; Ferguson, D. R.; Merkle, C. L.; Heck, P. H.; Lahti, D. J.

1973-01-01

The formulation and development of a computer analysis for the calculation of streamlines and pressure distributions around two-dimensional (planar and axisymmetric) isolated nacelles at transonic speeds are described. The computerized flow field analysis is designed to predict the transonic flow around long and short high-bypass-ratio fan duct nacelles with inlet flows and with exhaust flows having appropriate aerothermodynamic properties. The flow field boundaries are located as far upstream and downstream as necessary to obtain minimum disturbances at the boundary. The far-field lateral flow field boundary is analytically defined to exactly represent free-flight conditions or solid wind tunnel wall effects. The inviscid solution technique is based on a Streamtube Curvature Analysis. The computer program utilizes an automatic grid refinement procedure and solves the flow field equations with a matrix relaxation technique. The boundary layer displacement effects and the onset of turbulent separation are included, based on the compressible turbulent boundary layer solution method of Stratford and Beavers and on the turbulent separation prediction method of Stratford.

Probabilistic dual heuristic programming-based adaptive critic

NASA Astrophysics Data System (ADS)

Herzallah, Randa

2010-02-01

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.

Using business intelligence for efficient inter-facility patient transfer.

PubMed

Haque, Waqar; Derksen, Beth Ann; Calado, Devin; Foster, Lee

2015-01-01

In the context of inter-facility patient transfer, a transfer operator must be able to objectively identify a destination which meets the needs of a patient, while keeping in mind each facility's limitations. We propose a solution which uses Business Intelligence (BI) techniques to analyze data related to healthcare infrastructure and services, and provides a web based system to identify optimal destination(s). The proposed inter-facility transfer system uses a single data warehouse with an Online Analytical Processing (OLAP) cube built on top that supplies analytical data to multiple reports embedded in web pages. The data visualization tool includes map based navigation of the health authority as well as an interactive filtering mechanism which finds facilities meeting the selected criteria. The data visualization is backed by an intuitive data entry web form which safely constrains the data, ensuring consistency and a single version of truth. The overall time required to identify the destination for inter-facility transfers is reduced from hours to a few minutes with this interactive solution.

Resonant tunneling assisted propagation and amplification of plasmons in high electron mobility transistors

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

Bhardwaj, Shubhendu; Sensale-Rodriguez, Berardi; Xing, Huili Grace

A rigorous theoretical and computational model is developed for the plasma-wave propagation in high electron mobility transistor structures with electron injection from a resonant tunneling diode at the gate. We discuss the conditions in which low-loss and sustainable plasmon modes can be supported in such structures. The developed analytical model is used to derive the dispersion relation for these plasmon-modes. A non-linear full-wave-hydrodynamic numerical solver is also developed using a finite difference time domain algorithm. The developed analytical solutions are validated via the numerical solution. We also verify previous observations that were based on a simplified transmission line model. Itmore » is shown that at high levels of negative differential conductance, plasmon amplification is indeed possible. The proposed rigorous models can enable accurate design and optimization of practical resonant tunnel diode-based plasma-wave devices for terahertz sources, mixers, and detectors, by allowing a precise representation of their coupling when integrated with other electromagnetic structures.« less

Evaluation of groundwater pollution in a mining area using analytical solution: a case study of the Yimin open-pit mine in China.

PubMed

Li, Tianxin; Li, Li; Song, Hongqing; Meng, Linglong; Zhang, Shuli; Huang, Gang

2016-01-01

This study focused on using analytical and numerical models to develop and manage groundwater resources, and predict the effects of management measurements in the groundwater system. Movement of contaminants can be studied based on groundwater flow characteristics. This study can be used for prediction of ion concentration and evaluation of groundwater pollution as the theoretical basis. The Yimin open-pit mine is located in the northern part of the Inner Mongolia Autonomous Region of China. High concentrations of iron and manganese are observed in Yimin open-pit mine because of exploitation and pumping that have increased the concentration of the ions in groundwater. In this study, iron was considered as an index of contamination, and the solute model was calibrated using concentration observations from 14 wells in 2014. The groundwater flow model and analytical solutions were used in this study to forecast pollution concentration and variation trend after calibration. With continuous pumping, contaminants will migrate, and become enriched, towards the wellhead in the flow direction. The concentration of the contaminants and the range of pollution increase with the flow rate increased. The suitable flow rate of single well should be <380 m/day at Yimin open-pit for the standard value of pollution concentration.

Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

NASA Astrophysics Data System (ADS)

Chae, Jongchul; Litvinenko, Yuri E.

2017-08-01

The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na I D2 and Hα lines.

Amine-capped ZnS-Mn2+ nanocrystals for fluorescence detection of trace TNT explosive.

PubMed

Tu, Renyong; Liu, Bianhua; Wang, Zhenyang; Gao, Daming; Wang, Feng; Fang, Qunling; Zhang, Zhongping

2008-05-01

Mn2+-doped ZnS nanocrystals with an amine-capping layer have been synthesized and used for the fluorescence detection of ultratrace 2,4,6-trinitrotoluene (TNT) by quenching the strong orange Mn2+ photoluminescence. The organic amine-capped nanocrystals can bind TNT species from solution and atmosphere by the acid-base pairing interaction between electron-rich amino ligands and electron-deficient aromatic rings. The resultant TNT anions bound onto the amino monolayer can efficiently quench the Mn2+ photoluminescence through the electron transfer from the conductive band of ZnS to the lowest unoccupied molecular orbital (LUMO) of TNT anions. The amino ligands provide an amplified response to the binding events of nitroaromatic compounds by the 2- to approximately 5-fold increase in quenching constants. Moreover, a large difference in quenching efficiency was observed for different types of nitroaromatic analytes, dependent on the affinity of nitro analytes to the amino monolayer and their electron-accepting abilities. The amine-capped nanocrystals can sensitively detect down to 1 nM TNT in solution or several parts-per-billion of TNT vapor in atmosphere. The ion-doped nanocrystal sensors reported here show a remarkable air/solution stability, high quantum yield, and strong analyte affinity and, therefore, are well-suited for detecting the ultratrace TNT and distinguishing different nitro compounds.

