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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Experimental solution for scattered imaging of the interference of plasmonic and photonic mode waves launched by metal nano-slits.

PubMed

Li, Xing; Gao, Yaru; Jiang, Shuna; Ma, Li; Liu, Chunxiang; Cheng, Chuanfu

2015-02-09

Using an L-shaped metal nanoslit to generate waves of the pure photonic and plasmonic modes simultaneously, we perform an experimental solution for the scattered imaging of the interference of the two waves. From the fringe data of interference, the amplitudes and the wavevector components of the two waves are obtained. The initial phases of the two waves are obtained from the phase map reconstructed with the interference of the scattered image and the reference wave in the interferometer. The difference in the wavevector components gives rise to an additional phase delay. We introduce the scattering theory under Kirchhoff's approximation to metal slit regime and explain the wavevector difference reasonably. The solution of the quantities is a comprehensive reflection of excitation, scattering and interference of the two waves. By decomposing the polarized incident field with respect to the slit element, the scattered image produced by slit of arbitrary shape can be solved with the nanoscale Huygens-Fresnel principle. This is demonstrated by the experimental intensity pattern and phase map produced by a ring-slit and its consistency with the calculated results.

Dynamics of curved fronts in systems with power-law memory

NASA Astrophysics Data System (ADS)

Abu Hamed, M.; Nepomnyashchy, A. A.

2016-08-01

The dynamics of a curved front in a plane between two stable phases with equal potentials is modeled via two-dimensional fractional in time partial differential equation. A closed equation governing a slow motion of a small-curvature front is derived and applied for two typical examples of the potential function. Approximate axisymmetric and non-axisymmetric solutions are obtained.

Modeling a 400 Hz Signal Transmission Through the South China Sea Basin

DTIC Science & Technology

2009-03-01

TRACING ..........................8 1. General Ray Theory and the Eikonal Approximation .....................8 2. Hamiltonian Ray Tracing...HAMILTONIAN RAY TRACING 1. General Ray Theory and the Eikonal Approximation In general, modeling acoustic propagation through the ocean necessitates... eikonal and represents the phase component of the solution. Since solutions of constant phase represent wave fronts, and rays travel in a direction

A compositional multiphase model for groundwater contamination by petroleum products: 1. Theoretical considerations

USGS Publications Warehouse

Corapcioglu, M. Yavuz; Baehr, Arthur L.

1987-01-01

A mathematical model is developed to describe the fate of hydrocarbon constituents of petroleum products introduced to soils as an immiscible liquid from sources such as leaking underground storage tanks and ruptured pipelines. The problem is one of multiphase transport (oil (immiscible), air, and water phases) of a reactive contaminant with constituents such as benzene, toluene, and xylene found in refined petroleum products like gasoline. In the unsaturated zone, transport of each constituent can occur as a solute in the water phase, vapor in the air phase, and as an unaltered constituent in the oil phase. Additionally, the model allows for adsorption. Molecular transformations, microbially mediated or abiotic, are incorporated as sink terms in the conservation of mass equations. An equilibrium approximation, applicable to any immiscible organic contaminant is applied to partition constituent mass between the air, oil, water, and adsorbed phases for points in the region where the oil phase exists. Outside the oil plume the equilibrium approximation takes on a simpler form to partition constituent mass between the air, water, and adsorbed phases only. Microbial degradation of petroleum products is first discussed in a general model, then the conservation of mass equation for oxygen is incorporated into the analysis which takes advantage of the key role played by oxygen in the metabolism of hydrocarbon utilizing microbes in soil environments. Approximations to two subproblems, oil plume establishment in the unsaturated zone, and solute and vapor transport subsequent to immiscible plume establishment are then developed from the general model.

NUMERICAL ANALYSES FOR TREATING DIFFUSION IN SINGLE-, TWO-, AND THREE-PHASE BINARY ALLOY SYSTEMS

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1994-01-01

This package consists of a series of three computer programs for treating one-dimensional transient diffusion problems in single and multiple phase binary alloy systems. An accurate understanding of the diffusion process is important in the development and production of binary alloys. Previous solutions of the diffusion equations were highly restricted in their scope and application. The finite-difference solutions developed for this package are applicable for planar, cylindrical, and spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included to account for differences in modal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. In each analysis, an effort was made to achieve good accuracy while minimizing computation time. The solutions to the diffusion equations for single-, two-, and threephase binary alloy systems are numerically calculated by the three programs NAD1, NAD2, and NAD3. NAD1 treats the diffusion between pure metals which belong to a single-phase system. Diffusion in this system is described by a one-dimensional Fick's second law and will result in a continuous composition variation. For computational purposes, Fick's second law is expressed as an explicit second-order finite difference equation. Finite difference calculations are made by choosing the grid spacing small enough to give convergent solutions of acceptable accuracy. NAD2 treats diffusion between pure metals which form a two-phase system. Diffusion in the twophase system is described by two partial differential equations (a Fick's second law for each phase) and an interface-flux-balance equation which describes the location of the interface. Actual interface motion is obtained by a mass conservation procedure. To account for changes in the thicknesses of the two phases as diffusion progresses, a variable grid technique developed by Murray and Landis is employed. These equations are expressed in finite difference form and solved numerically. Program NAD3 treats diffusion between pure metals which form a two-phase system with an intermediate third phase. Diffusion in the three-phase system is described by three partial differential expressions of Fick's second law and two interface-flux-balance equations. As with the two-phase case, a variable grid finite difference is used to numerically solve the diffusion equations. Computation time is minimized without sacrificing solution accuracy by treating the three-phase problem as a two-phase problem when the thickness of the intermediate phase is less than a preset value. Comparisons between these programs and other solutions have shown excellent agreement. The programs are written in FORTRAN IV for batch execution on the CDC 6600 with a central memory requirement of approximately 51K (octal) 60 bit words.

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.

A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows

NASA Astrophysics Data System (ADS)

Joshi, Vaibhav; Jaiman, Rajeev K.

2018-05-01

We present a positivity preserving variational scheme for the phase-field modeling of incompressible two-phase flows with high density ratio. The variational finite element technique relies on the Allen-Cahn phase-field equation for capturing the phase interface on a fixed Eulerian mesh with mass conservative and energy-stable discretization. The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation. To make the scheme energy-stable in a variational sense, we discretize the spatial part of the Lagrange multiplier in the phase-field equation by the mid-point approximation. The proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second-order accuracy of both spatial and temporal discretizations. We integrate the Allen-Cahn phase-field equation with the incompressible Navier-Stokes equations for modeling a broad range of two-phase flow and fluid-fluid interface problems. The coupling of the implicit discretizations corresponding to the phase-field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure. Comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase-indicator field. We perform a standalone test to verify the accuracy and stability of the Allen-Cahn two-phase solver. We examine the convergence and accuracy properties of the coupled phase-field solver through the standard benchmarks of the Laplace-Young law and a sloshing tank problem. Two- and three-dimensional dam break problems are simulated to assess the capability of the phase-field solver for complex air-water interfaces involving topological changes on unstructured meshes. Finally, we demonstrate the phase-field solver for a practical offshore engineering application of wave-structure interaction.

The Kardar-Parisi-Zhang Equation as Scaling Limit of Weakly Asymmetric Interacting Brownian Motions

NASA Astrophysics Data System (ADS)

Diehl, Joscha; Gubinelli, Massimiliano; Perkowski, Nicolas

2017-09-01

We consider a system of infinitely many interacting Brownian motions that models the height of a one-dimensional interface between two bulk phases. We prove that the large scale fluctuations of the system are well approximated by the solution to the KPZ equation provided the microscopic interaction is weakly asymmetric. The proof is based on the martingale solutions of Gonçalves and Jara (Arch Ration Mech Anal 212(2):597-644, 2014) and the corresponding uniqueness result of Gubinelli and Perkowski (Energy solutions of KPZ are unique, 2015).

Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source.

PubMed

Kienle, A; Patterson, M S

1997-09-01

We investigate theoretically the errors in determining the reduced scattering and absorption coefficients of semi-infinite turbid media from frequency-domain reflectance measurements made at small distances between the source and the detector(s). The errors are due to the uncertainties in the measurement of the phase, the modulation and the steady-state reflectance as well as to the diffusion approximation which is used as a theoretical model to describe light propagation in tissue. Configurations using one and two detectors are examined for the measurement of the phase and the modulation and for the measurement of the phase and the steady-state reflectance. Three solutions of the diffusion equation are investigated. We show that measurements of the phase and the steady-state reflectance at two different distances are best suited for the determination of the optical properties close to the source. For this arrangement the errors in the absorption coefficient due to typical uncertainties in the measurement are greater than those resulting from the application of the diffusion approximation at a modulation frequency of 200 MHz. A Monte Carlo approach is also examined; this avoids the errors due to the diffusion approximation.

Gradient Augmented Level Set Method for Two Phase Flow Simulations with Phase Change

NASA Astrophysics Data System (ADS)

Anumolu, C. R. Lakshman; Trujillo, Mario F.

2016-11-01

A sharp interface capturing approach is presented for two-phase flow simulations with phase change. The Gradient Augmented Levelset method is coupled with the two-phase momentum and energy equations to advect the liquid-gas interface and predict heat transfer with phase change. The Ghost Fluid Method (GFM) is adopted for velocity to discretize the advection and diffusion terms in the interfacial region. Furthermore, the GFM is employed to treat the discontinuity in the stress tensor, velocity, and temperature gradient yielding an accurate treatment in handling jump conditions. Thermal convection and diffusion terms are approximated by explicitly identifying the interface location, resulting in a sharp treatment for the energy solution. This sharp treatment is extended to estimate the interfacial mass transfer rate. At the computational cell, a d-cubic Hermite interpolating polynomial is employed to describe the interface location, which is locally fourth-order accurate. This extent of subgrid level description provides an accurate methodology for treating various interfacial processes with a high degree of sharpness. The ability to predict the interface and temperature evolutions accurately is illustrated by comparing numerical results with existing 1D to 3D analytical solutions.

