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.

Directed transport by surface chemical potential gradients for enhancing analyte collection in nanoscale sensors.

PubMed

Sitt, Amit; Hess, Henry

2015-05-13

Nanoscale detectors hold great promise for single molecule detection and the analysis of small volumes of dilute samples. However, the probability of an analyte reaching the nanosensor in a dilute solution is extremely low due to the sensor's small size. Here, we examine the use of a chemical potential gradient along a surface to accelerate analyte capture by nanoscale sensors. Utilizing a simple model for transport induced by surface binding energy gradients, we study the effect of the gradient on the efficiency of collecting nanoparticles and single and double stranded DNA. The results indicate that chemical potential gradients along a surface can lead to an acceleration of analyte capture by several orders of magnitude compared to direct collection from the solution. The improvement in collection is limited to a relatively narrow window of gradient slopes, and its extent strongly depends on the size of the gradient patch. Our model allows the optimization of gradient layouts and sheds light on the fundamental characteristics of chemical potential gradient induced transport.

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.

Direct evidence on the existence of [Mo132]Keplerate-type species in aqueous solution.

PubMed

Roy, Soumyajit; Planken, Karel L; Kim, Robbert; Mandele, Dexx v d; Kegel, Willem K

2007-10-15

We demonstrate the existence of discrete single molecular [Mo(132)] Keplerate-type clusters in aqueous solution. Starting from a discrete spherical [Mo(132)] cluster, the formation of an open-basket-type [Mo(116)] defect structure is shown for the first time in solution using analytical ultracentrifugation sedimentation velocity experiments.

Exact solution for an optimal impermeable parachute problem

NASA Astrophysics Data System (ADS)

Lupu, Mircea; Scheiber, Ernest

2002-10-01

In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle--the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.

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

NASA Astrophysics Data System (ADS)

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

2014-07-01

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

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.

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.

Solution to Projectile Motion with Quadratic Drag and Graphing the Trajectory in Spreadsheets

ERIC Educational Resources Information Center

Benacka, Jan

2010-01-01

This note gives the analytical solution to projectile motion with quadratic drag by decomposing the velocity vector to "x," "y" coordinate directions. The solution is given by definite integrals. First, the impact angle is estimated from above, then the projectile coordinates are computed, and the trajectory is graphed at various launch angles and…

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)

Analytical theory of two-dimensional ring dark soliton in nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Chen, Wei; Wang, Qi; Shi, Jielong; Shen, Ming

2017-11-01

Completely stable two-dimensional ring dark soliton in nonlocal media with an arbitrary degree of nonlocality are investigated. The exact solution of the ring dark solitons is obtained with the variational method and a cylindrical nonlocal response function. The analytical results are confirmed by directly numerical simulations. We also analytically and numerically study the expansion dynamics of the gray ring dark solitons in detail.

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

Analytic solutions for single and multiple cylinders of gravitating polytropes in magnetostatic equilibrium

NASA Technical Reports Server (NTRS)

Lerche, I.; Low, B. C.

1980-01-01

Exact analytic solutions for the static equilibrium of a gravitating plasma polytrope in the presence of magnetic fields are presented. The means of generating various equilibrium configurations to illustrate directly the complex physical relationships between pressure, magnetic fields, and gravity in self-gravitating systems is demonstrated. One of the solutions is used to model interstellar clouds suspended by magnetic fields against the galactic gravity such as may be formed by the Parker (1966) instability. It is concluded that the pinching effect of closed loops of magnetic fields in the clouds may be a dominant agent in further collapsing the clouds following their formation.

Exact solutions of the population balance equation including particle transport, using group analysis

NASA Astrophysics Data System (ADS)

Lin, Fubiao; Meleshko, Sergey V.; Flood, Adrian E.

2018-06-01

The population balance equation (PBE) has received an unprecedented amount of attention in recent years from both academics and industrial practitioners because of its long history, widespread use in engineering, and applicability to a wide variety of particulate and discrete-phase processes. However it is typically impossible to obtain analytical solutions, although in almost every case a numerical solution of the PBEs can be obtained. In this article, the symmetries of PBEs with homogeneous coagulation kernels involving aggregation, breakage and growth processes and particle transport in one dimension are found by direct solving the determining equations. Using the optimal system of one and two-dimensional subalgebras, all invariant solutions and reduced equations are obtained. In particular, an explicit analytical physical solution is also presented.

Intimacy Is a Transdiagnostic Problem for Cognitive Behavior Therapy: Functional Analytical Psychotherapy Is a Solution

ERIC Educational Resources Information Center

Wetterneck, Chad T.; Hart, John M.

2012-01-01

Problems with intimacy and interpersonal issues are exhibited across most psychiatric disorders. However, most of the targets in Cognitive Behavioral Therapy are primarily intrapersonal in nature, with few directly involved in interpersonal functioning and effective intimacy. Functional Analytic Psychotherapy (FAP) provides a behavioral basis for…

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

NASA Astrophysics Data System (ADS)

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

2008-07-01

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

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.

Elasticity Theory Solution of the Problem on Plane Bending of a Narrow Layered Cantilever Beam by Loads at Its Free End

NASA Astrophysics Data System (ADS)

Goryk, A. V.; Koval'chuk, S. B.

2018-05-01

An exact elasticity theory solution for the problem on plane bending of a narrow layered composite cantilever beam by tangential and normal loads distributed on its free end is presented. Components of the stress-strain state are found for the whole layers package by directly integrating differential equations of the plane elasticity theory problem by using an analytic representation of piecewise constant functions of the mechanical characteristics of layer materials. The continuous solution obtained is realized for a four-layer beam with account of kinematic boundary conditions simulating the rigid fixation of its one end. The solution obtained allows one to predict the strength and stiffness of composite cantilever beams and to construct applied analytical solutions for various problems on the elastic bending of layered beams.

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

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.

Analytic theory of orbit contraction

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

Hankel-Bessel laser beams.

PubMed

Kotlyar, Victor V; Kovalev, Alexey A; Soifer, Victor A

2012-05-01

An analytical solution of the scalar Helmholtz equation to describe the propagation of a laser light beam in the positive direction of the optical axis is derived. The complex amplitude of such a beam is found to be in direct proportion to the product of two linearly independent solutions of Kummer's differential equation. Relationships for a particular case of such beams-namely, the Hankel-Bessel (HB) beams-are deduced. The focusing of the HB beams is studied. © 2012 Optical Society of America

Carbon nanotubes as adsorbent of solid-phase extraction and matrix for laser desorption/ionization mass spectrometry.

PubMed

Pan, Chensong; Xu, Songyun; Zou, Hanfa; Guo, Zhong; Zhang, Yu; Guo, Baochuan

2005-02-01

A method with carbon nanotubes functioning both as the adsorbent of solid-phase extraction (SPE) and the matrix for matrix assisted laser desorption/ionization mass spectrometry (MALDI-MS) to analyze small molecules in solution has been developed. In this method, 10 microL suspensions of carbon nanotubes in 50% (vol/vol) methanol were added to the sample solution to extract analytes onto surface of carbon nanotubes because of their dramatic hydrophobicity. Carbon nanotubes in solution are deposited onto the bottom of tube with centrifugation. After removing the supernatant fluid, carbon nanotubes are suspended again with dispersant and pipetted directly onto the sample target of the MALDI-MS to perform a mass spectrometric analysis. It was demonstrated by analysis of a variety of small molecules that the resolution of peaks and the efficiency of desorption/ionization on the carbon nanotubes are better than those on the activated carbon. It is found that with the addition of glycerol and sucrose to the dispersant, the intensity, the ratio of signal to noise (S/N), and the resolution of peaks for analytes by mass spectrometry increased greatly. Compared with the previously reported method by depositing sample solution onto thin layer of carbon nanotubes, it is observed that the detection limit for analytes can be enhanced about 10 to 100 times due to solid-phase extraction of analytes in solution by carbon nanotubes. An acceptable result of simultaneously quantitative analysis of three analytes in solution has been achieved. The application in determining drugs spiked into urine has also been realized.

Learning Analytics in Small-Scale Teacher-Led Innovations: Ethical and Data Privacy Issues

ERIC Educational Resources Information Center

Rodríguez-Triana, María Jesús; Martínez-Monés, Alejandra; Villagrá-Sobrino, Sara

2016-01-01

As a further step towards maturity, the field of learning analytics (LA) is working on the definition of frameworks that structure the legal and ethical issues that scholars and practitioners must take into account when planning and applying LA solutions to their learning contexts. However, current efforts in this direction tend to be focused on…

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

NASA Technical Reports Server (NTRS)

Lancaster, J. E.

1973-01-01

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

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.

An analytical and experimental study of crack extension in center-notched composites

NASA Technical Reports Server (NTRS)

Beuth, Jack L., Jr.; Herakovich, Carl T.

1987-01-01

The normal stress ratio theory for crack extension in anisotropic materials is studied analytically and experimentally. The theory is applied within a microscopic-level analysis of a single center notch of arbitrary orientation in a unidirectional composite material. The bulk of the analytical work of this study applies an elasticity solution for an infinite plate with a center line to obtain critical stress and crack growth direction predictions. An elasticity solution for an infinite plate with a center elliptical flaw is also used to obtain qualitative predictions of the location of crack initiation on the border of a rounded notch tip. The analytical portion of the study includes the formulation of a new crack growth theory that includes local shear stress. Normal stress ratio theory predictions are obtained for notched unidirectional tensile coupons and unidirectional Iosipescu shear specimens. These predictions are subsequently compared to experimental results.

Stimulating Creativity: Modulation of Convergent and Divergent Thinking by Transcranial Direct Current Stimulation (tDCS)

ERIC Educational Resources Information Center

Zmigrod, Sharon; Colzato, Lorenza S.; Hommel, Bernhard

2015-01-01

Creativity has been conceptualized as involving 2 distinct components; divergent thinking, the search for multiple solutions to a single problem, and convergent thinking, the quest for a single solution either through an analytical process or the experience of insight. Studies have demonstrated that these abilities can be improved by cognitive…

Direct Analysis of Samples of Various Origin and Composition Using Specific Types of Mass Spectrometry.

PubMed

Byliński, Hubert; Gębicki, Jacek; Dymerski, Tomasz; Namieśnik, Jacek

2017-07-04

One of the major sources of error that occur during chemical analysis utilizing the more conventional and established analytical techniques is the possibility of losing part of the analytes during the sample preparation stage. Unfortunately, this sample preparation stage is required to improve analytical sensitivity and precision. Direct techniques have helped to shorten or even bypass the sample preparation stage; and in this review, we comment of some of the new direct techniques that are mass-spectrometry based. The study presents information about the measurement techniques using mass spectrometry, which allow direct sample analysis, without sample preparation or limiting some pre-concentration steps. MALDI - MS, PTR - MS, SIFT - MS, DESI - MS techniques are discussed. These solutions have numerous applications in different fields of human activity due to their interesting properties. The advantages and disadvantages of these techniques are presented. The trends in development of direct analysis using the aforementioned techniques are also presented.

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

NASA Technical Reports Server (NTRS)

Ustino, Eugene A.

2006-01-01

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

In situ ionic liquid dispersive liquid-liquid microextraction and direct microvial insert thermal desorption for gas chromatographic determination of bisphenol compounds.

PubMed

Cacho, Juan Ignacio; Campillo, Natalia; Viñas, Pilar; Hernández-Córdoba, Manuel

2016-01-01

A new procedure based on direct insert microvial thermal desorption injection allows the direct analysis of ionic liquid extracts by gas chromatography and mass spectrometry (GC-MS). For this purpose, an in situ ionic liquid dispersive liquid-liquid microextraction (in situ IL DLLME) has been developed for the quantification of bisphenol A (BPA), bisphenol Z (BPZ) and bisphenol F (BPF). Different parameters affecting the extraction efficiency of the microextraction technique and the thermal desorption step were studied. The optimized procedure, determining the analytes as acetyl derivatives, provided detection limits of 26, 18 and 19 ng L(-1) for BPA, BPZ and BPF, respectively. The release of the three analytes from plastic containers was monitored using this newly developed analytical method. Analysis of the migration test solutions for 15 different plastic containers in daily use identified the presence of the analytes at concentrations ranging between 0.07 and 37 μg L(-1) in six of the samples studied, BPA being the most commonly found and at higher concentrations than the other analytes.

3D Tensorial Elastodynamics for Isotropic Media on Vertically Deformed Meshes

NASA Astrophysics Data System (ADS)

Shragge, J. C.

2017-12-01

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

Some new features of Direct Analysis in Real Time mass spectrometry utilizing the desorption at an angle option.

PubMed

Chernetsova, Elena S; Revelsky, Alexander I; Morlock, Gertrud E

2011-08-30

The present study is a first step towards the unexplored capabilities of Direct Analysis in Real Time (DART) mass spectrometry (MS) arising from the possibility of the desorption at an angle: scanning analysis of surfaces, including the coupling of thin-layer chromatography (TLC) with DART-MS, and a more sensitive analysis due to the preliminary concentration of analytes dissolved in large volumes of liquids on glass surfaces. In order to select the most favorable conditions for DART-MS analysis, proper positioning of samples is important. Therefore, a simple and cheap technique for the visualization of the impact region of the DART gas stream onto a substrate was developed. A filter paper or TLC plate, previously loaded with the analyte, was immersed in a derivatization solution. On this substrate, owing to the impact of the hot DART gas, reaction of the analyte to a colored product occurred. An improved capability of detection of DART-MS for the analysis of liquids was demonstrated by applying large volumes of model solutions of coumaphos into small glass vessels and drying these solutions prior to DART-MS analysis under ambient conditions. This allowed the introduction of, by up to more than two orders of magnitude, increased quantities of analyte compared with the conventional DART-MS analysis of liquids. Through this improved detectability, the capabilities of DART-MS in trace analysis could be strengthened. Copyright © 2011 John Wiley & Sons, Ltd.

Analytic topologically nontrivial solutions of the (3 +1 )-dimensional U (1 ) gauged Skyrme model and extended duality

NASA Astrophysics Data System (ADS)

Avilés, L.; Canfora, F.; Dimakis, N.; Hidalgo, D.

2017-12-01

We construct the first analytic examples of topologically nontrivial solutions of the (3 +1 )-dimensional U (1 ) gauged Skyrme model within a finite box in (3 +1 )-dimensional flat space-time. There are two types of gauged solitons. The first type corresponds to gauged Skyrmions living within a finite volume. The second corresponds to gauged time crystals (smooth solutions of the U (1 ) gauged Skyrme model whose periodic time dependence is protected by a winding number). The notion of electromagnetic duality can be extended for these two types of configurations in the sense that the electric and one of the magnetic components can be interchanged. These analytic solutions show very explicitly the Callan-Witten mechanism (according to which magnetic monopoles may "swallow" part of the topological charge of the Skyrmion) since the electromagnetic field contributes directly to the conserved topological charge of the gauged Skyrmions. As it happens in superconductors, the magnetic field is suppressed in the core of the gauged Skyrmions. On the other hand, the electric field is strongly suppresed in the core of gauged time crystals.

Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method

NASA Astrophysics Data System (ADS)

Shen-Shen, Chen; Juan, Wang; Qing-Hua, Li

2016-04-01

A scaled boundary node method (SBNM) is developed for two-dimensional fracture analysis of piezoelectric material, which allows the stress and electric displacement intensity factors to be calculated directly and accurately. As a boundary-type meshless method, the SBNM employs the moving Kriging (MK) interpolation technique to an approximate unknown field in the circumferential direction and therefore only a set of scattered nodes are required to discretize the boundary. As the shape functions satisfy Kronecker delta property, no special techniques are required to impose the essential boundary conditions. In the radial direction, the SBNM seeks analytical solutions by making use of analytical techniques available to solve ordinary differential equations. Numerical examples are investigated and satisfactory solutions are obtained, which validates the accuracy and simplicity of the proposed approach. Project supported by the National Natural Science Foundation of China (Grant Nos. 11462006 and 21466012), the Foundation of Jiangxi Provincial Educational Committee, China (Grant No. KJLD14041), and the Foundation of East China Jiaotong University, China (Grant No. 09130020).

Apparent dispersion in transient groundwater flow

USGS Publications Warehouse

Goode, Daniel J.; Konikow, Leonard F.

1990-01-01

This paper investigates the effects of large-scale temporal velocity fluctuations, particularly changes in the direction of flow, on solute spreading in a two-dimensional aquifer. Relations for apparent longitudinal and transverse dispersivity are developed through an analytical solution for dispersion in a fluctuating, quasi-steady uniform flow field, in which storativity is zero. For transient flow, spatial moments are evaluated from numerical solutions. Ignored or unknown transients in the direction of flow primarily act to increase the apparent transverse dispersivity because the longitudinal dispersivity is acting in a direction that is not the assumed flow direction. This increase is a function of the angle between the transient flow vector and the assumed steady state flow direction and the ratio of transverse to longitudinal dispersivity. The maximum effect on transverse dispersivity occurs if storativity is assumed to be zero, such that the flow field responds instantly to boundary condition changes.

Analytical Description of the H/D Exchange Kinetic of Macromolecule.

PubMed

Kostyukevich, Yury; Kononikhin, Alexey; Popov, Igor; Nikolaev, Eugene

2018-04-17

We present the accurate analytical solution obtained for the system of rate equations describing the isotope exchange process for molecules containing an arbitrary number of equivalent labile atoms. The exact solution was obtained using Mathematica 7.0 software, and this solution has the form of the time-dependent Gaussian distribution. For the case when forward exchange considerably overlaps the back exchange, it is possible to estimate the activation energy of the reaction by obtaining a temperature dependence of the reaction degree. Using a previously developed approach for performing H/D exchange directly in the ESI source, we have estimated the activation energies for ions with different functional groups and they were found to be in a range 0.04-0.3 eV. Since the value of the activation energy depends on the type of functional group, the developed approach can have potential analytical applications for determining types of functional groups in complex mixtures, such as petroleum, humic substances, bio-oil, and so on.

Oxidation kinetics of a continuous carbon phase in a nonreactive matrix

NASA Technical Reports Server (NTRS)

Eckel, Andrew J.; Cawley, James D.; Parthasarathy, Triplicane A.

1995-01-01

Analytical solutions of and experimental results on the oxidation kinetics of carbon in a pore are presented. Reaction rate, reaction sequence, oxidant partial pressure, total system pressure, pore/crack dimensions, and temperature are analyzed with respect to the influence of each on an overall linear-parabolic rate relationship. Direct measurement of carbon recession is performed using two microcomposite model systems oxidized in the temperature range of 700 to 1200 C, and for times to 35 h. Experimental results are evaluated using the derived analytical solutions. Implications on the oxidation resistance of continuous-fiber-reinforced ceramic-matrix composites containing a carbon constituent are 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.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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...

Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Weatherill, W. H.; Ehlers, F. E.; Yip, E.; Sebastian, J. D.

1980-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.

Synthetic Nano- and Micromachines in Analytical Chemistry: Sensing, Migration, Capture, Delivery, and Separation.

PubMed

Duan, Wentao; Wang, Wei; Das, Sambeeta; Yadav, Vinita; Mallouk, Thomas E; Sen, Ayusman

2015-01-01

Synthetic nano- and microscale machines move autonomously in solution or drive fluid flows by converting sources of energy into mechanical work. Their sizes are comparable to analytes (sub-nano- to microscale), and they respond to signals from each other and their surroundings, leading to emergent collective behavior. These machines can potentially enable hitherto difficult analytical applications. In this article, we review the development of different classes of synthetic nano- and micromotors and pumps and indicate their possible applications in real-time in situ chemical sensing, on-demand directional transport, cargo capture and delivery, as well as analyte isolation and separation.

Accurate determination of non-metallic impurities in high purity tetramethylammonium hydroxide using inductively coupled plasma tandem mass spectrometry

NASA Astrophysics Data System (ADS)

Fu, Liang; Xie, Hualin; Shi, Shuyun; Chen, Xiaoqing

2018-06-01

The content of non-metallic impurities in high-purity tetramethylammonium hydroxide (HPTMAH) aqueous solution has an important influence on the yield, electrical properties and reliability of the integrated circuit during the process of chip etching and cleaning. Therefore, an efficient analytical method to directly quantify the content of non-metallic impurities in HPTMAH aqueous solutions is necessary. The present study was aimed to develop a novel method that can accurately determine seven non-metallic impurities (B, Si, P, S, Cl, As, and Se) in an aqueous solution of HPTMAH by inductively coupled plasma tandem mass spectrometry (ICP-MS/MS). The samples were measured using a direct injection method. In the MS/MS mode, oxygen and hydrogen were used as reaction gases in the octopole reaction system (ORS) to eliminate mass spectral interferences during the analytical process. The detection limits of B, Si, P, S, Cl, As, and Se were 0.31, 0.48, 0.051, 0.27, 3.10, 0.008, and 0.005 μg L-1, respectively. The samples were analyzed by the developed method and the sector field inductively coupled plasma mass spectrometry (SF-ICP-MS) was used for contrastive analysis. The values of these seven elements measured using ICP-MS/MS were consistent with those measured by SF-ICP-MS. The proposed method can be utilized to analyze non-metallic impurities in HPTMAH aqueous solution. Table S2 Multiple potential interferences on the analytes. Table S3 Parameters of calibration curve and the detection limit (DL). Table S4 Results obtained for 25% concentration high-purity grade TMAH aqueous solution samples (μg L-1, mean ± standard deviation, n = 10).

Direct application of Padé approximant for solving nonlinear differential equations.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

2014-01-01

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

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.

Investigation of hydrophobic substrates for solution residue analysis utilizing an ambient desorption liquid sampling-atmospheric pressure glow discharge microplasma.

PubMed

Paing, Htoo W; Marcus, R Kenneth

2018-03-12

A practical method for preparation of solution residue samples for analysis utilizing the ambient desorption liquid sampling-atmospheric pressure glow discharge optical emission spectroscopy (AD-LS-APGD-OES) microplasma is described. Initial efforts involving placement of solution aliquots in wells drilled into copper substrates, proved unsuccessful. A design-of-experiment (DOE) approach was carried out to determine influential factors during sample deposition including solution volume, solute concentration, number of droplets deposited, and the solution matrix. These various aspects are manifested in the mass of analyte deposited as well as the size/shape of the product residue. Statistical analysis demonstrated that only those initial attributes were significant factors towards the emission response of the analyte. Various approaches were investigated to better control the location/uniformity of the deposited sample. Three alternative substrates, a glass slide, a poly(tetrafluoro)ethylene (PTFE) sheet, and a polydimethylsiloxane (PDMS)-coated glass slide, were evaluated towards the microplasma analytical performance. Co-deposition with simple organic dyes provided an accurate means of determining the location of the analyte with only minor influence on emission responses. The PDMS-coated glass provided the best performance by virtue of its providing a uniform spatial distribution of the residue material. This uniformity yielded an improved limits of detection by approximately 22× for 20 μL and 4 x for 2 μL over the other two substrates. While they operate by fundamentally different processes, this choice of substrate is not restricted to the LS-APGD, but may also be applicable to other AD methods such as DESI, DART, or LIBS. Further developments will be directed towards a field-deployable ambient desorption OES source for quantitative analysis of microvolume solution residues of nuclear forensics importance.

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.

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

NASA Astrophysics Data System (ADS)

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; Birkholzer, Jens T.

2017-11-01

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1-D, 2-D, and 3-D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, td. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, td0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the first two terms for high-accuracy approximations (with less than 10-7 relative error) for 1-D isotropic (spheres, cylinders, slabs) and 2-D/3-D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1-D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2-D/3-D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

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

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1D, 2D, and 3D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, t d0. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, t d0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the firstmore » two terms for high-accuracy approximations (with less than 10-7 relative error) for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2D/3D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.« less

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

DOE PAGES

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; ...

2017-10-24

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1D, 2D, and 3D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, t d0. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, t d0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the firstmore » two terms for high-accuracy approximations (with less than 10-7 relative error) for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2D/3D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.« less

Analytical and numerical construction of vertical periodic orbits about triangular libration points based on polynomial expansion relations among directions

NASA Astrophysics Data System (ADS)

Qian, Ying-Jing; Yang, Xiao-Dong; Zhai, Guan-Qiao; Zhang, Wei

2017-08-01

Innovated by the nonlinear modes concept in the vibrational dynamics, the vertical periodic orbits around the triangular libration points are revisited for the Circular Restricted Three-body Problem. The ζ -component motion is treated as the dominant motion and the ξ and η -component motions are treated as the slave motions. The slave motions are in nature related to the dominant motion through the approximate nonlinear polynomial expansions with respect to the ζ -position and ζ -velocity during the one of the periodic orbital motions. By employing the relations among the three directions, the three-dimensional system can be transferred into one-dimensional problem. Then the approximate three-dimensional vertical periodic solution can be analytically obtained by solving the dominant motion only on ζ -direction. To demonstrate the effectiveness of the proposed method, an accuracy study was carried out to validate the polynomial expansion (PE) method. As one of the applications, the invariant nonlinear relations in polynomial expansion form are used as constraints to obtain numerical solutions by differential correction. The nonlinear relations among the directions provide an alternative point of view to explore the overall dynamics of periodic orbits around libration points with general rules.

Analytical solutions for determining residual stresses in two-dimensional domains using the contour method

PubMed Central

Kartal, Mehmet E.

2013-01-01

The contour method is one of the most prevalent destructive techniques for residual stress measurement. Up to now, the method has involved the use of the finite-element (FE) method to determine the residual stresses from the experimental measurements. This paper presents analytical solutions, obtained for a semi-infinite strip and a finite rectangle, which can be used to calculate the residual stresses directly from the measured data; thereby, eliminating the need for an FE approach. The technique is then used to determine the residual stresses in a variable-polarity plasma-arc welded plate and the results show good agreement with independent neutron diffraction measurements. PMID:24204187

Effect of horizontal heat and fluid flow on the vertical temperature distribution in a semiconfining layer

USGS Publications Warehouse

Lu, Ning; Ge, Shemin

1996-01-01

By including the constant flow of heat and fluid in the horizontal direction, we develop an analytical solution for the vertical temperature distribution within the semiconfining layer of a typical aquifer system. The solution is an extension of the previous one-dimensional theory by Bredehoeft and Papadopulos [1965]. It provides a quantitative tool for analyzing the uncertainty of the horizontal heat and fluid flow. The analytical results demonstrate that horizontal flow of heat and fluid, if at values much smaller than those of the vertical, has a negligible effect on the vertical temperature distribution but becomes significant when it is comparable to the vertical.

Apparent Mass Nonlinearity for Paired Oscillating Plates

NASA Astrophysics Data System (ADS)

Granlund, Kenneth; Ol, Michael

2014-11-01

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

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

NASA Technical Reports Server (NTRS)

Fuller, C. R.

1986-01-01

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

Spatial derivatives of flow quantities behind curved shocks of all strengths

NASA Technical Reports Server (NTRS)

Darden, C. M.

1984-01-01

Explicit formulas in terms of shock curvature are developed for spatial derivatives of flow quantities behind a curved shock for two-dimensional inviscid steady flow. Factors which yield the equations indeterminate as the shock strength approaches 0 have been cancelled analytically so that formulas are valid for shocks of any strength. An application for the method is shown in the solution of shock coalescence when nonaxisymmetric effects are felt through derivatives in the circumferential direction. The solution of this problem requires flow derivatives behind the shock in both the axial and radial direction.

Sensitive ionization of non-volatile analytes using protein solutions as spray liquid in desorption electrospray ionization mass spectrometry.

PubMed

Zhu, Zhiqiang; Han, Jing; Zhang, Yan; Zhou, Yafei; Xu, Ning; Zhang, Bo; Gu, Haiwei; Chen, Huanwen

2012-12-15

Desorption electrospray ionization (DESI) is the most popular ambient ionization technique for direct analysis of complex samples without sample pretreatment. However, for many applications, especially for trace analysis, it is of interest to improve the sensitivity of DESI-mass spectrometry (MS). In traditional DESI-MS, a mixture of methanol/water/acetic acid is usually used to generate the primary ions. In this article, dilute protein solutions were electrosprayed in the DESI method to create multiply charged primary ions for the desorption ionization of trace analytes on various surfaces (e.g., filter paper, glass, Al-foil) without any sample pretreatment. The analyte ions were then detected and structurally characterized using a LTQ XL mass spectrometer. Compared with the methanol/water/acetic acid (49:49:2, v/v/v) solution, protein solutions significantly increased the signal levels of non-volatile compounds such as benzoic acid, TNT, o-toluidine, peptide and insulin in either positive or negative ion detection mode. For all the analytes tested, the limits of detection (LODs) were reduced to about half of the original values which were obtained using traditional DESI. The results showed that the signal enhancement is highly correlated with the molecular weight of the proteins and the selected solid surfaces. The proposed DESI method is a universal strategy for rapid and sensitive detection of trace amounts of strongly bound and/or non-volatile analytes, including explosives, peptides, and proteins. The results indicate that the sensitivity of DESI can be further improved by selecting larger proteins and appropriate solid surfaces. Copyright © 2012 John Wiley & Sons, Ltd.

1-D DC Resistivity Modeling and Interpretation in Anisotropic Media Using Particle Swarm Optimization

NASA Astrophysics Data System (ADS)

Pekşen, Ertan; Yas, Türker; Kıyak, Alper

2014-09-01

We examine the one-dimensional direct current method in anisotropic earth formation. We derive an analytic expression of a simple, two-layered anisotropic earth model. Further, we also consider a horizontally layered anisotropic earth response with respect to the digital filter method, which yields a quasi-analytic solution over anisotropic media. These analytic and quasi-analytic solutions are useful tests for numerical codes. A two-dimensional finite difference earth model in anisotropic media is presented in order to generate a synthetic data set for a simple one-dimensional earth. Further, we propose a particle swarm optimization method for estimating the model parameters of a layered anisotropic earth model such as horizontal and vertical resistivities, and thickness. The particle swarm optimization is a naturally inspired meta-heuristic algorithm. The proposed method finds model parameters quite successfully based on synthetic and field data. However, adding 5 % Gaussian noise to the synthetic data increases the ambiguity of the value of the model parameters. For this reason, the results should be controlled by a number of statistical tests. In this study, we use probability density function within 95 % confidence interval, parameter variation of each iteration and frequency distribution of the model parameters to reduce the ambiguity. The result is promising and the proposed method can be used for evaluating one-dimensional direct current data in anisotropic media.

Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-09-01

Nonlinear two-dimensional Kadomtsev-Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech-tanh, sinh-cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Heat as a groundwater tracer in shallow and deep heterogeneous media: Analytical solution, spreadsheet tool, and field applications

USGS Publications Warehouse

Kurylyk, Barret L.; Irvine, Dylan J.; Carey, Sean K.; Briggs, Martin A.; Werkema, Dale D.; Bonham, Mariah

2017-01-01

Groundwater flow advects heat, and thus, the deviation of subsurface temperatures from an expected conduction‐dominated regime can be analysed to estimate vertical water fluxes. A number of analytical approaches have been proposed for using heat as a groundwater tracer, and these have typically assumed a homogeneous medium. However, heterogeneous thermal properties are ubiquitous in subsurface environments, both at the scale of geologic strata and at finer scales in streambeds. Herein, we apply the analytical solution of Shan and Bodvarsson (2004), developed for estimating vertical water fluxes in layered systems, in 2 new environments distinct from previous vadose zone applications. The utility of the solution for studying groundwater‐surface water exchange is demonstrated using temperature data collected from an upwelling streambed with sediment layers, and a simple sensitivity analysis using these data indicates the solution is relatively robust. Also, a deeper temperature profile recorded in a borehole in South Australia is analysed to estimate deeper water fluxes. The analytical solution is able to match observed thermal gradients, including the change in slope at sediment interfaces. Results indicate that not accounting for layering can yield errors in the magnitude and even direction of the inferred Darcy fluxes. A simple automated spreadsheet tool (Flux‐LM) is presented to allow users to input temperature and layer data and solve the inverse problem to estimate groundwater flux rates from shallow (e.g., <1 m) or deep (e.g., up to 100 m) profiles. The solution is not transient, and thus, it should be cautiously applied where diel signals propagate or in deeper zones where multi‐decadal surface signals have disturbed subsurface thermal regimes.

Direct analyte-probed nanoextraction coupled to nanospray ionization-mass spectrometry of drug residues from latent fingerprints.

PubMed

Clemons, Kristina; Wiley, Rachel; Waverka, Kristin; Fox, James; Dziekonski, Eric; Verbeck, Guido F

2013-07-01

Here, we present a method of extracting drug residues from fingerprints via Direct Analyte-Probed Nanoextraction coupled to nanospray ionization-mass spectrometry (DAPNe-NSI-MS). This instrumental technique provides higher selectivity and lower detection limits over current methods, greatly reducing sample preparation, and does not compromise the integrity of latent fingerprints. This coupled to Raman microscopy is an advantageous supplement for location and identification of trace particles. DAPNe uses a nanomanipulator for extraction and differing microscopies for localization of chemicals of interest. A capillary tip with solvent of choice is placed in a nanopositioner. The surface to be analyzed is placed under a microscope, and a particle of interest is located. Using a pressure injector, the solvent is injected onto the surface where it dissolves the analyte, and then extracted back into the capillary tip. The solution is then directly analyzed via NSI-MS. Analyses of caffeine, cocaine, crystal methamphetamine, and ecstasy have been performed successfully. © 2013 American Academy of Forensic Sciences.