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.

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.

Constrained reduced-order models based on proper orthogonal decomposition

DOE PAGES

Reddy, Sohail R.; Freno, Brian Andrew; Cizmas, Paul G. A.; ...

2017-04-09

A novel approach is presented to constrain reduced-order models (ROM) based on proper orthogonal decomposition (POD). The Karush–Kuhn–Tucker (KKT) conditions were applied to the traditional reduced-order model to constrain the solution to user-defined bounds. The constrained reduced-order model (C-ROM) was applied and validated against the analytical solution to the first-order wave equation. C-ROM was also applied to the analysis of fluidized beds. Lastly, it was shown that the ROM and C-ROM produced accurate results and that C-ROM was less sensitive to error propagation through time than the ROM.

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

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

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

1979-03-01

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

Analytical and numerical 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.

Exact solutions for laminated composite cylindrical shells in cylindrical bending

NASA Technical Reports Server (NTRS)

Yuan, F. G.

1992-01-01

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

Analysis of 14C-bearing compounds released by the corrosion of irradiated steel using accelerator mass spectrometry.

PubMed

Cvetković, B Z; Salazar, G; Kunz, D; Szidat, S; Wieland, E

2018-06-25

The combination of ion chromatography (IC) with accelerator mass spectrometry (AMS) was developed to determine the speciation of 14C-(radiocarbon) bearing organic compounds in the femto to pico molar concentration range. The development of this compound-specific radiocarbon analysis (CSRA) of carboxylic acids is reported and the application of the method on a leaching solution from neutron-irradiated steel is demonstrated. The background and the dynamic range of the AMS-based method were quantified. On using 14C-labelled standards, the measurements demonstrate the repeatability of the analytical method and the reproducible recovery of the main target carboxylic acids (i.e., acetate, formate, malonate, and oxalate). The detection limit was determined to be in the mid fmol 14C per L level while the dynamic range of the analytical method covers three orders of magnitude from the low fmol to the mid pmol 14C per L level. Cross contamination was found to be negligible during IC fractionation and was accounted for during eluate processing and 14C detection by AMS. The 14C-bearing carboxylates released from an irradiated steel nut into an alkaline leaching solution were analysed using the CSRA-based analytical method with the aim to check the applicability of the approach and develop appropriate sample preparation. The concentrations of 14C-bearing formate and acetate, the main organic corrosion products, were at a low pmol 14C per L level for convenient dimensions of the alkaline leaching experiment which demonstrates that compound-specific 14C AMS is an extremely sensitive analytical method for analysing 14C-bearing compounds. The content of total organic 14C in solution (TO14C) determined by the direct measurement of an aliquot of the leaching solution agrees well with the sum of the 14C concentrations of the individual carboxylates within the uncertainty of the data. Furthermore, the TO14C content is in good agreement with the calculated value using the corrosion rate determined from the 60Co release and the 14C inventory of the irradiated steel specimen.

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.

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

Supersymmetric quantum mechanics method for the Fokker-Planck equation with applications to protein folding dynamics

NASA Astrophysics Data System (ADS)

Polotto, Franciele; Drigo Filho, Elso; Chahine, Jorge; Oliveira, Ronaldo Junio de

2018-03-01

This work developed analytical methods to explore the kinetics of the time-dependent probability distributions over thermodynamic free energy profiles of protein folding and compared the results with simulation. The Fokker-Planck equation is mapped onto a Schrödinger-type equation due to the well-known solutions of the latter. Through a semi-analytical description, the supersymmetric quantum mechanics formalism is invoked and the time-dependent probability distributions are obtained with numerical calculations by using the variational method. A coarse-grained structure-based model of the two-state protein Tm CSP was simulated at a Cα level of resolution and the thermodynamics and kinetics were fully characterized. Analytical solutions from non-equilibrium conditions were obtained with the simulated double-well free energy potential and kinetic folding times were calculated. It was found that analytical folding time as a function of temperature agrees, quantitatively, with simulations and experiments from the literature of Tm CSP having the well-known 'U' shape of the Chevron Plots. The simple analytical model developed in this study has a potential to be used by theoreticians and experimentalists willing to explore, quantitatively, rates and the kinetic behavior of their system by informing the thermally activated barrier. The theory developed describes a stochastic process and, therefore, can be applied to a variety of biological as well as condensed-phase two-state systems.

Uncertainty Estimation for the Determination of Ni, Pb and Al in Natural Water Samples by SPE-ICP-OES

NASA Astrophysics Data System (ADS)

Ghorbani, A.; Farahani, M. Mahmoodi; Rabbani, M.; Aflaki, F.; Waqifhosain, Syed

2008-01-01

In this paper we propose uncertainty estimation for the analytical results we obtained from determination of Ni, Pb and Al by solidphase extraction and inductively coupled plasma optical emission spectrometry (SPE-ICP-OES). The procedure is based on the retention of analytes in the form of 8-hydroxyquinoline (8-HQ) complexes on a mini column of XAD-4 resin and subsequent elution with nitric acid. The influence of various analytical parameters including the amount of solid phase, pH, elution factors (concentration and volume of eluting solution), volume of sample solution, and amount of ligand on the extraction efficiency of analytes was investigated. To estimate the uncertainty of analytical result obtained, we propose assessing trueness by employing spiked sample. Two types of bias are calculated in the assessment of trueness: a proportional bias and a constant bias. We applied Nested design for calculating proportional bias and Youden method to calculate the constant bias. The results we obtained for proportional bias are calculated from spiked samples. In this case, the concentration found is plotted against the concentration added and the slop of standard addition curve is an estimate of the method recovery. Estimated method of average recovery in Karaj river water is: (1.004±0.0085) for Ni, (0.999±0.010) for Pb and (0.987±0.008) for Al.