TWO-PHASE FORMATION IN SOLUTIONS OF TOBACCO MOSAIC VIRUS AND THE PROBLEM OF LONG-RANGE FORCES

PubMed Central

Oster, Gerald

1950-01-01

In a nearly salt-free medium, a dilute tobacco mosaic virus solution of rod-shaped virus particles of uniform length forms two phases; the bottom optically anisotropic phase has a greater virus concentration than has the top optically isotropic phase. For a sample containing particles of various lengths, the bottom phase contains longer particles than does the top and the concentrations top and bottom are nearly equal. The longer the particles the less the minimum concentration necessary for two-phase formation. Increasing the salt concentration increases the minimum concentration. The formation of two phases is explained in terms of geometrical considerations without recourse to the concept of long-range attractive forces. The minimum concentration for two-phase formation is that concentration at which correlation in orientation between the rod-shaped particles begins to take place. This concentration is determined by the thermodynamically effective size and shape of the particles as obtained from the concentration dependence of the osmotic pressure of the solutions measured by light scattering. The effective volume of the particles is introduced into the theory of Onsager for correlation of orientation of uniform size rods and good agreement with experiment is obtained. The theory is extended to a mixture of non-uniform size rods and to the case in which the salt concentration is varied, and agreement with experiment is obtained. The thermodynamically effective volume of the particles and its dependence on salt concentration are explained in terms of the shape of the particles and the electrostatic repulsion between them. Current theories of the hydration of proteins and of long-range forces are critically discussed. The bottom layer of freshly purified tobacco mosaic virus samples shows Bragg diffraction of visible light. The diffraction data indicate that the virus particles in solution form three-dimensional crystals approximately the size of crystalline inclusion bodies found in the cells of plants suffering from the disease. PMID:15422102

Tension responses to rapid pressure release in glycerinated rabbit muscle fibers.

PubMed Central

Fortune, N S; Geeves, M A; Ranatunga, K W

1991-01-01

We have previously shown that the isometric tension of a fully calcium-activated skinned rabbit psoas muscle fiber is reversibly depressed by increased hydrostatic pressure. We report here the characterization of tension transients induced by a rapid (less than 1-ms) release of increased pressure at 12 degrees C. The tension transient consists of three clear phases, an initial further decrease of tension in phase with pressure change followed by two phases of tension increase back to the level recorded at ambient pressure. The mean reciprocal relaxation time for phase 2 (1/tau 2) was approximately 17 s-1 and that for phase 3 (1/tau 3) was 3 s-1. The presence of 20 mM inorganic phosphate markedly increased 1/tau 2 to approximately 52 s-1 and decreased 1/tau 3 to approximately 1.7 s-1. These observations are interpreted in terms of a pressure-sensitive transition between two attached crossbridge states of low (or zero) and higher force. This is compatible with the pressure-sensitive isomerization of actomyosin previously observed in solution. The results presented allow us to propose a coupling between a specific pressure-sensitive isomerization of purified actomyosin, the phosphate release step of the ATPase pathway, and the force-generating event of the cross-bridge cycle. PMID:1871140

Liquid structure of the urea-water system studied by dielectric spectroscopy.

PubMed

Hayashi, Yoshihito; Katsumoto, Yoichi; Omori, Shinji; Kishii, Noriyuki; Yasuda, Akio

2007-02-08

Dielectric spectroscopy measurements for aqueous urea solutions were performed at 298 K through a concentration range from 0.5 to 9.0 M with frequencies between 200 MHz and 40 GHz. Observed dielectric spectra were well represented by the superposition of two Debye type relaxation processes attributable to the bulk-water clusters and the urea-water coclusters. Our quantitative analysis of the spectra shows that the number of hydration water molecules is approximately two per urea molecule for the lower concentration region below 5.0 M, while the previous molecular dynamics studies predicted approximately six water molecules. It was also indicated by those studies, however, that there are two types of hydration water molecule in urea solution, which are strongly and weakly associated to the urea molecule, respectively. Only the strongly associated water was distinguishable in our analysis, while the weakly associated water exhibited the same dynamic feature as bulk water. This implies that urea retains the weakly associated water in the tetrahedral structure and, thus, is not a strong structure breaker of water. We also verified the model of liquid water where water consists of two states: the icelike-ordered and dense-disordered phases. Our dielectric data did not agree with the theoretical prediction based on the two-phase model. The present work supports the argument that urea molecules can easily replace near-neighbor water in the hydrogen-bonding network and do not require the presence of the disordered phase of water to dissolve into water.

A higher-order split-step Fourier parabolic-equation sound propagation solution scheme.

PubMed

Lin, Ying-Tsong; Duda, Timothy F

2012-08-01

A three-dimensional Cartesian parabolic-equation model with a higher-order approximation to the square-root Helmholtz operator is presented for simulating underwater sound propagation in ocean waveguides. The higher-order approximation includes cross terms with the free-space square-root Helmholtz operator and the medium phase speed anomaly. It can be implemented with a split-step Fourier algorithm to solve for sound pressure in the model. Two idealized ocean waveguide examples are presented to demonstrate the performance of this numerical technique.

Analytical approximations to the dynamics of an array of coupled DC SQUIDs

NASA Astrophysics Data System (ADS)

Berggren, Susan; Palacios, Antonio

2014-04-01

Coupled dynamical systems that operate near the onset of a bifurcation can lead, under certain conditions, to strong signal amplification effects. Over the past years we have studied this generic feature on a wide range of systems, including: magnetic and electric fields sensors, gyroscopic devices, and arrays of loops of superconducting quantum interference devices, also known as SQUIDs. In this work, we consider an array of SQUID loops connected in series as a case study to derive asymptotic analytical approximations to the exact solutions through perturbation analysis. Two approaches are considered. First, a straightforward expansion in which the non-linear parameter related to the inductance of the DC SQUID is treated as the small perturbation parameter. Second, a more accurate procedure that considers the SQUID phase dynamics as non-uniform motion on a circle. This second procedure is readily extended to the series array and it could serve as a mathematical framework to find approximate solutions to related complex systems with high-dimensionality. To the best of our knowledge, an approximate analytical solutions to an array of SQUIDs has not been reported yet in the literature.

A multi-scale network method for two-phase flow in porous media

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

Khayrat, Karim, E-mail: khayratk@ifd.mavt.ethz.ch; Jenny, Patrick

Pore-network models of porous media are useful in the study of pore-scale flow in porous media. In order to extract macroscopic properties from flow simulations in pore-networks, it is crucial the networks are large enough to be considered representative elementary volumes. However, existing two-phase network flow solvers are limited to relatively small domains. For this purpose, a multi-scale pore-network (MSPN) method, which takes into account flow-rate effects and can simulate larger domains compared to existing methods, was developed. In our solution algorithm, a large pore network is partitioned into several smaller sub-networks. The algorithm to advance the fluid interfaces withinmore » each subnetwork consists of three steps. First, a global pressure problem on the network is solved approximately using the multiscale finite volume (MSFV) method. Next, the fluxes across the subnetworks are computed. Lastly, using fluxes as boundary conditions, a dynamic two-phase flow solver is used to advance the solution in time. Simulation results of drainage scenarios at different capillary numbers and unfavourable viscosity ratios are presented and used to validate the MSPN method against solutions obtained by an existing dynamic network flow solver.« less

On the Unreasonable Effectiveness of post-Newtonian Theory in Gravitational-Wave Physics

ScienceCinema

Will, Clifford M.

2017-12-22

The first indirect detection of gravitational waves involved a binary system of neutron stars.  In the future, the first direct detection may also involve binary systems -- inspiralling and merging binary neutron stars or black holes. This means that it is essential to understand in full detail the two-body system in general relativity, a notoriously difficult problem with a long history. Post-Newtonian approximation methods are thought to work only under slow motion and weak field conditions, while numerical solutions of Einstein's equations are thought to be limited to the final merger phase.  Recent results have shown that post-Newtonian approximations seem to remain unreasonably valid well into the relativistic regime, while advances in numerical relativity now permit solutions for numerous orbits before merger.  It is now possible to envision linking post-Newtonian theory and numerical relativity to obtain a complete "solution" of the general relativistic two-body problem.  These solutions will play a central role in detecting and understanding gravitational wave signals received by interferometric observatories on Earth and in space.

Atomic structure of a decagonal Al-Pd-Mn phase

NASA Astrophysics Data System (ADS)

Mihalkovič, Marek; Roth, Johannes; Trebin, Hans-Rainer

2017-12-01

We present a detailed structure solution for the 16 -Å decagonal quasicrystal in the Al-Pd-Mn system by means of cluster decoration and ab initio energy minimization. It is based on structure models of the ɛ and other approximant phases. The ɛ phases can be represented as subsets of a hexagon-boat-star (HBS) tiling. The decagonal phase comprises further HBS tiles. We have constructed several fictitious HBS approximants and optimized their structures individually. All tiles are decorated by two types of atomic clusters: the pseudo-Mackay icosahedron (PMI) and the large bicapped pentagonal prism (LBPP). It turns out that, whereas the PMI clusters can be kept essentially unchanged, the LBPP clusters must be adjusted in occupancy with Al atoms depending on their positions in the various tiles. In this way we obtain cluster decorations for all tiles of the decagonal quasicrystal. The calculations were confirmed by evaluation of an effective tile Hamiltonian.

Simulation of Two-Phase Flow Based on a Thermodynamically Constrained Averaging Theory Flow Model

NASA Astrophysics Data System (ADS)

Weigand, T. M.; Dye, A. L.; McClure, J. E.; Farthing, M. W.; Gray, W. G.; Miller, C. T.

2014-12-01

The thermodynamically constrained averaging theory (TCAT) has been used to formulate general classes of porous medium models, including new models for two-fluid-phase flow. The TCAT approach provides advantages that include a firm connection between the microscale, or pore scale, and the macroscale; a thermodynamically consistent basis; explicit inclusion of factors such as interfacial areas, contact angles, interfacial tension, and curvatures; and dynamics of interface movement and relaxation to an equilibrium state. In order to render the TCAT model solvable, certain closure relations are needed to relate fluid pressure, interfacial areas, curvatures, and relaxation rates. In this work, we formulate and solve a TCAT-based two-fluid-phase flow model. We detail the formulation of the model, which is a specific instance from a hierarchy of two-fluid-phase flow models that emerge from the theory. We show the closure problem that must be solved. Using recent results from high-resolution microscale simulations, we advance a set of closure relations that produce a closed model. Lastly, we use locally conservative spatial discretization and higher order temporal discretization methods to approximate the solution to this new model and compare the solution to the traditional model.

Model of two-temperature convective transfer in porous media

NASA Astrophysics Data System (ADS)

Gruais, Isabelle; Poliševski, Dan

2017-12-01

In this paper, we study the asymptotic behaviour of the solution of a convective heat transfer boundary problem in an ɛ -periodic domain which consists of two interwoven phases, solid and fluid, separated by an interface. The fluid flow and its dependence with respect to the temperature are governed by the Boussinesq approximation of the Stokes equations. The tensors of thermal diffusion of both phases are ɛ -periodic, as well as the heat transfer coefficient which is used to describe the first-order jump condition on the interface. We find by homogenization that the two-scale limits of the solutions verify the most common system used to describe local thermal non-equilibrium phenomena in porous media (see Nield and Bejan in Convection in porous media, Springer, New York, 1999; Rees and Pop in Transport phenomena in porous media III, Elsevier, Oxford, 2005). Since now, this system was justified only by volume averaging arguments.