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

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

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

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

2014-05-15

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

Interaction between mean flow and turbulence in two dimensions

PubMed Central

2016-01-01

This short note is written to call attention to an analytic approach to the interaction of developed turbulence with mean flows of simple geometry (jets and vortices). It is instructive to compare cases in two and three dimensions and see why the former are solvable and the latter are not (yet). We present the analytical solutions for two-dimensional mean flows generated by an inverse turbulent cascade on a sphere and in planar domains of different aspect ratios. These solutions are obtained in the limit of small friction when the flow is strong while turbulence can be considered weak and treated perturbatively. I then discuss when these simple solutions can be realized and when more complicated flows may appear instead. The next step of describing turbulence statistics inside a flow and directions of possible future progress are briefly discussed at the end. PMID:27493579

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.

Coronal emission-line polarization from the statistical equilibrium of magnetic sublevels. II. Fe XIV 5303 A

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

House, L.L.; Querfeld, C.W.; Rees, D.E.

1982-04-15

Coronal magnetic fields influence in the intensity and linear polarization of light scattered by coronal Fe XIV ions. To interpret polarization measurements of Fe XIV 5303 A coronal emission requires a detailed understanding of the dependence of the emitted Stokes vector on coronal magnetic field direction, electron density, and temperature and on height of origin. The required dependence is included in the solutions of statistical equilibrium for the ion which are solved explicitly for 34 magnetic sublevels in both the ground and four excited terms. The full solutions are reduced to equivalent simple analytic forms which clearly show the requiredmore » dependence on coronal conditions. The analytic forms of the reduced solutions are suitable for routine analysis of 5303 green line polarimetric data obtained at Pic du Midi and from the Solar Maximum Mission Coronagraph/Polarimeter.« less

Quantification of Water Flux in Vesicular Systems.

PubMed

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

2018-06-04

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

Relative tracking control of constellation satellites considering inter-satellite link

NASA Astrophysics Data System (ADS)

Fakoor, M.; Amozegary, F.; Bakhtiari, M.; Daneshjou, K.

2017-11-01

In this article, two main issues related to the large-scale relative motion of satellites in the constellation are investigated to establish the Inter Satellite Link (ISL) which means the dynamic and control problems. In the section related to dynamic problems, a detailed and effective analytical solution is initially provided for the problem of satellite relative motion considering perturbations. The direct geometric method utilizing spherical coordinates is employed to achieve this solution. The evaluation of simulation shows that the solution obtained from the geometric method calculates the relative motion of the satellite with high accuracy. Thus, the proposed analytical solution will be applicable and effective. In the section related to control problems, the relative tracking control system between two satellites will be designed in order to establish a communication link between the satellites utilizing analytical solution for relative motion of satellites with respect to the reference trajectory. Sliding mode control approach is employed to develop the relative tracking control system for body to body and payload to payload tracking control. Efficiency of sliding mode control approach is compared with PID and LQR controllers. Two types of payload to payload tracking control considering with and without payload degree of freedom are designed and suitable one for practical ISL applications is introduced. Also, Fuzzy controller is utilized to eliminate the control input in the sliding mode controller.

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

Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids.

PubMed

Ferrás, L L; Afonso, A M; Alves, M A; Nóbrega, J M; Pinho, F T

2014-04-15

In this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed. Copyright © 2013 Elsevier Inc. All rights reserved.

Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach.

PubMed

Achilleos, V; Richoux, O; Theocharis, G; Frantzeskakis, D J

2015-02-01

We report experimental results and study theoretically soliton formation and propagation in an air-filled acoustic waveguide side loaded with Helmholtz resonators. We propose a theoretical modeling of the system, which relies on a transmission-line approach, leading to a nonlinear dynamical lattice model. The latter allows for an analytical description of the various soliton solutions for the pressure, which are found by means of dynamical systems and multiscale expansion techniques. These solutions include Boussinesq-like and Korteweg-de Vries pulse-shaped solitons that are observed in the experiment, as well as nonlinear Schrödinger envelope solitons, that are predicted theoretically. The analytical predictions are in excellent agreement with direct numerical simulations and in qualitative agreement with the experimental observations.

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.

Analytical and numerical analysis of the slope of von Mises planar trusses

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

Kalina, M.; Frantík, P.

2016-06-08

In the present paper, there are presented post-critical stress states which will occur at loading by vertical shift of the top joint in the direction downwards. The formation of certain stress states depends on the size of the angle formed by a straight beam of the von Mises planar truss with horizontal plane. Numerical and analytical methods and their problems with finding the angle were described. The numerical solution applies the method of searching for a minimum of potential energy.

On the three-dimensional instability of strained vortices

NASA Technical Reports Server (NTRS)

Waleffe, Fabian

1990-01-01

The three-dimensional (3-D) instability of a two-dimensional (2-D) flow with elliptical streamlines has been proposed as a generic mechanism for the breakdown of many 2-D flows. A physical interpretation for the mechanism is presented together with an analytical treatment of the problem. It is shown that the stability of an elliptical flow is governed by an Ince equation. An analytical representation for a localized solution is given and establishes a direct link with previous computations and experiments.

Development of analytical procedures for the determination of hexavalent chromium in corrosion prevention coatings used in the automotive industry.

PubMed

Séby, F; Castetbon, A; Ortega, R; Guimon, C; Niveau, F; Barrois-Oudin, N; Garraud, H; Donard, O F X

2008-05-01

The European directive 2000/53/EC limits the use of Cr(VI) in vehicle manufacturing. Although a maximum of 2 g of Cr(VI) was authorised per vehicle for corrosion prevention coatings of key components, since July 2007 its use has been prohibited except for some particular applications. Therefore, the objective of this work was to develop direct analytical procedures for Cr(VI) determination in the different steel coatings used for screws. Instead of working directly with screws, the optimisation of the procedures was carried out with metallic plates homogeneously coated to improve the data comparability. Extraction of Cr(VI) from the metallic parts was performed by sonication. Two extraction solutions were tested: a direct water extraction solution used in standard protocols and an ammonium/ammonia buffer solution at pH 8.9. The extracts were further analysed for Cr speciation by high-performance liquid chromatography (HPLC) inductively coupled plasma (ICP) atomic emission spectrometry or HPLC ICP mass spectrometry depending on the concentration level. When possible, the coatings were also directly analysed by solid speciation techniques (X-ray photoelectron spectroscopy, XPS, and X-ray absorption near-edge structure, XANES) for validation of the results. Very good results between the different analytical approaches were obtained for the sample of coating made up of a heated paint containing Zn, Al and Cr when using the extracting buffer solution at pH 8.9. After a repeated four-step extraction procedure on the same portion test, taking into account the depth of the surface layer reached, good agreement with XPS and XANES results was obtained. In contrast, for the coatings composed of an alkaline Zn layer where Cr(VI) and Cr(III) are deposited, only the extraction procedure using water allowed the detection of Cr(VI). To elucidate the Cr(VI) reduction during extraction at pH 8.9, the reactivity of Cr(VI) towards different species of Zn generally present in the coatings (metallic Zn and zinc oxide) was studied. The results showed that metallic Zn rapidly reduces Cr(VI), whereas this reaction is less evident in the presence of zinc oxide. Water was then retained for coatings containing metallic Zn.

Bridging Numerical and Analytical Models of Transient Travel Time Distributions: Challenges and Opportunities

NASA Astrophysics Data System (ADS)

Danesh Yazdi, M.; Klaus, J.; Condon, L. E.; Maxwell, R. M.

2017-12-01

Recent advancements in analytical solutions to quantify water and solute time-variant travel time distributions (TTDs) and the related StorAge Selection (SAS) functions synthesize catchment complexity into a simplified, lumped representation. While these analytical approaches are easy and efficient in application, they require high frequency hydrochemical data for parameter estimation. Alternatively, integrated hydrologic models coupled to Lagrangian particle-tracking approaches can directly simulate age under different catchment geometries and complexity at a greater computational expense. Here, we compare and contrast the two approaches by exploring the influence of the spatial distribution of subsurface heterogeneity, interactions between distinct flow domains, diversity of flow pathways, and recharge rate on the shape of TTDs and the relating SAS functions. To this end, we use a parallel three-dimensional variably saturated groundwater model, ParFlow, to solve for the velocity fields in the subsurface. A particle-tracking model, SLIM, is then implemented to determine the age distributions at every real time and domain location, facilitating a direct characterization of the SAS functions as opposed to analytical approaches requiring calibration of such functions. Steady-state results reveal that the assumption of random age sampling scheme might only hold in the saturated region of homogeneous catchments resulting in an exponential TTD. This assumption is however violated when the vadose zone is included as the underlying SAS function gives a higher preference to older ages. The dynamical variability of the true SAS functions is also shown to be largely masked by the smooth analytical SAS functions. As the variability of subsurface spatial heterogeneity increases, the shape of TTD approaches a power-law distribution function, including a broader distribution of shorter and longer travel times. We further found that larger (smaller) magnitude of effective precipitation shifts the scale of TTD towards younger (older) travel times, while the shape of the TTD remains untouched. This work constitutes a first step in linking a numerical transport model and analytical solutions of TTD to study their assumptions and limitations, providing physical inferences for empirical parameters.

Chirped bright and dark solitons of (3 + 1)-dimensional coupled nonlinear Schrödinger equations in negative-index metamaterials with both electric and magnetic nonlinearity of Kerr type

NASA Astrophysics Data System (ADS)

Dai, Chao-Qing; Fan, Yan; Wang, Yue-Yue; Zheng, Jun

2018-02-01

The (3 + 1)-dimensional generalized coupled nonlinear Schrödinger equation with electric and magnetic nonlinearities of Kerr type and self-steepening effects is studied, and bright and dark soliton solutions are derived. Based on these analytical solutions, dynamical behaviors of bright and dark solitons are discussed. The amplitudes, widths and velocities of bright and dark solitons are all constants determined by the self-steepening effect parameters SE, SH. The phase chirp of a bright soliton diminishes in the pulse front of y-direction, however, it increases in the pulse back edge of y-direction. On the contrary, the phase chirp of a dark soliton increases in the pulse front of y-direction, however, it diminishes in the pulse back edge of y-direction. The phase chirps of a bright and dark soliton both shift along positive y -axis as time goes on. Moreover, the stability of the solutions is discussed.

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.

Development of a GC-MS-SPME Method for the Determination of Amines in Meteorites

NASA Astrophysics Data System (ADS)

Hilts, R. W.; Skelhorne, A. W.; Simkus, D.; Herd, C. D. K.

2016-08-01

A GC-MS-SPME analytical method for the direct determination of amines in aqueous solution has been developed. The key step in the procedure is the conversion of the amines into their non-volatile ammonium salts by protonation with HCl.

Analytical Solution for Low-Thrust Minimum Time Control of a Satellite Formation

DTIC Science & Technology

2004-09-01

The Classical Clohessy - Wiltshire Equations . . . . . . . . . A-1 A.1 Hill’s Rotating Coordinate Frame . . . . . . . . . . . . . . . A-1 A.2 Kinematics...9 A.1. The Clohessy and Wiltshire coordinate frame with x in the radial direction and y in the velocity direction. . . . . . . . . . . . . . . . A-1 B...coordinate system and approx- imations made by Clohessy and Wiltshire , combined with body-fixed thruster control, result in a linearized dynamic system. The

Effects of solar radiation pressure torque on the rotational motion of an artificial satellite

NASA Technical Reports Server (NTRS)

Zanardi, Maria Cecilia F. P. S.; Vilhenademoraes, Rodolpho

1992-01-01

The motion of an artificial satellite about its center of mass is studied considering torques due to the gravity gradient and direct solar radiation pressure. A model for direct solar radiation torque is derived for a circular cylindrical satellite. An analytical solution is obtained by the method of variation of the parameters. This solution shows that the angular variables have secular variation but that the modulus of the rotational angular momentum, the projection of rotational angular momentum on the z axis of the moment of inertia and inertial axis z, suffer only periodic variations. Considering a hypothetical artificial satellite, a numerical application is demonstrated.

Direct spectrophotometric method for analysis of food supplements containing synthetic polyhydroquinones

NASA Astrophysics Data System (ADS)

Vasilevsky, A. M.; Konoplev, G. A.; Stepanova, O. S.; Toropov, D. K.; Zagorsky, A. L.

2016-04-01

A novel direct spectrophotometric method for quantitative determination of Oxiphore® drug substance (synthetic polyhydroquinone complex) in food supplements is developed. Absorption spectra of Oxiphore® water solutions in the ultraviolet region are presented. Samples preparation procedures and mathematical methods of spectra post-analytical procession are discussed. Basic characteristics of the automatic CCD-based UV spectrophotometer and special software implementing the developed method are described. The results of the trials of the developed method and software are analyzed: the error of determination for Oxiphore® concentration in water solutions of the isolated substance and singlecomponent food supplements did not exceed 15% (average error was 7…10%).

An experimental study of wall-injected flows in a rectangular cylinder

NASA Astrophysics Data System (ADS)

Perrotta, A.; Romano, G. P.; Favini, B.

2018-01-01

An experimental investigation of the flow inside a rectangular cylinder with air injected continuously along the wall is performed. This kind of flow is a two-dimensional approximation of what happens inside a solid rocket motor, where the lateral grain burns expelling exhaust gas or in processes with air filtration or devices to attain uniform flows. We propose a brief derivation of some analytical solutions and a comparison between these solutions and experimental data, which are obtained using the particle image velocimetry technique, to provide a global reconstruction of the flowfield. The flow, which enters orthogonal to the injecting wall, turns suddenly its direction being pushed towards the exit of the chamber. Under the incompressible and inviscid flow hypothesis, two analytical solutions are reported and compared. The first one, known as Hart-McClure solution, is irrotational and the injection velocity is non-perpendicular to the injecting wall. The other one, due to Taylor and Culick, has non-zero vorticity and constant, vertical injection velocity. The comparison with laminar solutions is useful to assess whether transition to turbulence is reached and how the disturbance thrown in by the porous injection influences and modifies those solutions.

Study of a two-dimension transient heat propagation in cylindrical coordinates by means of two finite difference methods

NASA Astrophysics Data System (ADS)

Dumencu, A.; Horbaniuc, B.; Dumitraşcu, G.

2016-08-01

The analytical approach of unsteady conduction heat transfer under actual conditions represent a very difficult (if not insurmountable) problem due to the issues related to finding analytical solutions for the conduction heat transfer equation. Various techniques have been developed in order to overcome these difficulties, among which the alternate directions method and the decomposition method. Both of them are particularly suited for two-dimension heat propagation. The paper deals with both techniques in order to verify whether the results provided are in good accordance. The studied case consists of a long hollow cylinder, and considers that the time-dependent temperature field varies both in the radial and the axial directions. The implicit technique is used in both methods and involves the simultaneous solving of a set of equations for all of the nodes for each time step successively for each of the two directions. Gauss elimination is used to obtain the solution of the set, representing the nodal temperatures. After using the two techniques the results show a very good agreement, and since the decomposition is easier to use in terms of computer code and running time, this technique seems to be more recommendable.

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.

Investigations Concerning Hydrolysis and Stabilization of Antiradiation Compounds

DTIC Science & Technology

1982-01-01

Stability of Unencapsulated WR 2721 31 V. DISCUSSION 35 A. Microencapsulation 35 1. Microspheres 35 2. Microcapsules 35 B. Hydrolytic Stability of...in 1.5 hours at 370C in buffered solutions of pH 1.0 or 3.0. 3^ The more promising microspheres and microcapsules released the WR 2721 within two...hours at pH 7.5 in buffered solutions. 4) Analytical procedures were developed for: "♦ WR 2721 (directly) in microcapsules using an HPLC

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.

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

NASA Astrophysics Data System (ADS)

Batu, Vedat

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

Batu, Vedat

2012-01-01

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

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...

Petermann I and II spot size: Accurate semi analytical description involving Nelder-Mead method of nonlinear unconstrained optimization and three parameter fundamental modal field

NASA Astrophysics Data System (ADS)

Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal

2013-01-01

A semi-analytical model with three optimizing parameters and a novel non-Gaussian function as the fundamental modal field solution has been proposed to arrive at an accurate solution to predict various propagation parameters of graded-index fibers with less computational burden than numerical methods. In our semi analytical formulation the optimization of core parameter U which is usually uncertain, noisy or even discontinuous, is being calculated by Nelder-Mead method of nonlinear unconstrained minimizations as it is an efficient and compact direct search method and does not need any derivative information. Three optimizing parameters are included in the formulation of fundamental modal field of an optical fiber to make it more flexible and accurate than other available approximations. Employing variational technique, Petermann I and II spot sizes have been evaluated for triangular and trapezoidal-index fibers with the proposed fundamental modal field. It has been demonstrated that, the results of the proposed solution identically match with the numerical results over a wide range of normalized frequencies. This approximation can also be used in the study of doped and nonlinear fiber amplifier.

Exergy optimization in a steady moving bed heat exchanger.

PubMed

Soria-Verdugo, A; Almendros-Ibáñez, J A; Ruiz-Rivas, U; Santana, D

2009-04-01

This work provides an energy and exergy optimization analysis of a moving bed heat exchanger (MBHE). The exchanger is studied as a cross-flow heat exchanger where one of the phases is a moving granular medium. The optimal MBHE dimensions and the optimal particle diameter are obtained for a range of incoming fluid flow rates. The analyses are carried out over operation data of the exchanger obtained in two ways: a numerical simulation of the steady-state problem and an analytical solution of the simplified equations, neglecting the conduction terms. The numerical simulation considers, for the solid, the convection heat transfer to the fluid and the diffusion term in both directions, and for the fluid only the convection heat transfer to the solid. The results are compared with a well-known analytical solution (neglecting conduction effects) for the temperature distribution in the exchanger. Next, the analytical solution is used to derive an expression for the exergy destruction. The optimal length of the MBHE depends mainly on the flow rate and does not depend on particle diameter unless they become very small (thus increasing sharply the pressure drop). The exergy optimal length is always smaller than the thermal one, although the difference is itself small.

Well test mathematical model for fractures network in tight oil reservoirs

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam

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

Sharma, Pankaj, E-mail: psharma@rtu.ac.in; Parashar, Sandeep Kumar, E-mail: parashar2@yahoo.com

The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d{sub 15} effect. In piezoelectric actuators, the potential use of d{sub 15} effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d{sub 31} and d{sub 33}. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thicknessmore » direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.« less

Laser ablation in analytical chemistry - A review

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

Russo, Richard E.; Mao, Xianglei; Liu, Haichen

Laser ablation is becoming a dominant technology for direct solid sampling in analytical chemistry. Laser ablation refers to the process in which an intense burst of energy delivered by a short laser pulse is used to sample (remove a portion of) a material. The advantages of laser ablation chemical analysis include direct characterization of solids, no chemical procedures for dissolution, reduced risk of contamination or sample loss, analysis of very small samples not separable for solution analysis, and determination of spatial distributions of elemental composition. This review describes recent research to understand and utilize laser ablation for direct solid sampling,more » with emphasis on sample introduction to an inductively coupled plasma (ICP). Current research related to contemporary experimental systems, calibration and optimization, and fractionation is discussed, with a summary of applications in several areas.« less

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.

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.

Insight solutions are correct more often than analytic solutions

PubMed Central

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

2016-01-01

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

Liquid-core photonic crystal fiber platform for raman scattering measurements of microliter analyte solutions

NASA Astrophysics Data System (ADS)

Han, Yun; Oo, Maung Khaing; Zhu, Yinian; Sukhishvili, Svetlana; Xiao, Limin; Demokan, M. Süleyman; Jin, Wei; Du, Henry

2007-09-01

We have explored the use of index-guiding liquid-core photonic crystal fiber (LC-PCF) as a platform for sensing and measurements of analyte solutions of minute volume by normal and surface-enhanced Raman scattering (SERS). The index-guiding LC-PCF was fabricated by selectively sealing via fusion splicing the cladding air channels of a hollow-core PCF (HC-PCF) while leaving the center core open at both ends of the fiber. The center core of the resultant fiber was subsequently filled with water-ethanol solution mixtures at various ethanol concentrations for normal Raman scattering measurements and with water-thiocynate solutions containing Ag nanoparticle aggregates for SERS detection of thiocynate at trace concentrations. The light-guiding nature in the solution phase inside the LC-PCF allows direct and strong light-field overlap with the solution phase over the entire length of the PCF (~30 cm). This detection scheme also dramatically reduces the contribution of silica to Raman spectral background, compared with the solid-core counterpart, thus its potential interference in spectral analysis. These features attribute to ready normal Raman measurements of water, ethanol, and water (99 vol.%)-ethanol (1 vol.%) solutions as well as sensitive and reproducible SERS detection of ~10 ppb thiocynate in water, all at a volume of ~0.1 μL.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Analytical solutions for the dynamics of two trapped interacting ultracold atoms

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

Idziaszek, Zbigniew; Calarco, Tommaso; CNR-INFM BEC Center, I-38050 Povo

2006-08-15

We discuss exact solutions of the Schroedinger equation for the system of two ultracold atoms confined in an axially symmetric harmonic potential. We investigate different geometries of the trapping potential, in particular we study the properties of eigenenergies and eigenfunctions for quasi-one-dimensional and quasi-two-dimensional traps. We show that the quasi-one-dimensional and the quasi-two-dimensional regimes for two atoms can be already realized in the traps with moderately large (or small) ratios of the trapping frequencies in the axial and the transverse directions. Finally, we apply our theory to Feshbach resonances for trapped atoms. Introducing in our description an energy-dependent scattering lengthmore » we calculate analytically the eigenenergies for two trapped atoms in the presence of a Feshbach resonance.« less

Upscaling of Solute Transport in Heterogeneous Media with Non-uniform Flow and Dispersion Fields

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

Xu, Zhijie; Meakin, Paul

2013-10-01

An analytical and computational model for non-reactive solute transport in periodic heterogeneous media with arbitrary non-uniform flow and dispersion fields within the unit cell of length ε is described. The model lumps the effect of non-uniform flow and dispersion into an effective advection velocity Ve and an effective dispersion coefficient De. It is shown that both Ve and De are scale-dependent (dependent on the length scale of the microscopic heterogeneity, ε), dependent on the Péclet number Pe, and on a dimensionless parameter α that represents the effects of microscopic heterogeneity. The parameter α, confined to the range of [-0.5, 0.5]more » for the numerical example presented, depends on the flow direction and non-uniform flow and dispersion fields. Effective advection velocity Ve and dispersion coefficient De can be derived for any given flow and dispersion fields, and . Homogenized solutions describing the macroscopic variations can be obtained from the effective model. Solutions with sub-unit-cell accuracy can be constructed by homogenized solutions and its spatial derivatives. A numerical implementation of the model compared with direct numerical solutions using a fine grid, demonstrated that the new method was in good agreement with direct solutions, but with significant computational savings.« less

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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.

A sample preparation method for recovering suppressed analyte ions in MALDI TOF MS.

PubMed

Lou, Xianwen; de Waal, Bas F M; Milroy, Lech-Gustav; van Dongen, Joost L J

2015-05-01

In matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI TOF MS), analyte signals can be substantially suppressed by other compounds in the sample. In this technical note, we describe a modified thin-layer sample preparation method that significantly reduces the analyte suppression effect (ASE). In our method, analytes are deposited on top of the surface of matrix preloaded on the MALDI plate. To prevent embedding of analyte into the matrix crystals, the sample solution were prepared without matrix and efforts were taken not to re-dissolve the preloaded matrix. The results with model mixtures of peptides, synthetic polymers and lipids show that detection of analyte ions, which were completely suppressed using the conventional dried-droplet method, could be effectively recovered by using our method. Our findings suggest that the incorporation of analytes in the matrix crystals has an important contributory effect on ASE. By reducing ASE, our method should be useful for the direct MALDI MS analysis of multicomponent mixtures. Copyright © 2015 John Wiley & Sons, Ltd.

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.

Green aspects, developments and perspectives of liquid phase microextraction techniques.

PubMed

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

2014-02-01

Determination of analytes at trace levels in complex samples (e.g. biological or contaminated water or soils) are often required for the environmental assessment and monitoring as well as for scientific research in the field of environmental pollution. A limited number of analytical techniques are sensitive enough for the direct determination of trace components in samples and, because of that, a preliminary step of the analyte isolation/enrichment prior to analysis is required in many cases. In this work the newest trends and innovations in liquid phase microextraction, like: single-drop microextraction (SDME), hollow fiber liquid-phase microextraction (HF-LPME), and dispersive liquid-liquid microextraction (DLLME) have been discussed, including their critical evaluation and possible application in analytical practice. The described modifications of extraction techniques deal with system miniaturization and/or automation, the use of ultrasound and physical agitation, and electrochemical methods. Particular attention was given to pro-ecological aspects therefore the possible use of novel, non-toxic extracting agents, inter alia, ionic liquids, coacervates, surfactant solutions and reverse micelles in the liquid phase microextraction techniques has been evaluated in depth. Also, new methodological solutions and the related instruments and devices for the efficient liquid phase micoextraction of analytes, which have found application at the stage of procedure prior to chromatographic determination, are presented. © 2013 Published by Elsevier B.V.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

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.

Optimal starting conditions for the rendezvous maneuver: Analytical and computational approach

NASA Astrophysics Data System (ADS)

Ciarcia, Marco

The three-dimensional rendezvous between two spacecraft is considered: a target spacecraft on a circular orbit around the Earth and a chaser spacecraft initially on some elliptical orbit yet to be determined. The chaser spacecraft has variable mass, limited thrust, and its trajectory is governed by three controls, one determining the thrust magnitude and two determining the thrust direction. We seek the time history of the controls in such a way that the propellant mass required to execute the rendezvous maneuver is minimized. Two cases are considered: (i) time-to-rendezvous free and (ii) time-to-rendezvous given, respectively equivalent to (i) free angular travel and (ii) fixed angular travel for the target spacecraft. The above problem has been studied by several authors under the assumption that the initial separation coordinates and the initial separation velocities are given, hence known initial conditions for the chaser spacecraft. In this paper, it is assumed that both the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given so as to prevent the occurrence of trivial solutions. Two approaches are employed: optimal control formulation (Part A) and mathematical programming formulation (Part B). In Part A, analyses are performed with the multiple-subarc sequential gradient-restoration algorithm for optimal control problems. They show that the fuel-optimal trajectory is zero-bang, namely it is characterized by two subarcs: a long coasting zero-thrust subarc followed by a short powered max-thrust braking subarc. While the thrust direction of the powered subarc is continuously variable for the optimal trajectory, its replacement with a constant (yet optimized) thrust direction produces a very efficient guidance trajectory. Indeed, for all values of the initial distance, the fuel required by the guidance trajectory is within less than one percent of the fuel required by the optimal trajectory. For the guidance trajectory, because of the replacement of the variable thrust direction of the powered subarc with a constant thrust direction, the optimal control problem degenerates into a mathematical programming problem with a relatively small number of degrees of freedom, more precisely: three for case (i) time-to-rendezvous free and two for case (ii) time-to-rendezvous given. In particular, we consider the rendezvous between the Space Shuttle (chaser) and the International Space Station (target). Once a given initial distance SS-to-ISS is preselected, the present work supplies not only the best initial conditions for the rendezvous trajectory, but simultaneously the corresponding final conditions for the ascent trajectory. In Part B, an analytical solution of the Clohessy-Wiltshire equations is presented (i) neglecting the change of the spacecraft mass due to the fuel consumption and (ii) and assuming that the thrust is finite, that is, the trajectory includes powered subarcs flown with max thrust and coasting subarc flown with zero thrust. Then, employing the found analytical solution, we study the rendezvous problem under the assumption that the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given. The main contribution of Part B is the development of analytical solutions for the powered subarcs, an important extension of the analytical solutions already available for the coasting subarcs. One consequence is that the entire optimal trajectory can be described analytically. Another consequence is that the optimal control problems degenerate into mathematical programming problems. A further consequence is that, vis-a-vis the optimal control formulation, the mathematical programming formulation reduces the CPU time by a factor of order 1000. Key words. Space trajectories, rendezvous, optimization, guidance, optimal control, calculus of variations, Mayer problems, Bolza problems, transformation techniques, multiple-subarc sequential gradient-restoration algorithm.

A License to Lead? A New Leadership Agenda for America's Schools.

ERIC Educational Resources Information Center

Hess, Frederick M.

While considerable attention is paid to training and development for teachers, not enough is paid to the training of educational leaders, this paper contends. The aim of this paper is to provide an analytical groundwork and comprehensive direction for reform of educational leadership training to help policymakers design specific solutions to…

Nonlocal dark solitons under competing cubic-quintic nonlinearities.

PubMed

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

2013-01-01

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

Optimal control, optimization and asymptotic analysis of Purcell's microswimmer model

NASA Astrophysics Data System (ADS)

Wiezel, Oren; Or, Yizhar

2016-11-01

Purcell's swimmer (1977) is a classic model of a three-link microswimmer that moves by performing periodic shape changes. Becker et al. (2003) showed that the swimmer's direction of net motion is reversed upon increasing the stroke amplitude of joint angles. Tam and Hosoi (2007) used numerical optimization in order to find optimal gaits for maximizing either net displacement or Lighthill's energetic efficiency. In our work, we analytically derive leading-order expressions as well as next-order corrections for both net displacement and energetic efficiency of Purcell's microswimmer. Using these expressions enables us to explicitly show the reversal in direction of motion, as well as obtaining an estimate for the optimal stroke amplitude. We also find the optimal swimmer's geometry for maximizing either displacement or energetic efficiency. Additionally, the gait optimization problem is revisited and analytically formulated as an optimal control system with only two state variables, which can be solved using Pontryagin's maximum principle. It can be shown that the optimal solution must follow a "singular arc". Numerical solution of the boundary value problem is obtained, which exactly reproduces Tam and Hosoi's optimal gait.

Determination of arsenic and selenium by hydride generation and headspace solid phase microextraction coupled with optical emission spectrometry

NASA Astrophysics Data System (ADS)

Tyburska, Anna; Jankowski, Krzysztof; Rodzik, Agnieszka

2011-07-01

A hydride generation headspace solid phase microextraction technique has been developed in combination with optical emission spectrometry for determination of total arsenic and selenium. Hydrides were generated in a 10 mL volume septum-sealed vial and subsequently collected onto a polydimethylsiloxane/Carboxen solid phase microextraction fiber from the headspace of sample solution. After completion of the sorption, the fiber was transferred into a thermal desorption unit and the analytes were vaporized and directly introduced into argon inductively coupled plasma or helium microwave induced plasma radiation source. Experimental conditions of hydride formation reaction as well as sorption and desorption of analytes have been optimized showing the significant effect of the type of the solid phase microextraction fiber coating, the sorption time and hydrochloric acid concentration of the sample solution on analytical characteristics of the method developed. The limits of detection of arsenic and selenium were 0.1 and 0.8 ng mL - 1 , respectively. The limit of detection of selenium could be improved further using biosorption with baker's yeast Saccharomyces cerevisiae for analyte preconcentration. The technique was applied for the determination of total As and Se in real samples.

Development of new analytical methods for the determination of caffeine content in aqueous solution of green coffee beans.

PubMed

Weldegebreal, Blen; Redi-Abshiro, Mesfin; Chandravanshi, Bhagwan Singh

2017-12-05

This study was conducted to develop fast and cost effective methods for the determination of caffeine in green coffee beans. In the present work direct determination of caffeine in aqueous solution of green coffee bean was performed using FT-IR-ATR and fluorescence spectrophotometry. Caffeine was also directly determined in dimethylformamide solution using NIR spectroscopy with univariate calibration technique. The percentage of caffeine for the same sample of green coffee beans was determined using the three newly developed methods. The caffeine content of the green coffee beans was found to be 1.52 ± 0.09 (% w/w) using FT-IR-ATR, 1.50 ± 0.14 (% w/w) using NIR and 1.50 ± 0.05 (% w/w) using fluorescence spectroscopy. The means of the three methods were compared by applying one way analysis of variance and at p = 0.05 significance level the means were not significantly different. The percentage of caffeine in the same sample of green coffee bean was also determined by using the literature reported UV/Vis spectrophotometric method for comparison and found to be 1.40 ± 0.02 (% w/w). New simple, rapid and inexpensive methods were developed for direct determination of caffeine content in aqueous solution of green coffee beans using FT-IR-ATR and fluorescence spectrophotometries. NIR spectrophotometry can also be used as alternative choice of caffeine determination using reduced amount of organic solvent (dimethylformamide) and univariate calibration technique. These analytical methods may therefore, be recommended for the rapid, simple, safe and cost effective determination of caffeine in green coffee beans.