Optimal guidance law development for an advanced launch system

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Leung, Martin S. K.

1995-01-01

The objective of this research effort was to develop a real-time guidance approach for launch vehicles ascent to orbit injection. Various analytical approaches combined with a variety of model order and model complexity reduction have been investigated. Singular perturbation methods were first attempted and found to be unsatisfactory. The second approach based on regular perturbation analysis was subsequently investigated. It also fails because the aerodynamic effects (ignored in the zero order solution) are too large to be treated as perturbations. Therefore, the study demonstrates that perturbation methods alone (both regular and singular perturbations) are inadequate for use in developing a guidance algorithm for the atmospheric flight phase of a launch vehicle. During a second phase of the research effort, a hybrid analytic/numerical approach was developed and evaluated. The approach combines the numerical methods of collocation and the analytical method of regular perturbations. The concept of choosing intelligent interpolating functions is also introduced. Regular perturbation analysis allows the use of a crude representation for the collocation solution, and intelligent interpolating functions further reduce the number of elements without sacrificing the approximation accuracy. As a result, the combined method forms a powerful tool for solving real-time optimal control problems. Details of the approach are illustrated in a fourth order nonlinear example. The hybrid approach is then applied to the launch vehicle problem. The collocation solution is derived from a bilinear tangent steering law, and results in a guidance solution for the entire flight regime that includes both atmospheric and exoatmospheric flight phases.

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

PubMed

Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A

2015-12-01

Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

Electron Tomography: A Three-Dimensional Analytic Tool for Hard and Soft Materials Research.

PubMed

Ercius, Peter; Alaidi, Osama; Rames, Matthew J; Ren, Gang

2015-10-14

Three-dimensional (3D) structural analysis is essential to understand the relationship between the structure and function of an object. Many analytical techniques, such as X-ray diffraction, neutron spectroscopy, and electron microscopy imaging, are used to provide structural information. Transmission electron microscopy (TEM), one of the most popular analytic tools, has been widely used for structural analysis in both physical and biological sciences for many decades, in which 3D objects are projected into two-dimensional (2D) images. In many cases, 2D-projection images are insufficient to understand the relationship between the 3D structure and the function of nanoscale objects. Electron tomography (ET) is a technique that retrieves 3D structural information from a tilt series of 2D projections, and is gradually becoming a mature technology with sub-nanometer resolution. Distinct methods to overcome sample-based limitations have been separately developed in both physical and biological science, although they share some basic concepts of ET. This review discusses the common basis for 3D characterization, and specifies difficulties and solutions regarding both hard and soft materials research. It is hoped that novel solutions based on current state-of-the-art techniques for advanced applications in hybrid matter systems can be motivated. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Design and optimization of a nanoprobe comprising amphiphilic chitosan colloids and Au-nanorods: Sensitive detection of human serum albumin in simulated urine

NASA Astrophysics Data System (ADS)

Jean, Ren-Der; Larsson, Mikael; Cheng, Wei-Da; Hsu, Yu-Yuan; Bow, Jong-Shing; Liu, Dean-Mo

2016-12-01

Metallic nanoparticles have been utilized as analytical tools to detect a wide range of organic analytes. In most reports, gold (Au)-based nanosensors have been modified with ligands to introduce selectivity towards a specific target molecule. However, in a recent study a new concept was presented where bare Au-nanorods on self-assembled carboxymethyl-hexanoyl chitosan (CHC) nanocarriers achieved sensitive and selective detection of human serum albumin (HSA) after manipulation of the solution pH. Here this concept was further advanced through optimization of the ratio between Au-nanorods and CHC nanocarriers to create a nanotechnology-based sensor (termed CHC-AuNR nanoprobe) with an outstanding lower detection limit (LDL) for HSA. The CHC-AuNR nanoprobe was evaluated in simulated urine solution and a LDL as low as 1.5 pM was achieved at an estimated AuNR/CHC ratio of 2. Elemental mapping and protein adsorption kinetics over three orders of magnitude in HSA concentration confirmed accumulation of HSA on the nanorods and revealed the adsorption to be completed within 15 min for all investigated concentrations. The results suggest that the CHC-AuNR nanoprobe has potential to be utilized for cost-effective detection of analytes in complex liquids.

Electron Tomography: A Three-Dimensional Analytic Tool for Hard and Soft Materials Research

PubMed Central

Alaidi, Osama; Rames, Matthew J.

2016-01-01

Three-dimensional (3D) structural analysis is essential to understand the relationship between the structure and function of an object. Many analytical techniques, such as X-ray diffraction, neutron spectroscopy, and electron microscopy imaging, are used to provide structural information. Transmission electron microscopy (TEM), one of the most popular analytic tools, has been widely used for structural analysis in both physical and biological sciences for many decades, in which 3D objects are projected into two-dimensional (2D) images. In many cases, 2D-projection images are insufficient to understand the relationship between the 3D structure and the function of nanoscale objects. Electron tomography (ET) is a technique that retrieves 3D structural information from a tilt series of 2D projections, and is gradually becoming a mature technology with sub-nanometer resolution. Distinct methods to overcome sample-based limitations have been separately developed in both physical and biological science, although they share some basic concepts of ET. This review discusses the common basis for 3D characterization, and specifies difficulties and solutions regarding both hard and soft materials research. It is hoped that novel solutions based on current state-of-the-art techniques for advanced applications in hybrid matter systems can be motivated. PMID:26087941

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.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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.