X-Ray diffraction and mu-Raman investigation of the monoclinic-orthorhombic phase transition in Th(1-x)U(x)(C(2)O(4))(2).2H(2)O solid solutions.

PubMed

Clavier, Nicolas; Hingant, Nina; Rivenet, Murielle; Obbade, Saïd; Dacheux, Nicolas; Barré, Nicole; Abraham, Francis

2010-02-15

A complete Th(1-x)U(x)(C(2)O(4))(2).2H(2)O solid solution was prepared by mild hydrothermal synthesis from a mixture of hydrochloric solutions containing cations and oxalic acid. The crystal structure has been solved from twinned single crystals for x = 0, 0.5, and 1 with monoclinic symmetry, space group C2/c, leading to unit cell parameters of a approximately 10.5 A, b approximately 8.5 A, and c approximately 9.6 A. The crystal structure consists of a two-dimensional arrangement of actinide centers connected through bis-bidentate oxalate ions forming squares. The actinide metal is coordinated by eight oxygen atoms from four oxalate entities and two water oxygen atoms forming a bicapped square antiprism. The connection between the layers is assumed by hydrogen bonds between the water molecules and the oxygen of oxalate of an adjacent layer. Under these conditions, the unit cell contains two independent oxalate ions. From high-temperature mu-Raman and X-ray diffraction studies, the compounds were found to undergo a transition to an orthorhombic form (space group Ccca). The major differences in the structural arrangement concern the symmetry of uranium, which decreases from C2 to D2, leading to a unique oxalate group. Consequently, the nu(s)(C-O) double band observed in the Raman spectra recorded at room temperature turned into a singlet. This transformation was then used to make the phase transition temperature more precise as a function of the uranium content of the sample.

On the phase lag of turbulent dissipation in rotating tidal flows

NASA Astrophysics Data System (ADS)

Zhang, Qianjiang; Wu, Jiaxue

2018-03-01

Field observations of rotating tidal flows in a shallow tidally swept sea reveal that a notable phase lag of both shear production and turbulent dissipation increases with height above the seafloor. These vertical delays of turbulent quantities are approximately equivalent in magnitude to that of squared mean shear. The shear production approximately equals turbulent dissipation over the phase-lag column, and thus a main mechanism of phase lag of dissipation is mean shear, rather than vertical diffusion of turbulent kinetic energy. By relating the phase lag of dissipation to that of the mean shear, a simple formulation with constant eddy viscosity is developed to describe the phase lag in rotating tidal flows. An analytical solution indicates that the phase lag increases linearly with height subjected to a combined effect of tidal frequency, Coriolis parameter and eddy viscosity. The vertical diffusion of momentum associated with eddy viscosity produces the phase lag of squared mean shear, and resultant delay of turbulent quantities. Its magnitude is inhibited by Earth's rotation. Furthermore, a theoretical formulation of the phase lag with a parabolic eddy viscosity profile can be constructed. A first-order approximation of this formulation is still a linear function of height, and its magnitude is approximately 0.8 times that with constant viscosity. Finally, the theoretical solutions of phase lag with realistic viscosity can be satisfactorily justified by realistic phase lags of dissipation.

A Model for Displacements Between Parallel Plates That Shows Change of Type from Hyperbolic to Elliptic

NASA Astrophysics Data System (ADS)

Shariati, Maryam; Yortsos, Yannis; Talon, Laurent; Martin, Jerome; Rakotomalala, Nicole; Salin, Dominique

2003-11-01

We consider miscible displacement between parallel plates, where the viscosity is a function of the concentration. By selecting a piece-wise representation, the problem can be considered as ``three-phase'' flow. Assuming a lubrication-type approximation, the mathematical description is in terms of two quasi-linear hyperbolic equations. When the mobility of the middle phase is smaller than its neighbors, the system is genuinely hyperbolic and can be solved analytically. However, when it is larger, an elliptic region develops. This change-of-type behavior is for the first time proved here based on sound physical principles. Numerical solutions with a small diffusion are presented. Good agreement is obtained outside the elliptic region, but not inside, where the numerical results show unstable behavior. We conjecture that for the solution of the real problem in the mixed-type case, the full higher-dimensionality problem must be considered inside the elliptic region, in which the lubrication (parallel-flow) approximation is no longer appropriate. This is discussed in a companion presentation.

Immobilization of chromate in hyperalkaline waste streams by green rusts and zero-valent iron.

PubMed

Rogers, Christine M; Burke, Ian T; Ahmed, Imad A M; Shaw, Samuel

2014-01-01

Zero-valent iron (ZVI) and green rusts can be used as reductants to convert chromium from soluble, highly toxic Cr(VI) to insoluble Cr(III). This study compared the reduction rates of Cr(VI) by ZVI and two carbonate green rust phases in alkaline/hyperalkaline solutions. Batch experiments were carried out with synthetic chromate solutions at pH 7.7-12.3 and a chromite ore processing residue (COPR) leachate (pH approximately 12.2). Green rust removes chromate from high pH solutions (pH 10-12.5) very rapidly (<400 s). Chromate reduction rates for both green rust phases were consistently higher than for ZVI throughout the pH range studied; the surface area normalized rate constants were two orders of magnitude higher in the COPR leachate solution at pH 12.2. The performances of both green rusts were unaffected by changes in pH. In contrast, ZVI exhibited a marked decline in reduction rate with increasing pH to become almost ineffective above pH12.

Distortion of liquid film discharging from twin-fluid atomizer

NASA Astrophysics Data System (ADS)

Mehring, C.; Sirignano, W. A.

2001-11-01

The nonlinear distortion and disintegration of a thin liquid film exiting from a two-dimensional twin-fluid atomizer is analyzed numerically. Pulsed gas jets impacting on both sides of the discharging liquid film at the atomizer exit generate dilational and/or sinuous deformations of the film. Both liquid phase and gas phase are inviscid and incompressible. For the liquid phase the so-called long-wavelength approximation is employed yielding a system of unsteady one-dimensional equations for the planar film. Solution of Laplace's equation for the velocity potential yields the gas-phase velocity field on both sides of the liquid stream. Coupling between both phases is described through kinematic and dynamic boundary conditions at the phase interfaces, and includes the solution of the unsteady Bernoulli equation to determine the gas-phase pressure along the interfaces. Both gas- and liquid-phase equations are solved simultaneously. Solution of Laplace's equation for the gas streams is obtained by means of a boundary-element method. Numerical solutions for the liquid phase use the Lax-Wendroff method with Richtmyer splitting. Sheet distortion resulting from the stagnation pressure of the impacting gas jets and subsequent disturbance amplification due to Kelvin-Helmholtz effects are studied for various combinations of gas-pulse timing, gas-jet impact angles, gas-to-liquid-density ratio, liquid-phase Weber number and gas-jet-to-liquid-jet-momentum ratio. Dilational and sinuous oscillations of the liquid are examined and film pinch-off is predicted.

Interference effects in phased beam tracing using exact half-space solutions.

PubMed

Boucher, Matthew A; Pluymers, Bert; Desmet, Wim

2016-12-01

Geometrical acoustics provides a correct solution to the wave equation for rectangular rooms with rigid boundaries and is an accurate approximation at high frequencies with nearly hard walls. When interference effects are important, phased geometrical acoustics is employed in order to account for phase shifts due to propagation and reflection. Error increases, however, with more absorption, complex impedance values, grazing incidence, smaller volumes and lower frequencies. Replacing the plane wave reflection coefficient with a spherical one reduces the error but results in slower convergence. Frequency-dependent stopping criteria are then applied to avoid calculating higher order reflections for frequencies that have already converged. Exact half-space solutions are used to derive two additional spherical wave reflection coefficients: (i) the Sommerfeld integral, consisting of a plane wave decomposition of a point source and (ii) a line of image sources located at complex coordinates. Phased beam tracing using exact half-space solutions agrees well with the finite element method for rectangular rooms with absorbing boundaries, at low frequencies and for rooms with different aspect ratios. Results are accurate even for long source-to-receiver distances. Finally, the crossover frequency between the plane and spherical wave reflection coefficients is discussed.

Self-calibrating generalized phase-shifting interferometry of three phase-steps based on geometric concept of volume enclosed by a surface

NASA Astrophysics Data System (ADS)

Meneses-Fabian, Cruz

2016-12-01

This paper presents a non-iterative, fast, and simple algorithm for phase retrieval, in phase-shifting interferometry of three unknown and unequal phase-steps, based on the geometric concept of the volume enclosed by a surface. This approach can be divided in three stages; first the background is eliminated by the subtraction of two interferograms, for obtaining a secondary pattern; second, a surface is built by the product of two secondary patterns and the volume enclosed by this surface is computed; and third, the ratio between two enclosed volumes is approximated to a constant that depends on the phase-steps, with which a system of equations is established, and its solution allows the measurement of the phase-steps to be obtained. Additional advantages of this approach are its immunity to noise, and its capacity to support high spatial variations in the illumination. This approach is theoretically described and is numerically and experimentally verified.

Quantum preservation of the measurements precision using ultra-short strong pulses in exact analytical solution

NASA Astrophysics Data System (ADS)

Berrada, K.; Eleuch, H.

2017-09-01

Various schemes have been proposed to improve the parameter-estimation precision. In the present work, we suggest an alternative method to preserve the estimation precision by considering a model that closely describes a realistic experimental scenario. We explore this active way to control and enhance the measurements precision for a two-level quantum system interacting with classical electromagnetic field using ultra-short strong pulses with an exact analytical solution, i.e. beyond the rotating wave approximation. In particular, we investigate the variation of the precision with a few cycles pulse and a smooth phase jump over a finite time interval. We show that by acting on the shape of the phase transient and other parameters of the considered system, the amount of information may be increased and has smaller decay rate in the long time. These features make two-level systems incorporated in ultra-short, of-resonant and gradually changing phase good candidates for implementation of schemes for the quantum computation and the coherent information processing.

C1-Continuous relative permeability and hybrid upwind discretization of three phase flow in porous media

NASA Astrophysics Data System (ADS)

Lee, S. H.; Efendiev, Y.