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.

Analytic solution of the Spencer-Lewis angular-spatial moments equations

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

Filippone, W.L.

A closed-form solution for the angular-spatial moments of the Spencer-Lewis equation is presented that is valid for infinite homogeneous media. From the moments, the electron density distribution as a function of position and path length (energy) is reconstructed for several sample problems involving plane isotropic sources of electrons in aluminium. The results are in excellent agreement with those determined numerically using the streaming ray method. The primary use of the closed form solution will most likely be to generate accurate electron transport benchmark solutions. In principle, the electron density as a function of space, path length, and direction can bemore » determined for planar sources of arbitrary angular distribution.« less

Matrix Sturm-Liouville equation with a Bessel-type singularity on a finite interval

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia

2017-03-01

The matrix Sturm-Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. Special fundamental systems of solutions for this equation are constructed: analytic Bessel-type solutions with the prescribed behavior at the singular point and Birkhoff-type solutions with the known asymptotics for large values of the spectral parameter. The asymptotic formulas for Stokes multipliers, connecting these two fundamental systems of solutions, are derived. We also set boundary conditions and obtain asymptotic formulas for the spectral data (the eigenvalues and the weight matrices) of the boundary value problem. Our results will be useful in the theory of direct and inverse spectral problems.

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.

SPAR demonstration problems. [for stress analysis

NASA Technical Reports Server (NTRS)

Yen, C. L.; Moore, R. A.; Whetstone, W. D.

1974-01-01

A series of examples are presented to indicate some of the principal functions of the SPAR system and to illustrate SPAR's control card-data card structure. Information in the following categories is given: (1) a description of the problem and, in most cases, comparisons with analytical solutions; (2) a list of the input cards; (3) a printout of the table of contents of the direct access library into which all SPAR output was directed; and (4) a few representative plots.

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

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2005-01-01

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

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.

Multi-modal vibration amplitudes of taut inclined cables due to direct and/or parametric excitation

NASA Astrophysics Data System (ADS)

Macdonald, J. H. G.

2016-02-01

Cables are often prone to potentially damaging large amplitude vibrations. The dynamic excitation may be from external loading or motion of the cable ends, the latter including direct excitation, normally from components of end motion transverse to the cable, and parametric excitation induced by axial components of end motion causing dynamic tension variations. Geometric nonlinearity can be important, causing stiffening behaviour and nonlinear modal coupling. Previous analyses of the vibrations, often neglecting sag, have generally dealt with direct and parametric excitation separately or have reverted to numerical solutions of the responses. Here a nonlinear cable model is adopted, applicable to taut cables such as on cable-stayed bridges, that allows for cable inclination, small sag (such that the vibration modes are similar to those of a taut string), multiple modes in both planes and end motion and/or external forcing close to any natural frequency. Based on the method of scaling and averaging it is found that, for sinusoidal inputs and positive damping, non-zero steady state responses can only occur in the modes in each plane with natural frequencies close to the excitation frequency and those with natural frequencies close to half this frequency. Analytical solutions, in the form of non-dimensional polynomial equations, are derived for the steady state vibration amplitudes in up to three modes simultaneously: the directly excited mode, the corresponding nonlinearly coupled mode in the orthogonal plane and a parametrically excited mode with half the natural frequency. The stability of the solutions is also identified. The outputs of the equations are consistent with previous results, where available. Example results from the analytical solutions are presented for a typical inclined bridge cable subject to vertical excitation of the lower end, and they are validated by numerical integration of the equations of motion and against some previous experimental results. It is shown that the modal interactions and sag (although very small) affect the responses significantly.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Investigating Compaction by Intergranular Pressure Solution Using the Discrete Element Method

NASA Astrophysics Data System (ADS)

van den Ende, M. P. A.; Marketos, G.; Niemeijer, A. R.; Spiers, C. J.

2018-01-01

Intergranular pressure solution creep is an important deformation mechanism in the Earth's crust. The phenomenon has been frequently studied and several analytical models have been proposed that describe its constitutive behavior. These models require assumptions regarding the geometry of the aggregate and the grain size distribution in order to solve for the contact stresses and often neglect shear tractions. Furthermore, analytical models tend to overestimate experimental compaction rates at low porosities, an observation for which the underlying mechanisms remain to be elucidated. Here we present a conceptually simple, 3-D discrete element method (DEM) approach for simulating intergranular pressure solution creep that explicitly models individual grains, relaxing many of the assumptions that are required by analytical models. The DEM model is validated against experiments by direct comparison of macroscopic sample compaction rates. Furthermore, the sensitivity of the overall DEM compaction rate to the grain size and applied stress is tested. The effects of the interparticle friction and of a distributed grain size on macroscopic strain rates are subsequently investigated. Overall, we find that the DEM model is capable of reproducing realistic compaction behavior, and that the strain rates produced by the model are in good agreement with uniaxial compaction experiments. Characteristic features, such as the dependence of the strain rate on grain size and applied stress, as predicted by analytical models, are also observed in the simulations. DEM results show that interparticle friction and a distributed grain size affect the compaction rates by less than half an order of magnitude.

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.

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.

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.

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

Choi, Jeong

The research program reported here is focused on critical issues that represent conspicuous gaps in current understanding of rapid solidification, limiting our ability to predict and control microstructural evolution (i.e. morphological dynamics and microsegregation) at high undercooling, where conditions depart significantly from local equilibrium. More specifically, through careful application of phase-field modeling, using appropriate thin-interface and anti-trapping corrections and addressing important details such as transient effects and a velocity-dependent (i.e. adaptive) numerics, the current analysis provides a reasonable simulation-based picture of non-equilibrium solute partitioning and the corresponding oscillatory dynamics associated with single-phase rapid solidification and show that this method ismore » a suitable means for a self-consistent simulation of transient behavior and operating point selection under rapid growth conditions. Moving beyond the limitations of conventional theoretical/analytical treatments of non-equilibrium solute partitioning, these results serve to substantiate recent experimental findings and analytical treatments for single-phase rapid solidification. The departure from the equilibrium solid concentration at the solid-liquid interface was often observed during rapid solidification, and the energetic associated non-equilibrium solute partitioning has been treated in detail, providing possible ranges of interface concentrations for a given growth condition. Use of these treatments for analytical description of specific single-phase dendritic and cellular operating point selection, however, requires a model for solute partitioning under a given set of growth conditions. Therefore, analytical solute trapping models which describe the chemical partitioning as a function of steady state interface velocities have been developed and widely utilized in most of the theoretical investigations of rapid solidification. However, these solute trapping models are not rigorously verified due to the difficulty in experimentally measuring under rapid growth conditions. Moreover, since these solute trapping models include kinetic parameters which are difficult to directly measure from experiments, application of the solute trapping models or the associated analytic rapid solidification model is limited. These theoretical models for steady state rapid solidification which incorporate the solute trapping models do not describe the interdependency of solute diffusion, interface kinetics, and alloy thermodynamics. The phase-field approach allows calculating, spontaneously, the non-equilibrium growth effects of alloys and the associated time-dependent growth dynamics, without making the assumptions that solute partitioning is an explicit function of velocity, as is the current convention. In the research described here, by utilizing the phase-field model in the thin-interface limit, incorporating the anti-trapping current term, more quantitatively valid interface kinetics and solute diffusion across the interface are calculated. In order to sufficiently resolve the physical length scales (i.e. interface thickness and diffusion boundary length), grid spacings are continually adjusted in calculations. The full trajectories of transient planar growth dynamics under rapid directional solidification conditions with different pulling velocities are described. As a validation of a model, the predicted steady state conditions are consistent with the analytic approach for rapid growth. It was confirmed that rapid interface dynamics exhibits the abrupt acceleration of the planar front when the effect of the non-equilibrium solute partitioning at the interface becomes signi ficant. This is consistent with the previous linear stability analysis for the non-equilibrium interface dynamics. With an appropriate growth condition, the continuous oscillation dynamics was able to be simulated using continually adjusting grid spacings. This oscillatory dynamics including instantaneous jump of interface velocities are consistent with a previous phenomenological model by and a numerical investigation, which may cause the formation of banded structures. Additionally, the selection of the steady state growth dynamics in the highly undercooled melt is demonstrated. The transition of the growth morphology, interface velocity selection, and solute trapping phenomenon with increasing melt supersaturations was described by the phase-field simulation. The tip selection for the dendritic growth was consistent with Ivantsov's function, and the non-equilibrium chemical partitioning behavior shows good qualitative agreement with the Aziz's solute trapping model even though the model parameter(V D) remains as an arbitrary constant. This work is able to show the possibility of comprehensive description of rapid alloy growth over the entire time-dependent non-equilibrium phenomenon.« less

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.

On parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems

NASA Astrophysics Data System (ADS)

Lastra, A.; Malek, S.

2015-11-01

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

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

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

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...

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

NASA Astrophysics Data System (ADS)

Lane, M. T.

1989-06-01

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

Transition regime analytical solution to gas mass flow rate in a rectangular micro channel

NASA Astrophysics Data System (ADS)

Dadzie, S. Kokou; Dongari, Nishanth

2012-11-01

We present an analytical model predicting the experimentally observed gas mass flow rate in rectangular micro channels over slip and transition regimes without the use of any fitting parameter. Previously, Sone reported a class of pure continuum regime flows that requires terms of Burnett order in constitutive equations of shear stress to be predicted appropriately. The corrective terms to the conventional Navier-Stokes equation were named the ghost effect. We demonstrate in this paper similarity between Sone ghost effect model and newly so-called 'volume diffusion hydrodynamic model'. A generic analytical solution to gas mass flow rate in a rectangular micro channel is then obtained. It is shown that the volume diffusion hydrodynamics allows to accurately predict the gas mass flow rate up to Knudsen number of 5. This can be achieved without necessitating the use of adjustable parameters in boundary conditions or parametric scaling laws for constitutive relations. The present model predicts the non-linear variation of pressure profile along the axial direction and also captures the change in curvature with increase in rarefaction.

Collisionless kinetic theory of oblique tearing instabilities

DOE PAGES

Baalrud, S. D.; Bhattacharjee, A.; Daughton, W.

2018-02-15

The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes. In this paper, we find that this stabilization is associated with the density-gradient-driven diamagnetic drift. Themore » analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. Finally, a simple analytic estimate for the stability criterion is provided.« less

Analytical solutions of mushy layer equations describing directional solidification in the presence of nucleation

NASA Astrophysics Data System (ADS)

Alexandrov, Dmitri V.; Ivanov, Alexander A.; Alexandrova, Irina V.

2018-01-01

The processes of particle nucleation and their evolution in a moving metastable layer of phase transition (supercooled liquid or supersaturated solution) are studied analytically. The transient integro-differential model for the density distribution function and metastability level is solved for the kinetic and diffusionally controlled regimes of crystal growth. The Weber-Volmer-Frenkel-Zel'dovich and Meirs mechanisms for nucleation kinetics are used. We demonstrate that the phase transition boundary lying between the mushy and pure liquid layers evolves with time according to the following power dynamic law: , where Z1(t)=βt7/2 and Z1(t)=βt2 in cases of kinetic and diffusionally controlled scenarios. The growth rate parameters α, β and ε are determined analytically. We show that the phase transition interface in the presence of crystal nucleation and evolution propagates slower than in the absence of their nucleation. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.

Collisionless kinetic theory of oblique tearing instabilities

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

Baalrud, S. D.; Bhattacharjee, A.; Daughton, W.

The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes. In this paper, we find that this stabilization is associated with the density-gradient-driven diamagnetic drift. Themore » analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. Finally, a simple analytic estimate for the stability criterion is provided.« less

Collisionless kinetic theory of oblique tearing instabilities

NASA Astrophysics Data System (ADS)

Baalrud, S. D.; Bhattacharjee, A.; Daughton, W.

2018-02-01

The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes. We find that this stabilization is associated with the density-gradient-driven diamagnetic drift. The analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. A simple analytic estimate for the stability criterion is provided.

Analytical study of magnetohydrodynamic propulsion stability

NASA Astrophysics Data System (ADS)

Abdollahzadeh Jamalabadi, M. Y.

2014-09-01

In this paper an analytical solution for the stability of the fully developed flow drive in a magneto-hydro-dynamic pump with pulsating transverse Eletro-magnetic fields is presented. To do this, a theoretical model of the flow is developed and the analytical results are obtained for both the cylindrical and Cartesian configurations that are proper to use in the propulsion of marine vessels. The governing parabolic momentum PDEs are transformed into an ordinary differential equation using approximate velocity distribution. The numerical results are obtained and asymptotic analyses are built to discover the mathematical behavior of the solutions. The maximum velocity in a magneto-hydro-dynamic pump versus time for various values of the Stuart number, electro-magnetic interaction number, Reynolds number, aspect ratio, as well as the magnetic and electrical angular frequency and the shift of the phase angle is presented. Results show that for a high Stuart number there is a frequency limit for stability of the fluid flow in a certain direction of the flow. This stability frequency is dependent on the geometric parameters of a channel.

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.

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Ma, Wen-Xiu; Zhou, Yuan

2018-02-01

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

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.

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.

Small-amplitude oscillations of electrostatically levitated drops

NASA Astrophysics Data System (ADS)

Feng, J. Q.; Beard, K. V.

1990-07-01

The nature of axisymmetric oscillations of electrostatically levitated drops is examined using an analytical method of multiple-parameter perturbations. The solution for the quiescent equilibrium shape exhibits both stretching of the drop surface along the direction of the externally applied electric field and asymmetry about the drop's equatorial plane. In the presence of electric and gravitational fields, small-amplitude oscillations of charged drops differ from the linear modes first analyzed by Rayleigh. The oscillatory response at each frequency consists of several Legendre polynomials rather than just one, and the characteristic frequency for each axisymmetric mode decreases from that calculated by Rayleigh as the electric field strength increases. This lowering of the characteristic frequencies is enhanced by the net electric charge required for levitation against gravity. Since the contributions of the various forces appear explicitly in the analytic solutions, physical insight is readily gained into their causative role in drop behavior.

Peristalsis of nonconstant viscosity Jeffrey fluid with nanoparticles

NASA Astrophysics Data System (ADS)

Alvi, N.; Latif, T.; Hussain, Q.; Asghar, S.

Mixed convective peristaltic activity of variable viscosity nanofluids is addressed. Unlike the conventional consideration of constant viscosity; the viscosity is taken as temperature dependent. Constitutive relations for linear viscoelastic Jeffrey fluid are employed and uniform magnetic field is applied in the transverse direction. For nanofluids, the formulation is completed in presence of Brownian motion, thermophoresis, viscous dissipation and Joule heating. Consideration of temperature dependence of viscosity is not a choice but the realistic requirement of the wall temperature and the heat generated due to the viscous dissipation. Well established large wavelength and small Reynolds number approximations are invoked. Non-linear coupled system is analytically solved for the convergent series solutions identifying the interval of convergence explicitly. A comparative study between analytical and numerical solution is made for certainty. Influence of the parameters undertaken for the description of the problem is pointed out and its physics explained.

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.

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.

Hypercube Solutions for Conjugate Directions

DTIC Science & Technology

1991-12-01

1800s, Charles Babbage had designed his Difference Engine and proceeded to the more advanced Analytical Engine. These machines were 1 never completed...Consider his motivation. The following example was frequently cited by Charles Babbage (1792-1871) to justify the construction of his first computing...360 LIST OF REFERENCES [1] P. Morrison and E. Morrison, editors. Charles Babbage and His Calculating Engines. Dover Publications, Inc., New

Enhancing Information Awareness Through Directed Qualification of Semantic Relevancy Scoring Operations

DTIC Science & Technology

2014-06-01

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

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.

Simultaneous determination of glucose, triglycerides, urea, cholesterol, albumin and total protein in human plasma by Fourier transform infrared spectroscopy: direct clinical biochemistry without reagents.

PubMed

Jessen, Torben E; Höskuldsson, Agnar T; Bjerrum, Poul J; Verder, Henrik; Sørensen, Lars; Bratholm, Palle S; Christensen, Bo; Jensen, Lene S; Jensen, Maria A B

2014-09-01

Direct measurement of chemical constituents in complex biologic matrices without the use of analyte specific reagents could be a step forward toward the simplification of clinical biochemistry. Problems related to reagents such as production errors, improper handling, and lot-to-lot variations would be eliminated as well as errors occurring during assay execution. We describe and validate a reagent free method for direct measurement of six analytes in human plasma based on Fourier-transform infrared spectroscopy (FTIR). Blood plasma is analyzed without any sample preparation. FTIR spectrum of the raw plasma is recorded in a sampling cuvette specially designed for measurement of aqueous solutions. For each analyte, a mathematical calibration process is performed by a stepwise selection of wavelengths giving the optimal least-squares correlation between the measured FTIR signal and the analyte concentration measured by conventional clinical reference methods. The developed calibration algorithms are subsequently evaluated for their capability to predict the concentration of the six analytes in blinded patient samples. The correlation between the six FTIR methods and corresponding reference methods were 0.87

Direct determination of lead in biological samples by electrothermal vaporization inductively coupled plasma mass spectrometry (ETV-ICP-MS) after furnace-fusion in the sample cuvette-tungsten boat furnace.

PubMed

Okamoto, Y

2000-06-01

The newly conceived electrothermal vaporization (ETV) system using a tungsten boat furnace (TBF) sample cuvette was designed for the direct analysis of solid samples with detection by inductively coupled plasma mass spectrometry (ICP-MS). Into this small sample cuvette, a solid mixture of the biological samples and diammonium hydrogenphosphate powder as a fusion flux was placed and situated on a TBF. Tetramethylammonium hydroxide solution was added to the mixture. After the on-furnace digestion had been completed, the analyte in the cuvette was vaporized and introduced into the ICP mass spectrometer. The solid samples were analyzed by using a calibration curve prepared from the aqueous standard solutions. The detection limit was estimated to be 5.1 pg of lead, which corresponds to 10.2 ng g(-1) of lead in solid samples when a prepared sample amount of 1.0 mg was applied. The relative standard deviation for 8 replicate measurements obtained with 100 pg of lead was calculated to be 6.5%. The analytical results for various biological samples are described.

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...

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

NASA Astrophysics Data System (ADS)

Al Noufaey, K. S.

2018-06-01

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

Estimating Aquifer Properties Using Sinusoidal Pumping Tests

NASA Astrophysics Data System (ADS)

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

2001-12-01

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

Mitigation of solvent interference using a short packed column prior to ion mobility spectrometry.

PubMed

Jafari, Mohammad T; Saraji, Mohammad; Mossaddegh, Mehdi

2017-05-15

This paper introduces a novel approach to overcome the solvent interference in corona discharge-ion mobility spectrometry (CD-IMS) based on the time-resolved signals of the solvent and the analyte. To that end, a short Teflon tube was filled with a low amount of squalene or OV-1, which was prepared and located between the injection port and the entrance of the CD-IMS cell. Through this procedure, a sufficient delay (~5s) was obtained between the introduction of the solvent and the analyte into the reaction region of IMS. This resulted in removing the proton by solvent molecules, as well as increasing the effective collision during the analyte ionization, thereby providing an analysis with more sensitivity, accuracy, and precision. To show the column efficiency, ethion and diazinon (organophosphorus pesticides) were selected as the test compounds and their solutions were analyzed by the proposed method. The amount of sorbent, carrier gas flow rate, and the sorbent temperature affecting the sorbent efficiency were optimized by employing the response surface methodology and the central composite design. The proposed method was exhaustively validated in terms of sensitivity, linearity, and repeatability. In particular, the feasibility of direct injection was successfully verified by the satisfactory results, as compared with those achieved without the prior column. The methodology used in this study is very simple and inexpensive, which can overcome the solvent interference when a solution is directly injected into the CD-IMS. Copyright © 2017 Elsevier B.V. All rights reserved.

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.

Exact solution for four-order acousto-optic Bragg diffraction with arbitrary initial conditions.

PubMed

Pieper, Ron; Koslover, Deborah; Poon, Ting-Chung

2009-03-01

An exact solution to the four-order acousto-optic (AO) Bragg diffraction problem with arbitrary initial conditions compatible with exact Bragg angle incident light is developed. The solution, obtained by solving a 4th-order differential equation, is formalized into a transition matrix operator predicting diffracted light orders at the exit of the AO cell in terms of the same diffracted light orders at the entrance. It is shown that the transition matrix is unitary and that this unitary matrix condition is sufficient to guarantee energy conservation. A comparison of analytical solutions with numerical predictions validates the formalism. Although not directly related to the approach used to obtain the solution, it was discovered that all four generated eigenvalues from the four-order AO differential matrix operator are expressed simply in terms of Euclid's Divine Proportion.

Nonlinear dynamics of mushy layers induced by external stochastic fluctuations.

PubMed

Alexandrov, Dmitri V; Bashkirtseva, Irina A; Ryashko, Lev B

2018-02-28

The time-dependent process of directional crystallization in the presence of a mushy layer is considered with allowance for arbitrary fluctuations in the atmospheric temperature and friction velocity. A nonlinear set of mushy layer equations and boundary conditions is solved analytically when the heat and mass fluxes at the boundary between the mushy layer and liquid phase are induced by turbulent motion in the liquid and, as a result, have the corresponding convective form. Namely, the 'solid phase-mushy layer' and 'mushy layer-liquid phase' phase transition boundaries as well as the solid fraction, temperature and concentration (salinity) distributions are found. If the atmospheric temperature and friction velocity are constant, the analytical solution takes a parametric form. In the more common case when they represent arbitrary functions of time, the analytical solution is given by means of the standard Cauchy problem. The deterministic and stochastic behaviour of the phase transition process is analysed on the basis of the obtained analytical solutions. In the case of stochastic fluctuations in the atmospheric temperature and friction velocity, the phase transition interfaces (mushy layer boundaries) move faster than in the deterministic case. A cumulative effect of these noise contributions is revealed as well. In other words, when the atmospheric temperature and friction velocity fluctuate simultaneously due to the influence of different external processes and phenomena, the phase transition boundaries move even faster. This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'. © 2018 The Author(s).

Investigation of compositional segregation during unidirectional solidification of solid solution semiconducting alloys

NASA Technical Reports Server (NTRS)

Wang, J. C.

1982-01-01

Compositional segregation of solid solution semiconducting alloys in the radial direction during unidirectional solidification was investigated by calculating the effect of a curved solid liquid interface on solute concentration at the interface on the solid. The formulation is similar to that given by Coriell, Boisvert, Rehm, and Sekerka except that a more realistic cylindrical coordinate system which is moving with the interface is used. Analytical results were obtained for very small and very large values of beta with beta = VR/D, where V is the velocity of solidification, R the radius of the specimen, and D the diffusivity of solute in the liquid. For both very small and very large beta, the solute concentration at the interface in the solid C(si) approaches C(o) (original solute concentration) i.e., the deviation is minimal. The maximum deviation of C(si) from C(o) occurs for some intermediate value of beta.

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

NASA Astrophysics Data System (ADS)

Lefèvre, Victor; Lopez-Pamies, Oscar

2017-02-01

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

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

USGS Publications Warehouse

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

2014-01-01

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

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

EPA Science Inventory

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

DEFLECTION OF A HETEROGENEOUS WIDE-BEAM UNDER UNIFORM PRESSURE LOAD

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

T. V. Holschuh; T. K. Howard; W. R. Marcum

2014-07-01

Oregon State University (OSU) and the Idaho National Laboratory (INL) are currently collaborating on a test program which entails hydro-mechanical testing of a generic plate type fuel element, or generic test plate assembly (GTPA), for the purpose of qualitatively demonstrating mechanical integrity of uranium-molybdenum monolithic plates as compared to that of uranium aluminum dispersion, and aluminum fuel plates onset by hydraulic forces. This test program supports ongoing work conducted for/by the Global Threat Reduction Initiative (GTRI) Fuels Development Program. This study’s focus supports the ongoing collaborative effort by detailing the derivation of an analytic solution for deflection of a heterogeneousmore » plate under a uniform, distributed load in order to predict the deflection of test plates in the GTPA. The resulting analytical solutions for three specific boundary condition sets are then presented against several test cases of a homogeneous plate. In all test cases considered, the results for both homogeneous and heterogeneous plates are numerically identical to one another, demonstrating correct derivation of the heterogeneous solution. Two additional problems are presents herein that provide a representative deflection profile for the plates under consideration within the GTPA. Furthermore, qualitative observations are made about the influence of a more-rigid internal fuel-meat region and its influence on the overall deflection profile of a plate. Present work is being directed to experimentally confirm the analytical solution’s results using select materials.« less

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

NASA Astrophysics Data System (ADS)

Sarmah, Ratan; Tiwari, Shubham

2018-03-01

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

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

Modeling ultrasonic transient scattering from biological tissues including their dispersive properties directly in the time domain.

PubMed

Norton, G V; Novarini, J C

2007-06-01

Ultrasonic imaging in medical applications involves propagation and scattering of acoustic waves within and by biological tissues that are intrinsically dispersive. Analytical approaches for modeling propagation and scattering in inhomogeneous media are difficult and often require extremely simplifying approximations in order to achieve a solution. To avoid such approximations, the direct numerical solution of the wave equation via the method of finite differences offers the most direct tool, which takes into account diffraction and refraction. It also allows for detailed modeling of the real anatomic structure and combination/layering of tissues. In all cases the correct inclusion of the dispersive properties of the tissues can make the difference in the interpretation of the results. However, the inclusion of dispersion directly in the time domain proved until recently to be an elusive problem. In order to model the transient signal a convolution operator that takes into account the dispersive characteristics of the medium is introduced to the linear wave equation. To test the ability of this operator to handle scattering from localized scatterers, in this work, two-dimensional numerical modeling of scattering from an infinite cylinder with physical properties associated with biological tissue is calculated. The numerical solutions are compared with the exact solution synthesized from the frequency domain for a variety of tissues having distinct dispersive properties. It is shown that in all cases, the use of the convolutional propagation operator leads to the correct solution for the scattered field.

Protein associations and analytical ultracentrifugation

NASA Astrophysics Data System (ADS)

Laue, Tom

2010-03-01

Analytical ultracentrifugation (AUC) is a first principle method for characterizing the thermodynamics of macromolecules in solution. Since AUC directly assesses mass, it is particularly useful for characterizing both reversible and irreversible binding interactions between macromolecules. The principle measurement in AUC is the concentration as a function of radial position, which may be provided by either absorbance, interference or fluorescence detection. Each of these three different detectors may be used to characterize protein associations using either sedimentation equilibrium or sedimentation velocity analysis. Examples will be shown for characterizing irreversible (aggregate) formation, high-accuracy reversible association analysis, and the detection of protein interactions in complex and concentrated fluids (e.g. serum, cell cytosol).

Solvability of the electrocardiology inverse problem for a moving dipole.

PubMed

Tolkachev, V; Bershadsky, B; Nemirko, A

1993-01-01

New formulations of the direct and inverse problems for the moving dipole are offered. It has been suggested to limit the study by a small area on the chest surface. This lowers the role of the medium inhomogeneity. When formulating the direct problem, irregular components are considered. The algorithm of simultaneous determination of the dipole and regular noise parameters has been described and analytically investigated. It is shown that temporal overdetermination of the equations offers a single solution of the inverse problem for the four leads.

Macrosegregation during plane front directional solidification of Csl-1 wt. percent Tll alloy

NASA Technical Reports Server (NTRS)

Sidawi, I. M. S.; Tewari, S. N.

1991-01-01

Macrosegregation produced during vertical Bridgeman directional solidification of Csl-1 wt. pct. Tll in crucibles of varying diameter, from 0.5 to 2.0 cm, was examined. Gravity driven convection is present in the melt even in the smallest crucible diameter of 0.5 cm. Observed solutal profiles are in agreement with the analytical boundary layer model of Favier which describes macrosegregation in the presence of convection. The scintillation efficiency of Csl decreases along the specimen length as the thallium iodide content of the alloy increases.

Thermoelastic damping in thin microrings with two-dimensional heat conduction

NASA Astrophysics Data System (ADS)

Fang, Yuming; Li, Pu

2015-05-01

Accurate determination of thermoelastic damping (TED) is very challenging in the design of micro-resonators. Microrings are widely used in many micro-resonators. In the past, to model the TED effect on the microrings, some analytical models have been developed. However, in the previous works, the heat conduction within the microring is modeled by using the one-dimensional approach. The governing equation for heat conduction is solved only for the one-dimensional heat conduction along the radial thickness of the microring. This paper presents a simple analytical model for TED in microrings. The two-dimensional heat conduction over the thermoelastic temperature gradients along the radial thickness and the circumferential direction are considered in the present model. A two-dimensional heat conduction equation is developed. The solution of the equation is represented by the product of an assumed sine series along the radial thickness and an assumed trigonometric series along the circumferential direction. The analytical results obtained by the present 2-D model show a good agreement with the numerical (FEM) results. The limitations of the previous 1-D model are assessed.

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 YORP torques model with an improved temperature distribution function

NASA Astrophysics Data System (ADS)

Breiter, S.; Vokrouhlický, D.; Nesvorný, D.

2010-01-01

Previous models of the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect relied either on the zero thermal conductivity assumption, or on the solutions of the heat conduction equations assuming an infinite body size. We present the first YORP solution accounting for a finite size and non-radial direction of the surface normal vectors in the temperature distribution. The new thermal model implies the dependence of the YORP effect in rotation rate on asteroids conductivity. It is shown that the effect on small objects does not scale as the inverse square of diameter, but rather as the first power of the inverse.

Interactive program for analysis and design problems in advanced composites technology

NASA Technical Reports Server (NTRS)

Cruse, T. A.; Swedlow, J. L.

1971-01-01

During the past year an experimental program in the fracture of advanced fiber composites has been completed. The experimental program has given direction to additional experimental and theoretical work. A synthesis program for designing low weight multifastener joints in composites is proposed, based on extensive analytical background. A number of failed joints have been thoroughly analyzed to evaluate the failure hypothesis used in the synthesis procedure. Finally, a new solution is reported for isotropic and anisotropic laminates using the boundary-integral method. The solution method offers significant savings of computer core and time for important problems.

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.

MC ICP-MS δ(34)S(VCDT) measurement of dissolved sulfate in environmental aqueous samples after matrix separation by means of an anion exchange membrane.

PubMed

Hanousek, Ondrej; Berger, Torsten W; Prohaska, Thomas

2016-01-01

Analysis of (34)S/(32)S of sulfate in rainwater and soil solutions can be seen as a powerful tool for the study of the sulfur cycle. Therefore, it is considered as a useful means, e.g., for amelioration and calibration of ecological or biogeochemical models. Due to several analytical limitations, mainly caused by low sulfate concentration in rainwater, complex matrix of soil solutions, limited sample volume, and high number of samples in ecosystem studies, a straightforward analytical protocol is required to provide accurate S isotopic data on a large set of diverse samples. Therefore, sulfate separation by anion exchange membrane was combined with precise isotopic measurement by multicollector inductively coupled plasma mass spectrometry (MC ICP-MS). The separation method proved to be able to remove quantitatively sulfate from matrix cations (Ca, K, Na, or Li) which is a precondition in order to avoid a matrix-induced analytical bias in the mass spectrometer. Moreover, sulfate exchange on the resin is capable of preconcentrating sulfate from low concentrated solutions (to factor 3 in our protocol). No significant sulfur isotope fractionation was observed during separation and preconcentration. MC ICP-MS operated at edge mass resolution has enabled the direct (34)S/(32)S analysis of sulfate eluted from the membrane, with an expanded uncertainty U (k = 2) down to 0.3 ‰ (a single measurement). The protocol was optimized and validated using different sulfate solutions and different matrix compositions. The optimized method was applied in a study on solute samples retrieved in a beech (Fagus sylvatica) forest in the Vienna Woods. Both rainwater (precipitation and tree throughfall) and soil solution δ (34)SVCDT ranged between 4 and 6 ‰, the ratio in soil solution being slightly lower. The lower ratio indicates that a considerable portion of the atmospherically deposited sulfate is cycled through the organic S pool before being released to the soil solution. Nearly the same trends and variations were observed in soil solution and rainwater δ (34)SVCDT values showing that sulfate adsorption/desorption are not important processes in the studied soil.

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

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.

An algebraic program for the states associated with the U(5) ⊃ O(5) ⊃ O(3) chain of groups

NASA Astrophysics Data System (ADS)

Yannouleas, C.; Pacheco, J. M.

1988-12-01

A REDUCE program is presented that calculates algebraically the γ-dependent part of the states associated with the U(5) ⊃ O(5) ⊃ O(3) chain of groups, familiar from nuclear-structure problems. The method of solution is a direct implementation of the analytic expressions given by Chacón and Moshinsky.

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

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

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

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

Passive non-linear microrheology for determining extensional viscosity

NASA Astrophysics Data System (ADS)

Hsiao, Kai-Wen; Dinic, Jelena; Ren, Yi; Sharma, Vivek; Schroeder, Charles M.