Use of computer programs STLK1 and STWT1 for analysis of stream-aquifer hydraulic interaction

USGS Publications Warehouse

Desimone, Leslie A.; Barlow, Paul M.

1999-01-01

Quantifying the hydraulic interaction of aquifers and streams is important in the analysis of stream base fow, flood-wave effects, and contaminant transport between surface- and ground-water systems. This report describes the use of two computer programs, STLK1 and STWT1, to analyze the hydraulic interaction of streams with confined, leaky, and water-table aquifers during periods of stream-stage fuctuations and uniform, areal recharge. The computer programs are based on analytical solutions to the ground-water-flow equation in stream-aquifer settings and calculate ground-water levels, seepage rates across the stream-aquifer boundary, and bank storage that result from arbitrarily varying stream stage or recharge. Analysis of idealized, hypothetical stream-aquifer systems is used to show how aquifer type, aquifer boundaries, and aquifer and streambank hydraulic properties affect aquifer response to stresses. Published data from alluvial and stratifed-drift aquifers in Kentucky, Massachusetts, and Iowa are used to demonstrate application of the programs to field settings. Analytical models of these three stream-aquifer systems are developed on the basis of available hydrogeologic information. Stream-stage fluctuations and recharge are applied to the systems as hydraulic stresses. The models are calibrated by matching ground-water levels calculated with computer program STLK1 or STWT1 to measured ground-water levels. The analytical models are used to estimate hydraulic properties of the aquifer, aquitard, and streambank; to evaluate hydrologic conditions in the aquifer; and to estimate seepage rates and bank-storage volumes resulting from flood waves and recharge. Analysis of field examples demonstrates the accuracy and limitations of the analytical solutions and programs when applied to actual ground-water systems and the potential uses of the analytical methods as alternatives to numerical modeling for quantifying stream-aquifer interactions.

Relativistic electron kinetic effects on laser diagnostics in burning plasmas

NASA Astrophysics Data System (ADS)

Mirnov, V. V.; Den Hartog, D. J.

2018-02-01

Toroidal interferometry/polarimetry (TIP), poloidal polarimetry (PoPola), and Thomson scattering systems (TS) are major optical diagnostics being designed and developed for ITER. Each of them relies upon a sophisticated quantitative understanding of the electron response to laser light propagating through a burning plasma. Review of the theoretical results for two different applications is presented: interferometry/polarimetry (I/P) and polarization of Thomson scattered light, unified by the importance of relativistic (quadratic in vTe/c) electron kinetic effects. For I/P applications, rigorous analytical results are obtained perturbatively by expansion in powers of the small parameter τ = Te/me c2, where Te is electron temperature and me is electron rest mass. Experimental validation of the analytical models has been made by analyzing data of more than 1200 pulses collected from high-Te JET discharges. Based on this validation the relativistic analytical expressions are included in the error analysis and design projects of the ITER TIP and PoPola systems. The polarization properties of incoherent Thomson scattered light are being examined as a method of Te measurement relevant to ITER operational regimes. The theory is based on Stokes vector transformation and Mueller matrices formalism. The general approach is subdivided into frequency-integrated and frequency-resolved cases. For each of them, the exact analytical relativistic solutions are presented in the form of Mueller matrix elements averaged over the relativistic Maxwellian distribution function. New results related to the detailed verification of the frequency-resolved solutions are reported. The precise analytic expressions provide output much more rapidly than relativistic kinetic numerical codes allowing for direct real-time feedback control of ITER device operation.

Magnetic solid-phase extraction using carbon nanotubes as sorbents: a review.

PubMed

Herrero-Latorre, C; Barciela-García, J; García-Martín, S; Peña-Crecente, R M; Otárola-Jiménez, J

2015-09-10

Magnetic solid-phase extraction (M-SPE) is a procedure based on the use of magnetic sorbents for the separation and preconcentration of different organic and inorganic analytes from large sample volumes. The magnetic sorbent is added to the sample solution and the target analyte is adsorbed onto the surface of the magnetic sorbent particles (M-SPs). Analyte-M-SPs are separated from the sample solution by applying an external magnetic field and, after elution with the appropriate solvent, the recovered analyte is analyzed. This approach has several advantages over traditional solid phase extraction as it avoids time-consuming and tedious on-column SPE procedures and it provides a rapid and simple analyte separation that avoids the need for centrifugation or filtration steps. As a consequence, in the past few years a great deal of research has been focused on M-SPE, including the development of new sorbents and novel automation strategies. In recent years, the use of magnetic carbon nanotubes (M-CNTs) as a sorption substrate in M-SPE has become an active area of research. These materials have exceptional mechanical, electrical, optical and magnetic properties and they also have an extremely large surface area and varied possibilities for functionalization. This review covers the synthesis of M-CNTs and the different approaches for the use of these compounds in M-SPE. The performance, general characteristics and applications of M-SPE based on magnetic carbon nanotubes for organic and inorganic analysis have been evaluated on the basis of more than 110 references. Finally, some important challenges with respect the use of magnetic carbon nanotubes in M-SPE are discussed. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

Data visualisation in surveillance for injury prevention and control: conceptual bases and case studies.