2016-10-01

Three-phase flow in a reservoir model has been a major challenge in simulation studies due to slowly convergent iterations in Newton solution of nonlinear transport equations. In this paper, we examine the numerical characteristics of three-phase flow and propose a consistent, "C1-continuous discretization" (to be clarified later) of transport equations that ensures a convergent solution in finite difference approximation. First, we examine three-phase relative permeabilities that are critical in solving nonlinear transport equations. Three-phase relative permeabilities are difficult to measure in the laboratory, and they are often correlated with two-phase relative permeabilities (e.g., oil-gas and water-oil systems). Numerical convergence of non-linear transport equations entails that three-phase relative permeability correlations are a monotonically increasing function of the phase saturation and the consistency conditions of phase transitions are satisfied. The Modified Stone's Method II and the Linear Interpolation Method for three-phase relative permeability are closely examined for their mathematical properties. We show that the Linear Interpolation Method yields C1-continuous three-phase relative permeabilities for smooth solutions if the two phase relative permeabilities are monotonic and continuously differentiable. In the second part of the paper, we extend a Hybrid-Upwinding (HU) method of two-phase flow (Lee, Efendiev and Tchelepi, ADWR 82 (2015) 27-38) to three phase flow. In the HU method, the phase flux is divided into two parts based on the driving forces (in general, it can be divided into several parts): viscous and buoyancy. The viscous-driven and buoyancy-driven fluxes are upwinded differently. Specifically, the viscous flux, which is always co-current, is upwinded based on the direction of the total velocity. The pure buoyancy-induced flux is shown to be only dependent on saturation distributions and counter-current. In three-phase flow, the buoyancy effect can be expressed as a sum of two buoyancy effects from two-phase flows, i.e., oil-water and oil-gas systems. We propose an upwind scheme for the buoyancy flux term from three-phase flow as a sum of two buoyancy terms from two-phase flows. The upwind direction of the buoyancy flux in two phase flow is always fixed such that the heavier fluid goes downward and the lighter fluid goes upward. It is shown that the Implicit Hybrid-Upwinding (IHU) scheme for three-phase flow is locally conservative and produces physically-consistent numerical solutions. As in two phase flow, the primary advantage of the IHU scheme is that the flux of a fluid phase remains continuous and differentiable as the flow regime changes between co-current and counter-current conditions as a function of time, or (Newton) iterations. This is in contrast to the standard phase-potential-based upwinding scheme, in which the overall fractional-flow (flux) function is non-differentiable across the transition between co-current and counter-current flows.

ANALYZING NUMERICAL ERRORS IN DOMAIN HEAT TRANSPORT MODELS USING THE CVBEM.

USGS Publications Warehouse

Hromadka, T.V.; ,

1985-01-01

Besides providing an exact solution for steady-state heat conduction processes (Laplace Poisson equations), the CVBEM (complex variable boundary element method) can be used for the numerical error analysis of domain model solutions. For problems where soil water phase change latent heat effects dominate the thermal regime, heat transport can be approximately modeled as a time-stepped steady-state condition in the thawed and frozen regions, respectively. The CVBEM provides an exact solution of the two-dimensional steady-state heat transport problem, and also provides the error in matching the prescribed boundary conditions by the development of a modeling error distribution or an approximative boundary generation. This error evaluation can be used to develop highly accurate CVBEM models of the heat transport process, and the resulting model can be used as a test case for evaluating the precision of domain models based on finite elements or finite differences.

Phase slips in superconducting weak links

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

Kimmel, Gregory; Glatz, Andreas; Aranson, Igor S.

2017-01-01

Superconducting vortices and phase slips are primary mechanisms of dissipation in superconducting, superfluid, and cold-atom systems. While the dynamics of vortices is fairly well described, phase slips occurring in quasi-one- dimensional superconducting wires still elude understanding. The main reason is that phase slips are strongly nonlinear time-dependent phenomena that cannot be cast in terms of small perturbations of the superconducting state. Here we study phase slips occurring in superconducting weak links. Thanks to partial suppression of superconductivity in weak links, we employ a weakly nonlinear approximation for dynamic phase slips. This approximation is not valid for homogeneous superconducting wires andmore » slabs. Using the numerical solution of the time-dependent Ginzburg-Landau equation and bifurcation analysis of stationary solutions, we show that the onset of phase slips occurs via an infinite period bifurcation, which is manifested in a specific voltage-current dependence. Our analytical results are in good agreement with simulations.« less

Fluid displacement between two parallel plates: a non-empirical model displaying change of type from hyperbolic to elliptic equations

NASA Astrophysics Data System (ADS)

Shariati, M.; Talon, L.; Martin, J.; Rakotomalala, N.; Salin, D.; Yortsos, Y. C.

2004-11-01

We consider miscible displacement between parallel plates in the absence of diffusion, with a concentration-dependent viscosity. By selecting a piecewise viscosity function, this can also be considered as ‘three-fluid’ flow in the same geometry. Assuming symmetry across the gap and based on the lubrication (‘equilibrium’) approximation, a description in terms of two quasi-linear hyperbolic equations is obtained. We find that the system is hyperbolic and can be solved analytically, when the mobility profile is monotonic, or when the mobility of the middle phase is smaller than its neighbours. When the mobility of the middle phase is larger, a change of type is displayed, an elliptic region developing in the composition space. Numerical solutions of Riemann problems of the hyperbolic system spanning the elliptic region, with small diffusion added, show good agreement with the analytical outside, but an unstable behaviour inside the elliptic region. In these problems, the elliptic region arises precisely at the displacement front. Crossing the elliptic region requires the solution of essentially an eigenvalue problem of the full higher-dimensional model, obtained here using lattice BGK simulations. The hyperbolic-to-elliptic change-of-type reflects the failing of the lubrication approximation, underlying the quasi-linear hyperbolic formalism, to describe the problem uniformly. The obtained solution is analogous to non-classical shocks recently suggested in problems with change of type.

Design of an Evolutionary Approach for Intrusion Detection

PubMed Central

2013-01-01

A novel evolutionary approach is proposed for effective intrusion detection based on benchmark datasets. The proposed approach can generate a pool of noninferior individual solutions and ensemble solutions thereof. The generated ensembles can be used to detect the intrusions accurately. For intrusion detection problem, the proposed approach could consider conflicting objectives simultaneously like detection rate of each attack class, error rate, accuracy, diversity, and so forth. The proposed approach can generate a pool of noninferior solutions and ensembles thereof having optimized trade-offs values of multiple conflicting objectives. In this paper, a three-phase, approach is proposed to generate solutions to a simple chromosome design in the first phase. In the first phase, a Pareto front of noninferior individual solutions is approximated. In the second phase of the proposed approach, the entire solution set is further refined to determine effective ensemble solutions considering solution interaction. In this phase, another improved Pareto front of ensemble solutions over that of individual solutions is approximated. The ensemble solutions in improved Pareto front reported improved detection results based on benchmark datasets for intrusion detection. In the third phase, a combination method like majority voting method is used to fuse the predictions of individual solutions for determining prediction of ensemble solution. Benchmark datasets, namely, KDD cup 1999 and ISCX 2012 dataset, are used to demonstrate and validate the performance of the proposed approach for intrusion detection. The proposed approach can discover individual solutions and ensemble solutions thereof with a good support and a detection rate from benchmark datasets (in comparison with well-known ensemble methods like bagging and boosting). In addition, the proposed approach is a generalized classification approach that is applicable to the problem of any field having multiple conflicting objectives, and a dataset can be represented in the form of labelled instances in terms of its features. PMID:24376390

Measuring optical phase digitally in coherent metrology systems

NASA Astrophysics Data System (ADS)

Kelly, Damien P.; Ryle, James; Zhao, Liang; Sheridan, John T.

2017-05-01

The accurate measurement of optical phase has many applications in metrology. For biological samples, which appear transparent, the phase data provides information about the refractive index of the sample. In speckle metrology, the phase can be used to estimate stress and strains of a rough surface with high sensitivity. In this theoretical manuscript we compare and contrast the properties of two techniques for estimating the phase distribution of a wave field under the paraxial approximation: (I) A digital holographic system, and (II) An idealized phase retrieval system. Both systems use a CCD or CMOS array to measure the intensities of the wave fields that are reflected from or transmitted through the sample of interest. This introduces a numerical aspect to the problem. For the two systems above we examine how numerical calculations can limit the performance of these systems leading to a near-infinite number of possible solutions.

Analytical treatment of self-phase-modulation beyond the slowly varying envelope approximation

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

Syrchin, M.S.; Zheltikov, A.M.; International Laser Center, M.V. Lomonosov Moscow State University, 119899 Moscow

Analytical treatment of the self-phase-modulation of an ultrashort light pulse is extended beyond the slowly varying envelope approximation. The resulting wave equation is modified to include corrections to self-phase-modulation due to higher-order spatial and temporal derivatives. Analytical solutions are found in the limiting regimes of high nonlinearities and very short pulses. Our results reveal features that can significantly impact both pulse shape and the evolution of the phase.

Releasing intracellular product to prepare whole cell biocatalyst for biosynthesis of Monascus pigments in water-edible oil two-phase system.

PubMed

Hu, Minglue; Zhang, Xuehong; Wang, Zhilong

2016-11-01

Selective releasing intracellular product in Triton X-100 micelle aqueous solution to prepare whole cell biocatalyst is a novel strategy for biosynthesis of Monascus pigments, in which cell suspension culture exhibits some advantages comparing with the corresponding growing cell submerged culture. In the present work, the nonionic surfactant Triton X-100 was successfully replaced by edible plant oils for releasing intracellular Monascus pigments. High concentration of Monascus pigments (with absorbance nearly 710 AU at 470 nm in the oil phase, normalized to the aqueous phase volume approximately 142 AU) was achieved by cell suspension culture in peanut oil-water two-phase system. Furthermore, the utilization of edible oil as extractant also fulfills the demand for application of Monascus pigments as natural food colorant.

Aqueous Biphasic Systems for the Synthesis of Formates by Catalytic CO2 Hydrogenation: Integrated Reaction and Catalyst Separation for CO2 -Scrubbing Solutions.

PubMed

Scott, Martin; Blas Molinos, Beatriz; Westhues, Christian; Franciò, Giancarlo; Leitner, Walter

2017-03-22

Aqueous biphasic systems were investigated for the production of formate-amine adducts by metal-catalyzed CO 2 hydrogenation, including typical scrubbing solutions as feedstocks. Different hydrophobic organic solvents and ionic liquids could be employed as the stationary phase for cis-[Ru(dppm) 2 Cl 2 ] (dppm=bis-diphenylphosphinomethane) as prototypical catalyst without any modification or tagging of the complex. The amines were found to partition between the two phases depending on their structure, whereas the formate-amine adducts were nearly quantitatively extracted into the aqueous phase, providing a favorable phase behavior for the envisaged integrated reaction/separation sequence. The solvent pair of methyl isobutyl carbinol (MIBC) and water led to the most practical and productive system and repeated use of the catalyst phase was demonstrated. The highest single batch activity with a TOF av of approximately 35 000 h -1 and an initial TOF of approximately 180 000 h -1 was achieved in the presence of NEt 3 . Owing to higher stability, the highest productivities were obtained with methyl diethanolamine (Aminosol CST 115) and monoethanolamine (MEA), which are used in commercial scale CO 2 -scrubbing processes. Saturated aqueous solutions (CO 2 overpressure 5-10 bar) of MEA could be converted into the corresponding formate adducts with average turnover frequencies up to 14×10 3  h -1 with an overall yield of 70 % based on the amine, corresponding to a total turnover number of 150 000 over eleven recycling experiments. This opens the possibility for integrated approaches to carbon capture and utilization. © 2017 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.