2017-12-01

Extensional viscosity is a key property of complex fluids that greatly influences the non-equilibrium behavior and processing of polymer solutions, melts, and colloidal suspensions. In this work, we use microfluidics to determine steady extensional viscosity for polymer solutions by directly observing particle migration in planar extensional flow. Tracer particles are suspended in semi-dilute solutions of DNA and polyethylene oxide, and a Stokes trap is used to confine single particles in extensional flows of polymer solutions in a cross-slot device. Particles are observed to migrate in the direction transverse to flow due to normal stresses, and particle migration is tracked and quantified using a piezo-nanopositioning stage during the microfluidic flow experiment. Particle migration trajectories are then analyzed using a second-order fluid model that accurately predicts that migration arises due to normal stress differences. Using this analytical framework, extensional viscosities can be determined from particle migration experiments, and the results are in reasonable agreement with bulk rheological measurements of extensional viscosity based on a dripping-onto-substrate method. Overall, this work demonstrates that non-equilibrium properties of complex fluids can be determined by passive yet non-linear microrheology.

Solution-based analysis of multiple analytes by a sensor array: toward the development of an electronic tongue

NASA Astrophysics Data System (ADS)

Savoy, Steven M.; Lavigne, John J.; Yoo, J. S.; Wright, John; Rodriguez, Marc; Goodey, Adrian; McDoniel, Bridget; McDevitt, John T.; Anslyn, Eric V.; Shear, Jason B.; Ellington, Andrew D.; Neikirk, Dean P.

1998-12-01

A micromachined sensor array has been developed for the rapid characterization of multi-component mixtures in aqueous media. The sensor functions in a manner analogous to that of the mammalian tongue, using an array composed of individually immobilized polystyrene-polyethylene glycol composite microspheres selectively arranged in micromachined etch cavities localized o n silicon wafers. Sensing occurs via colorimetric or fluorometric changes to indicator molecules that are covalently bound to amine termination sites on the polymeric microspheres. The hybrid micromachined structure has been interfaced directly to a charged-coupled-device that is used for the simultaneous acquisition of the optical data from the individually addressable `taste bud' elements. With the miniature sensor array, acquisition of data streams composed of red, green, and blue color patterns distinctive for the analytes in the solution are rapidly acquired. The unique combination of carefully chosen reporter molecules with water permeable microspheres allows for the simultaneous detection and quantification of a variety of analytes. The fabrication of the sensor structures and the initial colorimetric and fluorescent responses for pH, Ca+2, Ce+3, and sugar are reported. Interface to microfluidic components should also be possible, producing a complete sampling/sensing system.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Rapid computation of directional wellbore drawdown in a confined aquifer via Poisson resummation

NASA Astrophysics Data System (ADS)

Blumenthal, Benjamin J.; Zhan, Hongbin

2016-08-01

We have derived a rapidly computed analytical solution for drawdown caused by a partially or fully penetrating directional wellbore (vertical, horizontal, or slant) via Green's function method. The mathematical model assumes an anisotropic, homogeneous, confined, box-shaped aquifer. Any dimension of the box can have one of six possible boundary conditions: 1) both sides no-flux; 2) one side no-flux - one side constant-head; 3) both sides constant-head; 4) one side no-flux; 5) one side constant-head; 6) free boundary conditions. The solution has been optimized for rapid computation via Poisson Resummation, derivation of convergence rates, and numerical optimization of integration techniques. Upon application of the Poisson Resummation method, we were able to derive two sets of solutions with inverse convergence rates, namely an early-time rapidly convergent series (solution-A) and a late-time rapidly convergent series (solution-B). From this work we were able to link Green's function method (solution-B) back to image well theory (solution-A). We then derived an equation defining when the convergence rate between solution-A and solution-B is the same, which we termed the switch time. Utilizing the more rapidly convergent solution at the appropriate time, we obtained rapid convergence at all times. We have also shown that one may simplify each of the three infinite series for the three-dimensional solution to 11 terms and still maintain a maximum relative error of less than 10-14.

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

Riemann-Hilbert technique scattering analysis of metamaterial-based asymmetric 2D open resonators

NASA Astrophysics Data System (ADS)

Kamiński, Piotr M.; Ziolkowski, Richard W.; Arslanagić, Samel

2017-12-01

The scattering properties of metamaterial-based asymmetric two-dimensional open resonators excited by an electric line source are investigated analytically. The resonators are, in general, composed of two infinite and concentric cylindrical layers covered with an infinitely thin, perfect conducting shell that has an infinite axial aperture. The line source is oriented parallel to the cylinder axis. An exact analytical solution of this problem is derived. It is based on the dual-series approach and its transformation to the equivalent Riemann-Hilbert problem. Asymmetric metamaterial-based configurations are found to lead simultaneously to large enhancements of the radiated power and to highly steerable Huygens-like directivity patterns; properties not attainable with the corresponding structurally symmetric resonators. The presented open resonator designs are thus interesting candidates for many scientific and engineering applications where enhanced directional near- and far-field responses, tailored with beam shaping and steering capabilities, are highly desired.

Directly oxidized chemiluminescence of 2-substituted-4,5-di(2-furyl)-1H -imidazole by acidic potassium permanganate and its analytical application for determination of albumin.

PubMed

Kang, Jing; Zhang, Yumin; Huang, Zhongxiu; Han, Lu; Tang, Jieli; Wang, Shuaijun; Zhang, Yihua

2011-07-01

In the paper, 2,4,5-tri(2-furyl)-1H-imidazole (TFI) and 2-phenyl-4,5-di(2-furyl)-1H-imidazole (PDFI), were chosen to investigate chemiluminescence (CL) properties of 2-substituted-4,5-di(2-furyl)-1H-imidazoles. The directly oxidized CL of analytes by potassium permanganate (KMnO(4)) was in detail studied. The KMnO(4) could directly oxidize TFI/PDFI to produce strong CL emission in acidic solution. The effects of experimental conditions were investigated. Under the optimal conditions, the effect of albumin on the TFI/PDFI-KMnO(4) system was investigated. It was found that the addition of albumin into the system could induce enhancement of CL signal, and the enhanced CL intensity is linearly related to the logarithm of concentration of albumin. Based on this study, a novel CL method has been developed for the determination of albumin with high sensitivity and good selectivity. The method was applied to the determination of albumin in human serum samples, and the results were in agreement with those obtained by the bromcresol green (BCG) method. The relative errors for the analytical results were from -5.8% to 4.2%. These new phenomena would further enable people to exploit more CL analytical application of the heterocyclic imidazole derivatives. © Springer Science+Business Media, LLC 2011

A reduced-order model from high-dimensional frictional hysteresis

PubMed Central

Biswas, Saurabh; Chatterjee, Anindya

2014-01-01

Hysteresis in material behaviour includes both signum nonlinearities as well as high dimensionality. Available models for component-level hysteretic behaviour are empirical. Here, we derive a low-order model for rate-independent hysteresis from a high-dimensional massless frictional system. The original system, being given in terms of signs of velocities, is first solved incrementally using a linear complementarity problem formulation. From this numerical solution, to develop a reduced-order model, basis vectors are chosen using the singular value decomposition. The slip direction in generalized coordinates is identified as the minimizer of a dissipation-related function. That function includes terms for frictional dissipation through signum nonlinearities at many friction sites. Luckily, it allows a convenient analytical approximation. Upon solution of the approximated minimization problem, the slip direction is found. A final evolution equation for a few states is then obtained that gives a good match with the full solution. The model obtained here may lead to new insights into hysteresis as well as better empirical modelling thereof. PMID:24910522

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.

Simultaneous determination of thirteen different steroid hormones using micro UHPLC-MS/MS with on-line SPE system.

PubMed

Márta, Zoltán; Bobály, Balázs; Fekete, Jenő; Magda, Balázs; Imre, Tímea; Mészáros, Katalin Viola; Bálint, Mária; Szabó, Pál Tamás

2018-02-20

Ultratrace analysis of sample components requires excellent analytical performance in terms of limits of quantitation (LOQ). Micro UHPLC coupled to sensitive tandem mass spectrometry provides state of the art solution for such analytical problems. Using on-line SPE with column switching on a micro UHPLC-MS/MS system allowed to decrease LOQ without any complex sample preparation protocol. The presented method is capable of reaching satisfactory low LOQ values for analysis of thirteen different steroid molecules from human plasma without the most commonly used off-line SPE or compound derivatization. Steroids were determined by using two simple sample preparation methods, based on lower and higher plasma steroid concentrations. In the first method, higher analyte concentrations were directly determined after protein precipitation with methanol. The organic phase obtained from the precipitation was diluted with water and directly injected into the LC-MS system. In the second method, low steroid levels were determined by concentrating the organic phase after steroid extraction. In this case, analytes were extracted with ethyl acetate and reconstituted in 90/10 water/acetonitrile following evaporation to dryness. This step provided much lower LOQs, outperforming previously published values. The method has been validated and subsequently applied to clinical laboratory measurement. Copyright © 2017 Elsevier B.V. All rights reserved.

Aerosol dilution as a simple strategy for analysis of complex samples by ICP-MS.

PubMed

Barros, Ariane I; Pinheiro, Fernanda C; Amaral, Clarice D B; Lorençatto, Rodolfo; Nóbrega, Joaquim A

2018-02-01

This study investigated the capability of High Matrix Introduction (HMI) strategy for analysis of dialysis solution and urine samples using inductively coupled plasma mass spectrometry. The use of HMI enables the direct introduction of urine samples and dialysis solutions 2-fold diluted with 0.14molL -1 HNO 3 . Bismuth, Ge, Ir, Li, Pt, Rh, Sc and Tl were evaluated as internal standards for Al, Ag, As, Be, Cd, Cr, Pb, Sb, Se, Tl, and Hg determination in dialysis solution and As, Cd, Hg and Pb determination in urine samples. Helium collision cell mode (4.5mLmin -1 ) was efficient to overcome polyatomic interferences in As, Se and Cr determinations. Mercury memory effects were evaluated by washing with 0.12molL -1 HCl or an alkaline diluent solution prepared with n-butanol, NH 4 OH, EDTA, and Triton X-100. This later solution was efficient for avoiding Hg memory effects in 6h of analysis. Linear calibration curves were obtained for all analytes and detection limits were lower than maximum amounts allowed by Brazilian legislations. Recoveries for all analytes in dialysis solutions and urine samples ranged from 82% to 125% and relative standard deviations for all elements and samples were lower than 7%. Analysis of control internal urine samples was in agreement with certified values at 95% confidence level (t-test; p < 0.05). Copyright © 2017 Elsevier B.V. All rights reserved.

Approximate analytical solution for non-Darcian flow toward a partially penetrating well in a confined aquifer

NASA Astrophysics Data System (ADS)

Wen, Zhang; Liu, Kai; Chen, Xiaolian

2013-08-01

In this study, non-Darcian flow to a partially penetrating well in a confined aquifer was investigated. The flow in the horizontal direction was assumed to be non-Darcian, while the flow in the vertical direction was assumed to be Darcian. The Izbash equation was employed to describe the non-Darcian flow in the horizontal direction of the aquifer. We used a linearization procedure to approximate the non-linear term in the governing equation enabling the mathematical model to be solved using a combination of Laplace and Fourier cosine transforms. Approximate analytical solutions for the drawdown were obtained and the impacts of different parameters on the drawdown were analyzed. The results indicated that a larger power index n in the Izbash equation leads to a larger drawdown at early times, while a larger n results in a smaller drawdown at late times. The drawdowns along the vertical direction z are symmetric if the well screen is located in the center of the aquifer, and the drawdown at the center of the aquifer is the largest along the vertical direction for this case. The length of the well screen w has little impact on the drawdown at early times, while a larger length of the well screen results in a smaller drawdown at late times. The drawdown increases with Kr at early times, while it decreases as Kr increases at late times, in which Kr is the apparent radial hydraulic conductivity. A sensitivity analysis of the parameters, i.e., the specific storage Ss, w, n and Kr, indicated that the drawdown is not sensitive to them at early times, while it is very sensitive to these parameters at late times especially to the power index n.

Analytical optical scattering in clouds

NASA Technical Reports Server (NTRS)

Phanord, Dieudonne D.

1989-01-01

An analytical optical model for scattering of light due to lightning by clouds of different geometry is being developed. The self-consistent approach and the equivalent medium concept of Twersky was used to treat the case corresponding to outside illumination. Thus, the resulting multiple scattering problem is transformed with the knowledge of the bulk parameters, into scattering by a single obstacle in isolation. Based on the size parameter of a typical water droplet as compared to the incident wave length, the problem for the single scatterer equivalent to the distribution of cloud particles can be solved either by Mie or Rayleigh scattering theory. The super computing code of Wiscombe can be used immediately to produce results that can be compared to the Monte Carlo computer simulation for outside incidence. A fairly reasonable inverse approach using the solution of the outside illumination case was proposed to model analytically the situation for point sources located inside the thick optical cloud. Its mathematical details are still being investigated. When finished, it will provide scientists an enhanced capability to study more realistic clouds. For testing purposes, the direct approach to the inside illumination of clouds by lightning is under consideration. Presently, an analytical solution for the cubic cloud will soon be obtained. For cylindrical or spherical clouds, preliminary results are needed for scattering by bounded obstacles above or below a penetrable surface interface.

Gust Acoustics Computation with a Space-Time CE/SE Parallel 3D Solver

NASA Technical Reports Server (NTRS)

Wang, X. Y.; Himansu, A.; Chang, S. C.; Jorgenson, P. C. E.; Reddy, D. R. (Technical Monitor)

2002-01-01

The benchmark Problem 2 in Category 3 of the Third Computational Aero-Acoustics (CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem concerns the unsteady response of an isolated finite-span swept flat-plate airfoil bounded by two parallel walls to an incident gust. The acoustic field generated by the interaction of the gust with the flat-plate airfoil is computed by solving the 3D (three-dimensional) Euler equations in the time domain using a parallel version of a 3D CE/SE solver. The effect of the gust orientation on the far-field directivity is studied. Numerical solutions are presented and compared with analytical solutions, showing a reasonable agreement.

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.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 2: Derivation of finite-element equations and comparisons with analytical solutions

USGS Publications Warehouse

Cooley, Richard L.

1992-01-01

MODFE, a modular finite-element model for simulating steady- or unsteady-state, area1 or axisymmetric flow of ground water in a heterogeneous anisotropic aquifer is documented in a three-part series of reports. In this report, part 2, the finite-element equations are derived by minimizing a functional of the difference between the true and approximate hydraulic head, which produces equations that are equivalent to those obtained by either classical variational or Galerkin techniques. Spatial finite elements are triangular with linear basis functions, and temporal finite elements are one dimensional with linear basis functions. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining units; (3) specified recharge or discharge at points, along lines, or areally; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining units combined with aquifer dewatering, and evapotranspiration. The matrix equations produced by the finite-element method are solved by the direct symmetric-Doolittle method or the iterative modified incomplete-Cholesky conjugate-gradient method. The direct method can be efficient for small- to medium-sized problems (less than about 500 nodes), and the iterative method is generally more efficient for larger-sized problems. Comparison of finite-element solutions with analytical solutions for five example problems demonstrates that the finite-element model can yield accurate solutions to ground-water flow problems.

Exact and approximate solutions for the decades-old Michaelis-Menten equation: Progress-curve analysis through integrated rate equations.

PubMed

Goličnik, Marko

2011-01-01

The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate V, and the Michaelis constant K(M) ) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to understand fully, or can even be misunderstood, by students when based only on the differential form of the Michaelis-Menten equation, and the variety of methods available to calculate the kinetic constants from rate versus substrate concentration "textbook data." Consequently, enzyme kinetics can be confusing if an analytical solution of the Michaelis-Menten equation is not available. Therefore, the still rarely known exact solution to the Michaelis-Menten equation is presented here through the explicit closed-form equation in terms of the Lambert W(x) function. Unfortunately, as the W(x) is not available in standard curve-fitting computer programs, the practical use of this direct solution is limited for most life-science students. Thus, the purpose of this article is to provide analytical approximations to the equation for modeling Michaelis-Menten kinetics. The elementary and explicit nature of these approximations can provide students with direct and simple estimations of kinetic parameters from raw experimental time-course data. The Michaelis-Menten kinetics studied in the latter context can provide an ideal alternative to the 100-year-old problems of data transformation, graphical visualization, and data analysis of enzyme-catalyzed reactions. Hence, the content of the course presented here could gradually become an important component of the modern biochemistry curriculum in the 21st century. Copyright © 2011 Wiley Periodicals, Inc.

Chemical Transport in a Fissured Rock: Verification of a Numerical Model

NASA Astrophysics Data System (ADS)

Rasmuson, A.; Narasimhan, T. N.; Neretnieks, I.

1982-10-01

Numerical models for simulating chemical transport in fissured rocks constitute powerful tools for evaluating the acceptability of geological nuclear waste repositories. Due to the very long-term, high toxicity of some nuclear waste products, the models are required to predict, in certain cases, the spatial and temporal distribution of chemical concentration less than 0.001% of the concentration released from the repository. Whether numerical models can provide such accuracies is a major question addressed in the present work. To this end we have verified a numerical model, TRUMP, which solves the advective diffusion equation in general three dimensions, with or without decay and source terms. The method is based on an integrated finite difference approach. The model was verified against known analytic solution of the one-dimensional advection-diffusion problem, as well as the problem of advection-diffusion in a system of parallel fractures separated by spherical particles. The studies show that as long as the magnitude of advectance is equal to or less than that of conductance for the closed surface bounding any volume element in the region (that is, numerical Peclet number <2), the numerical method can indeed match the analytic solution within errors of ±10-3% or less. The realistic input parameters used in the sample calculations suggest that such a range of Peclet numbers is indeed likely to characterize deep groundwater systems in granitic and ancient argillaceous systems. Thus TRUMP in its present form does provide a viable tool for use in nuclear waste evaluation studies. A sensitivity analysis based on the analytic solution suggests that the errors in prediction introduced due to uncertainties in input parameters are likely to be larger than the computational inaccuracies introduced by the numerical model. Currently, a disadvantage in the TRUMP model is that the iterative method of solving the set of simultaneous equations is rather slow when time constants vary widely over the flow region. Although the iterative solution may be very desirable for large three-dimensional problems in order to minimize computer storage, it seems desirable to use a direct solver technique in conjunction with the mixed explicit-implicit approach whenever possible. Work in this direction is in progress.

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.

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.

Magnetohydrodynamic Jump Conditions for Oblique Relativistic Shocks with Gyrotropic Pressure

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

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

PubMed

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

2016-01-01

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

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

USGS Publications Warehouse

Wexler, Eliezer J.

1992-01-01

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

The interplay between pH sensitivity and label-free protein detection in immunologically modified nano-scaled field-effect transistor.

PubMed

Shalev, Gil; Rosenwaks, Yossi; Levy, Ilan

2012-01-15

We present experimental results in order to establish a correlation between pH sensitivity of immunologically modified nano-scaled field-effect transistor (NS-ImmunoFET) with their sensing capacity for label-free detection. The NS-ImmunoFETs are fabricated from silicon-on-insulator (SOI) wafers and are fully-depleted with thickness of ~20 nm. The data shows that higher sensitivity to pH entails enhanced sensitivity to analyte detection. This suggests that the mechanism of analyte detection as pure electrostatic perturbation induced by antibody-analyte interaction is over simplified. The fundamental assumption, in existing models for field-effect sensing mechanism assumes that the analyte molecules do not directly interact with the surface but rather stand 'deep' in the solution and away from the dielectric surface. Recent studies clearly provide contradicting evidence demonstrating that antibodies lie down flat on the surface. These observations led us to propose that the proteins that cover the gate area intimately interact with active sites on the surface thus forming a network of interacting sites. Since sensitivity to pH is directly correlated with the amount of amphoteric sites, we witness a direct correlation between sensitivity to pH and analyte detection. The highest and lowest threshold voltage shift for a label-free and specific detection of 6.5 nM IgG were 40 mV and 2.3 mV for NS-ImmunoFETs with pH sensitivity of 35 mV/decade and 15 mV/decade, respectively. Finally, physical modeling of the NS-ImmunoFET is presented and charge of a single IgG protein at pH 6 is calculated. The obtained value is consistent with charge of IgG protein cited in literature. Copyright © 2011 Elsevier B.V. All rights reserved.

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

Feasibility of corona discharge ion mobility spectrometry for direct analysis of samples extracted by dispersive liquid-liquid microextraction.

PubMed

Jafari, Mohammad T; Riahi, Farhad

2014-05-23

The capability of corona discharge ionization ion mobility spectrometry (CD-IMS) for direct analysis of the samples extracted by dispersive liquid-liquid microextraction (DLLME) was investigated and evaluated, for the first time. To that end, an appropriate new injection port was designed and constructed, resulting in possibility of direct injection of the known sample volume, without tedious sample preparation steps (e.g. derivatization, solvent evaporation, and re-solving in another solvent…). Malathion as a test compound was extracted from different matrices by a rapid and convenient DLLME method. The positive ion mobility spectra of the extracted malathion were obtained after direct injection of carbon tetrachloride or methanol solutions. The analyte responses were compared and the statistical results revealed the feasibility of direct analysis of the extracted samples in carbon tetrachloride, resulting in a convenient methodology. The coupled method of DLLME-CD-IMS was exhaustively validated in terms of sensitivity, dynamic range, recovery, and enrichment factor. Finally, various real samples of apple, river and underground water were analyzed, all verifying the feasibility and success of the proposed method for the easy extraction of the analyte using DLLME separation before the direct analysis by CD-IMS. Copyright © 2014 Elsevier B.V. All rights reserved.

Developing automated analytical methods for scientific environments using LabVIEW.

PubMed

Wagner, Christoph; Armenta, Sergio; Lendl, Bernhard

2010-01-15

The development of new analytical techniques often requires the building of specially designed devices, each requiring its own dedicated control software. Especially in the research and development phase, LabVIEW has proven to be one highly useful tool for developing this software. Yet, it is still common practice to develop individual solutions for different instruments. In contrast to this, we present here a single LabVIEW-based program that can be directly applied to various analytical tasks without having to change the program code. Driven by a set of simple script commands, it can control a whole range of instruments, from valves and pumps to full-scale spectrometers. Fluid sample (pre-)treatment and separation procedures can thus be flexibly coupled to a wide range of analytical detection methods. Here, the capabilities of the program have been demonstrated by using it for the control of both a sequential injection analysis - capillary electrophoresis (SIA-CE) system with UV detection, and an analytical setup for studying the inhibition of enzymatic reactions using a SIA system with FTIR detection.

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

PubMed

Shim, Jaesool; Yoo, Kisoo; Dutta, Prashanta

2017-03-01

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

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

PubMed

Yang, Yong; Liu, Yongzhong; Yu, Bo; Ding, Tian

2016-06-01

Volatile contaminants may migrate with carbon dioxide (CO2) injection or leakage in subsurface formations, which leads to the risk of the CO2 storage and the ecological environment. This study aims to develop an analytical model that could predict the contaminant migration process induced by CO2 storage. The analytical model with two moving boundaries is obtained through the simplification of the fully coupled model for the CO2-aqueous phase -stagnant phase displacement system. The analytical solutions are confirmed and assessed through the comparison with the numerical simulations of the fully coupled model. Then, some key variables in the analytical solutions, including the critical time, the locations of the dual moving boundaries and the advance velocity, are discussed to present the characteristics of contaminant migration in the multi-phase displacement system. The results show that these key variables are determined by four dimensionless numbers, Pe, RD, Sh and RF, which represent the effects of the convection, the dispersion, the interphase mass transfer and the retention factor of contaminant, respectively. The proposed analytical solutions could be used for tracking the migration of the injected CO2 and the contaminants in subsurface formations, and also provide an analytical tool for other solute transport in multi-phase displacement system. Copyright © 2016 Elsevier B.V. All rights reserved.

Direct Push Chemical Sensors for DNAPL

DTIC Science & Technology

2007-01-01

System Improvements Problem Solution 1. Insufficient thermal protection Implemented use of microporous insulation . Lab and field tests have shown...screw thread cap with Teflon lined septum. The soil and methanol were mixed by hand and the vial was placed in an insulated cooler on ice until...Teflon lined septum. The vials were stored within an insulated cooler on ice until shipped to Columbia Analytical Services for analysis by U.S. EPA

Fluorescent probes for the simultaneous detection of multiple analytes in biology.

PubMed

Kolanowski, Jacek L; Liu, Fei; New, Elizabeth J

2018-01-02

Many of the key questions facing cellular biology concern the location and concentration of chemical species, from signalling molecules to metabolites to exogenous toxins. Fluorescent sensors (probes) have revolutionised the understanding of biological systems through their exquisite sensitivity to specific analytes. Probe design has focussed on selective sensors for individual analytes, but many of the most pertinent biological questions are related to the interaction of more than one chemical species. While it is possible to simultaneously use multiple sensors for such applications, data interpretation will be confounded by the fact that sensors will have different uptake, localisation and metabolism profiles. An alternative solution is to instead use a single probe that responds to two analytes, termed a dual-responsive probe. Recent progress in this field has yielded exciting probes, some of which have demonstrated biological application. Here we review work that has been carried out to date, and suggest future research directions that will harness the considerable potential of dual-responsive fluorescent probes.

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.

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

USDA-ARS?s Scientific Manuscript database

Analytical solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subj...

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

NASA Technical Reports Server (NTRS)

Rose, Cheryl A.; Herakovich, Carl T.

1991-01-01

An improved approximate analytical solution for interlaminar stresses in finite width, symmetric, angle-ply laminated coupons subjected to axial loading is presented. The solution is based upon statically admissible stress fields which take into consideration local property mismatch effects and global equilibrium requirements. Unknown constants in the admissible stress states are determined through minimization of the complementary energy. Typical results are presented for through-the-thickness and interlaminar stress distributions for angle-ply laminates. It is shown that the results represent an improved approximate analytical solution for interlaminar stresses.

Modeling the Nab Experiment Electronics in SPICE

NASA Astrophysics Data System (ADS)

Blose, Alexander; Crawford, Christopher; Sprow, Aaron; Nab Collaboration

2017-09-01

The goal of the Nab experiment is to measure the neutron decay coefficients a, the electron-neutrino correlation, as well as b, the Fierz interference term to precisely test the Standard Model, as well as probe for Beyond the Standard Model physics. In this experiment, protons from the beta decay of the neutron are guided through a magnetic field into a Silicon detector. Event reconstruction will be achieved via time-of-flight measurement for the proton and direct measurement of the coincident electron energy in highly segmented silicon detectors, so the amplification circuitry needs to preserve fast timing, provide good amplitude resolution, and be packaged in a high-density format. We have designed a SPICE simulation to model the full electronics chain for the Nab experiment in order to understand the contributions of each stage and optimize them for performance. Additionally, analytic solutions to each of the components have been determined where available. We will present a comparison of the output from the SPICE model, analytic solution, and empirically determined data.

Symmetry breaking in optimal timing of traffic signals on an idealized two-way street.

PubMed

Panaggio, Mark J; Ottino-Löffler, Bertand J; Hu, Peiguang; Abrams, Daniel M

2013-09-01

Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal world, traffic signals would be timed such that consecutive lights turned green just as vehicles arrived, eliminating the need to stop at each block. Unfortunately, this "green-wave" scenario is generally unworkable due to frustration imposed by competing demands of traffic moving in different directions. Until now this has typically been resolved by numerical simulation and optimization. Here, we develop a theory for the flow in an idealized system consisting of a long two-way road with periodic intersections. We show that optimal signal timing can be understood analytically and that there are counterintuitive asymmetric solutions to this signal coordination problem. We further explore how these theoretical solutions degrade as traffic conditions vary and automotive density increases.

Symmetry breaking in optimal timing of traffic signals on an idealized two-way street

NASA Astrophysics Data System (ADS)

Panaggio, Mark J.; Ottino-Löffler, Bertand J.; Hu, Peiguang; Abrams, Daniel M.

2013-09-01

Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal world, traffic signals would be timed such that consecutive lights turned green just as vehicles arrived, eliminating the need to stop at each block. Unfortunately, this “green-wave” scenario is generally unworkable due to frustration imposed by competing demands of traffic moving in different directions. Until now this has typically been resolved by numerical simulation and optimization. Here, we develop a theory for the flow in an idealized system consisting of a long two-way road with periodic intersections. We show that optimal signal timing can be understood analytically and that there are counterintuitive asymmetric solutions to this signal coordination problem. We further explore how these theoretical solutions degrade as traffic conditions vary and automotive density increases.

Indentation theory on a half-space of transversely isotropic multi-ferroic composite medium: sliding friction effect

NASA Astrophysics Data System (ADS)

Wu, F.; Wu, T.-H.; Li, X.-Y.

2018-03-01

This article aims to present a systematic indentation theory on a half-space of multi-ferroic composite medium with transverse isotropy. The effect of sliding friction between the indenter and substrate is taken into account. The cylindrical flat-ended indenter is assumed to be electrically/magnetically conducting or insulating, which leads to four sets of mixed boundary-value problems. The indentation forces in the normal and tangential directions are related to the Coulomb friction law. For each case, the integral equations governing the contact behavior are developed by means of the generalized method of potential theory, and the corresponding coupling field is obtained in terms of elementary functions. The effect of sliding on the contact behavior is investigated. Finite element method (FEM) in the context of magneto-electro-elasticity is developed to discuss the validity of the analytical solutions. The obtained analytical solutions may serve as benchmarks to various simplified analyses and numerical codes and as a guide for future experimental studies.

Rotor Vortex Filaments: Living on the Slipstream's Edge

NASA Technical Reports Server (NTRS)

Young, Larry A.

1997-01-01

The purpose of this paper is to gain a better understanding of rotor wake evolution in hover and axial flow by deriving an analytical solution for the time dependent behavior of vortex filament circulation and core size. This solution is applicable only for vortex filaments in the rotor far-wake. A primarily inviscid vortex/shear layer interaction (where the slipstream boundary is modeled as a shear layer) has been identified in this analytical treatment. This vortex/shear layer interaction results in decreasing, vortex filament circulation and core size with time. The inviscid vortex/shear layer interaction is shown, in a first-order treatment, to be of greater magnitude than viscous diffusion effects. The rate of contraction, and ultimate collapse, of the vortex filament core is found to be directly proportional to the rotor inflow velocity. This new insight into vortex filament decay promises to help reconcile several disparate observations made in the literature and will, hopefully, promote new advances in theoretical modeling of rotor wakes.

Planar light bullets under conditions of second-harmonic generation.

PubMed

Sazonov, Sergey V; Mamaikin, Mikhail S; Komissarova, Maria V; Zakharova, Irina G

2017-08-01

We study solutions to second-harmonic-generation equations in two-dimensional media with anomalous dispersion. The analytical solution is obtained in an approximate form of the planar spatiotemporal two-component soliton by means of the averaged Lagrangian method. It is shown that a decrease in the amplitudes of both soliton components and an increase in the value of the transverse coordinate are accompanied by an increase in their temporal duration. Within this variational approach, we have managed to find a stability criterion for the light bullet and a period of oscillations of soliton parameters. Then, we use the obtained form as an initial configuration to carry out the direct numerical simulation of soliton dynamics. We demonstrate stable propagation of spatiotemporal solitons undergoing small oscillations predicted analytically for a long distance. The formation of a two-component light bullet is shown when we launch a pulse only at the fundamental frequency. In addition, we investigate the phase and group-velocity mismatch effects on the propagation of pulses.

Current to the ionosphere following a lightning stroke

NASA Technical Reports Server (NTRS)

Hale, L. C.; Baginski, M. E.

1987-01-01

A simple analytical expression for calculating the total current waveform to the ionosphere after a lightning stroke is derived. The validity of this expression is demonstrated by comparison with a more rigorous computer solution of Maxwell's equations. The analytic model demonstrates that the temporal variation of the current induced in the ionosphere and global circuit and the corresponding return current in the earth depends on the conductivity profile at intervening altitudes in the middle atmosphere. A conclusion is that capacitative coupling may provide tighter coupling between the lower atmosphere and the ionosphere than usually considered, in both directions, which may help to explain observations which seem to indicate that magnetospheric phenomena may in some instances trigger lightning.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Simplified computational methods for elastic and elastic-plastic fracture problems

NASA Technical Reports Server (NTRS)

Atluri, Satya N.

1992-01-01

An overview is given of some of the recent (1984-1991) developments in computational/analytical methods in the mechanics of fractures. Topics covered include analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids, with crack faces being subjected to arbitrary tractions; finite element or boundary element alternating methods for two or three dimensional crack problems; a 'direct stiffness' method for stiffened panels with flexible fasteners and with multiple cracks; multiple site damage near a row of fastener holes; an analysis of cracks with bonded repair patches; methods for the generation of weight functions for two and three dimensional crack problems; and domain-integral methods for elastic-plastic or inelastic crack mechanics.