PubMed

Martinez, Ramon; Ordunez, Pedro; Soliz, Patricia N; Ballesteros, Michael F

2016-04-01

The complexity of current injury-related health issues demands the usage of diverse and massive data sets for comprehensive analyses, and application of novel methods to communicate data effectively to the public health community, decision-makers and the public. Recent advances in information visualisation, availability of new visual analytic methods and tools, and progress on information technology provide an opportunity for shaping the next generation of injury surveillance. To introduce data visualisation conceptual bases, and propose a visual analytic and visualisation platform in public health surveillance for injury prevention and control. The paper introduces data visualisation conceptual bases, describes a visual analytic and visualisation platform, and presents two real-world case studies illustrating their application in public health surveillance for injury prevention and control. Application of visual analytic and visualisation platform is presented as solution for improved access to heterogeneous data sources, enhance data exploration and analysis, communicate data effectively, and support decision-making. Applications of data visualisation concepts and visual analytic platform could play a key role to shape the next generation of injury surveillance. Visual analytic and visualisation platform could improve data use, the analytic capacity, and ability to effectively communicate findings and key messages. The public health surveillance community is encouraged to identify opportunities to develop and expand its use in injury prevention and control. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

Investigations of Some Liquid Matrixes for Analyte Quantification by MALDI

NASA Astrophysics Data System (ADS)

Moon, Jeong Hee; Park, Kyung Man; Ahn, Sung Hee; Lee, Seong Hoon; Kim, Myung Soo

2015-06-01

Sample inhomogeneity is one of the obstacles preventing the generation of reproducible mass spectra by MALDI and to their use for the purpose of analyte quantification. As a potential solution to this problem, we investigated MALDI with some liquid matrixes prepared by nonstoichiometric mixing of acids and bases. Out of 27 combinations of acids and bases, liquid matrixes could be produced from seven. When the overall spectral features were considered, two liquid matrixes using α-cyano-4-hydroxycinnamic acid as the acid and 3-aminoquinoline and N,N-diethylaniline as bases were the best choices. In our previous study of MALDI with solid matrixes, we found that three requirements had to be met for the generation of reproducible spectra and for analyte quantification: (1) controlling the temperature by fixing the total ion count, (2) plotting the analyte-to-matrix ion ratio versus the analyte concentration as the calibration curve, and (3) keeping the matrix suppression below a critical value. We found that the same requirements had to be met in MALDI with liquid matrixes as well. In particular, although the liquid matrixes tested here were homogeneous, they failed to display spot-to-spot spectral reproducibility unless the first requirement above was met. We also found that analyte-derived ions could not be produced efficiently by MALDI with the above liquid matrixes unless the analyte was sufficiently basic. In this sense, MALDI processes with solid and liquid matrixes should be regarded as complementary techniques rather than as competing ones.

Investigations of Some Liquid Matrixes for Analyte Quantification by MALDI.

PubMed

Moon, Jeong Hee; Park, Kyung Man; Ahn, Sung Hee; Lee, Seong Hoon; Kim, Myung Soo

2015-10-01

Sample inhomogeneity is one of the obstacles preventing the generation of reproducible mass spectra by MALDI and to their use for the purpose of analyte quantification. As a potential solution to this problem, we investigated MALDI with some liquid matrixes prepared by nonstoichiometric mixing of acids and bases. Out of 27 combinations of acids and bases, liquid matrixes could be produced from seven. When the overall spectral features were considered, two liquid matrixes using α-cyano-4-hydroxycinnamic acid as the acid and 3-aminoquinoline and N,N-diethylaniline as bases were the best choices. In our previous study of MALDI with solid matrixes, we found that three requirements had to be met for the generation of reproducible spectra and for analyte quantification: (1) controlling the temperature by fixing the total ion count, (2) plotting the analyte-to-matrix ion ratio versus the analyte concentration as the calibration curve, and (3) keeping the matrix suppression below a critical value. We found that the same requirements had to be met in MALDI with liquid matrixes as well. In particular, although the liquid matrixes tested here were homogeneous, they failed to display spot-to-spot spectral reproducibility unless the first requirement above was met. We also found that analyte-derived ions could not be produced efficiently by MALDI with the above liquid matrixes unless the analyte was sufficiently basic. In this sense, MALDI processes with solid and liquid matrixes should be regarded as complementary techniques rather than as competing ones.

Recent Advances in Paper-Based Sensors

PubMed Central

Liana, Devi D.; Raguse, Burkhard; Gooding, J. Justin; Chow, Edith

2012-01-01

Paper-based sensors are a new alternative technology for fabricating simple, low-cost, portable and disposable analytical devices for many application areas including clinical diagnosis, food quality control and environmental monitoring. The unique properties of paper which allow passive liquid transport and compatibility with chemicals/biochemicals are the main advantages of using paper as a sensing platform. Depending on the main goal to be achieved in paper-based sensors, the fabrication methods and the analysis techniques can be tuned to fulfill the needs of the end-user. Current paper-based sensors are focused on microfluidic delivery of solution to the detection site whereas more advanced designs involve complex 3-D geometries based on the same microfluidic principles. Although paper-based sensors are very promising, they still suffer from certain limitations such as accuracy and sensitivity. However, it is anticipated that in the future, with advances in fabrication and analytical techniques, that there will be more new and innovative developments in paper-based sensors. These sensors could better meet the current objectives of a viable low-cost and portable device in addition to offering high sensitivity and selectivity, and multiple analyte discrimination. This paper is a review of recent advances in paper-based sensors and covers the following topics: existing fabrication techniques, analytical methods and application areas. Finally, the present challenges and future outlooks are discussed. PMID:23112667

Microfluidic-Based sample chips for radioactive solutions

DOE PAGES

Tripp, J. L.; Law, J. D.; Smith, T. E.; ...