Aqueous Biphasic Systems for the Synthesis of Formates by Catalytic CO2 Hydrogenation: Integrated Reaction and Catalyst Separation for CO2‐Scrubbing Solutions

PubMed Central

Scott, Martin; Blas Molinos, Beatriz; Westhues, Christian

2017-01-01

Abstract Aqueous biphasic systems were investigated for the production of formate–amine adducts by metal‐catalyzed CO2 hydrogenation, including typical scrubbing solutions as feedstocks. Different hydrophobic organic solvents and ionic liquids could be employed as the stationary phase for cis‐[Ru(dppm)2Cl2] (dppm=bis‐diphenylphosphinomethane) as prototypical catalyst without any modification or tagging of the complex. The amines were found to partition between the two phases depending on their structure, whereas the formate–amine adducts were nearly quantitatively extracted into the aqueous phase, providing a favorable phase behavior for the envisaged integrated reaction/separation sequence. The solvent pair of methyl isobutyl carbinol (MIBC) and water led to the most practical and productive system and repeated use of the catalyst phase was demonstrated. The highest single batch activity with a TOFav of approximately 35 000 h−1 and an initial TOF of approximately 180 000 h−1 was achieved in the presence of NEt3. Owing to higher stability, the highest productivities were obtained with methyl diethanolamine (Aminosol CST 115) and monoethanolamine (MEA), which are used in commercial scale CO2‐scrubbing processes. Saturated aqueous solutions (CO2 overpressure 5–10 bar) of MEA could be converted into the corresponding formate adducts with average turnover frequencies up to 14×103 h−1 with an overall yield of 70 % based on the amine, corresponding to a total turnover number of 150 000 over eleven recycling experiments. This opens the possibility for integrated approaches to carbon capture and utilization. PMID:28103428

Switching dynamics of doped CoFeB trilayers and a comparison to the quasistatic approximation

NASA Astrophysics Data System (ADS)

Forrester, Michael; Kusmartsev, Feodor; Kovács, Endre

2013-05-01

The investigation of the switching times of the magnetization reversal of two interacting CoFeB nanomagnets, with dimensions small enough to maintain a single-domain structure, has been carried out. A quasistatic approximation is shown to give valid results and to compare well to the damped dynamical solutions of the Landau-Lifshitz-Gilbert equations. The characteristics of the switching are shown in the associated hysteresis loops and we build a complete phase diagram of the various parallel, antiparallel, and scissoring states of the magnetization in terms of the coupling energy between the nanomagnets, magnetic anisotropy, and the interaction with an applied magnetic field. The phase diagram summarizes the different kinds of hysteresis associated with the magnetization reversal phenomena. The switching fields and times are estimated and the vulnerabilities of the magnetic phases to thermally induced magnetic field variations are examined. The stability of the phases is a fine balance between intrinsic and extrinsic magnetism and we examine its precarious nature. Our work identifies the structures that have the most robust magnetization states and hence a design ethic for creating nanomagnetic heterostructures with outstanding magnetoresistance properties based upon the two magnetic elements.

Self-organization of a wedge-shaped surfactant in monolayers and multilayers.

PubMed

Cain, Nicholas; Van Bogaert, Josh; Gin, Douglas L; Hammond, Scott R; Schwartz, Daniel K

2007-01-16

The self-organization behavior of a wedge-shaped surfactant, disodium-3,4,5-tris(dodecyloxy)phenylmethylphosphonate, was studied in Langmuir monolayers (at the air-water interface), Langmuir-Blodgett (LB) monolayers and multilayers, and films adsorbed spontaneously from isooctane solution onto a mica substrate (self-assembled films). This compound forms an inverted hexagonal lyotropic liquid crystal phase in the bulk and in thick adsorbed films. Surface pressure isotherm and Brewster angle microscope (BAM) studies of Langmuir monolayers revealed three phases: gas (G), liquid expanded (LE), and liquid condensed (LC). The surface pressure-temperature phase diagram was determined in detail; a triple point was found at approximately 10 degrees C. Atomic force microscope (AFM) images of LB monolayers transferred from various regions of the phase diagram were consistent with the BAM images and indicated that the LE regions are approximately 0.5 nm thinner than the LC regions. AFM images were also obtained of self-assembled films after various adsorption times. For short adsorption times, when monolayer self-assembly was incomplete, the film topography indicated the coexistence of two distinct monolayer phases. The height difference between these two phases was again 0.5 nm, suggesting a correspondence with the LE/LC coexistence observed in the Langmuir monolayers. For longer immersion times, adsorbed multilayers assembled into highly organized periodic arrays of inverse cylindrical micelles. Similar periodic structures, with the same repeat distance of 4.5 nm, were also observed in three-layer LB films. However, the regions of organized periodic structure were much smaller and more poorly correlated in the LB multilayers than in the films adsorbed from solution. Collectively, these observations indicate a high degree of similarity between the molecular organization in Langmuir layers/LB films and adsorbed self-assembled films. In both cases, monolayers progress through an LE phase, into LE/LC coexistence, and finally into LC phase as surface density increases. Following the deposition of an additional bilayer, the film reorganizes to form an array of inverted cylindrical micelles.

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

Dechant, Lawrence J.

Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler,more » closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.« less

Groebner Basis Methods for Stationary Solutions of a Low-Dimensional Model for a Shear Flow

NASA Astrophysics Data System (ADS)

Pausch, Marina; Grossmann, Florian; Eckhardt, Bruno; Romanovski, Valery G.

2014-10-01

We use Groebner basis methods to extract all stationary solutions for the nine-mode shear flow model described in Moehlis et al. (New J Phys 6:56, 2004). Using rational approximations to irrational wave numbers and algebraic manipulation techniques we reduce the problem of determining all stationary states to finding roots of a polynomial of order 30. The coefficients differ by 30 powers of 10, so that algorithms for extended precision are needed to extract the roots reliably. We find that there are eight stationary solutions consisting of two distinct states, each of which appears in four symmetry-related phases. We discuss extensions of these results for other flows.

Hybridized Multiscale Discontinuous Galerkin Methods for Multiphysics

DTIC Science & Technology

2015-09-14

discontinuous Galerkin method for the numerical solution of the Helmholtz equation , J. Comp. Phys., 290, 318–335, 2015. [14] N.C. NGUYEN, J. PERAIRE...approximations of the Helmholtz equation for a very wide range of wave frequencies. Our approach combines the hybridizable discontinuous Galerkin methodology...local approximation spaces of the hybridizable discontinuous Galerkin methods with precomputed phases which are solutions of the eikonal equation in

Intermolecular interactions in the condensed phase: Evaluation of semi-empirical quantum mechanical methods

NASA Astrophysics Data System (ADS)

Christensen, Anders S.; Kromann, Jimmy C.; Jensen, Jan H.; Cui, Qiang

2017-10-01

To facilitate further development of approximate quantum mechanical methods for condensed phase applications, we present a new benchmark dataset of intermolecular interaction energies in the solution phase for a set of 15 dimers, each containing one charged monomer. The reference interaction energy in solution is computed via a thermodynamic cycle that integrates dimer binding energy in the gas phase at the coupled cluster level and solute-solvent interaction with density functional theory; the estimated uncertainty of such calculated interaction energy is ±1.5 kcal/mol. The dataset is used to benchmark the performance of a set of semi-empirical quantum mechanical (SQM) methods that include DFTB3-D3, DFTB3/CPE-D3, OM2-D3, PM6-D3, PM6-D3H+, and PM7 as well as the HF-3c method. We find that while all tested SQM methods tend to underestimate binding energies in the gas phase with a root-mean-squared error (RMSE) of 2-5 kcal/mol, they overestimate binding energies in the solution phase with an RMSE of 3-4 kcal/mol, with the exception of DFTB3/CPE-D3 and OM2-D3, for which the systematic deviation is less pronounced. In addition, we find that HF-3c systematically overestimates binding energies in both gas and solution phases. As most approximate QM methods are parametrized and evaluated using data measured or calculated in the gas phase, the dataset represents an important first step toward calibrating QM based methods for application in the condensed phase where polarization and exchange repulsion need to be treated in a balanced fashion.

Coupled radial Schrödinger equations written as Dirac-type equations: application to an amplitude-phase approach

NASA Astrophysics Data System (ADS)

Thylwe, Karl-Erik; McCabe, Patrick

2012-04-01

The classical amplitude-phase method due to Milne, Wilson, Young and Wheeler in the 1930s is known to be a powerful computational tool for determining phase shifts and energy eigenvalues in cases where a sufficiently slowly varying amplitude function can be found. The key for the efficient computations is that the original single-state radial Schrödinger equation is transformed to a nonlinear equation, the Milne equation. Such an equation has solutions that may or may not oscillate, depending on boundary conditions, which then requires a robust recipe for locating the (optimal) ‘almost constant’ solutions for its use in the method. For scattering problems the solutions of the amplitude equations always approach constants as the radial distance r tends to infinity, and there is no problem locating the ‘optimal’ amplitude functions from a low-order semiclassical approximation. In the present work, the amplitude-phase approach is generalized to two coupled Schrödinger equations similar to an earlier generalization to radial Dirac equations. The original scalar amplitude then becomes a vector quantity, and the original Milne equation is generalized accordingly. Numerical applications to resonant electron-atom scattering are illustrated.

Spatially resolved micro-Raman observation on the phase separation of effloresced sea salt droplets.

PubMed

Xiao, Han-Shuang; Dong, Jin-Ling; Wang, Liang-Yu; Zhao, Li-Jun; Wang, Feng; Zhang, Yun-Hong

2008-12-01

We report on the investigation of the phase separation of individual seawater droplets in the efflorescence processes with the spatially resolved Raman system. Upon decreasing the relative humidity (RH), CaSO4.0.5H2O separated out foremost fromthe droplet atan unexpectedly high RH of approcimately 90%. Occasionally, CaSO4.2H2O substituted for CaSO4.O.5H2O crystallizing first at approximately 78% RH. Relatively large NaCI solids followed to crystallize at approximately 55% RH and led to the great loss of the solution. Then, the KMgCl3.6H2O crystallites separated out from the residual solutions, adjacentto NaCl at approximately 44% RH. Moreover, a shell structure of dried sea salt particle was found to form at low RHs, with the NaCl crystals in the core and minor supersaturated solutions covered with MgSO4 gel coating on the surface. Ultimately, the shielded solution partly effloresced into MgSO4 hydrates at very dry state (<5% RH).