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

NASA Astrophysics Data System (ADS)

Zinati, Reza Farshbaf; Manafian, Jalil

2017-04-01

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

A new amperometric nanostructured sensor for the analytical determination of hydrogen peroxide.

PubMed

Guascito, M R; Filippo, E; Malitesta, C; Manno, D; Serra, A; Turco, A

2008-12-01

A new amperometric, nanostructured sensor for the analytical determination of hydrogen peroxide is proposed. This sensor was constructed by immobilizing silver nanoparticles in a polyvinyl alcohol (PVA) film on a platinum electrode, which was performed by direct drop-casting silver nanoparticles that were capped in a PVA colloidal suspension. UV-vis spectroscopy, X-ray diffraction and transmission electron microscopy were used to give a complete characterization of the nanostructured film. Cyclic voltammetry experiments yielded evidence that silver nanoparticles facilitate hydrogen peroxide reduction, showing excellent catalytic activity. Moreover, the cronoamperometric response of modified sensors was dependent on nanoparticle lifetime. Experiments were performed, using freshly prepared solutions, after 4 and 8 days. Results concerning the quantitative analysis of hydrogen peroxide, in terms of detection limit, linear range, sensitivity and standard deviation (STD), are discussed for each tested sensor type. Utilization of two different linear ranges (40 microM to 6mM and 1.25 microM to 1.0mM) enabled the assessment of concentration intervals having up to three orders of magnitude. Moreover, the electrode made using a 4-day-old solution showed the maximal sensitivity of 128 nA microM(-1)(4090 nA microM(-1)cm(-2)), yielding a limit of detection of 1 microuM and STD of 2.5 microAmM(-1). All of these analytical parameters make the constructed sensors suitable for peroxide determination in aqueous solution.

Isothermal Bondi Accretion in Jaffe and Hernquist Galaxies with a Central Black Hole: Fully Analytical Solutions

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

Ciotti, Luca; Pellegrini, Silvia, E-mail: luca.ciotti@unibo.it

One of the most active fields of research of modern-day astrophysics is that of massive black hole formation and coevolution with the host galaxy. In these investigations, ranging from cosmological simulations, to semi-analytical modeling, to observational studies, the Bondi solution for accretion on a central point-mass is widely adopted. In this work we generalize the classical Bondi accretion theory to take into account the effects of the gravitational potential of the host galaxy, and of radiation pressure in the optically thin limit. Then, we present the fully analytical solution, in terms of the Lambert–Euler W -function, for isothermal accretion inmore » Jaffe and Hernquist galaxies with a central black hole. The flow structure is found to be sensitive to the shape of the mass profile of the host galaxy. These results and the formulae that are provided, most importantly, the one for the critical accretion parameter, allow for a direct evaluation of all flow properties, and are then useful for the abovementioned studies. As an application, we examine the departure from the true mass accretion rate of estimates obtained using the gas properties at various distances from the black hole, under the hypothesis of classical Bondi accretion. An overestimate is obtained from regions close to the black hole, and an underestimate outside a few Bondi radii; the exact position of the transition between the two kinds of departure depends on the galaxy model.« less

Evaporation-induced flow in an inviscid liquid line at any contact angle

NASA Astrophysics Data System (ADS)

Petsi, A. J.; Burganos, V. N.

2006-04-01

The problem of potential flow inside an evaporating liquid line, shaped as an infinitely long cylindrical segment lying on a flat surface, is considered and an analytical solution is obtained for any contact angle in (0,π) . In this way, microflow details inside linear liquid bodies evaporating on hydrophilic, hydrophobic, and strongly hydrophobic substrates can now be obtained. The mathematical formulation employs the velocity potential and stream function formulations in bipolar coordinates and the solution is obtained using the technique of Fourier transform. Both pinned and depinned contact lines are considered. The solution is applicable to any evaporation mechanism but for illustration purposes numerical results are presented here for the particular case of kinetically controlled evaporation. For hydrophilic substrates, the flow inside the evaporating liquid line is directed towards the edges for pinned contact lines, thus, promoting a coffee stain effect. The opposite flow direction is observed for depinned contact lines. However, for strongly hydrophobic substrates, flow is directed outwards for both pinned and depinned contact lines, but owing to its low magnitude compared to that on hydrophilic substrates, a craterlike colloidal deposit should be expected rather than a ringlike deposit, in agreement with experimental observations.

The Minimum-Mass Surface Density of the Solar Nebula using the Disk Evolution Equation

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

2005-01-01

The Hayashi minimum-mass power law representation of the pre-solar nebula (Hayashi 1981, Prog. Theo. Phys.70,35) is revisited using analytic solutions of the disk evolution equation. A new cumulative-planetary-mass-model (an integrated form of the surface density) is shown to predict a smoother surface density compared with methods based on direct estimates of surface density from planetary data. First, a best-fit transcendental function is applied directly to the cumulative planetary mass data with the surface density obtained by direct differentiation. Next a solution to the time-dependent disk evolution equation is parametrically adapted to the planetary data. The latter model indicates a decay rate of r -1/2 in the inner disk followed by a rapid decay which results in a sharper outer boundary than predicted by the minimum mass model. The model is shown to be a good approximation to the finite-size early Solar Nebula and by extension to extra solar protoplanetary disks.

Statistical theory on the analytical form of cloud particle size distributions

NASA Astrophysics Data System (ADS)

Wu, Wei; McFarquhar, Greg

2017-11-01

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

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.

Back analysis of geomechanical parameters in underground engineering using artificial bee colony.

PubMed

Zhu, Changxing; Zhao, Hongbo; Zhao, Ming

2014-01-01

Accurate geomechanical parameters are critical in tunneling excavation, design, and supporting. In this paper, a displacements back analysis based on artificial bee colony (ABC) algorithm is proposed to identify geomechanical parameters from monitored displacements. ABC was used as global optimal algorithm to search the unknown geomechanical parameters for the problem with analytical solution. To the problem without analytical solution, optimal back analysis is time-consuming, and least square support vector machine (LSSVM) was used to build the relationship between unknown geomechanical parameters and displacement and improve the efficiency of back analysis. The proposed method was applied to a tunnel with analytical solution and a tunnel without analytical solution. The results show the proposed method is feasible.

Analytical solution and simplified analysis of coupled parent-daughter steady-state transport with multirate mass transfer

Treesearch

R. Haggerty

2013-01-01

In this technical note, a steady-state analytical solution of concentrations of a parent solute reacting to a daughter solute, both of which are undergoing transport and multirate mass transfer, is presented. Although the governing equations are complicated, the resulting solution can be expressed in simple terms. A function of the ratio of concentrations, In (daughter...

AN ANALYTICAL SOLUTION TO RICHARDS' EQUATIONS FOR A DRAINING SOIL PROFILE

EPA Science Inventory

Analytical solutions are developed for the Richards' equation following the analysis of Broadbridge and White. Included here is the solution for drainage and redistribution of a partially or deeply wetted profile. Additionally, infiltration for various initial conditions is exami...

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result.

PubMed

Wu, Yang; Kelly, Damien P

2014-12-12

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of [Formula: see text] and [Formula: see text] type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Formula: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Formula: see text], where [Formula: see text] is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result

NASA Astrophysics Data System (ADS)

Wu, Yang; Kelly, Damien P.

2014-12-01

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of ? and ? type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of ? and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by ?, where ? is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

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

USGS Publications Warehouse

Wexler, Eliezer J.

1989-01-01

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

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

PubMed

Gai, Litao; Bilige, Sudao; Jie, Yingmo

2016-01-01

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

Determination of copper in tap water using solid-phase spectrophotometry

NASA Technical Reports Server (NTRS)

Hill, Carol M.; Street, Kenneth W.; Philipp, Warren H.; Tanner, Stephen P.

1994-01-01

A new application of ion exchange films is presented. The films are used in a simple analytical method of directly determining low concentrations of Cu(2+) in aqueous solutions, in particular, drinking water. The basis for this new test method is the color and absorption intensity of the ion when adsorbed onto the film. The film takes on the characteristic color of the adsorbed cation, which is concentrated on the film by many orders of magnitude. The linear relationship between absorbance (corrected for variations in film thickness) and solution concentration makes the determinations possible. These determinations agree well with flame atomic absorption determinations.

A mean spherical model for soft potentials: The hard core revealed as a perturbation

NASA Technical Reports Server (NTRS)

Rosenfeld, Y.; Ashcroft, N. W.

1978-01-01

The mean spherical approximation for fluids is extended to treat the case of dense systems interacting via soft-potentials. The extension takes the form of a generalized statement concerning the behavior of the direct correlation function c(r) and radial distribution g(r). From a detailed analysis that views the hard core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions.

Laminar film condensation along a vertical plate embedded in an anisotropic porous medium with oblique principal axes

NASA Astrophysics Data System (ADS)

Degan, Gérard; Sanya, Arthur; Akowanou, Christian

2016-10-01

This work analytically investigates the problem of steady film condensation along a vertical surface embedded in an anisotropic porous medium filled with a dry saturated vapor. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction which is oblique to the gravity vector. On the basis of the generalized Darcy's law and within the boundary layer approximations, similar solutions have been obtained for the temperature and flow patterns in the condensate. Moreover, closed form solutions for the boundary layer thickness and heat transfer rate have been obtained in terms of the governing parameters of the problem.

Dispersive distortions of a radio-wave pulse in a double-resonance gaseous medium

NASA Astrophysics Data System (ADS)

Strelkov, G. M.

2017-03-01

The problem on dispersive distortions of an electromagnetic pulse in a gaseous medium with two isolated resonant frequencies is solved analytically. The solution is obtained directly in the time region and, thus, is not the result of calculations of the Fourier integral. Without introducing additional assumptions, it is possible to study the regularities and the features of the process of propagation of pulses caused by variations of both their initial characteristics and the parameters of the propagation medium. As an example, the solution is applied to describe the distortions of the two-frequency pulse of subnanosecond duration in the terrestrial atmosphere.

ICANT, a code for the self-consistent computation of ICRH antenna coupling

NASA Astrophysics Data System (ADS)

Pécoul, S.; Heuraux, S.; Koch, R.; Leclert, G.

1996-02-01

The code deals with 3D antenna structures (finite length antennae) that are used to launch electromagnetic waves into tokamak plasmas. The antenna radiation problem is solved using a finite boundary element technique combined with a spectral solution of the interior problem. The slab approximation is used, and periodicity in y and z directions is introduced to account for toroidal geometry. We present results for various types of antennae radiating in vacuum: antenna with a finite Faraday screen and ideal Faraday screen, antenna with side limiters and phased antenna arrays. The results (radiated power, current profile) obtained are very close to analytical solutions when available.

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.

Immuno Nanosensor for the Ultrasensitive Naked Eye Detection of Tuberculosis.

PubMed

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

2018-06-14

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

Applicability of direct total reflection X-ray fluorescence analysis for selenium determination in solutions related to environmental and geochemical studies

NASA Astrophysics Data System (ADS)

Marguí, E.; Floor, G. H.; Hidalgo, M.; Kregsamer, P.; Roman-Ross, G.; Streli, C.; Queralt, I.

2010-12-01

A significant amount of environmental studies related to selenium determination in different environmental compartments have been published in the last years due to the narrow range between the Se nutritious requirement as essential element and toxic effects upon exposure. However, the direct analysis of complex liquid samples like natural waters and extraction solutions presents significant problems related to the low Se concentrations and the complicated matrix of this type of samples. The goal of the present research was to study the applicability of direct TXRF analysis of different type of solutions commonly used in environmental and geochemical studies, confirm the absence or presence of matrix effects and evaluate the limits of detection and accuracy for Se determination in the different matrices. Good analytical results were obtained for the direct analysis of ground and rain water samples with limits of detection for Se two orders of magnitude lower than the permissible Se concentration in drinking waters ([Se] = 10 μg/L) according to the WHO. However, the Se detection limits for more complex liquid samples such as thermal waters and extraction solutions were in the μg/L range due to the presence of high contents of other elements present in the matrix (i.e., Br, Fe, Zn) or the high background of the TXRF spectrum that hamper the Se determination at trace levels. Our results give insight into the possibilities and drawbacks of direct TXRF analysis and to a certain extent the potential applications in the environmental and geochemical field.

On the Directional Dependence and Null Space Freedom in Uncertainty Bound Identification

NASA Technical Reports Server (NTRS)

Lim, K. B.; Giesy, D. P.

1997-01-01

In previous work, the determination of uncertainty models via minimum norm model validation is based on a single set of input and output measurement data. Since uncertainty bounds at each frequency is directionally dependent for multivariable systems, this will lead to optimistic uncertainty levels. In addition, the design freedom in the uncertainty model has not been utilized to further reduce uncertainty levels. The above issues are addressed by formulating a min- max problem. An analytical solution to the min-max problem is given to within a generalized eigenvalue problem, thus avoiding a direct numerical approach. This result will lead to less conservative and more realistic uncertainty models for use in robust control.

A Comprehensive Analytical Solution of the Nonlinear Pendulum

ERIC Educational Resources Information Center

Ochs, Karlheinz

2011-01-01

In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions…

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

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

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

2014-05-15

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

Analysis of n-alkanes at sub microgram per liter level after direct solid phase microextraction from aqueous samples.

PubMed

Farajzadeh, Mirali; Hatami, Mehdi

2002-11-01

This work describes the application of the previously presented solid phase microextraction (SPME) fiber in direct mode for sampling of C10-C20 n-alkanes from aqueous solution. The fiber has simple composition and is constructed from activated charcoal:PVC suspension in tetrahydrofuran. When the composition of the fiber was optimized that the optimum composition was 90:10 (activated charcoal:PVC) for direct mode, whereas it was 75:25 for sampling from the headspace of aqueous samples. This fiber is completely stable in contact with water. The extraction efficiency is improved in the presence of 0.1 M NaCl. The value is between 17.8-38.5% for the first extraction, which better than the efficiency of similar commercial fibers. After seven extractions, all analytes are removed from the aqueous samples nearly 100%. Single fiber repeatability and fiber-to-fiber reproducibility are good and both are less than 13% for all studied alkanes. Finally, direct mode SPME was used in the determination of n-alkanes in the range of sub microg L(-1) without any additional preconcentration procedure. Gas chromatography along with flame ionization detection were used for separation and detection of the studied analytes.

Mathematical models for the synthesis and optimization of spiral bevel gear tooth surfaces. [for helicopter transmissions

NASA Technical Reports Server (NTRS)

Litvin, F. L.; Rahman, P.; Goldrich, R. N.

1982-01-01

The geometry of spiral bevel gears and to their rational design are studied. The nonconjugate tooth surfaces of spiral bevel gears are, in theory, replaced (or approximated) by conjugated tooth surfaces. These surfaces can be generated by two conical surfaces, and by a conical surface and a revolution. Although these conjugated tooth surfaces are simpler than the actual ones, the determination of their principal curvatures and directions is still a complicated problem. Therefore, a new approach, to the solution of these is proposed. Direct relationships between the principal curvatures and directions of the tool surface and those of the generated gear surface are obtained. With the aid of these analytical tools, the Hertzian contact problem for conjugate tooth surfaces can be solved. These results are useful in determining compressive load capacity and surface fatigue life of spiral bevel gears. A general theory of kinematical errors exerted by manufacturing and assembly errors is developed. This theory is used to determine the analytical relationship between gear misalignments and kinematical errors. This is important to the study of noise and vibration in geared systems.

Sedimentary Geothermal Feasibility Study: October 2016

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

Augustine, Chad; Zerpa, Luis

The objective of this project is to analyze the feasibility of commercial geothermal projects using numerical reservoir simulation, considering a sedimentary reservoir with low permeability that requires productivity enhancement. A commercial thermal reservoir simulator (STARS, from Computer Modeling Group, CMG) is used in this work for numerical modeling. In the first stage of this project (FY14), a hypothetical numerical reservoir model was developed, and validated against an analytical solution. The following model parameters were considered to obtain an acceptable match between the numerical and analytical solutions: grid block size, time step and reservoir areal dimensions; the latter related to boundarymore » effects on the numerical solution. Systematic model runs showed that insufficient grid sizing generates numerical dispersion that causes the numerical model to underestimate the thermal breakthrough time compared to the analytic model. As grid sizing is decreased, the model results converge on a solution. Likewise, insufficient reservoir model area introduces boundary effects in the numerical solution that cause the model results to differ from the analytical solution.« less

Geometric model of pseudo-distance measurement in satellite location systems

NASA Astrophysics Data System (ADS)

Panchuk, K. L.; Lyashkov, A. A.; Lyubchinov, E. V.

2018-04-01

The existing mathematical model of pseudo-distance measurement in satellite location systems does not provide a precise solution of the problem, but rather an approximate one. The existence of such inaccuracy, as well as bias in measurement of distance from satellite to receiver, results in inaccuracy level of several meters. Thereupon, relevance of refinement of the current mathematical model becomes obvious. The solution of the system of quadratic equations used in the current mathematical model is based on linearization. The objective of the paper is refinement of current mathematical model and derivation of analytical solution of the system of equations on its basis. In order to attain the objective, geometric analysis is performed; geometric interpretation of the equations is given. As a result, an equivalent system of equations, which allows analytical solution, is derived. An example of analytical solution implementation is presented. Application of analytical solution algorithm to the problem of pseudo-distance measurement in satellite location systems allows to improve the accuracy such measurements.

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

On the nonlinear dynamics of trolling-mode AFM: Analytical solution using multiple time scales method

NASA Astrophysics Data System (ADS)

Sajjadi, Mohammadreza; Pishkenari, Hossein Nejat; Vossoughi, Gholamreza

2018-06-01

Trolling mode atomic force microscopy (TR-AFM) has resolved many imaging problems by a considerable reduction of the liquid-resonator interaction forces in liquid environments. The present study develops a nonlinear model of the meniscus force exerted to the nanoneedle of TR-AFM and presents an analytical solution to the distributed-parameter model of TR-AFM resonator utilizing multiple time scales (MTS) method. Based on the developed analytical solution, the frequency-response curves of the resonator operation in air and liquid (for different penetration length of the nanoneedle) are obtained. The closed-form analytical solution and the frequency-response curves are validated by the comparison with both the finite element solution of the main partial differential equations and the experimental observations. The effect of excitation angle of the resonator on horizontal oscillation of the probe tip and the effect of different parameters on the frequency-response of the system are investigated.

Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells.

PubMed

Ahmadi, S M; Campoli, G; Amin Yavari, S; Sajadi, B; Wauthle, R; Schrooten, J; Weinans, H; Zadpoor, A A

2014-06-01

Cellular structures with highly controlled micro-architectures are promising materials for orthopedic applications that require bone-substituting biomaterials or implants. The availability of additive manufacturing techniques has enabled manufacturing of biomaterials made of one or multiple types of unit cells. The diamond lattice unit cell is one of the relatively new types of unit cells that are used in manufacturing of regular porous biomaterials. As opposed to many other types of unit cells, there is currently no analytical solution that could be used for prediction of the mechanical properties of cellular structures made of the diamond lattice unit cells. In this paper, we present new analytical solutions and closed-form relationships for predicting the elastic modulus, Poisson׳s ratio, critical buckling load, and yield (plateau) stress of cellular structures made of the diamond lattice unit cell. The mechanical properties predicted using the analytical solutions are compared with those obtained using finite element models. A number of solid and porous titanium (Ti6Al4V) specimens were manufactured using selective laser melting. A series of experiments were then performed to determine the mechanical properties of the matrix material and cellular structures. The experimentally measured mechanical properties were compared with those obtained using analytical solutions and finite element (FE) models. It has been shown that, for small apparent density values, the mechanical properties obtained using analytical and numerical solutions are in agreement with each other and with experimental observations. The properties estimated using an analytical solution based on the Euler-Bernoulli theory markedly deviated from experimental results for large apparent density values. The mechanical properties estimated using FE models and another analytical solution based on the Timoshenko beam theory better matched the experimental observations. Copyright © 2014 Elsevier Ltd. All rights reserved.

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.

Parametric study of minimum reactor mass in energy-storage dc-to-dc converters

NASA Technical Reports Server (NTRS)

Wong, R. C.; Owen, H. A., Jr.; Wilson, T. G.

1981-01-01

Closed-form analytical solutions for the design equations of a minimum-mass reactor for a two-winding voltage-or-current step-up converter are derived. A quantitative relationship between the three parameters - minimum total reactor mass, maximum output power, and switching frequency - is extracted from these analytical solutions. The validity of the closed-form solution is verified by a numerical minimization procedure. A computer-aided design procedure using commercially available toroidal cores and magnet wires is also used to examine how the results from practical designs follow the predictions of the analytical solutions.

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

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

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

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

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

NASA Astrophysics Data System (ADS)

Norouzi, M.; Biglari, N.

2013-05-01

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

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.

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

NASA Astrophysics Data System (ADS)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

Finite Element Analysis of Magnetic Damping Effects on G-Jitter Induced Fluid Flow

NASA Technical Reports Server (NTRS)

Pan, Bo; Li, Ben Q.; deGroh, Henry C., III

1997-01-01

This paper reports some interim results on numerical modeling and analyses of magnetic damping of g-jitter driven fluid flow in microgravity. A finite element model is developed to represent the fluid flow, thermal and solute transport phenomena in a 2-D cavity under g-jitter conditions with and without an applied magnetic field. The numerical model is checked by comparing with analytical solutions obtained for a simple parallel plate channel flow driven by g-jitter in a transverse magnetic field. The model is then applied to study the effect of steady state g-jitter induced oscillation and on the solute redistribution in the liquid that bears direct relevance to the Bridgman-Stockbarger single crystal growth processes. A selection of computed results is presented and the results indicate that an applied magnetic field can effectively damp the velocity caused by g-jitter and help to reduce the time variation of solute redistribution.

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations.

PubMed

Slunyaev, A; Pelinovsky, E; Sergeeva, A; Chabchoub, A; Hoffmann, N; Onorato, M; Akhmediev, N

2013-07-01

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

Numerical Modeling of Ablation Heat Transfer

NASA Technical Reports Server (NTRS)

Ewing, Mark E.; Laker, Travis S.; Walker, David T.

2013-01-01

A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.

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.

Analytical method development for directed enzyme evolution research: a high throughput high-performance liquid chromatography method for analysis of ribose and ribitol and a capillary electrophoresis method for the separation of ribose enantiomers.

PubMed

Sun, Baoguo; Miller, Gregory; Lee, Wan Yee; Ho, Kelvin; Crowe, Michael A; Partridge, Leslie

2013-01-04

Analytical methods were developed for a directed enzyme evolution research programme, which pursued high performance enzymes to produce high quality L-ribose using large scale biocatalytic reaction. A high throughput HPLC method with evaporative light-scattering detection was developed to test ribose and ribitol in the enzymatic reaction, a β-cyclobond 2000 analytical column separated ribose and ribitol in 2.3 min, a C(18) guard column was used as an on-line filter to clean up the enzyme sample matrix and a short gradient was applied to wash the column, the enzymatic reaction solution can be directly injected after quenching. Total run time of each sample was approx. 4 min which provided capability of screening 4×96-well plates/day/instrument. Meanwhile, a capillary electrophoresis method was developed for the separation of ribose enantiomers, while 7-aminonaphthalene-1,3-disulfonic acid was used as derivatisation reagent and 25 mM tetraborate with 5 mM β-cyclodextrin was used as electrolyte. 0.35%of D-ribose in L-ribose can be detected which can be translated into 99.3% ee of L-ribose. Derivatisation reagent and sample matrix did not interfere with the measurement. Copyright © 2012 Elsevier B.V. All rights reserved.

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.

FDVIBSPC16: Sheath Flow SERS for Chemical Profiling in Urine

PubMed Central

Riordan, Colleen M.; Jacobs, Kevin T.; Negri, Pierre; Schultz, Zachary D.

2016-01-01

The molecular specificity and sensitivity of surface enhanced Raman scattering (SERS) makes it an attractive method for biomedical diagnostics. Here we present results demonstrating the utility and complications for SERS characterization in urine. The chemical fingerprint characteristic of Raman spectra suggests use as a label free diagnostic; however, the complex composition of biological fluids presents a tremendous challenge. In particular, the limited number of surface sites and competing absorption tend to mask the presence of analytes in solution, particularly when the solution contains multiple analytes. To address these problems and characterize biological fluids we have demonstrated a sheath-flow interface for SERS detection. This sheath-flow SERS interface uses hydrodynamic focusing to confine analyte molecules eluting out of a column onto a planar SERS substrate where the molecules are detected by their intrinsic SERS signal. In this report we compare direct detection of benzoylecgonine in urine using DSERS with chemical profiling by capillary zone electrophoresis and sheath-flow SERS detection. The SERS spectrum from the observed migration peaks can identify benzoylecgonine and other distinct spectra are also observed, suggesting improved chemical diagnostics in urine. With over 2000 reported compounds in urine, identification of each of the detected species is an enormous task. Nonetheless, these samples provide a benchmark to establish the potential clinical utility of sheath-flow SERS detection. PMID:27034996

Determination of fluorine concentrations using wavelength dispersive X-ray fluorescence (WDXRF) spectrometry to analyze fluoride precipitates.

NASA Astrophysics Data System (ADS)

Lee, H. A.; Lee, J.; Kwon, E.; Kim, D.; Yoon, H. O.

2015-12-01

In recent times, fluorine has been receiving increasing attention due to the possibility for chemical (HF) leakage accidents and its high toxicity to human and environment. In this respect, a novel approach for the determination of fluorine concentrations in water samples using wavelength dispersive X-ray fluorescence (WDXRF) spectrometry was investigated in this study. The main disadvantage of WDXRF technique for fluorine analysis is low analytical sensitivity for light elements with atomic number (Z) less than 15. To overcome this problem, we employed the precipitation reaction which fluoride is reacted with cation such as Al3+ and/or Ca2+ prior to WDXRF analysis because of their high analytical sensitivity. The cation was added in fluoride solutions to form precipitate (AlF3 and/or CaF2) and then the solution was filtered through Whatman filter. After drying at 60 °C for 5 min, the filter was coated with X-ray film and directly analyzed using WDXRF spectrometry. Consequently, we analyzed the cation on filter and subsequently fluorine concentration was calculated inversely based on chemical form of precipitate. This method can improve the analytical sensitivity of WDXRF technique for fluorine analysis and be applicable to various elements that can make precipitate.

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 solution for multi-species contaminant transport in finite media with time-varying boundary conditions

USDA-ARS?s Scientific Manuscript database

Most analytical solutions available for the equations governing the advective-dispersive transport of multiple solutes undergoing sequential first-order decay reactions have been developed for infinite or semi-infinite spatial domains and steady-state boundary conditions. In this work we present an ...

APPROXIMATE AND ANALYTICAL SOLUTIONS FOR SOLUTE TRANSPORT FROM AN INJECTION WELL INTO A SINGLE FRACTURE

EPA Science Inventory

In dealing with problems related to land-based nuclear waste management, a number of analytical and approximate solutions were developed to quantify radionuclide transport through fractures contained in the porous formation. t has been reported that by treating the radioactive de...

Analytical solution for vacuum preloading considering the nonlinear distribution of horizontal permeability within the smear zone.

PubMed

Peng, Jie; He, Xiang; Ye, Hanming

2015-01-01

The vacuum preloading is an effective method which is widely used in ground treatment. In consolidation analysis, the soil around prefabricated vertical drain (PVD) is traditionally divided into smear zone and undisturbed zone, both with constant permeability. In reality, the permeability of soil changes continuously within the smear zone. In this study, the horizontal permeability coefficient of soil within the smear zone is described by an exponential function of radial distance. A solution for vacuum preloading consolidation considers the nonlinear distribution of horizontal permeability within the smear zone is presented and compared with previous analytical results as well as a numerical solution, the results show that the presented solution correlates well with the numerical solution, and is more precise than previous analytical solution.

Analytical solution for vacuum preloading considering the nonlinear distribution of horizontal permeability within the smear zone

PubMed Central

Peng, Jie; He, Xiang; Ye, Hanming

2015-01-01

The vacuum preloading is an effective method which is widely used in ground treatment. In consolidation analysis, the soil around prefabricated vertical drain (PVD) is traditionally divided into smear zone and undisturbed zone, both with constant permeability. In reality, the permeability of soil changes continuously within the smear zone. In this study, the horizontal permeability coefficient of soil within the smear zone is described by an exponential function of radial distance. A solution for vacuum preloading consolidation considers the nonlinear distribution of horizontal permeability within the smear zone is presented and compared with previous analytical results as well as a numerical solution, the results show that the presented solution correlates well with the numerical solution, and is more precise than previous analytical solution. PMID:26447973

Analytic solution and pulse area theorem for three-level atoms

NASA Astrophysics Data System (ADS)

Shchedrin, Gavriil; O'Brien, Chris; Rostovtsev, Yuri; Scully, Marlan O.

2015-12-01

We report an analytic solution for a three-level atom driven by arbitrary time-dependent electromagnetic pulses. In particular, we consider far-detuned driving pulses and show an excellent match between our analytic result and the numerical simulations. We use our solution to derive a pulse area theorem for three-level V and Λ systems without making the rotating wave approximation. Formulated as an energy conservation law, this pulse area theorem can be used to understand pulse propagation through three-level media.

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.

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.

A mathematical solution for the parameters of three interfering resonances

NASA Astrophysics Data System (ADS)

Han, X.; Shen, C. P.

2018-04-01

The multiple-solution problem in determining the parameters of three interfering resonances from a fit to an experimentally measured distribution is considered from a mathematical viewpoint. It is shown that there are four numerical solutions for a fit with three coherent Breit-Wigner functions. Although explicit analytical formulae cannot be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, a numerical method is provided to derive the other solutions from that already obtained, based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The good agreement between the solutions found using this mathematical method and those directly from the fit verifies the correctness of the constraint equations and mathematical methodology used. Supported by National Natural Science Foundation of China (NSFC) (11575017, 11761141009), the Ministry of Science and Technology of China (2015CB856701) and the CAS Center for Excellence in Particle Physics (CCEPP)

Hydraulic modeling of riverbank filtration systems with curved boundaries using analytic elements and series solutions

NASA Astrophysics Data System (ADS)

Bakker, Mark

2010-08-01

A new analytic solution approach is presented for the modeling of steady flow to pumping wells near rivers in strip aquifers; all boundaries of the river and strip aquifer may be curved. The river penetrates the aquifer only partially and has a leaky stream bed. The water level in the river may vary spatially. Flow in the aquifer below the river is semi-confined while flow in the aquifer adjacent to the river is confined or unconfined and may be subject to areal recharge. Analytic solutions are obtained through superposition of analytic elements and Fourier series. Boundary conditions are specified at collocation points along the boundaries. The number of collocation points is larger than the number of coefficients in the Fourier series and a solution is obtained in the least squares sense. The solution is analytic while boundary conditions are met approximately. Very accurate solutions are obtained when enough terms are used in the series. Several examples are presented for domains with straight and curved boundaries, including a well pumping near a meandering river with a varying water level. The area of the river bottom where water infiltrates into the aquifer is delineated and the fraction of river water in the well water is computed for several cases.

Improved partition equilibrium model for predicting analyte response in electrospray ionization mass spectrometry.

PubMed

Du, Lihong; White, Robert L

2009-02-01

A previously proposed partition equilibrium model for quantitative prediction of analyte response in electrospray ionization mass spectrometry is modified to yield an improved linear relationship. Analyte mass spectrometer response is modeled by a competition mechanism between analyte and background electrolytes that is based on partition equilibrium considerations. The correlation between analyte response and solution composition is described by the linear model over a wide concentration range and the improved model is shown to be valid for a wide range of experimental conditions. The behavior of an analyte in a salt solution, which could not be explained by the original model, is correctly predicted. The ion suppression effects of 16:0 lysophosphatidylcholine (LPC) on analyte signals are attributed to a combination of competition for excess charge and reduction of total charge due to surface tension effects. In contrast to the complicated mathematical forms that comprise the original model, the simplified model described here can more easily be employed to predict analyte mass spectrometer responses for solutions containing multiple components. Copyright (c) 2008 John Wiley & Sons, Ltd.

Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere

NASA Technical Reports Server (NTRS)

Weinman, J. A.; Twitty, J. T.; Browning, S. R.; Herman, B. M.

1975-01-01

The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical small-angle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosol-laden model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few per cent. The analytical solution to the problem which considers an aerosol-laden atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.

Exact solutions of magnetohydrodynamics for describing different structural disturbances in solar wind

NASA Astrophysics Data System (ADS)

Grib, S. A.; Leora, S. N.