2015-01-01

Historical nuclear fuel cycle process sampling techniques required sample volumes ranging in the tens of milliliters. The radiation levels experienced by analytical personnel and equipment, in addition to the waste volumes generated from analysis of these samples, have been significant. These sample volumes also impacted accountability inventories of required analytes during process operations. To mitigate radiation dose and other issues associated with the historically larger sample volumes, a microcapillary sample chip was chosen for further investigation. The ability to obtain microliter volume samples coupled with a remote automated means of sample loading, tracking, and transporting to the analytical instrument wouldmore » greatly improve analytical efficiency while reducing both personnel exposure and radioactive waste volumes. Sample chip testing was completed to determine the accuracy, repeatability, and issues associated with the use of microfluidic sample chips used to supply µL sample volumes of lanthanide analytes dissolved in nitric acid for introduction to an analytical instrument for elemental analysis.« less

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.

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.

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.

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.

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.

A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies

NASA Astrophysics Data System (ADS)

Liang, Hui; Chen, Xiaobo

2017-10-01

A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN2] and Neumann-to-Dirichlet [ND2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier-Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier-Laguerre expansion.

Supersaturated Electrolyte Solutions: Theory and Experiment

NASA Technical Reports Server (NTRS)

Izmailov, Alexander F.; Myerson, Allan S.; Na, Han-Soo

1995-01-01

Highly supersaturated electrolyte solutions can be prepared and studied employing an electrodynamic levitator trap (ELT) technique. The ELT technique involves containerless suspension of a microdroplet thus eliminating dust, dirt, and container walls which normally cause heterogeneous nucleation. This allows very high supersaturations to be achieved. A theoretical study of the experimental results obtained for the water activity in microdroplets of various electrolyte solutions is based on the development of the Cahn-Hilliard formalism for electrolyte solutions. In the approach suggested the metastable state for electrolyte solutions is described in terms of the conserved order parameter omega(r,t) associated with fluctuations of the mean solute concentration n(sub 0). Parameters of the corresponding Ginzburg-Landau free energy functional which defines the dynamics of metastable state relaxation are determined and expressed through the experimentally measured quantities. A correspondence of 96-99 % between theory and experiment for all solutions studied was achieved and allowed the determination of an analytical expression for the spinodal concentration n(sub spin), and its calculation for various electrolyte solutions at 298 K. The assumption that subcritical solute clusters consist of the electrically neutral Bjerrum pairs has allowed both analytical and numerical investigation of the number-size N(sub c) of nucleation monomers (aggregates of the Bjerrum pairs) which are elementary units of the solute critical clusters. This has also allowed estimations for the surface tension Alpha, and equilibrium bulk energy Beta per solute molecule in the nucleation monomers. The dependence of these properties on the temperature T and on the solute concentration n(sub 0) through the entire metastable zone (from saturation concentration n(sub sat) to spinodal n(sub spin) is examined. It has been demonstrated that there are the following asymptotics: N(sub c), = I at spinodal concentration and N(sub c) = infinity at saturation.

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.

Vacuum-assisted headspace-solid phase microextraction for determining volatile free fatty acids and phenols. Investigations on the effect of pressure on competitive adsorption phenomena in a multicomponent system.

PubMed

Trujillo-Rodríguez, María J; Pino, Verónica; Psillakis, Elefteria; Anderson, Jared L; Ayala, Juan H; Yiantzi, Evangelia; Afonso, Ana M

2017-04-15

This work proposes a new vacuum headspace solid-phase microextraction (Vac-HSSPME) method combined to gas chromatography-flame ionization detection for the determination of free fatty acids (FFAs) and phenols. All target analytes of the multicomponent solution were volatiles but their low Henry's Law constants rendered them amenable to Vac-HSSPME. The ability of a new and easy to construct Vac-HSSPME sampler to maintain low-pressure conditions for extended sampling times was concurrently demonstrated. Vac-HSSPME and regular HSSPME methods were independently optimized and the results were compared at all times. The performances of four commercial SPME fibers and two polymeric ionic liquid (PIL)-based SPME fibers were evaluated and the best overall results were obtained with the adsorbent-type CAR/PDMS fiber. For the concentrations used here, competitive displacement became more intense for the smaller and more volatile analytes of the multi-component solution when lowering the sampling pressure. The extraction time profiles showed that Vac-HSSPME had a dramatic positive effect on extraction kinetics. The local maxima of adsorbed analytes recorded with Vac-HSSPME occurred faster, but were always lower than that with regular HSSPME due to the faster analyte-loading from the multicomponent solution. Increasing the sampling temperature during Vac-HSSPME reduced the extraction efficiency of smaller analytes due to the enhancement in water molecule collisions with the fiber. This effect was not recorded for the larger phenolic compounds. Based on the optimum values selected, Vac-HSSPME required a shorter extraction time and milder sampling conditions than regular HSSPME: 20 min and 35 °C for Vac-HSSPME versus 40 min and 45 °C for regular HSSPME. The performance of the optimized Vac-HSSPME and regular HSSPME procedures were assessed and Vac-HSSPME method proved to be more sensitive, with lower limits of detection (from 0.14 to 13 μg L -1 ), and better intra-day precision (relative standard deviations values < 10% at the lowest spiked level) than regular HSSPME for almost all target analytes. The proposed Vac-HSSPME method was successfully applied to quantify FFAs and phenols in milk and milk derivatives samples. Copyright © 2017 Elsevier B.V. All rights reserved.