Charge pattern matching as a ‘fuzzy’ mode of molecular recognition for the functional phase separations of intrinsically disordered proteins

NASA Astrophysics Data System (ADS)

Lin, Yi-Hsuan; Brady, Jacob P.; Forman-Kay, Julie D.; Chan, Hue Sun

2017-11-01

Biologically functional liquid-liquid phase separation of intrinsically disordered proteins (IDPs) is driven by interactions encoded by their amino acid sequences. Little is currently known about the molecular recognition mechanisms for distributing different IDP sequences into various cellular membraneless compartments. Pertinent physics was addressed recently by applying random-phase-approximation (RPA) polymer theory to electrostatics, which is a major energetic component governing IDP phase properties. RPA accounts for charge patterns and thus has advantages over Flory-Huggins (FH) and Overbeek-Voorn mean-field theories. To make progress toward deciphering the phase behaviors of multiple IDP sequences, the RPA formulation for one IDP species plus solvent is hereby extended to treat polyampholyte solutions containing two IDP species plus solvent. The new formulation generally allows for binary coexistence of two phases, each containing a different set of volume fractions ({φ }1,{φ }2) for the two different IDP sequences. The asymmetry between the two predicted coexisting phases with regard to their {φ }1/{φ }2 ratios for the two sequences increases with increasing mismatch between their charge patterns. This finding points to a multivalent, stochastic, ‘fuzzy’ mode of molecular recognition that helps populate various IDP sequences differentially into separate phase compartments. An intuitive illustration of this trend is provided by FH models, whereby a hypothetical case of ternary coexistence is also explored. Augmentations of the present RPA theory with a relative permittivity {ɛ }{{r}}(φ ) that depends on IDP volume fraction φ ={φ }1+{φ }2 lead to higher propensities to phase separate, in line with the case with one IDP species we studied previously. Notably, the cooperative, phase-separation-enhancing effects predicted by the prescriptions for {ɛ }{{r}}(φ ) we deem physically plausible are much more prominent than that entailed by common effective medium approximations based on Maxwell Garnett and Bruggeman mixing formulas. Ramifications of our findings on further theoretical development for IDP phase separation are discussed.

Effects of various assumptions on the calculated liquid fraction in isentropic saturated equilibrium expansions

NASA Technical Reports Server (NTRS)

Bursik, J. W.; Hall, R. M.

1980-01-01

The saturated equilibrium expansion approximation for two phase flow often involves ideal-gas and latent-heat assumptions to simplify the solution procedure. This approach is well documented by Wegener and Mack and works best at low pressures where deviations from ideal-gas behavior are small. A thermodynamic expression for liquid mass fraction that is decoupled from the equations of fluid mechanics is used to compare the effects of the various assumptions on nitrogen-gas saturated equilibrium expansion flow starting at 8.81 atm, 2.99 atm, and 0.45 atm, which are conditions representative of transonic cryogenic wind tunnels. For the highest pressure case, the entire set of ideal-gas and latent-heat assumptions are shown to be in error by 62 percent for the values of heat capacity and latent heat. An approximation of the exact, real-gas expression is also developed using a constant, two phase isentropic expansion coefficient which results in an error of only 2 percent for the high pressure case.

Volterra integral equation-factorisation method and nucleus-nucleus elastic scattering

NASA Astrophysics Data System (ADS)

Laha, U.; Majumder, M.; Bhoi, J.

2018-04-01

An approximate solution for the nuclear Hulthén plus atomic Hulthén potentials is constructed by solving the associated Volterra integral equation by series substitution method. Within the framework of supersymmetry-inspired factorisation method, this solution is exploited to construct higher partial wave interactions. The merit of our approach is examined by computing elastic scattering phases of the α {-}α system by the judicious use of phase function method. Reasonable agreements in phase shifts are obtained with standard data.

Planetary spectra for anisotropic scattering

NASA Technical Reports Server (NTRS)

Chamberlain, J. W.

1976-01-01

Some effects on planetary spectra that would be produced by departures from isotropic scattering are examined. The phase function is the simplest departure to handle analytically and the only phase function, other than the isotropic one, that can be incorporated into a Chandrasekhar first approximation. This approach has the advantage of illustrating effects resulting from anisotropies while retaining the simplicity that yields analytic solutions. The curve of growth is the sine qua non of planetary spectroscopy. The discussion emphasizes the difficulties and importance of ascertaining curves of growth as functions of observing geometry. A plea is made to observers to analyze their empirical curves of growth, whenever it seems feasible, in terms of coefficients of which are the leading terms in radiative-transfer analysis. An algebraic solution to the two sets of anisotropic H functions is developed which gives emergent intensities accurate to 0.3%.

Interaction between blood and solid particles propagating through a capillary with slip effects.

PubMed

Zeeshan, A; Fatima, A; Khalid, F; Bhatti, M M

2018-04-18

This article describes the interaction between solid particles and blood propagating through a capillary. A slip condition is considered on the walls of the capillary. The rheological features of the blood are discussed by considering as a two-phase Newtonian fluid model, i.e., the suspension of cells in plasma. A perturbation method is successfully applied to obtain the series solution of the governing coupled differential equations. The series solution for both fluid and particle phase are presented up to second order approximation. The expressions for the velocity and pressure distributions under slip effects are determined within a tube. Furthermore, the current results are beneficial to understand the rheological features of blood which will be helpful to interpret and analyze more complex blood flow models. Copyright © 2018 Elsevier Inc. All rights reserved.

Early-time solution of the horizontal unconfined aquifer in the build-up phase

NASA Astrophysics Data System (ADS)

Gravanis, Elias; Akylas, Evangelos

2017-04-01

The Boussinesq equation is a dynamical equation for the free surface of saturated subsurface flows over an impervious bed. Boussinesq equation is non-linear. The non-linearity comes from the reduction of the dimensionality of the problem: The flow is assumed to be vertically homogeneous, therefore the flow rate through a cross section of the flow is proportional to the free surface height times the hydraulic gradient, which is assumed to be equal to the slope of the free surface (Dupuit approximation). In general, 'vertically' means normally on the bed; combining the Dupuit approximation with the continuity equation leads to the Boussinesq equation. There are very few transient exact solutions. Self- similar solutions have been constructed in the past by various authors. A power series type of solution was derived for a self-similar Boussinesq equation by Barenblatt in 1990. That type of solution has generated a certain amount of literature. For the unconfined flow case for zero recharge rate Boussinesq derived for the horizontal aquifer an exact solution assuming separation of variables. This is actually an exact asymptotic solution of the horizontal aquifer recession phase for late times. The kinematic wave is an interesting solution obtained by dropping the non-linear term in the Boussinesq equation. Although it is an approximate solution, and holds well only for small values of the Henderson and Wooding λ parameter (that is, for steep slopes, high conductivity or small recharge rate), it becomes less and less approximate for smaller values of the parameter, that is, it is asymptotically exact with respect to that parameter. In the present work we consider the case of the unconfined subsurface flow over horizontal bed in the build-up phase under constant recharge rate. This is a case with an infinite Henderson and Wooding parameter, that is, it is the limiting case where the non-linear term is present in the Boussinesq while the linear spatial derivative term goes away. Nonetheless, no analogue of the kinematic wave or the Boussinesq separable solution exists in this case. The late time state of the build-up phase under constant recharge rate is very simply the steady state solution. Our aim is to construct the early time asymptotic solution of this problem. The solution is expressed as a power series of a suitable similarity variable, which is constructed so that to satisfy the boundary conditions at both ends of the aquifer, that is, it is a polynomial approximation of the exact solution. The series turn out to be asymptotic and it is regularized by re-summation techniques which are used to define divergent series. The outflow rate in this regime is linear in time, and the (dimensionless) coefficient is calculated to eight significant figures. The local error of the series is quantified by its deviation from satisfying the self-similar Boussinesq equation at every point. The local error turns out to be everywhere positive, hence, so is the integrated error, which in turn quantifies the degree of convergence of the series to the exact solution.

An effective solution to the nonlinear, nonstationary Navier-Stokes equations for two dimensions

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.

1975-01-01

A sequence of approximate solutions for the nonlinear, nonstationary Navier-Stokes equations for a two-dimensional domain, from which explicit error estimates and rates of convergence are obtained, is described. This sequence of approximate solutions is based primarily on the Newton-Kantorovich method.

Study of the hard-disk system at high densities: the fluid-hexatic phase transition.

PubMed

Mier-Y-Terán, Luis; Machorro-Martínez, Brian Ignacio; Chapela, Gustavo A; Del Río, Fernando

2018-06-21

Integral equations of uniform fluids have been considered unable to predict any characteristic feature of the fluid-solid phase transition, including the shoulder that arises in the second peak of the fluid-phase radial distribution function, RDF, of hard-core systems obtained by computer simulations, at fluid densities very close to the structural two-step phase transition. This reasoning is based on the results of traditional integral approximations, like Percus-Yevick, PY, which does not show such a shoulder in hard-core systems, neither in two nor three dimensions. In this work, we present results of three Ansätze, based on the PY theory, that were proposed to remedy the lack of PY analytical solutions in two dimensions. This comparative study shows that one of those Ansätze does develop a shoulder in the second peak of the RDF at densities very close to the phase transition, qualitatively describing this feature. Since the shoulder grows into a peak at still higher densities, this integral equation approach predicts the appearance of an orientational order characteristic of the hexatic phase in a continuous fluid-hexatic phase transition.

A Riemann solver for single-phase and two-phase shallow flow models based on relaxation. Relations with Roe and VFRoe solvers

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

Pelanti, Marica, E-mail: Marica.Pelanti@ens.f; Bouchut, Francois, E-mail: francois.bouchut@univ-mlv.f; Mangeney, Anne, E-mail: mangeney@ipgp.jussieu.f

2011-02-01

We present a Riemann solver derived by a relaxation technique for classical single-phase shallow flow equations and for a two-phase shallow flow model describing a mixture of solid granular material and fluid. Our primary interest is the numerical approximation of this two-phase solid/fluid model, whose complexity poses numerical difficulties that cannot be efficiently addressed by existing solvers. In particular, we are concerned with ensuring a robust treatment of dry bed states. The relaxation system used by the proposed solver is formulated by introducing auxiliary variables that replace the momenta in the spatial gradients of the original model systems. The resultingmore » relaxation solver is related to Roe solver in that its Riemann solution for the flow height and relaxation variables is formally computed as Roe's Riemann solution. The relaxation solver has the advantage of a certain degree of freedom in the specification of the wave structure through the choice of the relaxation parameters. This flexibility can be exploited to handle robustly vacuum states, which is a well known difficulty of standard Roe's method, while maintaining Roe's low diffusivity. For the single-phase model positivity of flow height is rigorously preserved. For the two-phase model positivity of volume fractions in general is not ensured, and a suitable restriction on the CFL number might be needed. Nonetheless, numerical experiments suggest that the proposed two-phase flow solver efficiently models wet/dry fronts and vacuum formation for a large range of flow conditions. As a corollary of our study, we show that for single-phase shallow flow equations the relaxation solver is formally equivalent to the VFRoe solver with conservative variables of Gallouet and Masella [T. Gallouet, J.-M. Masella, Un schema de Godunov approche C.R. Acad. Sci. Paris, Serie I, 323 (1996) 77-84]. The relaxation interpretation allows establishing positivity conditions for this VFRoe method.« less

The Stefan problem of solidification of ternary systems in the presence of moving phase transition regions

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

Alexandrov, D. V., E-mail: Dmitri.Alexandrov@usu.ru; Ivanov, A. A.