2016-03-01

We use analytical methods of magnetohydrodynamics to describe the behavior of cosmic plasma. This approach makes it possible to describe different structural fields of disturbances in solar wind: shock waves, direction discontinuities, magnetic clouds and magnetic holes, and their interaction with each other and with the Earth's magnetosphere. We note that the wave problems of solar-terrestrial physics can be efficiently solved by the methods designed for solving classical problems of mathematical physics. We find that the generalized Riemann solution particularly simplifies the consideration of secondary waves in the magnetosheath and makes it possible to describe in detail the classical solutions of boundary value problems. We consider the appearance of a fast compression wave in the Earth's magnetosheath, which is reflected from the magnetosphere and can nonlinearly overturn to generate a back shock wave. We propose a new mechanism for the formation of a plateau with protons of increased density and a magnetic field trough in the magnetosheath due to slow secondary shock waves. Most of our findings are confirmed by direct observations conducted on spacecrafts (WIND, ACE, Geotail, Voyager-2, SDO and others).

Ensemble solute transport in two-dimensional operator-scaling random fields

NASA Astrophysics Data System (ADS)

Monnig, Nathan D.; Benson, David A.; Meerschaert, Mark M.

2008-02-01

Motivated by field measurements of aquifer hydraulic conductivity (K), recent techniques were developed to construct anisotropic fractal random fields in which the scaling, or self-similarity parameter, varies with direction and is defined by a matrix. Ensemble numerical results are analyzed for solute transport through these two-dimensional "operator-scaling" fractional Brownian motion ln(K) fields. Both the longitudinal and transverse Hurst coefficients, as well as the "radius of isotropy" are important to both plume growth rates and the timing and duration of breakthrough. It is possible to create operator-scaling fractional Brownian motion fields that have more "continuity" or stratification in the direction of transport. The effects on a conservative solute plume are continually faster-than-Fickian growth rates, highly non-Gaussian shapes, and a heavier tail early in the breakthrough curve. Contrary to some analytic stochastic theories for monofractal K fields, the plume growth rates never exceed A. Mercado's (1967) purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent superstratified growth must be the result of other demonstrable factors, such as initial plume size.

Column Number Density Expressions Through M = 0 and M = 1 Point Source Plumes Along Any Straight Path

NASA Technical Reports Server (NTRS)

Woronowicz, Michael S.

2016-01-01

Analytical expressions for column number density (CND) are developed for optical line of sight paths through a variety of steady free molecule point source models including directionally-constrained effusion (Mach number M = 0) and flow from a sonic orifice (M 1). Sonic orifice solutions are approximate, developed using a fair simulacrum fitted to the free molecule solution. Expressions are also developed for a spherically-symmetric thermal expansion (M = 0). CND solutions are found for the most general paths relative to these sources and briefly explored. It is determined that the maximum CND from a distant location through directed effusion and sonic orifice cases occurs along the path parallel to the source plane that intersects the plume axis. For the effusive case this value is exactly twice the CND found along the ray originating from that point of intersection and extending to infinity along the plumes axis. For sonic plumes this ratio is reduced to about 43. For high Mach number cases the maximum CND will be found along the axial centerline path.

An analytical computation of magnetic field generated from a cylinder ferromagnet

NASA Astrophysics Data System (ADS)

Taniguchi, Tomohiro

2018-04-01

An analytical formulation to compute a magnetic field generated from an uniformly magnetized cylinder ferromagnet is developed. Exact solutions of the magnetic field generated from the magnetization pointing in an arbitrary direction are derived, which are applicable both inside and outside the ferromagnet. The validities of the present formulas are confirmed by comparing them with demagnetization coefficients estimated in earlier works. The results will be useful for designing practical applications, such as high-density magnetic recording and microwave generators, where nanostructured ferromagnets are coupled to each other through the dipole interactions and show cooperative phenomena such as synchronization. As an example, the magnetic field generated from a spin torque oscillator for magnetic recording based on microwave assisted magnetization reversal is studied.

ANALYTIC MODELING OF STARSHADES

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

Cash, Webster

2011-09-01

External occulters, otherwise known as starshades, have been proposed as a solution to one of the highest priority yet technically vexing problems facing astrophysics-the direct imaging and characterization of terrestrial planets around other stars. New apodization functions, developed over the past few years, now enable starshades of just a few tens of meters diameter to occult central stars so efficiently that the orbiting exoplanets can be revealed and other high-contrast imaging challenges addressed. In this paper, an analytic approach to the analysis of these apodization functions is presented. It is used to develop a tolerance analysis suitable for use inmore » designing practical starshades. The results provide a mathematical basis for understanding starshades and a quantitative approach to setting tolerances.« less

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.

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

Modification of a method-of-characteristics solute-transport model to incorporate decay and equilibrium-controlled sorption or ion exchange

USGS Publications Warehouse

Goode, D.J.; Konikow, Leonard F.

1989-01-01

The U.S. Geological Survey computer model of two-dimensional solute transport and dispersion in ground water (Konikow and Bredehoeft, 1978) has been modified to incorporate the following types of chemical reactions: (1) first-order irreversible rate-reaction, such as radioactive decay; (2) reversible equilibrium-controlled sorption with linear, Freundlich, or Langmuir isotherms; and (3) reversible equilibrium-controlled ion exchange for monovalent or divalent ions. Numerical procedures are developed to incorporate these processes in the general solution scheme that uses method-of- characteristics with particle tracking for advection and finite-difference methods for dispersion. The first type of reaction is accounted for by an exponential decay term applied directly to the particle concentration. The second and third types of reactions are incorporated through a retardation factor, which is a function of concentration for nonlinear cases. The model is evaluated and verified by comparison with analytical solutions for linear sorption and decay, and by comparison with other numerical solutions for nonlinear sorption and ion exchange.

Periodic waves in fiber Bragg gratings

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

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

2008-02-15

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

Nanomanipulation-Coupled Matrix-Assisted Laser Desorption/ Ionization-Direct Organelle Mass Spectrometry: A Technique for the Detailed Analysis of Single Organelles

NASA Astrophysics Data System (ADS)

Phelps, Mandy S.; Sturtevant, Drew; Chapman, Kent D.; Verbeck, Guido F.

2016-02-01

We describe a novel technique combining precise organelle microextraction with deposition and matrix-assisted laser desorption/ionization (MALDI) for a rapid, minimally invasive mass spectrometry (MS) analysis of single organelles from living cells. A dual-positioner nanomanipulator workstation was utilized for both extraction of organelle content and precise co-deposition of analyte and matrix solution for MALDI-direct organelle mass spectrometry (DOMS) analysis. Here, the triacylglycerol (TAG) profiles of single lipid droplets from 3T3-L1 adipocytes were acquired and results validated with nanoelectrospray ionization (NSI) MS. The results demonstrate the utility of the MALDI-DOMS technique as it enabled longer mass analysis time, higher ionization efficiency, MS imaging of the co-deposited spot, and subsequent MS/MS capabilities of localized lipid content in comparison to NSI-DOMS. This method provides selective organellar resolution, which complements current biochemical analyses and prompts for subsequent subcellular studies to be performed where limited samples and analyte volume are of concern.

Continuous, Real-Time Monitoring of Cocaine in Undiluted Blood Serum via a Microfluidic, Electrochemical Aptamer-Based Sensor

PubMed Central

Swensen, James S.; Xiao, Yi; Ferguson, Brian S.; Lubin, Arica A.; Lai, Rebecca Y.; Heeger, Alan J.; Plaxco, Kevin W.; Soh, H. Tom.

2009-01-01

The development of a biosensor system capable of continuous, real-time measurement of small-molecule analytes directly in complex, unprocessed aqueous samples has been a significant challenge, and successful implementation has been achieved for only a limited number of targets. Towards a general solution to this problem, we report here the Microfluidic Electrochemical Aptamer-based Sensor (MECAS) chip wherein we integrate target-specific DNA aptamers that fold, and thus generate an electrochemical signal, in response to the analyte with a microfluidic detection system. As a model, we demonstrate the continuous, real-time (~1 minute time resolution) detection of the small molecule drug cocaine at near physiological, low micromolar concentrations directly in undiluted, otherwise unmodified blood serum. We believe our approach of integrating folding-based electrochemical sensors with miniaturized detection systems may lay the ground work for the real-time, point-of-care detection of a wide variety of molecular targets. PMID:19271708

Some Interaction Solutions of a Reduced Generalised (3+1)-Dimensional Shallow Water Wave Equation for Lump Solutions and a Pair of Resonance Solitons

NASA Astrophysics Data System (ADS)

Wang, Yao; Chen, Mei-Dan; Li, Xian; Li, Biao

2017-05-01

Through Hirota bilinear transformation and symbolic computation with Maple, a class of lump solutions, rationally localised in all directions in the space, to a reduced generalised (3+1)-dimensional shallow water wave (SWW) equation are prensented. The resulting lump solutions all contain six parameters, two of which are free due to the translation invariance of the SWW equation and the other four of which must satisfy a nonzero determinant condition guaranteeing analyticity and rational localisation of the solutions. Then we derived the interaction solutions for lump solutions and one stripe soliton and the result shows that the particular lump solutions with specific values of the involved parameters will be drowned or swallowed by the stripe soliton. Furthermore, we extend this method to a more general combination of positive quadratic function and hyperbolic functions. Especially, it is interesting that a rogue wave is found to be aroused by the interaction between lump solutions and a pair of resonance stripe solitons. By choosing the values of the parameters, the dynamic properties of lump solutions, interaction solutions for lump solutions and one stripe soliton and interaction solutions for lump solutions and a pair of resonance solitons, are shown by dynamic graphs.

Mechanical Properties of Additively Manufactured Thick Honeycombs.

PubMed

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

2016-07-23

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

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

PubMed

Khan, Farman U; Qamar, Shamsul

2017-05-01

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

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.

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

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the monotone and stable discrete-analytical numerical schemes [1]-[3] conserving the positivity of the chemical substance concentrations and possessing the properties of energy and mass balance that are postulated in the general variational principle for integrated models. All algorithms for solution of transport, diffusion and transformation problems are direct (without iterations). The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References Penenko V., Tsvetova E. Discrete-analytical methods for the implementation of variational principles in environmental applications// Journal of computational and applied mathematics, 2009, v. 226, 319-330. Penenko A.V. Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods// Numerical Analysis and Applications, 2012, V. 5, pp 326-341. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models //Numerical Analysis and Applications, 2013 (in press).

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.

Low-Cost Chemical-Responsive Adhesive Sensing Chips.

PubMed

Tan, Weirui; Zhang, Liyuan; Shen, Wei

2017-12-06

Chemical-responsive adhesive sensing chip is a new low-cost analytical platform that uses adhesive tape loaded with indicator reagents to detect or quantify the target analytes by directly sticking the tape to the samples of interest. The chemical-responsive adhesive sensing chips can be used with paper to analyze aqueous samples; they can also be used to detect and quantify solid, particulate, and powder analytes. The colorimetric indicators become immediately visible as the contact between the functionalized adhesives and target samples is made. The chemical-responsive adhesive sensing chip expands the capability of paper-based analytical devices to analyze solid, particulate, or powder materials via one-step operation. It is also a simpler alternative way, to the covalent chemical modification of paper, to eliminate indicator leaching from the dipstick-style paper sensors. Chemical-responsive adhesive chips can display analytical results in the form of colorimetric dot patterns, symbols, and texts, enabling clear understanding of assay results by even nonprofessional users. In this work, we demonstrate the analyses of heavy metal salts in silica powder matrix, heavy metal ions in water, and bovine serum albumin in an aqueous solution. The detection is one-step, specific, sensitive, and easy-to-operate.

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.

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.

Nonlocal Symmetries, Consistent Riccati Expansion, and Analytical Solutions of the Variant Boussinesq System

NASA Astrophysics Data System (ADS)

Feng, Lian-Li; Tian, Shou-Fu; Zhang, Tian-Tian; Zhou, Jun

2017-07-01

Under investigation in this paper is the variant Boussinesq system, which describes the propagation of surface long wave towards two directions in a certain deep trough. With the help of the truncated Painlevé expansion, we construct its nonlocal symmetry, Bäcklund transformation, and Schwarzian form, respectively. The nonlocal symmetries can be localised to provide the corresponding nonlocal group, and finite symmetry transformations and similarity reductions are computed. Furthermore, we verify that the variant Boussinesq system is solvable via the consistent Riccati expansion (CRE). By considering the consistent tan-function expansion (CTE), which is a special form of CRE, the interaction solutions between soliton and cnoidal periodic wave are explicitly studied.

Homoclinic orbits in three-dimensional Shilnikov-type chaotic systems

NASA Astrophysics Data System (ADS)

Feng, Jing-Jing; Zhang, Qi-Chang; Wang, Wei; Hao, Shu-Ying

2013-09-01

In this paper, the Padé approximant and analytic solution in the neighborhood of the initial value are introduced into the process of constructing the Shilnikov type homoclinic trajectories in three-dimensional nonlinear dynamical systems. The PID controller system with quadratic and cubic nonlinearities, the simplified solar-wind-driven-magnetosphere-ionosphere system, and the human DNA sequence system are considered. With the aid of presenting a new condition, the solutions of solving the boundary-value problems which are formulated for the trajectory and evaluating the initial amplitude values become available. At the same time, the value of the bifurcation parameter is obtained directly, which is almost consistent with the numerical result.

A novel and sensitive fluorescence sensor for glutathione detection by controlling the surface passivation degree of carbon quantum dots.

PubMed

Pan, Jiahong; Zheng, Zengyao; Yang, Jianying; Wu, Yaoyu; Lu, Fushen; Chen, Yaowen; Gao, Wenhua

2017-05-01

A novel fluorescence sensor based on controlling the surface passivation degree of carbon quantum dots (CQDs) was developed for glutathione (GSH) detection. First, we found that the fluorescence intensity of the CQDs which was obtained by directly pyrolyzing citric acid would increased largely after the surface passivation treatment by 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide (EDC). In the light of this phenomenon, we designed a simple, rapid and selective fluorescence sensor based on the surface passivated CQDs. A certain and excess amount of EDC were mixed with GSH, part of EDC would form a stable complex with GSH owing to the exposed sulfhydryl group of GSH. As the synthesized CQDs were added into the above mixture solution, the fluorescence intensity of the (EDC/GSH)/CQDs mixture solution could be directly related to the amount of GSH. Compared to other fluorescence analytical methods, the fluorescence sensor we design is neither the traditional fluorescent "turn on" probes nor "turn off" probes. It is a new fluorescence analytical method that target object indirectly control the surface passivation degree of CQDs so that it can realize the detection of the target object. Moreover, the proposed method manifested great advantages including short analysis time, low cost and ease of operation. Copyright © 2017 Elsevier B.V. All rights reserved.

Multistability and switching in oppositely-directed saturated coupler

NASA Astrophysics Data System (ADS)

Nithyanandan, K.; Shafeeque Ali, A. K.; Porsezian, K.; Nishad, M. P. M.; Tchofo Dinda, P.; Grelu, Ph.

2018-06-01

We investigate theoretically the optical multistability that takes place in a two-core oppositely-directed saturated coupler (ODSC) having negative index material (NIM) channel. The dynamics are studied using the Lagrangian variational method, and analytical solutions are constructed with Jacobi elliptic functions. The ODSC exhibits a bandgap as a consequence of the effective feedback mechanism due to the opposite directionality of the phase velocity and the Poynting vector in the NIM channel. Depending on the strength of the nonlinear saturation, the system admits multiple stable states. Considering the additional degrees of design freedom with respect to conventional nonlinear couplers, the ODSC could become an attractive choice for all-optical switching. The existence of multiple transmission resonance windows could also facilitate the realization of gap solitons.

Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions

NASA Astrophysics Data System (ADS)

Gordon, Dan; Gordon, Rachel; Turkel, Eli

2015-09-01

We consider several compact high order absorbing boundary conditions (ABCs) for the Helmholtz equation in three dimensions. A technique called "the gradient method" (GM) for ABCs is also introduced and combined with the high order ABCs. GM is based on the principle of using directional derivatives in the direction of the wavefront propagation. The new ABCs are used together with the recently introduced compact sixth order finite difference scheme for variable wave numbers. Experiments on problems with known analytic solutions produced very accurate results, demonstrating the efficacy of the high order schemes, particularly when combined with GM. The new ABCs are then applied to the SEG/EAGE Salt model, showing the advantages of the new schemes.

A simple and effective method for detecting precipitated proteins in MALDI-TOF MS.

PubMed

Oshikane, Hiroyuki; Watabe, Masahiko; Nakaki, Toshio

2018-04-01

MALDI-TOF MS has developed rapidly into an essential analytical tool for the life sciences. Cinnamic acid derivatives are generally employed in routine molecular weight determinations of intact proteins using MALDI-TOF MS. However, a protein of interest may precipitate when mixed with matrix solution, perhaps preventing MS detection. We herein provide a simple approach to enable the MS detection of such precipitated protein species by means of a "direct deposition method" -- loading the precipitant directly onto the sample plate. It is thus expected to improve routine MS analysis of intact proteins. Copyright © 2018. Published by Elsevier Inc.

The Surface Density Distribution in the Solar Nebula

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

2004-01-01

The commonly used minimum mass power law representation of the pre-solar nebula is reanalyzed using a new cumulative-mass-model. This model predicts a smoother surface density approximation compared with methods based on direct computation of surface density. The density is quantified using two independent analytical formulations. First, a best-fit transcendental function is applied directly to the basic planetary data. Next a solution to the time-dependent disk evolution equation is parametrically adapted to the solar nebula data. The latter model is shown to be a good approximation to the finite-size early Solar Nebula, and by extension to other extra solar protoplanetary disks.

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

DOE PAGES

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

2014-12-17

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

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

NASA Astrophysics Data System (ADS)

Alvarez, Orlando; Haddad, Matthew

2018-03-01

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

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

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

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

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

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

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

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

2016-06-08

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

The propagation of the shock wave from a strong explosion in a plane-parallel stratified medium: the Kompaneets approximation

NASA Astrophysics Data System (ADS)

Olano, C. A.

2009-11-01

Context: Using certain simplifications, Kompaneets derived a partial differential equation that states the local geometrical and kinematical conditions that each surface element of a shock wave, created by a point blast in a stratified gaseous medium, must satisfy. Kompaneets could solve his equation analytically for the case of a wave propagating in an exponentially stratified medium, obtaining the form of the shock front at progressive evolutionary stages. Complete analytical solutions of the Kompaneets equation for shock wave motion in further plane-parallel stratified media were not found, except for radially stratified media. Aims: We aim to analytically solve the Kompaneets equation for the motion of a shock wave in different plane-parallel stratified media that can reflect a wide variety of astrophysical contexts. We were particularly interested in solving the Kompaneets equation for a strong explosion in the interstellar medium of the Galactic disk, in which, due to intense winds and explosions of stars, gigantic gaseous structures known as superbubbles and supershells are formed. Methods: Using the Kompaneets approximation, we derived a pair of equations that we call adapted Kompaneets equations, that govern the propagation of a shock wave in a stratified medium and that permit us to obtain solutions in parametric form. The solutions provided by the system of adapted Kompaneets equations are equivalent to those of the Kompaneets equation. We solved the adapted Kompaneets equations for shock wave propagation in a generic stratified medium by means of a power-series method. Results: Using the series solution for a shock wave in a generic medium, we obtained the series solutions for four specific media whose respective density distributions in the direction perpendicular to the stratification plane are of an exponential, power-law type (one with exponent k=-1 and the other with k =-2) and a quadratic hyperbolic-secant. From these series solutions, we deduced exact solutions for the four media in terms of elemental functions. The exact solution for shock wave propagation in a medium of quadratic hyperbolic-secant density distribution is very appropriate to describe the growth of superbubbles in the Galactic disk. Member of the Carrera del Investigador Científico del CONICET, Argentina.

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

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

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

2016-12-20

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

Ionization Efficiency of Doubly Charged Ions Formed from Polyprotic Acids in Electrospray Negative Mode

NASA Astrophysics Data System (ADS)

Liigand, Piia; Kaupmees, Karl; Kruve, Anneli

2016-07-01

The ability of polyprotic acids to give doubly charged ions in negative mode electrospray was studied and related to physicochemical properties of the acids via linear discriminant analysis (LDA). It was discovered that the compound has to be strongly acidic (low p K a1 and p K a2) and to have high hydrophobicity (log P ow) to become multiply charged. Ability to give multiply charged ions in ESI/MS cannot be directly predicted from the solution phase acidities. Therefore, for the first time, a quantitative model to predict the charge state of the analyte in ESI/MS is proposed and validated for small anions. Also, a model to predict ionization efficiencies of these analytes was developed. Results indicate that acidity of the analyte, its octanol-water partition coefficient, and charge delocalization are important factors that influence ionization efficiencies as well as charge states of the analytes. The pH of the solvent was also found to be an important factor influencing the ionization efficiency of doubly charged ions.

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.

Electrokinetic flow in a capillary with a charge-regulating surface polymer layer.

PubMed

Keh, Huan J; Ding, Jau M

2003-07-15

An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson-Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.

Dynamic Characteristics of Micro-Beams Considering the Effect of Flexible Supports

PubMed Central

Zhong, Zuo-Yang; Zhang, Wen-Ming; Meng, Guang

2013-01-01

Normally, the boundaries are assumed to allow small deflections and moments for MEMS beams with flexible supports. The non-ideal boundary conditions have a significant effect on the qualitative dynamical behavior. In this paper, by employing the principle of energy equivalence, rigorous theoretical solutions of the tangential and rotational equivalent stiffness are derived based on the Boussinesq's and Cerruti's displacement equations. The non-dimensional differential partial equation of the motion, as well as coupled boundary conditions, are solved analytically using the method of multiple time scales. The closed-form solution provides a direct insight into the relationship between the boundary conditions and vibration characteristics of the dynamic system, in which resonance frequencies increase with the nonlinear mechanical spring effect but decrease with the effect of flexible supports. The obtained results of frequencies and mode shapes are compared with the cases of ideal boundary conditions, and the differences between them are contrasted on frequency response curves. The influences of the support material property on the equivalent stiffness and resonance frequency shift are also discussed. It is demonstrated that the proposed model with the flexible supports boundary conditions has significant effect on the rigorous quantitative dynamical analysis of the MEMS beams. Moreover, the proposed analytical solutions are in good agreement with those obtained from finite element analyses.

Fractional dynamics pharmacokinetics–pharmacodynamic models

PubMed Central

2010-01-01

While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics. PMID:20455076

A one-step method for modelling longitudinal data with differential equations.

PubMed

Hu, Yueqin; Treinen, Raymond

2018-04-06

Differential equation models are frequently used to describe non-linear trajectories of longitudinal data. This study proposes a new approach to estimate the parameters in differential equation models. Instead of estimating derivatives from the observed data first and then fitting a differential equation to the derivatives, our new approach directly fits the analytic solution of a differential equation to the observed data, and therefore simplifies the procedure and avoids bias from derivative estimations. A simulation study indicates that the analytic solutions of differential equations (ASDE) approach obtains unbiased estimates of parameters and their standard errors. Compared with other approaches that estimate derivatives first, ASDE has smaller standard error, larger statistical power and accurate Type I error. Although ASDE obtains biased estimation when the system has sudden phase change, the bias is not serious and a solution is also provided to solve the phase problem. The ASDE method is illustrated and applied to a two-week study on consumers' shopping behaviour after a sale promotion, and to a set of public data tracking participants' grammatical facial expression in sign language. R codes for ASDE, recommendations for sample size and starting values are provided. Limitations and several possible expansions of ASDE are also discussed. © 2018 The British Psychological Society.

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.

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.

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.

Curvature Effect in Shear Flow: Slowdown of Turbulent Flame Speeds with Markstein Number

NASA Astrophysics Data System (ADS)

Lyu, Jiancheng; Xin, Jack; Yu, Yifeng

2017-12-01

It is well-known in the combustion community that curvature effect in general slows down flame propagation speeds because it smooths out wrinkled flames. However, such a folklore has never been justified rigorously. In this paper, as the first theoretical result in this direction, we prove that the turbulent flame speed (an effective burning velocity) is decreasing with respect to the curvature diffusivity (Markstein number) for shear flows in the well-known G-equation model. Our proof involves several novel and rather sophisticated inequalities arising from the nonlinear structure of the equation. On a related fundamental issue, we solve the selection problem of weak solutions or find the "physical fluctuations" when the Markstein number goes to zero and solutions approach those of the inviscid G-equation model. The limiting solution is given by a closed form analytical formula.

Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss-Bonnet term

NASA Astrophysics Data System (ADS)

de la Cruz-Dombriz, Álvaro; Farrugia, Gabriel; Levi Said, Jackson; Sáez-Chillón Gómez, Diego

2017-12-01

In the context of extended teleparallel gravity theories with a 3  +  1 dimensions Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological solutions. In particular when applied to a Friedmann-Lemaître-Robertson-Walker geometry in four-dimensional spacetime with standard fluids exclusively. We study different types of gravitational Lagrangians and reconstruct solutions provided by analytical expressions for either the cosmological scale factor or the Hubble parameter. We also show that it is possible to find Lagrangians of this type without a cosmological constant such that the behaviour of the ΛCDM model is precisely mimicked. The new Lagrangians may also lead to other phenomenological consequences opening up the possibility for new theories to compete directly with other extensions of General Relativity.

International Conference on Numerical Methods in Fluid Dynamics, 7th, Stanford University, Stanford and Moffett Field, CA, June 23-27, 1980, Proceedings

NASA Technical Reports Server (NTRS)

Reynolds, W. C. (Editor); Maccormack, R. W.

1981-01-01

Topics discussed include polygon transformations in fluid mechanics, computation of three-dimensional horseshoe vortex flow using the Navier-Stokes equations, an improved surface velocity method for transonic finite-volume solutions, transonic flow calculations with higher order finite elements, the numerical calculation of transonic axial turbomachinery flows, and the simultaneous solutions of inviscid flow and boundary layer at transonic speeds. Also considered are analytical solutions for the reflection of unsteady shock waves and relevant numerical tests, reformulation of the method of characteristics for multidimensional flows, direct numerical simulations of turbulent shear flows, the stability and separation of freely interacting boundary layers, computational models of convective motions at fluid interfaces, viscous transonic flow over airfoils, and mixed spectral/finite difference approximations for slightly viscous flows.

Chemical transport in a fissured rock: Verification of a numerical model

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

Rasmuson, A.; Narasimhan, T. N.; Neretnieks, I.

1982-10-01

Numerical models for simulating chemical transport in fissured rocks constitute powerful tools for evaluating the acceptability of geological nuclear waste repositories. Due to the very long-term, high toxicity of some nuclear waste products, the models are required to predict, in certain cases, the spatial and temporal distribution of chemical concentration less than 0.001% of the concentration released from the repository. Whether numerical models can provide such accuracies is a major question addressed in the present work. To this end, we have verified a numerical model, TRUMP, which solves the advective diffusion equation in general three dimensions with or without decaymore » and source terms. The method is based on an integrated finite-difference approach. The model was verified against known analytic solution of the one-dimensional advection-diffusion problem as well as the problem of advection-diffusion in a system of parallel fractures separated by spherical particles. The studies show that as long as the magnitude of advectance is equal to or less than that of conductance for the closed surface bounding any volume element in the region (that is, numerical Peclet number <2), the numerical method can indeed match the analytic solution within errors of ±10{sup -3} % or less. The realistic input parameters used in the sample calculations suggest that such a range of Peclet numbers is indeed likely to characterize deep groundwater systems in granitic and ancient argillaceous systems. Thus TRUMP in its present form does provide a viable tool for use in nuclear waste evaluation studies. A sensitivity analysis based on the analytic solution suggests that the errors in prediction introduced due to uncertainties in input parameters is likely to be larger than the computational inaccuracies introduced by the numerical model. Currently, a disadvantage in the TRUMP model is that the iterative method of solving the set of simultaneous equations is rather slow when time constants vary widely over the flow region. Although the iterative solution may be very desirable for large three-dimensional problems in order to minimize computer storage, it seems desirable to use a direct solver technique in conjunction with the mixed explicit-implicit approach whenever possible. work in this direction is in progress.« less

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

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

NASA Astrophysics Data System (ADS)

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

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

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.

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

NASA Astrophysics Data System (ADS)

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

2015-02-01

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

Motions about a fixed point by hypergeometric functions: new non-complex analytical solutions and integration of the herpolhode

NASA Astrophysics Data System (ADS)

Mingari Scarpello, Giovanni; Ritelli, Daniele

2018-06-01

The present study highlights the dynamics of a body moving about a fixed point and provides analytical closed form solutions. Firstly, for the symmetrical heavy body, that is the Lagrange-Poisson case, we compute the second (precession, ψ ) and third (spin, φ) Euler angles in explicit and real form by means of multiple hypergeometric (Lauricella) functions. Secondly, releasing the weight assumption but adding the complication of the asymmetry, by means of elliptic integrals of third kind, we provide the precession angle ψ completing the treatment of the Euler-Poinsot case. Thirdly, by integrating the relevant differential equation, we reach the finite polar equation of a special motion trajectory named the herpolhode. Finally, we keep the symmetry of the first problem, but without weight, and take into account a viscous dissipation. The use of motion first integrals—adopted for the first two problems—is no longer practicable in this situation; therefore, the Euler equations, faced directly, are driving to particular occurrences of Bessel functions of order - 1/2.

Dynamic modes of quasispherical vesicles: exact analytical solutions.

PubMed

Guedda, M; Abaidi, M; Benlahsen, M; Misbah, C

2012-11-01

In this paper we introduce a simple mathematical analysis to reexamine vesicle dynamics in the quasispherical limit (small deformation) under a shear flow. In this context, a recent paper [Misbah, Phys. Rev. Lett. 96, 028104 (2006)] revealed a dynamic referred to as the vacillating-breathing (VB) mode where the vesicle main axis oscillates about the flow direction and the shape undergoes a breathinglike motion, as well as the tank-treading and tumbling (TB) regimes. Our goal here is to identify these three modes by obtaining explicit analytical expressions of the vesicle inclination angle and the shape deformation. In particular, the VB regime is put in evidence and the transition dynamics is discussed. Not surprisingly, our finding confirms the Keller-Skalak solutions (for rigid particles) and shows that the VB and TB modes coexist, and whether one prevails over the other depends on the initial conditions. An interesting additional element in the discussion is the prediction of the TB and VB modes as functions of a control parameter Γ, which can be identified as a TB-VB parameter.

Coupled Electro-Hydrodynamic Effects of Electro-Osmosis from Pore Scale to Darcy Scale

NASA Astrophysics Data System (ADS)

Schotting, R.; Joekar-Niasar, V.; Leijnse, A.

2011-12-01

Electro-osmosis is "movement of a fluid under the effect of an electric field in a porous medium". This phenomenon has many applications in civil engineering (slope stabilization, dewatering), environmental engineering (soil remediation, sludge dewatering), chemical engineering (micro- or nano- mixers), medical engineering (drug delivery), etc. The key factor in electro-osmosis is the competition between the electrochemical and hydrodynamic forces as well as the coupling between the solid surface and the electrolyte properties. The objective of this research is to understand the influence of pore-scale heterogeneities of surface properties on the Darcy-scale behavior. We develop novel analytical solutions for the flow and transport of electrolyte including electro-hydrodynamic forces in a single micro-channel. We propose the complete analytical solution for monovalent electrolyte at full range overlapping double layers, and nonlinear electric field, including the Donan effect in transport of ions. These pore-scale formulations are numerically upscaled to obtain the Darcy-scale behavior. Our results show the contribution of electro-osmotic, chemical-osmotic and hydrodynamic components of the flow equation on pressure field evolution and multi-directional flow field at Darcy scale.

Response of a shell structure subject to distributed harmonic excitation

NASA Astrophysics Data System (ADS)

Cao, Rui; Bolton, J. Stuart

2016-09-01

Previously, a coupled, two-dimensional structural-acoustic ring model was constructed to simulate the dynamic and acoustical behavior of pneumatic tires. Analytical forced solutions were obtained and were experimentally verified through laser velocimeter measurement made using automobile tires. However, the two-dimensional ring model is incapable of representing higher order, in-plane modal motion in either the circumferential or axial directions. Therefore, in this paper, a three-dimensional pressurized circular shell model is proposed to study the in-plane shearing motion and the effect of different forcing conditions. Closed form analytical solutions were obtained for both free and forced vibrations of the shell under simply supported boundary conditions. Dispersion relations were calculated and different wave types were identified by their different speeds. Shell surface mobility results under various input distributions were also studied and compared. Spatial Fourier series decompositions were also performed on the spatial mobility results to give the forced dispersion relations, which illustrate clearly the influence of input force spatial distribution. Such a model has practical application in identifying the sources of noise and vibration problems in automotive tires.

Semi-active control of a sandwich beam partially filled with magnetorheological elastomer

NASA Astrophysics Data System (ADS)

Dyniewicz, Bartłomiej; Bajkowski, Jacek M.; Bajer, Czesław I.