Local Modelling of Groundwater Flow Using Analytic Element Method Three-dimensional Transient Unconfined Groundwater Flow With Partially Penetrating Wells and Ellipsoidal Inhomogeneites

NASA Astrophysics Data System (ADS)

Jankovic, I.; Barnes, R. J.; Soule, R.

2001-12-01

The analytic element method is used to model local three-dimensional flow in the vicinity of partially penetrating wells. The flow domain is bounded by an impermeable horizontal base, a phreatic surface with recharge and a cylindrical lateral boundary. The analytic element solution for this problem contains (1) a fictitious source technique to satisfy the head and the discharge conditions along the phreatic surface, (2) a fictitious source technique to satisfy specified head conditions along the cylindrical boundary, (3) a method of imaging to satisfy the no-flow condition across the impermeable base, (4) the classical analytic solution for a well and (5) spheroidal harmonics to account for the influence of the inhomogeneities in hydraulic conductivity. Temporal variations of the flow system due to time-dependent recharge and pumping are represented by combining the analytic element method with a finite difference method: analytic element method is used to represent spatial changes in head and discharge, while the finite difference method represents temporal variations. The solution provides a very detailed description of local groundwater flow with an arbitrary number of wells of any orientation and an arbitrary number of ellipsoidal inhomogeneities of any size and conductivity. These inhomogeneities may be used to model local hydrogeologic features (such as gravel packs and clay lenses) that significantly influence the flow in the vicinity of partially penetrating wells. Several options for specifying head values along the lateral domain boundary are available. These options allow for inclusion of the model into steady and transient regional groundwater models. The head values along the lateral domain boundary may be specified directly (as time series). The head values along the lateral boundary may also be assigned by specifying the water-table gradient and a head value at a single point (as time series). A case study is included to demonstrate the application of the model in local modeling of the groundwater flow. Transient three-dimensional capture zones are delineated for a site on Prairie Island, MN. Prairie Island is located on the Mississippi River 40 miles south of the Twin Cities metropolitan area. The case study focuses on a well that has been known to contain viral DNA. The objective of the study was to assess the potential for pathogen migration toward the well.

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

Quantifying non-Markovianity of continuous-variable Gaussian dynamical maps

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

Vasile, Ruggero; Maniscalco, Sabrina; Paris, Matteo G. A.

2011-11-15

We introduce a non-Markovianity measure for continuous-variable open quantum systems based on the idea put forward in H.-P. Breuer et al.[Phys. Rev. Lett. 103, 210401 (2009);], that is, by quantifying the flow of information from the environment back to the open system. Instead of the trace distance we use here the fidelity to assess distinguishability of quantum states. We employ our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels: the purely damping channel and the quantum Brownian motion channel with Ohmic environment. We consider different classes of Gaussian states and look for pairs of states maximizing the backflow ofmore » information. For coherent states we find simple analytical solutions, whereas for squeezed states we provide both exact numerical and approximate analytical solutions in the weak coupling limit.« less

Computer-Based Mathematics Instructions for Engineering Students

NASA Technical Reports Server (NTRS)

Khan, Mustaq A.; Wall, Curtiss E.

1996-01-01

Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.

Solution of the mean spherical approximation for polydisperse multi-Yukawa hard-sphere fluid mixture using orthogonal polynomial expansions

NASA Astrophysics Data System (ADS)

Kalyuzhnyi, Yurij V.; Cummings, Peter T.

2006-03-01

The Blum-Høye [J. Stat. Phys. 19 317 (1978)] solution of the mean spherical approximation for a multicomponent multi-Yukawa hard-sphere fluid is extended to a polydisperse multi-Yukawa hard-sphere fluid. Our extension is based on the application of the orthogonal polynomial expansion method of Lado [Phys. Rev. E 54, 4411 (1996)]. Closed form analytical expressions for the structural and thermodynamic properties of the model are presented. They are given in terms of the parameters that follow directly from the solution. By way of illustration the method of solution is applied to describe the thermodynamic properties of the one- and two-Yukawa versions of the model.

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.

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.

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.

Motion-Based pH Sensing Based on the Cartridge-Case-like Micromotor.

PubMed

Su, Yajun; Ge, Ya; Liu, Limei; Zhang, Lina; Liu, Mei; Sun, Yunyu; Zhang, Hui; Dong, Bin

2016-02-17

In this paper, we report a novel cartridge-case-like micromotor. The micromotor, which is fabricated by the template synthesis method, consists of a gelatin shell with platinum nanoparticles decorating its inner surface. Intriguingly, the resulting cartridge-case-like structure exhibits a pH-dependent "open and close" feature, which originates from the pH responsiveness of the gelatin material. On the basis of the catalytic activity of the platinum nanoparticle inside the gelatin shell, the resulting cartridge-case-like structure is capable of moving autonomously in the aqueous solution containing the hydrogen peroxide fuel. More interestingly, we find out that the micromotor can be utilized as a motion-based pH sensor over the whole pH range. The moving velocity of the micromotor increases monotonically with the increase of pH of the analyte solution. Three different factors are considered to be responsible for the proportional relation between the motion speed and pH of the analyte solution: the peroxidase-like and oxidase-like catalytic behavior of the platinum nanoparticle at low and high pH, the volumetric decomposition of the hydrogen peroxide under the basic condition and the pH-dependent catalytic activity of the platinum nanoparticle caused by the swelling/deswelling behavior of the gelatin material. The current work highlights the impact of the material properties on the motion behavior of a micromotor, thus paving the way toward its application in the motion-based sensing field.