2009-05-15

The process of solidification of ternary systems in the presence of moving phase transition regions has been investigated theoretically in terms of the nonlinear equation of the liquidus surface. A mathematical model is developed and an approximate analytical solution to the Stefan problem is constructed for a linear temperature profile in two-phase zones. The temperature and impurity concentration distributions are determined, the solid-phase fractions in the phase transition regions are obtained, and the laws of motion of their boundaries are established. It is demonstrated that all boundaries move in accordance with the laws of direct proportionality to the square rootmore » of time, which is a general property of self-similar processes. It is substantiated that the concentration of an impurity of the substance undergoing a phase transition only in the cotectic zone increases in this zone and decreases in the main two-phase zone in which the other component of the substance undergoes a phase transition. In the process, the concentration reaches a maximum at the interface between the main two-phase zone and the cotectic two-phase zone. The revealed laws of motion of the outer boundaries of the entire phase transition region do not depend on the amount of the components under consideration and hold true for crystallization of a multicomponent system.« less

COMMERCIALLY PURE TITANIUM-ARSENIC ALLOYS. CONSTITUTION AND ROOM- TEMPERATURE TENSILE PROPERTIES

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

Haynes, R.

1960-02-01

Titanium--arsenic alloys undergo a peritectoid reaction at approximately 900 deg C, in which beta solid solution reacts with a compound, shown to be Ti/sub 4/As, to form alpha phase containing approximately 0.05 wt.% (0.03 at.%) arsenic. Solubility of arsenic in beta phase increases slowly with temperature, reaching a maximum of approximately 1.6 wt.% (1 at.%) at the eutectic temperature, 1351 plus or minus 15 deg C. The eutectic composition is approximately 17.5 wt.% (12 at.%) arsenic. Up to 1 wt.% arsenic exerts only a slight strengthening effect on commercially pure titanium, accompanied by a small loss in ductility. Solution-treatment atmore » temperatures in the beta field increases the strength above the level obtained by annealing in the ( alpha + Ti/ sub 4/As) field and this strengthening can be further enhanced by ageing at 550 deg C. Optimum properties obtainable are similar to those of low-strength titunium alloys. (auth)« less

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1982-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

Analytical approximations for effective relative permeability in the capillary limit

NASA Astrophysics Data System (ADS)

Rabinovich, Avinoam; Li, Boxiao; Durlofsky, Louis J.

2016-10-01

We present an analytical method for calculating two-phase effective relative permeability, krjeff, where j designates phase (here CO2 and water), under steady state and capillary-limit assumptions. These effective relative permeabilities may be applied in experimental settings and for upscaling in the context of numerical flow simulations, e.g., for CO2 storage. An exact solution for effective absolute permeability, keff, in two-dimensional log-normally distributed isotropic permeability (k) fields is the geometric mean. We show that this does not hold for krjeff since log normality is not maintained in the capillary-limit phase permeability field (Kj=k·krj) when capillary pressure, and thus the saturation field, is varied. Nevertheless, the geometric mean is still shown to be suitable for approximating krjeff when the variance of ln⁡k is low. For high-variance cases, we apply a correction to the geometric average gas effective relative permeability using a Winsorized mean, which neglects large and small Kj values symmetrically. The analytical method is extended to anisotropically correlated log-normal permeability fields using power law averaging. In these cases, the Winsorized mean treatment is applied to the gas curves for cases described by negative power law exponents (flow across incomplete layers). The accuracy of our analytical expressions for krjeff is demonstrated through extensive numerical tests, using low-variance and high-variance permeability realizations with a range of correlation structures. We also present integral expressions for geometric-mean and power law average krjeff for the systems considered, which enable derivation of closed-form series solutions for krjeff without generating permeability realizations.

Effects of Solute Concentrations on Kinetic Pathways in Ni-Al-Cr Alloys

NASA Technical Reports Server (NTRS)

Booth-Morrison, Christopher; Weninger, Jessica; Sudbrack, Chantal K.; Mao, Zugang; Seidman, David N.; Noebe, Ronald D.

2008-01-01

The kinetic pathways resulting from the formation of coherent gamma'-precipitates from the gamma-matrix are studied for two Ni-Al-Cr alloys with similar gamma'-precipitate volume fractions at 873 K. The details of the phase decompositions of Ni-7.5Al-8.5Cr at.% and Ni-5.2Al-14.2Cr at.% for aging times from 1/6 to 1024 h are investigated by atom-probe tomography, and are found to differ significantly from a mean-field description of coarsening. The morphologies of the gamma'-precipitates of the alloys are similar, though the degrees of gamma'-precipitate coagulation and coalescence differ. Quantification within the framework of classical nucleation theory reveals that differences in the chemical driving forces for phase decomposition result in differences in the nucleation behavior of the two alloys. The temporal evolution of the gamma'-precipitate average radii and the gamma-matrix supersaturations follow the predictions of classical coarsening models. The compositional trajectories of the gamma-matrix phases of the alloys are found to follow approximately the equilibrium tie-lines, while the trajectories of the gamma'-precipitates do not, resulting in significant differences in the partitioning ratios of the solute elements.

Closure to new results for an approximate method for calculating two-dimensional furrow infiltration

USDA-ARS?s Scientific Manuscript database

In a discussion paper, Ebrahimian and Noury (2015) raised several concerns about an approximate solution to the two-dimensional Richards equation presented by Bautista et al (2014). The solution is based on a procedure originally proposed by Warrick et al. (2007). Such a solution is of practical i...

Three FORTRAN programs for finite-difference solutions to binary diffusion in one and two phases with composition-and time-dependent diffusion coefficients

USGS Publications Warehouse

Sanford, R.F.

1982-01-01

Geological examples of binary diffusion are numerous. They are potential indicators of the duration and rates of geological processes. Analytical solutions to the diffusion equations generally do not allow for variable diffusion coefficients, changing boundary conditions, and impingement of diffusion fields. The three programs presented here are based on Crank-Nicholson finite-difference approximations, which can take into account these complicating factors. Program 1 describes the diffusion of a component into an initially homogeneous phase that has a constant surface composition. Specifically it is written for Fe-Mg exchange in olivine at oxygen fugacities appropriate for the lunar crust, but other components, phases, or fugacities may be substituted by changing the values of the diffusion coefficient. Program 2 simulates the growth of exsolution lamellae. Program 3 describes the growth of reaction rims. These two programs are written for pseudobinary Ca-(Mg, Fe) exchange in pyroxenes. In all three programs, the diffusion coefficients and boundary conditions can be varied systematically with time. To enable users to employ widely different numerical values for diffusion coefficients and diffusion distance, the grid spacing in the space dimension and the increment by which the grid spacing in the time dimension is increased at each time step are input constants that can be varied each time the programs are run to yield a solution of the desired accuracy. ?? 1982.

Charge-patterning phase transition on a surface lattice of titratable sites adjacent to an electrolyte solution

NASA Astrophysics Data System (ADS)

Shore, Joel; Thurston, George

We discuss a model for a charge-patterning phase transition on a two-dimensional square lattice of titratable sites, here regarded as protonation sites, placed on a square lattice in a dielectric medium just below the planar interface between this medium and an aqueous salt solution. Within Debye-Huckel theory, the analytical form of the electrostatic repulsion between protonated sites exhibits an approximate inverse cubic power-law decrease beyond short distances. The problem can thus be mapped onto the two-dimensional antiferromagnetic Ising model with this longer-range interaction, which we study with Monte Carlo simulations. As we increase pH, the occupation probability of a site decreases from 1 at low pH to 0 at high pH. For sufficiently-strong interaction strengths, a phase transition occurs as the occupation probability of 1/2 is approached: the charges arrange themselves into a checkerboard pattern. This ordered phase persists over a range of pH until a transition occurs back to a disordered state. This state is the analogue of the Neel state in the antiferromagnetic Ising spin model. More complicated ordered phases are expected for sufficiently strong interactions (with occupation probabilities of 1/4 and 3/4) and if the lattice is triangular rather than square. This work was supported by NIH EY018249 (GMT).

Analytic Description of Critical Point Nuclei in a Spherical-Axially Deformed Shape Phase Transition

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

Iachello, F.

2001-07-30

An approximate solution at the critical point of the spherical to axially deformed shape phase transition in nuclei is presented. The eigenvalues of the Hamiltonian are expressed in terms of zeros of Bessel functions of irrational order.

Benchmarks for single-phase flow in fractured porous media

NASA Astrophysics Data System (ADS)

Flemisch, Bernd; Berre, Inga; Boon, Wietse; Fumagalli, Alessio; Schwenck, Nicolas; Scotti, Anna; Stefansson, Ivar; Tatomir, Alexandru

2018-01-01

This paper presents several test cases intended to be benchmarks for numerical schemes for single-phase fluid flow in fractured porous media. A number of solution strategies are compared, including a vertex and two cell-centred finite volume methods, a non-conforming embedded discrete fracture model, a primal and a dual extended finite element formulation, and a mortar discrete fracture model. The proposed benchmarks test the schemes by increasing the difficulties in terms of network geometry, e.g. intersecting fractures, and physical parameters, e.g. low and high fracture-matrix permeability ratio as well as heterogeneous fracture permeabilities. For each problem, the results presented are the number of unknowns, the approximation errors in the porous matrix and in the fractures with respect to a reference solution, and the sparsity and condition number of the discretized linear system. All data and meshes used in this study are publicly available for further comparisons.

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of the s=3/2 Ising model from renormalization-group theory.