2015-08-01

The paper deals with the semi-active control of vibrations of structural elements. Elastomer composites with ferromagnetic particles that act as magnetorheological fluids are used. The damping coefficient and the shear modulus of the elastomer increases when it is exposed to an electro-magnetic field. The control of this process in time allows us to reduce vibrations more effectively than if the elastomer is permanently exposed to a magnetic field. First the analytical solution for the vibrations of a sandwich beam filled with an elastomer is given. Then the control problem is defined and applied to the analytical formula. The numerical solution of the minimization problem results in a periodic, perfectly rectangular control function if free vibrations are considered. Such a temporarily acting magnetic field is more efficient than a constantly acting one. The surplus reaches 20-50% or more, depending on the filling ratio of the elastomer. The resulting control was verified experimentally in the vibrations of a cantilever sandwich beam. The proposed semi-active control can be directly applied to engineering vibrating structural elements, for example helicopter rotors, aircraft wings, pads under machines, and vehicles.

Three-dimensional analytical solution for the instability of a parallel array of mutually attracting identical simply supported piezoelectric microplates

NASA Astrophysics Data System (ADS)

Liu, Lei; Wang, Xu

2017-12-01

Three-dimensional analytical solutions are derived for the structural instability of a parallel array of mutually attracting identical simply supported orthotropic piezoelectric rectangular microplates by means of a linear perturbation analysis. The two surfaces of each plate can be either insulating or conducting. By considering the fact that the shear stresses and the normal electric displacement (or electric potential) are zero on the two surfaces of each plate, a 2 × 2 transfer matrix for a plate can be obtained directly from the 8 × 8 fundamental piezoelectricity matrix without resolving the original Stroh eigenrelation. The critical interaction coefficient can be determined by solving the resulting generalized eigenvalue problem for the piezoelectric plate array. Also considered in our analysis is the in-plane uniform edge compression acting on the four sides of each piezoelectric plate. Our results indicate that the stabilizing influence of the piezoelectric effect on the structural instability is unignorable; the edge compression always plays a destabilizing role in the structural instability of the plate array with interactions.

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.

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.

Rapid determination of benzodiazepines, zolpidem and their metabolites in urine using direct injection liquid chromatography-tandem mass spectrometry.

PubMed

Jeong, Yu-Dong; Kim, Min Kyung; Suh, Sung Ill; In, Moon Kyo; Kim, Jin Young; Paeng, Ki-Jung

2015-12-01

Benzodiazepines and zolpidem are generally prescribed as sedative, hypnotics, anxiolytics or anticonvulsants. These drugs, however, are frequently misused in drug-facilitated crime. Therefore, a rapid and simple liquid chromatography-tandem mass spectrometric (LC-MS/MS) method was developed for identification and quantification of benzodiazepines, zolpidem and their metabolites in urine using deuterium labeled internal standards (IS). Urine samples (120 μL) mixed with 80 μL of the IS solution were centrifuged. An aliquot (5 μL) of the sample solution was directly injected into the LC-MS/MS system for analysis. The mobile phases consisted of water and acetonitrile containing 2mM ammonium trifluoroacetate and 0.2% acetic acid. The analytical column was a Zorbax SB-C18 (100 mm × 2.1 mm i.d., 3.5 μm, Agilent). The separation and detection of 18 analytes were achieved within 10 min. Calibration curves were linear over the concentration ranges of 0.5-20 ng/mL (zolpidem), 1.0-40 ng/mL (flurazepam and temazepam), 2.5-100 ng/mL (7-aminoclonazepam, 1-hydroxymidazolam, midazolam, flunitrazepam and alprazolam), 5.0-200 ng/mL (zolpidem phenyl-4-carboxylic acid, α-hydroxyalprazolam, oxazepam, nordiazepam, triazolam, diazepam and α-hydroxytriazolam), 10-400 ng/mL (lorazepam and desalkylflurazepam) and 10-100 ng/mL (N-desmethylflunitrazepam) with the coefficients of determination (r(2)) above 0.9971. The dilution integrity of the analytes was examined for supplementation of short linear range. Dilution precision and accuracy were tested using two, four and ten-folds dilutions and they ranged from 3.7 to 14.4% and -12.8 to 12.5%, respectively. The process efficiency for this method was 63.0-104.6%. Intra- and inter-day precisions were less than 11.8% and 9.1%, while intra- and inter-day accuracies were less than -10.0 to 8.2%, respectively. The lower limits of quantification were lower than 10 ng/mL for each analyte. The applicability of the developed method was successfully verified with human urine samples from drug users (n=21). Direct urine sample injection and optimized mobile phases were introduced for simple sample preparation and high-sensitivity with the desired separation. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

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

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

Yeh, T.C.J.

1995-02-01

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

Rotorcraft Diagnostics

NASA Technical Reports Server (NTRS)

Haste, Deepak; Azam, Mohammad; Ghoshal, Sudipto; Monte, James

2012-01-01

Health management (HM) in any engineering systems requires adequate understanding about the system s functioning; a sufficient amount of monitored data; the capability to extract, analyze, and collate information; and the capability to combine understanding and information for HM-related estimation and decision-making. Rotorcraft systems are, in general, highly complex. Obtaining adequate understanding about functioning of such systems is quite difficult, because of the proprietary (restricted access) nature of their designs and dynamic models. Development of an EIM (exact inverse map) solution for rotorcraft requires a process that can overcome the abovementioned difficulties and maximally utilize monitored information for HM facilitation via employing advanced analytic techniques. The goal was to develop a versatile HM solution for rotorcraft for facilitation of the Condition Based Maintenance Plus (CBM+) capabilities. The effort was geared towards developing analytic and reasoning techniques, and proving the ability to embed the required capabilities on a rotorcraft platform, paving the way for implementing the solution on an aircraft-level system for consolidation and reporting. The solution for rotorcraft can he used offboard or embedded directly onto a rotorcraft system. The envisioned solution utilizes available monitored and archived data for real-time fault detection and identification, failure precursor identification, and offline fault detection and diagnostics, health condition forecasting, optimal guided troubleshooting, and maintenance decision support. A variant of the onboard version is a self-contained hardware and software (HW+SW) package that can be embedded on rotorcraft systems. The HM solution comprises components that gather/ingest data and information, perform information/feature extraction, analyze information in conjunction with the dependency/diagnostic model of the target system, facilitate optimal guided troubleshooting, and offer decision support for optimal maintenance.

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.

On the analytic and numeric optimisation of airplane trajectories under real atmospheric conditions

NASA Astrophysics Data System (ADS)

Gonzalo, J.; Domínguez, D.; López, D.

2014-12-01

From the beginning of aviation era, economic constraints have forced operators to continuously improve the planning of the flights. The revenue is proportional to the cost per flight and the airspace occupancy. Many methods, the first started in the middle of last century, have explore analytical, numerical and artificial intelligence resources to reach the optimal flight planning. In parallel, advances in meteorology and communications allow an almost real-time knowledge of the atmospheric conditions and a reliable, error-bounded forecast for the near future. Thus, apart from weather risks to be avoided, airplanes can dynamically adapt their trajectories to minimise their costs. International regulators are aware about these capabilities, so it is reasonable to envisage some changes to allow this dynamic planning negotiation to soon become operational. Moreover, current unmanned airplanes, very popular and often small, suffer the impact of winds and other weather conditions in form of dramatic changes in their performance. The present paper reviews analytic and numeric solutions for typical trajectory planning problems. Analytic methods are those trying to solve the problem using the Pontryagin principle, where influence parameters are added to state variables to form a split condition differential equation problem. The system can be solved numerically -indirect optimisation- or using parameterised functions -direct optimisation-. On the other hand, numerical methods are based on Bellman's dynamic programming (or Dijkstra algorithms), where the fact that two optimal trajectories can be concatenated to form a new optimal one if the joint point is demonstrated to belong to the final optimal solution. There is no a-priori conditions for the best method. Traditionally, analytic has been more employed for continuous problems whereas numeric for discrete ones. In the current problem, airplane behaviour is defined by continuous equations, while wind fields are given in a discrete grid at certain time intervals. The research demonstrates advantages and disadvantages of each method as well as performance figures of the solutions found for typical flight conditions under static and dynamic atmospheres. This provides significant parameters to be used in the selection of solvers for optimal trajectories.

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.

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.

Revisitation of the dipole tracer test for heterogeneous porous formations

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Mechanical Properties of Additively Manufactured Thick Honeycombs

PubMed Central

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

2016-01-01

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

Functionalized magnetic nanoparticle analyte sensor

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

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

2014-03-25

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

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.

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.

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.

A rapid and high-precision method for sulfur isotope δ(34)S determination with a multiple-collector inductively coupled plasma mass spectrometer: matrix effect correction and applications for water samples without chemical purification.

PubMed

Lin, An-Jun; Yang, Tao; Jiang, Shao-Yong

2014-04-15

Previous studies have indicated that prior chemical purification of samples, although complex and time-consuming, is essential in obtaining precise and accurate results for sulfur isotope ratios using multiple-collector inductively coupled plasma mass spectrometry (MC-ICP-MS). In this study, we introduce a new, rapid and precise MC-ICP-MS method for sulfur isotope determination from water samples without chemical purification. The analytical work was performed on an MC-ICP-MS instrument with medium mass resolution (m/Δm ~ 3000). Standard-sample bracketing (SSB) was used to correct samples throughout the analytical sessions. Reference materials included an Alfa-S (ammonium sulfate) standard solution, ammonium sulfate provided by the lab of the authors and fresh seawater from the South China Sea. A range of matrix-matched Alfa-S standard solutions and ammonium sulfate solutions was used to investigate the matrix (salinity) effect (matrix was added in the form of NaCl). A seawater sample was used to confirm the reliability of the method. Using matrix-matched (salinity-matched) Alfa-S as the working standard, the measured δ(34)S value of AS (-6.73 ± 0.09‰) was consistent with the reference value (-6.78 ± 0.07‰) within the uncertainty, suggesting that this method could be recommended for the measurement of water samples without prior chemical purification. The δ(34)S value determination for the unpurified seawater also yielded excellent results (21.03 ± 0.18‰) that are consistent with the reference value (20.99‰), thus confirming the feasibility of the technique. The data and the results indicate that it is feasible to use MC-ICP-MS and matrix-matched working standards to measure the sulfur isotopic compositions of water samples directly without chemical purification. In comparison with the existing MC-ICP-MS techniques, the new method is better for directly measuring δ(34)S values in water samples with complex matrices; therefore, it can significantly accelerate analytical turnover. Copyright © 2014 John Wiley & Sons, Ltd.

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

Asano, Keiji G; Ford, Michael J; Tomkins, Bruce A

A self-aspirating heated nebulizer probe is described and demonstrated for use in the direct analysis of analytes on surfaces and in liquid samples by atmospheric pressure chemical ionization (APCI) mass spectrometry. Functionality and performance of the probe as a self-aspirating APCI source is demonstrated using reserpine and progesterone as test compounds. The utility of the probe to sample analytes directly from surfaces was demonstrated first by scanning development lanes of a reversed-phase thin-layer chromatography plate in which a three-component dye mixture, viz., Fat Red 7B, Solvent Green 3, and Solvent Blue 35, was spotted and the components were separated. Developmentmore » lanes were scanned by the sampling probe operated under computer control (x, y plane) while full-scan mass spectra were recorded using a quadrupole ion trap mass spectrometer. In addition, the ability to sample the surface of pharmaceutical tablets (viz., Extra Strength Tylenol(reg. sign) and Evista(reg. sign) tablets) and to detect the active ingredients (acetaminophen and raloxifene, respectively) selectively was demonstrated using tandem mass spectrometry (MS/MS). Finally, the capability to sample analyte solutions from the wells of a 384-well microtiter plate and to perform quantitative analyses using MS/MS detection was illustrated with cotinine standards spiked with cotinine-d{sub 3} as an internal standard.« less

Gas chromatography with mass spectrometry for the determination of phthalates preconcentrated by microextraction based on an ionic liquid.

PubMed

Cacho, Juan Ignacio; Campillo, Natalia; Viñas, Pilar; Hernández-Córdoba, Manuel

2017-03-01

A new procedure is proposed for the analysis of migration test solutions obtained from plastic bottles used in the packaging of edible oils. Ultrasound-assisted emulsification microextraction with ionic liquids was applied for the preconcentration of six phthalate esters: dimethylphthalate, diethylphthalate, di-n-butylphthalate, n-butylbenzylphthalate, di-2-ethylhexylphthalate, and di-n-octylphthalate. The enriched ionic liquid was directly analyzed by gas chromatography and mass spectrometry using direct insert microvial thermal desorption. The different factors affecting the microextraction efficiency, such as volume of the extracting phase (30 μL of the ionic liquid) and ultrasound application time (25 s), and the thermal desorption step, such as desorption temperature and time, and gas flow rate, were studied. Under the selected conditions, detection limits for the analytes were in the 0.012-0.18 μg/L range, while recovery assays provided values ranging from 80 to 112%. The use of butyl benzoate as internal standard increased the reproducibility of the analytical procedure. When the release of the six phthalate esters from the tested plastic bottles to liquid simulants was monitored using the optimized procedure, analyte concentrations of between 1.0 and 273 μg/L were detected. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

NASA Astrophysics Data System (ADS)

Deng, Baoqing; Si, Yinbing; Wang, Jia

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

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

1993-09-01

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

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.

An Analytical Model of Periodic Waves in Shallow Water,

DTIC Science & Technology

1984-07-01

the KP equation , "f’ + 6f +x + 3 f 0 (1.8) "’ S(t o x yy describes their evolution if they are weakly two-dimensional ( Kadomtsev & Petviashvili ...directions. Both short-crested and long-crested waves are available from the model. Every wave pattern is an exact solution of the Kadomtsev - Petviashvili ...vol. 9, pp 65-66 Kadomtsev , B. B. & V. I. Petviashvili , 1970, Soy. Phys. Doklady, vol. 15, pp 539-541 Korteweg, D. J. & G. de~ries, 1895, Phil Mag

Wideband Low-Reflection Inhomogeneous Dielectric Structures

NASA Astrophysics Data System (ADS)

Denisova, N. A.; Rezvov, A. V.

2017-08-01

We consider reflection of electromagnetic waves from two-layer dielectric films with finite thickness, whose refractive indices vary in the direction of wave propagation, which is perpendicular to the substrate boundary. The profiles of the refractive indices of the structures having low reflection coefficients in a wide frequency range are found. The obtained results are based on exact analytical solutions of the Helmholtz equation for one type of the layered inhomogeneous dielectric medium. The possibility of creating new low-reflection wideband inhomogeneous dielectric structures is demonstrated.

Comparison of procedures for correction of matrix interferences in the analysis of soils by ICP-OES with CCD detection

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

Sadler, D.A.; Sun, F.; Littlejohn, D.

1995-12-31

ICP-OES is a useful technique for multi-element analysis of soils. However, as a number of elements are present in relatively high concentrations, matrix interferences can occur and examples have been widely reported. The availability of CCD detectors has increased the opportunities for rapid multi-element, multi-wave-length determination of elemental concentrations in soils and other environmental samples. As the composition of soils from industrial sites can vary considerably, especially when taken from different pit horizons, procedures are required to assess the extent of interferences and correct the effects, on a simultaneous multi-element basis. In single element analysis, plasma operating conditions can sometimesmore » be varied to minimize or even remove multiplicative interferences. In simultaneous multi-element analysis, the scope for this approach may be limited, depending on the spectrochemical characteristics of the emitting analyte species. Matrix matching, by addition of major sample components to the analyte calibrant solutions, can be used to minimize inaccuracies. However, there are also limitations to this procedure, when the sample composition varies significantly. Multiplicative interference effects can also be assessed by a {open_quotes}single standard addition{close_quotes} of each analyte to the sample solution and the information obtained may be used to correct the analyte concentrations determined directly. Each of these approaches has been evaluated to ascertain the best procedure for multi-element analysis of industrial soils by ICP-OES with CCD detection at multiple wavelengths. Standard reference materials and field samples have been analyzed to illustrate the efficacy of each procedure.« less

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.

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

Robust Vision-Based Pose Estimation Algorithm for AN Uav with Known Gravity Vector

NASA Astrophysics Data System (ADS)

Kniaz, V. V.

2016-06-01

Accurate estimation of camera external orientation with respect to a known object is one of the central problems in photogrammetry and computer vision. In recent years this problem is gaining an increasing attention in the field of UAV autonomous flight. Such application requires a real-time performance and robustness of the external orientation estimation algorithm. The accuracy of the solution is strongly dependent on the number of reference points visible on the given image. The problem only has an analytical solution if 3 or more reference points are visible. However, in limited visibility conditions it is often needed to perform external orientation with only 2 visible reference points. In such case the solution could be found if the gravity vector direction in the camera coordinate system is known. A number of algorithms for external orientation estimation for the case of 2 known reference points and a gravity vector were developed to date. Most of these algorithms provide analytical solution in the form of polynomial equation that is subject to large errors in the case of complex reference points configurations. This paper is focused on the development of a new computationally effective and robust algorithm for external orientation based on positions of 2 known reference points and a gravity vector. The algorithm implementation for guidance of a Parrot AR.Drone 2.0 micro-UAV is discussed. The experimental evaluation of the algorithm proved its computational efficiency and robustness against errors in reference points positions and complex configurations.

Singularity-free next-to-leading order ΔS = 1 renormalization group evolution and ɛ K ' /ɛK in the Standard Model and beyond

NASA Astrophysics Data System (ADS)

Kitahara, Teppei; Nierste, Ulrich; Tremper, Paul

2016-12-01

The standard analytic solution of the renormalization group (RG) evolution for the Δ S = 1 Wilson coefficients involves several singularities, which complicate analytic solutions. In this paper we derive a singularity-free solution of the next-to-leading order (NLO) RG equations, which greatly facilitates the calculation of ɛ K ' , the measure of direct CP violation in K → ππ decays. Using our new RG evolution and the latest lattice results for the hadronic matrix elements, we calculate the ratio ɛ K ' /ɛ K (with ɛ K quantifying indirect CP violation) in the Standard Model (SM) at NLO to ɛ K ' /ɛ K = (1.06 ± 5.07) × 10- 4, which is 2 .8 σ below the experimental value. We also present the evolution matrix in the high-energy regime for calculations of new physics contributions and derive easy-to-use approximate formulae. We find that the RG amplification of new-physics contributions to Wilson coefficients of the electroweak penguin operators is further enhanced by the NLO corrections: if the new contribution is generated at the scale of 1-10 TeV, the RG evolution between the new-physics scale and the electroweak scale enhances these coefficients by 50-100%. Our solution contains a term of order α EM 2 / α s 2 , which is numerically unimportant for the SM case but should be included in studies of high-scale new-physics.

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Symmetry-plane model of 3D Euler flows: Mapping to regular systems and numerical solutions of blowup

NASA Astrophysics Data System (ADS)

Mulungye, Rachel M.; Lucas, Dan; Bustamante, Miguel D.

2014-11-01

We introduce a family of 2D models describing the dynamics on the so-called symmetry plane of the full 3D Euler fluid equations. These models depend on a free real parameter and can be solved analytically. For selected representative values of the free parameter, we apply the method introduced in [M.D. Bustamante, Physica D: Nonlinear Phenom. 240, 1092 (2011)] to map the fluid equations bijectively to globally regular systems. By comparing the analytical solutions with the results of numerical simulations, we establish that the numerical simulations of the mapped regular systems are far more accurate than the numerical simulations of the original systems, at the same spatial resolution and CPU time. In particular, the numerical integrations of the mapped regular systems produce robust estimates for the growth exponent and singularity time of the main blowup quantity (vorticity stretching rate), converging well to the analytically-predicted values even beyond the time at which the flow becomes under-resolved (i.e. the reliability time). In contrast, direct numerical integrations of the original systems develop unstable oscillations near the reliability time. We discuss the reasons for this improvement in accuracy, and explain how to extend the analysis to the full 3D case. Supported under the programme for Research in Third Level Institutions (PRTLI) Cycle 5 and co-funded by the European Regional Development Fund.

Piezoelectric trace vapor calibrator

NASA Astrophysics Data System (ADS)

Verkouteren, R. Michael; Gillen, Greg; Taylor, David W.

2006-08-01

The design and performance of a vapor generator for calibration and testing of trace chemical sensors are described. The device utilizes piezoelectric ink-jet nozzles to dispense and vaporize precisely known amounts of analyte solutions as monodisperse droplets onto a hot ceramic surface, where the generated vapors are mixed with air before exiting the device. Injected droplets are monitored by microscope with strobed illumination, and the reproducibility of droplet volumes is optimized by adjustment of piezoelectric wave form parameters. Complete vaporization of the droplets occurs only across a 10°C window within the transition boiling regime of the solvent, and the minimum and maximum rates of trace analyte that may be injected and evaporated are determined by thermodynamic principles and empirical observations of droplet formation and stability. By varying solution concentrations, droplet injection rates, air flow, and the number of active nozzles, the system is designed to deliver—on demand—continuous vapor concentrations across more than six orders of magnitude (nominally 290fg/lto1.05μg/l). Vapor pulses containing femtogram to microgram quantities of analyte may also be generated. Calibrated ranges of three explosive vapors at ng/l levels were generated by the device and directly measured by ion mobility spectrometry (IMS). These data demonstrate expected linear trends within the limited working range of the IMS detector and also exhibit subtle nonlinear behavior from the IMS measurement process.

Multifunctional Au NPs-polydopamine-polyvinylidene fluoride membrane chips as probe for enrichment and rapid detection of organic contaminants.

PubMed

Wang, Saihua; Niu, Hongyun; Cai, Yaqi; Cao, Dong

2018-05-01

High-throughput and rapid detection of hazardous compounds in complicated samples is essential for the solution of environmental problems. We have prepared a "pH-paper-like" chip which can rapidly "indicate" the occurrence of organic contaminants just through dipping the chip in water samples for short time followed by fast analysis with surface-assisted laser desorption/ionization time-of-flight mass spectrometry (SALDI-TOF MS). The chips are composed of polyvinylidene fluoride membrane (PVDFM), polydopamine (PDA) film and Au nanoparticles (Au NPs), which are layer-by-layer assembled according to the adhesion, self-polymerization and reduction property of dopamine. In the Au NPs loaded polydopamine-polyvinylidene fluoride membrane (Au NPs-PDA-PVDFM) chips, PVDFM combined with PDA film are responsible for the enrichment of organic analyte through hydrophobic interactions and π-π stacking; Au NPs serve as effective SALDI matrix for the rapid detection of target analyte. After dipping into water solution for minutes, the Au-PDA-PVDFM chips with enriched organic analytes can be detected directly with SALDI-TOF MS. The good solid-phase extraction performance of the PDA-PVDFM components, remarkable matrix effect of the loaded AuNPs, and sensitivity of the SALDI-TOF MS technique ensure excellent sensitivity and reproducibility for the quantification of trace levels of organic contaminants in environmental water samples. Copyright © 2018 Elsevier B.V. All rights reserved.

Tornado model for a magnetised plasma

NASA Astrophysics Data System (ADS)

Onishchenko, O. G.; Fedun, V.; Smolyakov, A.; Horton, W.; Pokhotelov, O. A.; Verth, G.

2018-05-01

A new analytical model of axially-symmetric magnetic vortices with both a twisted fluid flow and a magnetic field is proposed. The exact solution for the three-dimensional structure of the fluid velocity and the magnetic field is obtained within the framework of the ideal magnetohydrodynamic equations for an incompressible fluid in a gravitational field. A quasi-stationary localised vortex arises when the radial flow that tends to concentrate vorticity in a narrow column around the axis of symmetry is balanced by the vertical vortex advection in the axial direction. The explicit expressions for the velocity and magnetic field components are obtained. The proposed analytic model may be used to parameterise the observed solar tornadoes and can provide a new indirect way for estimating magnetic twist from the observed azimuthal velocity profiles.

Maximum drag reduction asymptotes and the cross-over to the Newtonian plug

NASA Astrophysics Data System (ADS)

Benzi, R.; de Angelis, E.; L'Vov, V. S.; Procaccia, I.; Tiberkevich, V.

2006-03-01

We employ the full FENE-P model of the hydrodynamics of a dilute polymer solution to derive a theoretical approach to drag reduction in wall-bounded turbulence. We recapture the results of a recent simplified theory which derived the universal maximum drag reduction (MDR) asymptote, and complement that theory with a discussion of the cross-over from the MDR to the Newtonian plug when the drag reduction saturates. The FENE-P model gives rise to a rather complex theory due to the interaction of the velocity field with the polymeric conformation tensor, making analytic estimates quite taxing. To overcome this we develop the theory in a computer-assisted manner, checking at each point the analytic estimates by direct numerical simulations (DNS) of viscoelastic turbulence in a channel.

Quantum Effects at a Proton Relaxation at Low Temperatures

NASA Astrophysics Data System (ADS)

Kalytka, V. A.; Korovkin, M. V.

2016-11-01

Quantum effects during migratory polarization in multi-well crystals (including multi-well silicates and crystalline hydrates) are investigated in a variable electric field at low temperatures by direct quantum-mechanical calculations. Based on analytical solution of the quantum Liouville kinetic equation in the linear approximation for the polarizing field, the non-stationary density matrix is calculated for an ensemble of non-interacting protons moving in the field of one-dimensional multi-well crystal potential relief of rectangular shape. An expression for the complex dielectric constant convenient for a comparison with experiment and calculation of relaxer parameters is derived using the nonequilibrium polarization density matrix. The density matrix apparatus can be used for analytical investigation of the quantum mechanism of spontaneous polarization of a ferroelectric material (KDP and DKDP).

Analytical investigations on the thermal properties of microscale inorganic light-emitting diodes on an orthotropic substrate

NASA Astrophysics Data System (ADS)

Li, Y.; Chen, J.; Xing, Y.; Song, J.

2017-03-01

The microscale inorganic light-emitting diodes (μ-ILEDs) create novel opportunities in biointegrated applications such as wound healing acceleration and optogenetics. Analytical expressions, validated by finite element analysis, are obtained for the temperature increase of a rectangular μ-ILED device on an orthotropic substrate, which could offer an appealing advantage in controlling the heat flow direction to achieve the goal in thermal management. The influences of various parameters (e.g., thermal conductivities of orthotropic substrate, loading parameters) on the temperature increase of the μ-ILED are investigated based on the obtained closed-form solutions. These results provide a novel route to control the temperature distribution in the μ-ILED system and provide easily interpretable guidelines to minimize the adverse thermal effects.

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.

Axisymmetric capillary-gravity waves at the interface of two viscous, immiscible fluids - Initial value problem

NASA Astrophysics Data System (ADS)

Farsoiya, Palas Kumar; Dasgupta, Ratul

2017-11-01

When the interface between two radially unbounded, viscous fluids lying vertically in a stable configuration (denser fluid below) at rest, is perturbed, radially propagating capillary-gravity waves are formed which damp out with time. We study this process analytically using a recently developed linearised theory. For small amplitude initial perturbations, the analytical solution to the initial value problem, represented as a linear superposition of Bessel modes at time t = 0 , is found to agree very well with results obtained from direct numerical simulations of the Navier-Stokes equations, for a range of initial conditions. Our study extends the earlier work by John W. Miles who studied this initial value problem analytically, taking into account, a single viscous fluid only. Implications of this study for the mechanistic understanding of droplet impact into a deep pool, will be discussed. Some preliminary, qualitative comparison with experiments will also be presented. We thank SERB Dept. Science & Technology, Govt. of India, Grant No. EMR/2016/000830 for financial support.

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

NASA Astrophysics Data System (ADS)

Liu, X.; Zhan, H.

2017-12-01

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

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

PubMed Central

Qiu, Chenchen; Li, Yande

2017-01-01

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

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

DOE PAGES

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

2017-06-15

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

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

NASA Technical Reports Server (NTRS)

Lancaster, J. E.

1973-01-01

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

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.

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

On the use of formulations in person-centred, solution-focused short-term psychotherapy.

PubMed

Fitzgerald, Pamela; Leudar, Ivan

2012-01-01

According to Carl Rogers, therapy must be non-directive in order to be effective. This means that the therapist needs to be trained to work within the clients' frame of reference and do so in their practice. Conversation analytic research, however, suggests that therapists who claim to practise non-directive, non-authoritarian therapy nevertheless exercise subtle means of influencing their clients (e.g. through active listening, see Fitzgerald and Leudar 2010). The questions are: what in practice counts as being non-directive and how (relatively) nondirective psychotherapy is accomplished in practice. The present paper focuses on formulations which are one of the therapist's most useful tools and we demonstrate how these are used to guide clients to think along lines conducive to change.

Lie symmetry analysis, conservation laws, solitary and periodic waves for a coupled Burger equation

NASA Astrophysics Data System (ADS)

Xu, Mei-Juan; Tian, Shou-Fu; Tu, Jian-Min; Zhang, Tian-Tian

2017-01-01

Under investigation in this paper is a generalized (2 + 1)-dimensional coupled Burger equation with variable coefficients, which describes lots of nonlinear physical phenomena in geophysical fluid dynamics, condense matter physics and lattice dynamics. By employing the Lie group method, the symmetry reductions and exact explicit solutions are obtained, respectively. Based on a direct method, the conservations laws of the equation are also derived. Furthermore, by virtue of the Painlevé analysis, we successfully obtain the integrable condition on the variable coefficients, which plays an important role in further studying the integrability of the equation. Finally, its auto-Bäcklund transformation as well as some new analytic solutions including solitary and periodic waves are also presented via algebraic and differential manipulation.

ICANT, a code for the self-consistent computation of ICRH antenna coupling

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

Pecoul, S.; Heuraux, S.; Koch, R.

1996-02-01

The code deals with 3D antenna structures (finite length antennae) that are used to launch electromagnetic waves into tokamak plasmas. The antenna radiation problem is solved using a finite boundary element technique combined with a spectral solution of the interior problem. The slab approximation is used, and periodicity in {ital y} and {ital z} directions is introduced to account for toroidal geometry. We present results for various types of antennae radiating in vacuum: antenna with a finite Faraday screen and ideal Faraday screen, antenna with side limiters and phased antenna arrays. The results (radiated power, current profile) obtained are verymore » close to analytical solutions when available. {copyright} {ital 1996 American Institute of Physics.}« less

Water hammer prediction and control: the Green's function method

NASA Astrophysics Data System (ADS)

Xuan, Li-Jun; Mao, Feng; Wu, Jie-Zhi

2012-04-01

By Green's function method we show that the water hammer (WH) can be analytically predicted for both laminar and turbulent flows (for the latter, with an eddy viscosity depending solely on the space coordinates), and thus its hazardous effect can be rationally controlled and minimized. To this end, we generalize a laminar water hammer equation of Wang et al. (J. Hydrodynamics, B2, 51, 1995) to include arbitrary initial condition and variable viscosity, and obtain its solution by Green's function method. The predicted characteristic WH behaviors by the solutions are in excellent agreement with both direct numerical simulation of the original governing equations and, by adjusting the eddy viscosity coefficient, experimentally measured turbulent flow data. Optimal WH control principle is thereby constructed and demonstrated.

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.

Efficient implementation of three-dimensional reference interaction site model self-consistent-field method: Application to solvatochromic shift calculations

NASA Astrophysics Data System (ADS)

Minezawa, Noriyuki; Kato, Shigeki

2007-02-01

The authors present an implementation of the three-dimensional reference interaction site model self-consistent-field (3D-RISM-SCF) method. First, they introduce a robust and efficient algorithm for solving the 3D-RISM equation. The algorithm is a hybrid of the Newton-Raphson and Picard methods. The Jacobian matrix is analytically expressed in a computationally useful form. Second, they discuss the solute-solvent electrostatic interaction. For the solute to solvent route, the electrostatic potential (ESP) map on a 3D grid is constructed directly from the electron density. The charge fitting procedure is not required to determine the ESP. For the solvent to solute route, the ESP acting on the solute molecule is derived from the solvent charge distribution obtained by solving the 3D-RISM equation. Matrix elements of the solute-solvent interaction are evaluated by the direct numerical integration. A remarkable reduction in the computational time is observed in both routes. Finally, the authors implement the first derivatives of the free energy with respect to the solute nuclear coordinates. They apply the present method to "solute" water and formaldehyde in aqueous solvent using the simple point charge model, and the results are compared with those from other methods: the six-dimensional molecular Ornstein-Zernike SCF, the one-dimensional site-site RISM-SCF, and the polarizable continuum model. The authors also calculate the solvatochromic shifts of acetone, benzonitrile, and nitrobenzene using the present method and compare them with the experimental and other theoretical results.

Efficient implementation of three-dimensional reference interaction site model self-consistent-field method: application to solvatochromic shift calculations.