Analytical study of the critical behavior of the nonlinear pendulum

NASA Astrophysics Data System (ADS)

Lima, F. M. S.

2010-11-01

The dynamics of a simple pendulum consisting of a small bob and a massless rigid rod has three possible regimes depending on its total energy E: Oscillatory (when E is not enough for the pendulum to reach the top position), "perpetual ascent" when E is exactly the energy needed to reach the top, and nonoscillatory for greater energies. In the latter regime, the pendulum rotates periodically without velocity inversions. In contrast to the oscillatory regime, for which an exact analytic solution is known, the other two regimes are usually studied by solving the equation of motion numerically. By applying conservation of energy, I derive exact analytical solutions to both the perpetual ascent and nonoscillatory regimes and an exact expression for the pendulum period in the nonoscillatory regime. Based on Cromer's approximation for the large-angle pendulum period, I find a simple approximate expression for the decrease of the period with the initial velocity in the nonoscillatory regime, valid near the critical velocity. This expression is used to study the critical slowing down, which is observed near the transition between the oscillatory and nonoscillatory regimes.

Sound Emission of Rotor Induced Deformations of Generator Casings

NASA Technical Reports Server (NTRS)

Polifke, W.; Mueller, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)

2001-01-01

The casing of large electrical generators can be deformed slightly by the rotor's magnetic field. The sound emission produced by these periodic deformations, which could possibly exceed guaranteed noise emission limits, is analysed analytically and numerically. From the deformation of the casing, the normal velocity of the generator's surface is computed. Taking into account the corresponding symmetry, an analytical solution for the acoustic pressure outside the generator is round in terms of the Hankel function of second order. The normal velocity or the generator surface provides the required boundary condition for the acoustic pressure and determines the magnitude of pressure oscillations. For the numerical simulation, the nonlinear 2D Euler equations are formulated In a perturbation form for low Mach number Computational Aeroacoustics (CAA). The spatial derivatives are discretized by the classical sixth-order central interior scheme and a third-order boundary scheme. Spurious high frequency oscillations are damped by a characteristic-based artificial compression method (ACM) filter. The time derivatives are approximated by the classical 4th-order Runge-Kutta method. The numerical results are In excellent agreement with the analytical solution.

Development of paper-based microfluidic analytical device for iron assay using photomask printed with 3D printer for fabrication of hydrophilic and hydrophobic zones on paper by photolithography.

PubMed

Asano, Hitoshi; Shiraishi, Yukihide

2015-07-09

This paper describes a paper-based microfluidic analytical device for iron assay using a photomask printed with a 3D printer for fabrication of hydrophilic and hydrophobic zones on the paper by photolithography. Several designed photomasks for patterning paper-based microfluidic analytical devices can be printed with a 3D printer easily, rapidly and inexpensively. A chromatography paper was impregnated with the octadecyltrichlorosilane n-hexane solution and hydrophobized. After the hydrophobic zone of the paper was exposed to the UV light through the photomask, the hydrophilic zone was generated. The smallest functional hydrophilic channel and hydrophobic barrier were ca. 500 μm and ca. 100 μm in width, respectively. The fabrication method has high stability, resolution and precision for hydrophilic channel and hydrophobic barrier. This test paper was applied to the analysis of iron in water samples using a colorimetry with phenanthroline. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

Numerical simulation for solution of space-time fractional telegraphs equations with local fractional derivatives via HAFSTM

NASA Astrophysics Data System (ADS)

Pandey, Rishi Kumar; Mishra, Hradyesh Kumar

2017-11-01

In this paper, the semi-analytic numerical technique for the solution of time-space fractional telegraph equation is applied. This numerical technique is based on coupling of the homotopy analysis method and sumudu transform. It shows the clear advantage with mess methods like finite difference method and also with polynomial methods similar to perturbation and Adomian decomposition methods. It is easily transform the complex fractional order derivatives in simple time domain and interpret the results in same meaning.

Exact analysis of two kinds of piezoelectric actuator

NASA Astrophysics Data System (ADS)

Rong, Han; Zhifei, Shi

2008-02-01

Two kinds of piezoelectric hollow cylinder actuator are studied in this paper. One is the expansion actuator and the other is the contraction actuator. Using the Airy stress function method, the analytical solutions of these two kinds of actuators are obtained based on the theory of piezo-elasticity. The solutions are compared with numerical results and good agreement is found. Inherent properties of these two kinds of piezoelectric cylinder actuator are presented and discussed. Findings have applications in the field of micromechanics and microengineering.

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

Preston, Leiph

Although using standard Taylor series coefficients for finite-difference operators is optimal in the sense that in the limit of infinitesimal space and time discretization, the solution approaches the correct analytic solution to the acousto-dynamic system of differential equations, other finite-difference operators may provide optimal computational run time given certain error bounds or source bandwidth constraints. This report describes the results of investigation of alternative optimal finite-difference coefficients based on several optimization/accuracy scenarios and provides recommendations for minimizing run time while retaining error within given error bounds.

The influence of thermal and conductive temperatures in a nanoscale resonator

NASA Astrophysics Data System (ADS)

Hobiny, Aatef; Abbas, Ibrahim A.

2018-06-01

In this work, the thermoelastic interaction in a nano-scale resonator based on two-temperature Green-Naghdi model is established. The nanoscale resonator ends were simply supported. In the Laplace's domain, the analytical solution of conductivity temperature and thermodynamic temperature, the displacement and the stress components are obtained. The eigenvalue approach resorted to for solutions. In the vector-matrix differential equations form, the essential equations were written. The numerical results for all variables are presented and are illustrated graphically.

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.