PubMed

Minezawa, Noriyuki; Kato, Shigeki

2007-02-07

The authors present an implementation of the three-dimensional reference interaction site model self-consistent-field (3D-RISM-SCF) method. First, they introduce a robust and efficient algorithm for solving the 3D-RISM equation. The algorithm is a hybrid of the Newton-Raphson and Picard methods. The Jacobian matrix is analytically expressed in a computationally useful form. Second, they discuss the solute-solvent electrostatic interaction. For the solute to solvent route, the electrostatic potential (ESP) map on a 3D grid is constructed directly from the electron density. The charge fitting procedure is not required to determine the ESP. For the solvent to solute route, the ESP acting on the solute molecule is derived from the solvent charge distribution obtained by solving the 3D-RISM equation. Matrix elements of the solute-solvent interaction are evaluated by the direct numerical integration. A remarkable reduction in the computational time is observed in both routes. Finally, the authors implement the first derivatives of the free energy with respect to the solute nuclear coordinates. They apply the present method to "solute" water and formaldehyde in aqueous solvent using the simple point charge model, and the results are compared with those from other methods: the six-dimensional molecular Ornstein-Zernike SCF, the one-dimensional site-site RISM-SCF, and the polarizable continuum model. The authors also calculate the solvatochromic shifts of acetone, benzonitrile, and nitrobenzene using the present method and compare them with the experimental and other theoretical results.

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

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

Transcritical flow of a Bose-Einstein condensate through a penetrable barrier

NASA Astrophysics Data System (ADS)

Leszczyszyn, A. M.; El, G. A.; Gladush, Yu. G.; Kamchatnov, A. M.

2009-06-01

The problem of the transcritical flow of a Bose-Einstein condensate through a wide repulsive penetrable barrier is studied analytically using the combination of the locally steady “hydraulic” solution of the one-dimensional Gross-Pitaevskii equation and the solutions of the Whitham modulation equations describing the resolution of the upstream and downstream discontinuities through dispersive shocks. It is shown that within the physically reasonable range of parameters, the downstream dispersive shock is attached to the barrier and effectively represents the train of very slow dark solitons, which can be observed in experiments. The rate of the soliton emission, the amplitudes of the solitons in the train, and the drag force are determined in terms of the Bose-Einstein condensate oncoming flow velocity and the strength of the potential barrier. Good agreement with direct numerical solutions is demonstrated. Connection with recent experiments is discussed.

Discrete Spring Model for Predicting Delamination Growth in Z-Fiber Reinforced DCB Specimens

NASA Technical Reports Server (NTRS)

Ratcliffe, James G.; OBrien, T. Kevin

2004-01-01

Beam theory analysis was applied to predict delamination growth in Double Cantilever Beam (DCB) specimens reinforced in the thickness direction with pultruded pins, known as Z-fibers. The specimen arms were modeled as cantilever beams supported by discrete springs, which were included to represent the pins. A bi-linear, irreversible damage law was used to represent Z-fiber damage, the parameters of which were obtained from previous experiments. Closed-form solutions were developed for specimen compliance and displacements corresponding to Z-fiber row locations. A solution strategy was formulated to predict delamination growth, in which the parent laminate mode I critical strain energy release rate was used as the criterion for delamination growth. The solution procedure was coded into FORTRAN 90, giving a dedicated software tool for performing the delamination prediction. Comparison of analysis results with previous analysis and experiment showed good agreement, yielding an initial verification for the analytical procedure.

Discrete Spring Model for Predicting Delamination Growth in Z-Fiber Reinforced DCB Specimens

NASA Technical Reports Server (NTRS)

Ratcliffe, James G.; O'Brien, T. Kevin

2004-01-01

Beam theory analysis was applied to predict delamination growth in DCB specimens reinforced in the thickness direction with pultruded pins, known as Z-fibers. The specimen arms were modeled as cantilever beams supported by discrete springs, which were included to represent the pins. A bi-linear, irreversible damage law was used to represent Z-fiber damage, the parameters of which were obtained from previous experiments. Closed-form solutions were developed for specimen compliance and displacements corresponding to Z-fiber row locations. A solution strategy was formulated to predict delamination growth, in which the parent laminate mode I fracture toughness was used as the criterion for delamination growth. The solution procedure was coded into FORTRAN 90, giving a dedicated software tool for performing the delamination prediction. Comparison of analysis results with previous analysis and experiment showed good agreement, yielding an initial verification for the analytical procedure.

A compatible high-order meshless method for the Stokes equations with applications to suspension flows

NASA Astrophysics Data System (ADS)

Trask, Nathaniel; Maxey, Martin; Hu, Xiaozhe

2018-02-01

A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a discretization that couples a staggered scheme for pressure approximation with a divergence-free velocity reconstruction to obtain an adaptive, high-order, finite difference-like discretization that can be efficiently solved with conventional algebraic multigrid techniques. We use analytic benchmarks to demonstrate equal-order convergence for both velocity and pressure when solving problems with curvilinear geometries. In order to study problems in dense suspensions, we couple the solution for the flow to the equations of motion for freely suspended particles in an implicit monolithic scheme. The combination of high-order accuracy with fully-implicit schemes allows the accurate resolution of stiff lubrication forces directly from the solution of the Stokes problem without the need to introduce sub-grid lubrication models.

Bessel-Gauss beams as rigorous solutions of the Helmholtz equation.

PubMed

April, Alexandre

2011-10-01

The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel-Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre-Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.

Stable oxygen and hydrogen isotopes of brines - comparing isotope ratio mass spectrometry and isotope ratio infrared spectroscopy

NASA Astrophysics Data System (ADS)

Ahrens, Christian; Koeniger, Paul; van Geldern, Robert; Stadler, Susanne

2013-04-01

Today's standard analytical methods for high precision stable isotope analysis of fluids are gas-water equilibration and high temperature pyrolysis coupled to isotope ratio mass spectrometers (IRMS). In recent years, relatively new laser-based analytical instruments entered the market that are said to allow high isotope precision data on nearly every media. This optical technique is referred to as isotope ratio infrared spectroscopy (IRIS). The objective of this study is to evaluate the capability of this new instrument type for highly saline solutions and a comparison of the analytical results with traditional IRMS analysis. It has been shown for the equilibration method that the presence of salts influences the measured isotope values depending on the salt concentration (see Lécuyer et al, 2009; Martineau, 2012). This so-called 'isotope salt effect' depends on the salt type and salt concentration. These factors change the activity in the fluid and therefore shift the isotope ratios measured by the equilibration method. Consequently, correction factors have to be applied to these analytical data. Direct conversion techniques like pyrolysis or the new laser instruments allow the measurement of the water molecule from the sample directly and should therefore not suffer from the salt effect, i.e. no corrections of raw values are necessary. However, due to high salt concentrations this might cause technical problems with the analytical hardware and may require labor-intensive sample preparation (e.g. vacuum distillation). This study evaluates the salt isotope effect for the IRMS equilibration technique (Thermo Gasbench II coupled to Delta Plus XP) and the laser-based IRIS instruments with liquid injection (Picarro L2120-i). Synthetic salt solutions (NaCl, KCl, CaCl2, MgCl2, MgSO4, CaSO4) and natural brines collected from the Stassfurt Salt Anticline (Germany; Stadler et al., 2012) were analysed with both techniques. Salt concentrations ranged from seawater salinity up to full saturation. References Lécuyer, C. et al. (2009). Chem. Geol., 264, 122-126. [doi:10.1016/j.chemgeo.2009.02.017] Martineau, F. et al. (2012). Chem. Geol., 291, 236-240. [doi:10.1016/j.chemgeo.2011.10.017] Stadler, S. et al. (2012). Chem. Geol., 294-295, 226-242. [doi:10.1016/j.chemgeo.2011.12.006

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.

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.

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.

Column Number Density Expressions Through M = 0 and M = 1 Point Source Plumes Along Any Straight Path

NASA Technical Reports Server (NTRS)

Woronowicz, Michael

2016-01-01

Analytical expressions for column number density (CND) are developed for optical line of sight paths through a variety of steady free molecule point source models including directionally-constrained effusion (Mach number M = 0) and flow from a sonic orifice (M = 1). Sonic orifice solutions are approximate, developed using a fair simulacrum fitted to the free molecule solution. Expressions are also developed for a spherically-symmetric thermal expansion (M = 0). CND solutions are found for the most general paths relative to these sources and briefly explored. It is determined that the maximum CND from a distant location through directed effusion and sonic orifice cases occurs along the path parallel to the source plane that intersects the plume axis. For the effusive case this value is exactly twice the CND found along the ray originating from that point of intersection and extending to infinity along the plume's axis. For sonic plumes this ratio is reduced to about 4/3. For high Mach number cases the maximum CND will be found along the axial centerline path. Keywords: column number density, plume flows, outgassing, free molecule flow.

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

NASA Astrophysics Data System (ADS)

Pástor, P.

2016-07-01

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

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

USGS Publications Warehouse

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

1981-01-01

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

A Computing Method for Sound Propagation Through a Nonuniform Jet Stream

NASA Technical Reports Server (NTRS)

Padula, S. L.; Liu, C. H.

1974-01-01

Understanding the principles of jet noise propagation is an essential ingredient of systematic noise reduction research. High speed computer methods offer a unique potential for dealing with complex real life physical systems whereas analytical solutions are restricted to sophisticated idealized models. The classical formulation of sound propagation through a jet flow was found to be inadequate for computer solutions and a more suitable approach was needed. Previous investigations selected the phase and amplitude of the acoustic pressure as dependent variables requiring the solution of a system of nonlinear algebraic equations. The nonlinearities complicated both the analysis and the computation. A reformulation of the convective wave equation in terms of a new set of dependent variables is developed with a special emphasis on its suitability for numerical solutions on fast computers. The technique is very attractive because the resulting equations are linear in nonwaving variables. The computer solution to such a linear system of algebraic equations may be obtained by well-defined and direct means which are conservative of computer time and storage space. Typical examples are illustrated and computational results are compared with available numerical and experimental data.

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

PubMed

Mikula, Shawn; Niebur, Ernst

2008-11-01

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

Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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

USDA-ARS?s Scientific Manuscript database

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

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

NASA Technical Reports Server (NTRS)

Schonfeld, D.; Lansing, F. L.

1983-01-01

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

Analytic solutions for Long's equation and its generalization

NASA Astrophysics Data System (ADS)

Humi, Mayer

2017-12-01

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

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.

Triangular dislocation: an analytical, artefact-free solution

NASA Astrophysics Data System (ADS)

Nikkhoo, Mehdi; Walter, Thomas R.

2015-05-01

Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space {R}3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

An analytical model for solute transport through a GCL-based two-layered liner considering biodegradation.

PubMed

Guan, C; Xie, H J; Wang, Y Z; Chen, Y M; Jiang, Y S; Tang, X W

2014-01-01

An analytical model for solute advection and dispersion in a two-layered liner consisting of a geosynthetic clay liner (GCL) and a soil liner (SL) considering the effect of biodegradation was proposed. The analytical solution was derived by Laplace transformation and was validated over a range of parameters using the finite-layer method based software Pollute v7.0. Results show that if the half-life of the solute in GCL is larger than 1 year, the degradation in GCL can be neglected for solute transport in GCL/SL. When the half-life of GCL is less than 1 year, neglecting the effect of degradation in GCL on solute migration will result in a large difference of relative base concentration of GCL/SL (e.g., 32% for the case with half-life of 0.01 year). The 100-year solute base concentration can be reduced by a factor of 2.2 when the hydraulic conductivity of the SL was reduced by an order of magnitude. The 100-year base concentration was reduced by a factor of 155 when the half life of the contaminant in the SL was reduced by an order of magnitude. The effect of degradation is more important in approving the groundwater protection level than the hydraulic conductivity. The analytical solution can be used for experimental data fitting, verification of complicated numerical models and preliminary design of landfill liner systems. © 2013.

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.

Reverberation effects on directionality and response of stationary monopole and dipole sources in a wind tunnel

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1985-01-01

Analytical solutions for the three dimensional inhomogeneous wave equation with flow in a hardwall rectangular wind tunnel and in the free field are presented for a stationary monopole noise source. Dipole noise sources are calculated by combining two monopoles 180 deg out of phase. Numerical calculations for the modal content, spectral response and directivity for both monopole and dipole sources are presented. In addition, the effect of tunnel alterations, such as the addition of a mounting plate, on the tunnels reverberant response are considered. In the frequency range of practical importance for the turboprop response, important features of the free field directivity can be approximated in a hardwall wind tunnel with flow if the major lobe of the noise source is not directed upstream. However, for an omnidirectional source, such as a monopole, the hardwall wind tunnel and free field response are not comparable.

Rapid process development of chromatographic process using direct analysis in real time mass spectrometry as a process analytical technology tool.

PubMed

Yan, Binjun; Chen, Teng; Xu, Zhilin; Qu, Haibin

2014-06-01

The concept of quality by design (QbD) is widely applied in the process development of pharmaceuticals. However, the additional cost and time have caused some resistance about QbD implementation. To show a possible solution, this work proposed a rapid process development method, which used direct analysis in real time mass spectrometry (DART-MS) as a process analytical technology (PAT) tool for studying the chromatographic process of Ginkgo biloba L., as an example. The breakthrough curves were fast determined by DART-MS at-line. A high correlation coefficient of 0.9520 was found between the concentrations of ginkgolide A determined by DART-MS and HPLC. Based on the PAT tool, the impacts of process parameters on the adsorption capacity were discovered rapidly, which showed a decreased adsorption capacity with the increase of the flow rate. This work has shown the feasibility and advantages of integrating PAT into QbD implementation for rapid process development. Copyright © 2014 Elsevier B.V. All rights reserved.

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.

Linear and nonlinear evolution of azimuthal clumping instabilities in a Z-pinch wire array

DOE PAGES

Tang, Wilkin; Strickler, T. S.; Lau, Y. Y.; ...

2007-01-31

This study presents an analytic theory on the linear and nonlinear evolution of the most unstable azimuthal clumping mode, known as the pi-mode, in a discrete wire array. In the pi-mode, neighboring wires of the array pair-up as a result of the mutual attraction of the wires which carry current in the same direction. The analytic solution displays two regimes, where the collective interactions of all wires dominate, versus where the interaction of the neighboring, single wire dominates. This solution was corroborated by two vastly different numerical codes which were used to simulate arrays with both high wire numbers (upmore » to 600) and low wire number (8). All solutions show that azimuthal clumping of discrete wires occurs before appreciable radial motion of the wires. Thus, absence of azimuthal clumping of wires in comparison with the wires’ radial motion may imply substantial lack of wire currents. Finally, while the present theory and simulations have ignored the plasma corona and axial variations, it is argued that their effects, and the complete account of the three-dimensional feature of the pi-mode, together with a scaling study of the wire number, may be expediently simulated by using only one single wire in an annular wedge with a reflection condition imposed on the wedge’s boundary.« less

Maybe Small Is Too Small a Term: Introduction to Advancing Small Sample Prevention Science.

PubMed

Fok, Carlotta Ching Ting; Henry, David; Allen, James

2015-10-01

Prevention research addressing health disparities often involves work with small population groups experiencing such disparities. The goals of this special section are to (1) address the question of what constitutes a small sample; (2) identify some of the key research design and analytic issues that arise in prevention research with small samples; (3) develop applied, problem-oriented, and methodologically innovative solutions to these design and analytic issues; and (4) evaluate the potential role of these innovative solutions in describing phenomena, testing theory, and evaluating interventions in prevention research. Through these efforts, we hope to promote broader application of these methodological innovations. We also seek whenever possible, to explore their implications in more general problems that appear in research with small samples but concern all areas of prevention research. This special section includes two sections. The first section aims to provide input for researchers at the design phase, while the second focuses on analysis. Each article describes an innovative solution to one or more challenges posed by the analysis of small samples, with special emphasis on testing for intervention effects in prevention research. A concluding article summarizes some of their broader implications, along with conclusions regarding future directions in research with small samples in prevention science. Finally, a commentary provides the perspective of the federal agencies that sponsored the conference that gave rise to this special section.

Axisymmetric Plume Simulations with NASA's DSMC Analysis Code

NASA Technical Reports Server (NTRS)

Stewart, B. D.; Lumpkin, F. E., III

2012-01-01

A comparison of axisymmetric Direct Simulation Monte Carlo (DSMC) Analysis Code (DAC) results to analytic and Computational Fluid Dynamics (CFD) solutions in the near continuum regime and to 3D DAC solutions in the rarefied regime for expansion plumes into a vacuum is performed to investigate the validity of the newest DAC axisymmetric implementation. This new implementation, based on the standard DSMC axisymmetric approach where the representative molecules are allowed to move in all three dimensions but are rotated back to the plane of symmetry by the end of the move step, has been fully integrated into the 3D-based DAC code and therefore retains all of DAC s features, such as being able to compute flow over complex geometries and to model chemistry. Axisymmetric DAC results for a spherically symmetric isentropic expansion are in very good agreement with a source flow analytic solution in the continuum regime and show departure from equilibrium downstream of the estimated breakdown location. Axisymmetric density contours also compare favorably against CFD results for the R1E thruster while temperature contours depart from equilibrium very rapidly away from the estimated breakdown surface. Finally, axisymmetric and 3D DAC results are in very good agreement over the entire plume region and, as expected, this new axisymmetric implementation shows a significant reduction in computer resources required to achieve accurate simulations for this problem over the 3D simulations.

High-Fidelity Generalization Method of Cells for Inelastic Periodic Multiphase Materials

NASA Technical Reports Server (NTRS)

Aboudi, Jacob; Pindera, Marek-Jerzy; Arnold, Steven M.

2002-01-01

An extension of a recently-developed linear thermoelastic theory for multiphase periodic materials is presented which admits inelastic behavior of the constituent phases. The extended theory is capable of accurately estimating both the effective inelastic response of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstructure. The model's analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite-element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading. The model's predictive accuracy in generating both the effective inelastic stress-strain response and the local stress said inelastic strain fields is demonstrated by comparison with the results of an analytical inelastic solution for the axisymmetric and axial shear response of a unidirectional composite based on the concentric cylinder model, and with finite-element results for transverse loading.

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

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

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

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

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

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

Integral Equations in Computational Electromagnetics: Formulations, Properties and Isogeometric Analysis

NASA Astrophysics Data System (ADS)

Lovell, Amy Elizabeth

Computational electromagnetics (CEM) provides numerical methods to simulate electromagnetic waves interacting with its environment. Boundary integral equation (BIE) based methods, that solve the Maxwell's equations in the homogeneous or piecewise homogeneous medium, are both efficient and accurate, especially for scattering and radiation problems. Development and analysis electromagnetic BIEs has been a very active topic in CEM research. Indeed, there are still many open problems that need to be addressed or further studied. A short and important list includes (1) closed-form or quasi-analytical solutions to time-domain integral equations, (2) catastrophic cancellations at low frequencies, (3) ill-conditioning due to high mesh density, multi-scale discretization, and growing electrical size, and (4) lack of flexibility due to re-meshing when increasing number of forward numerical simulations are involved in the electromagnetic design process. This dissertation will address those several aspects of boundary integral equations in computational electromagnetics. The first contribution of the dissertation is to construct quasi-analytical solutions to time-dependent boundary integral equations using a direct approach. Direct inverse Fourier transform of the time-harmonic solutions is not stable due to the non-existence of the inverse Fourier transform of spherical Hankel functions. Using new addition theorems for the time-domain Green's function and dyadic Green's functions, time-domain integral equations governing transient scattering problems of spherical objects are solved directly and stably for the first time. Additional, the direct time-dependent solutions, together with the newly proposed time-domain dyadic Green's functions, can enrich the time-domain spherical multipole theory. The second contribution is to create a novel method of moments (MoM) framework to solve electromagnetic boundary integral equation on subdivision surfaces. The aim is to avoid the meshing and re-meshing stages to accelerate the design process when the geometry needs to be updated. Two schemes to construct basis functions on the subdivision surface have been explored. One is to use the div-conforming basis function, and the other one is to create a rigorous iso-geometric approach based on the subdivision basis function with better smoothness properties. This new framework provides us better accuracy, more stability and high flexibility. The third contribution is a new stable integral equation formulation to avoid catastrophic cancellations due to low-frequency breakdown or dense-mesh breakdown. Many of the conventional integral equations and their associated post-processing operations suffer from numerical catastrophic cancellations, which can lead to ill-conditioning of the linear systems or serious accuracy problems. Examples includes low-frequency breakdown and dense mesh breakdown. Another instability may come from nontrivial null spaces of involving integral operators that might be related with spurious resonance or topology breakdown. This dissertation presents several sets of new boundary integral equations and studies their analytical properties. The first proposed formulation leads to the scalar boundary integral equations where only scalar unknowns are involved. Besides the requirements of gaining more stability and better conditioning in the resulting linear systems, multi-physics simulation is another driving force for new formulations. Scalar and vector potentials (rather than electromagnetic field) based formulation have been studied for this purpose. Those new contributions focus on different stages of boundary integral equations in an almost independent manner, e.g. isogeometric analysis framework can be used to solve different boundary integral equations, and the time-dependent solutions to integral equations from different formulations can be achieved through the same methodology proposed.

A novel analytical description of periodic volume coil geometries in MRI

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Volumetric Interpretation of Protein Adsorption: Interfacial Packing of Protein Adsorbed to Hydrophobic Surfaces from Surface-Saturating Solution Concentrations

PubMed Central

Kao, Ping; Parhi, Purnendu; Krishnan, Anandi; Noh, Hyeran; Haider, Waseem; Tadigadapa, Srinivas; Allara, David L.; Vogler, Erwin A.

2010-01-01

The maximum capacity of a hydrophobic adsorbent is interpreted in terms of square or hexagonal (cubic and face-centered-cubic, FCC) interfacial packing models of adsorbed blood proteins in a way that accommodates experimental measurements by the solution-depletion method and quartz-crystal-microbalance (QCM) for the human proteins serum albumin (HSA, 66 kDa), immunoglobulin G (IgG, 160 kDa), fibrinogen (Fib, 341 kDa), and immunoglobulin M (IgM, 1000 kDa). A simple analysis shows that adsorbent capacity is capped by a fixed mass/volume (e.g. mg/mL) surface-region (interphase) concentration and not molar concentration. Nearly analytical agreement between the packing models and experiment suggests that, at surface saturation, above-mentioned proteins assemble within the interphase in a manner that approximates a well-ordered array. HSA saturates a hydrophobic adsorbent with the equivalent of a single square-or-hexagonally-packed layer of hydrated molecules whereas the larger proteins occupy two-or-more layers, depending on the specific protein under consideration and analytical method used to measure adsorbate mass (solution depletion or QCM). Square-or-hexagonal (cubic and FCC) packing models cannot be clearly distinguished by comparison to experimental data. QCM measurement of adsorbent capacity is shown to be significantly different than that measured by solution depletion for similar hydrophobic adsorbents. The underlying reason is traced to the fact that QCM measures contribution of both core protein, water of hydration, and interphase water whereas solution depletion measures only the contribution of core protein. It is further shown that thickness of the interphase directly measured by QCM systematically exceeds that inferred from solution-depletion measurements, presumably because the static model used to interpret solution depletion does not accurately capture the complexities of the viscoelastic interfacial environment probed by QCM. PMID:21035180

Volumetric interpretation of protein adsorption: interfacial packing of protein adsorbed to hydrophobic surfaces from surface-saturating solution concentrations.

PubMed

Kao, Ping; Parhi, Purnendu; Krishnan, Anandi; Noh, Hyeran; Haider, Waseem; Tadigadapa, Srinivas; Allara, David L; Vogler, Erwin A

2011-02-01

The maximum capacity of a hydrophobic adsorbent is interpreted in terms of square or hexagonal (cubic and face-centered-cubic, FCC) interfacial packing models of adsorbed blood proteins in a way that accommodates experimental measurements by the solution-depletion method and quartz-crystal-microbalance (QCM) for the human proteins serum albumin (HSA, 66 kDa), immunoglobulin G (IgG, 160 kDa), fibrinogen (Fib, 341 kDa), and immunoglobulin M (IgM, 1000 kDa). A simple analysis shows that adsorbent capacity is capped by a fixed mass/volume (e.g. mg/mL) surface-region (interphase) concentration and not molar concentration. Nearly analytical agreement between the packing models and experiment suggests that, at surface saturation, above-mentioned proteins assemble within the interphase in a manner that approximates a well-ordered array. HSA saturates a hydrophobic adsorbent with the equivalent of a single square or hexagonally-packed layer of hydrated molecules whereas the larger proteins occupy two-or-more layers, depending on the specific protein under consideration and analytical method used to measure adsorbate mass (solution depletion or QCM). Square or hexagonal (cubic and FCC) packing models cannot be clearly distinguished by comparison to experimental data. QCM measurement of adsorbent capacity is shown to be significantly different than that measured by solution depletion for similar hydrophobic adsorbents. The underlying reason is traced to the fact that QCM measures contribution of both core protein, water of hydration, and interphase water whereas solution depletion measures only the contribution of core protein. It is further shown that thickness of the interphase directly measured by QCM systematically exceeds that inferred from solution-depletion measurements, presumably because the static model used to interpret solution depletion does not accurately capture the complexities of the viscoelastic interfacial environment probed by QCM. Copyright © 2010 Elsevier Ltd. All rights reserved.

Validation of the SINDA/FLUINT code using several analytical solutions

NASA Technical Reports Server (NTRS)

Keller, John R.

1995-01-01

The Systems Improved Numerical Differencing Analyzer and Fluid Integrator (SINDA/FLUINT) code has often been used to determine the transient and steady-state response of various thermal and fluid flow networks. While this code is an often used design and analysis tool, the validation of this program has been limited to a few simple studies. For the current study, the SINDA/FLUINT code was compared to four different analytical solutions. The thermal analyzer portion of the code (conduction and radiative heat transfer, SINDA portion) was first compared to two separate solutions. The first comparison examined a semi-infinite slab with a periodic surface temperature boundary condition. Next, a small, uniform temperature object (lumped capacitance) was allowed to radiate to a fixed temperature sink. The fluid portion of the code (FLUINT) was also compared to two different analytical solutions. The first study examined a tank filling process by an ideal gas in which there is both control volume work and heat transfer. The final comparison considered the flow in a pipe joining two infinite reservoirs of pressure. The results of all these studies showed that for the situations examined here, the SINDA/FLUINT code was able to match the results of the analytical solutions.

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

EPA Science Inventory

Several numerical and analytical solutions of the radiative transfer equation (RTE) for plane albedo were compared for solar light reflection by sea water. The study incorporated the simplest case, that being a semi-infinite one-dimensional plane-parallel absorbing and scattering...

Analytic solutions for colloid transport with time- or depth-dependent retention in porous media

USDA-ARS?s Scientific Manuscript database

Elucidating and quantifying the transport of industrial nanoparticles (e.g. silver, carbon nanotubes, and graphene oxide) and other colloid-size particles such as viruses and bacteria is important to safeguard and manage the quality of the subsurface environment. Analytic solutions were derived for...

Convection equation modeling: A non-iterative direct matrix solution algorithm for use with SINDA

NASA Technical Reports Server (NTRS)

Schrage, Dean S.

1993-01-01

The determination of the boundary conditions for a component-level analysis, applying discrete finite element and finite difference modeling techniques often requires an analysis of complex coupled phenomenon that cannot be described algebraically. For example, an analysis of the temperature field of a coldplate surface with an integral fluid loop requires a solution to the parabolic heat equation and also requires the boundary conditions that describe the local fluid temperature. However, the local fluid temperature is described by a convection equation that can only be solved with the knowledge of the locally-coupled coldplate temperatures. Generally speaking, it is not computationally efficient, and sometimes, not even possible to perform a direct, coupled phenomenon analysis of the component-level and boundary condition models within a single analysis code. An alternative is to perform a disjoint analysis, but transmit the necessary information between models during the simulation to provide an indirect coupling. For this approach to be effective, the component-level model retains full detail while the boundary condition model is simplified to provide a fast, first-order prediction of the phenomenon in question. Specifically for the present study, the coldplate structure is analyzed with a discrete, numerical model (SINDA) while the fluid loop convection equation is analyzed with a discrete, analytical model (direct matrix solution). This indirect coupling allows a satisfactory prediction of the boundary condition, while not subjugating the overall computational efficiency of the component-level analysis. In the present study a discussion of the complete analysis of the derivation and direct matrix solution algorithm of the convection equation is presented. Discretization is analyzed and discussed to extend of solution accuracy, stability and computation speed. Case studies considering a pulsed and harmonic inlet disturbance to the fluid loop are analyzed to assist in the discussion of numerical dissipation and accuracy. In addition, the issues of code melding or integration with standard class solvers such as SINDA are discussed to advise the user of the potential problems to be encountered.

Exact Analytic Solution for a Ballistic Orbiting Wind

NASA Astrophysics Data System (ADS)

Wilkin, Francis P.; Hausner, Harry

2017-07-01

Much theoretical and observational work has been done on stellar winds within binary systems. We present a new solution for a ballistic wind launched from a source in a circular orbit. The solution is that of a single wind—no second wind is included in the system and the shocks that arise are those due to the orbiting wind interacting with itself. Our method emphasizes the curved streamlines in the corotating frame, where the flow is steady-state, allowing us to obtain an exact solution for the mass density at all pre-shock locations. Assuming an initially isotropic wind, fluid elements launched from the interior hemisphere of the wind will be the first to cross other streamlines, resulting in a spiral structure bounded by two shock surfaces. Streamlines from the outer wind hemisphere later intersect these shocks as well. An analytic solution is obtained for the geometry of the two shock surfaces. Although the inner and outer shock surfaces asymptotically trace Archimedean spirals, our tail solution suggests many crossings where the shocks overlap, beyond which the analytic solution cannot be continued. Our solution can be readily extended to an initially anisotropic wind.

Anisotropic cosmological solutions in R + R^2 gravity

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Angular correlations of photons from solution diffraction at a free-electron laser encode molecular structure

DOE PAGES

Mendez, Derek; Watkins, Herschel; Qiao, Shenglan; ...

2016-09-26

During X-ray exposure of a molecular solution, photons scattered from the same molecule are correlated. If molecular motion is insignificant during exposure, then differences in momentum transfer between correlated photons are direct measurements of the molecular structure. In conventional small- and wide-angle solution scattering, photon correlations are ignored. This report presents advances in a new biomolecular structural analysis technique, correlated X-ray scattering (CXS), which uses angular intensity correlations to recover hidden structural details from molecules in solution. Due to its intense rapid pulses, an X-ray free electron laser (XFEL) is an excellent tool for CXS experiments. A protocol is outlinedmore » for analysis of a CXS data set comprising a total of half a million X-ray exposures of solutions of small gold nanoparticles recorded at the Spring-8 Ångström Compact XFEL facility (SACLA). From the scattered intensities and their correlations, two populations of nanoparticle domains within the solution are distinguished: small twinned, and large probably non-twinned domains. Finally, it is shown analytically how, in a solution measurement, twinning information is only accessible via intensity correlations, demonstrating how CXS reveals atomic-level information from a disordered solution of like molecules.« less

ALARA: The next link in a chain of activation codes

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

Wilson, P.P.H.; Henderson, D.L.

1996-12-31

The Adaptive Laplace and Analytic Radioactivity Analysis [ALARA] code has been developed as the next link in the chain of DKR radioactivity codes. Its methods address the criticisms of DKR while retaining its best features. While DKR ignored loops in the transmutation/decay scheme to preserve the exactness of the mathematical solution, ALARA incorporates new computational approaches without jeopardizing the most important features of DKR`s physical modelling and mathematical methods. The physical model uses `straightened-loop, linear chains` to achieve the same accuracy in the loop solutions as is demanded in the rest of the scheme. In cases where a chain hasmore » no loops, the exact DKR solution is used. Otherwise, ALARA adaptively chooses between a direct Laplace inversion technique and a Laplace expansion inversion technique to optimize the accuracy and speed of the solution. All of these methods result in matrix solutions which allow the fastest and most accurate solution of exact pulsing histories. Since the entire history is solved for each chain as it is created, ALARA achieves the optimum combination of high accuracy, high speed and low memory usage. 8 refs., 2 figs.« less

Solid-phase microextraction for qualitative and quantitative determination of migrated degradation products of antioxidants in an organic aqueous solution.

PubMed

Burman, Lina; Albertsson, Ann-Christine; Höglund, Anders

2005-07-08

Low molecular weight aromatic substances may migrate out from plastic packaging to their contents, especially if they consist of organic aqueous solutions or oils. It is, therefore, extremely important to be able to identify and quantify any migrated substances in such solutions, even at very low concentrations. We have in this work investigated and evaluated the use of solid-phase microextraction for the specific task of extraction from an organic aqueous solution such as a simulated pharmaceutical solution consisting of 10 vol.% ethanol in water. The goal was furthermore to investigate the possibility of simultaneously identifying and quantifying the substances in spite of differences in their chemical structures. Methods were developed and evaluated for extraction both with direct sampling and with headspace sampling. Difficulties appeared due to the ethanol in the solution and the minute amounts of substances present. We have shown that a simultaneous quantification of migrated low molecular weight degradation products of antioxidants using only one fibre is possible if the extraction method and temperature are adjusted in relation to the concentration levels of the analytes. Comparions were made with solid-phase extraction.

Physics of heat pipe rewetting

NASA Technical Reports Server (NTRS)

Chan, S. H.

1992-01-01

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