PubMed

Yunus, Çağın; Renklioğlu, Başak; Keskin, Mustafa; Berker, A Nihat

2016-06-01

The spin-3/2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d=3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d=3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589

ADIABATIC DISPERSED TWO-PHASE FLOW: FURTHER RESULTS ON THE INFLUENCE OF PHYSICAL PROPERTIES ON PRESSURE DROP AND FILM THICKNESS. Topical Report No. 6

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

Casagrande, I.; Cravarolo, L.; Hassid, A.

1963-05-01

A discussion is given of the experimental data obtained at CISE on two- phase adiabatic flow under the following conditions: vertical upward (dispersed regime) flow; circular conduit (15 to 25 mm diameter); gaseous phase argon or nitrogen; liquid phase water or ethyl alcohol-water solution (,90% by wt. of alcohol); gas fiow rate of 15 to 82 g/ cm/sup 2/; liquid flow rate of 20 to 208 g/ cm/sup 2/ sec; temperature of 18 to 20 deg C; pressure of up to approximates 22 kg/cm/sup 2/. The measured quantities are pressure drop and liquid film thickness on the wall of themore » conduit. The pressure loss and film flow rate are evaluated. The experimental data are discussed and the influence of surface tension and gas and liquid viscosity investigated. A simple relationship for the pressure loss over a wide range of experimental conditions in adiabatic dispersed regime is given. (auth)« less

Phase-space finite elements in a least-squares solution of the transport equation

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

Drumm, C.; Fan, W.; Pautz, S.

2013-07-01

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less

The application of rational approximation in the calculation of a temperature field with a non-linear surface heat-transfer coefficient during quenching for 42CrMo steel cylinder

NASA Astrophysics Data System (ADS)

Cheng, Heming; Huang, Xieqing; Fan, Jiang; Wang, Honggang

1999-10-01

The calculation of a temperature field has a great influence upon the analysis of thermal stresses and stains during quenching. In this paper, a 42CrMo steel cylinder was used an example for investigation. From the TTT diagram of the 42CrMo steel, the CCT diagram was simulated by mathematical transformation, and the volume fraction of phase constituents was calculated. The thermal physical properties were treated as functions of temperature and the volume fraction of phase constituents. The rational approximation was applied to the finite element method. The temperature field with phase transformation and non-linear surface heat-transfer coefficients was calculated using this technique, which can effectively avoid oscillationin the numerical solution for a small time step. The experimental results of the temperature field calculation coincide with the numerical solutions.

Superalloy for high-temperature hydrogen environmental applications

NASA Technical Reports Server (NTRS)

McKannan, Eugene C. (Inventor); McPherson, William B. (Inventor); Ahmed, Shaffiq (Inventor); Chandler, Shirley S. (Inventor)

1991-01-01

A nickel-based superalloy is provided which is resistant to deterioration in hydrogen at high operating temperatures and pressures, and which thus can be used in hydrogen-fueled spacecraft such as the Space Shuttle. The superalloy is characterized by a two-phase microstructure and consists of a gamma-prime precipitated phase in a gamma matrix. The gamma matrix phase is a primary solid solution and the gamma precipitated phase will be an intermetallic compound of the type A.sub.3 B, such as nickel aluminide or titanide. Both phases are coherent, ordered, and compatible, and thus will retain most of their strength at elevated temperatures. The alloy consists essentially of (by weight): Ni 50-60%, Cr 10-20%, Al 2-6%, Co 2-5%, Ti 3-8%, W 5-12%, Mo 5-10%, Nb 1-3%, wherein the ratio W/MO is approximately equal to 1, and Ti/Al ranges from about 1 to about 2.

Anion-exchange behavior of several alkylsilica reversed-phase columns.

PubMed

Marchand, D H; Snyder, L R

2008-10-31

Some alkylsilica columns carry a positive charge at low pH, as determined by anion-exchange with nitrate ion. In the present study, the relative positive charge for 14 alkylsilica columns was measured for a mobile-phase pH 3.0. All but 3 of these columns were found to carry a significant positive charge under these conditions. The relative positive charge on these columns was found to correlate approximately with two other column characteristics: relative cation-exchange behavior as measured by the hydrophobic-subtraction model (values of C-2.8), and slow equilibration of the column to changes in the mobile-phase-as evidenced by a slow change in the retention of anionic and cationic solutes with time. The origin of this positive charge may arise from the bonding process, with incorporation of some cationic entity into the stationary phase.

Electronic structure calculation by nonlinear optimization: Application to metals

NASA Astrophysics Data System (ADS)

Benedek, R.; Min, B. I.; Woodward, C.; Garner, J.

1988-04-01

There is considerable interest in the development of novel algorithms for the calculation of electronic structure (e.g., at the level of the local-density approximation of density-functional theory). In this paper we consider a first-order equation-of-motion method. Two methods of solution are described, one proposed by Williams and Soler, and the other base on a Born-Dyson series expansion. The extension of the approach to metallic systems is outlined and preliminary numerical calculations for Zintl-phase NaTl are presented.

Determinants of relaxation rate in rabbit skinned skeletal muscle fibres

PubMed Central

Luo, Ye; Davis, Jonathan P; Smillie, Lawrence B; Rall, Jack A

2002-01-01

The influence of Ca2+-activated force, the rate of dissociation of Ca2+ from troponin C (TnC) and decreased crossbridge detachment rate on the time course of relaxation induced by flash photolysis of diazo-2 in rabbit skinned psoas fibres was investigated at 15 °C. The rate of relaxation increased as the diazo-2 chelating capacity (i.e. free [diazo-2]/free [Ca2+]) increased. At a constant diazo-2 chelating capacity, the rate of relaxation was independent of the pre-photolysis Ca2+-activated force in the range 0.3-0.8 of maximum isometric force. A TnC mutant that exhibited increased Ca2+ sensitivity caused by a decreased Ca2+ dissociation rate in solution (M82Q TnC) also increased the Ca2+ sensitivity of steady-state force and decreased the rate of relaxation in fibres by approximately twofold. In contrast, a TnC mutant with decreased Ca2+ sensitivity caused by an increased Ca2+ dissociation rate in solution (NHdel TnC) decreased the Ca2+ sensitivity of steady-state force but did not accelerate relaxation. Decreasing the rate of crossbridge kinetics by reducing intracellular inorganic phosphate concentration ([Pi]) slowed relaxation by approximately twofold and led to two phases of relaxation, a slow linear phase followed by a fast exponential phase. In fibres, M82Q TnC further slowed relaxation in low [Pi] conditions by approximately twofold, whereas NHdel TnC had no significant effect on relaxation. These results are consistent with the interpretation that the Ca2+-dissociation rate and crossbridge detachment rate are similar in fast-twitch skeletal muscle, such that decreasing either rate slows relaxation, but accelerating Ca2+ dissociation has little effect on relaxation. PMID:12482894

Mixture-mixture design for the fingerprint optimization of chromatographic mobile phases and extraction solutions for Camellia sinensis.

PubMed

Borges, Cleber N; Bruns, Roy E; Almeida, Aline A; Scarminio, Ieda S

2007-07-09

A composite simplex centroid-simplex centroid mixture design is proposed for simultaneously optimizing two mixture systems. The complementary model is formed by multiplying special cubic models for the two systems. The design was applied to the simultaneous optimization of both mobile phase chromatographic mixtures and extraction mixtures for the Camellia sinensis Chinese tea plant. The extraction mixtures investigated contained varying proportions of ethyl acetate, ethanol and dichloromethane while the mobile phase was made up of varying proportions of methanol, acetonitrile and a methanol-acetonitrile-water (MAW) 15%:15%:70% mixture. The experiments were block randomized corresponding to a split-plot error structure to minimize laboratory work and reduce environmental impact. Coefficients of an initial saturated model were obtained using Scheffe-type equations. A cumulative probability graph was used to determine an approximate reduced model. The split-plot error structure was then introduced into the reduced model by applying generalized least square equations with variance components calculated using the restricted maximum likelihood approach. A model was developed to calculate the number of peaks observed with the chromatographic detector at 210 nm. A 20-term model contained essentially all the statistical information of the initial model and had a root mean square calibration error of 1.38. The model was used to predict the number of peaks eluted in chromatograms obtained from extraction solutions that correspond to axial points of the simplex centroid design. The significant model coefficients are interpreted in terms of interacting linear, quadratic and cubic effects of the mobile phase and extraction solution components.

Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problems

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

Ng, C.; Bhattacharjee, A.; Skiff, F.

2006-05-15

Landau damping and Bernstein-Greene-Kruskal (BGK) modes are among the most fundamental concepts in plasma physics. While the former describes the surprising damping of linear plasma waves in a collisionless plasma, the latter describes exact undamped nonlinear solutions of the Vlasov equation. There does exist a relationship between the two: Landau damping can be described as the phase mixing of undamped eigenmodes, the so-called Case-Van Kampen modes, which can be viewed as BGK modes in the linear limit. While these concepts have been around for a long time, unexpected new results are still being discovered. For Landau damping, we show thatmore » the textbook picture of phase mixing is altered profoundly in the presence of collision. In particular, the continuous spectrum of Case-Van Kampen modes is eliminated and replaced by a discrete spectrum, even in the limit of zero collision. Furthermore, we show that these discrete eigenmodes form a complete set of solutions. Landau-damped solutions are then recovered as true eigenmodes (which they are not in the collisionless theory). For BGK modes, our interest is motivated by recent discoveries of electrostatic solitary waves in magnetospheric plasmas. While one-dimensional BGK theory is quite mature, there appear to be no exact three-dimensional solutions in the literature (except for the limiting case when the magnetic field is sufficiently strong so that one can apply the guiding-center approximation). We show, in fact, that two- and three-dimensional solutions that depend only on energy do not exist. However, if solutions depend on both energy and angular momentum, we can construct exact three-dimensional solutions for the unmagnetized case, and two-dimensional solutions for the case with a finite magnetic field. The latter are shown to be exact, fully electromagnetic solutions of the steady-state Vlasov-Poisson-Ampere system.« less

The design of an Fe-12Mn-O.2Ti alloy steel for low temperature use

NASA Technical Reports Server (NTRS)

Hwang, S. K.; Morris, J. W., Jr.

1977-01-01

An investigation was made to improve the low temperature mechanical properties of Fe-8 approximately 12% Mn-O 2Ti alloy steels. A two-phase(alpha + gamma) tempering in combination with cold working or hot working was identified as an effective treatment. A potential application as a Ni-free cryogenic steel was shown for this alloy. It was also shown that an Fe-8Mn steel could be grain-refined by a purely thermal treatment because of its dislocated martensitic structure and absence of epsilon phase. A significant reduction of the ductile-brittle transition temperature was obtained in this alloy. The nature and origin of brittle fracture in Fe-Mn alloys were also investigated. Two embrittling regions were found in a cooling curve of an Fe-12Mn-O 2Ti steel which was shown to be responsible for intergranular fracture. Auger electron spectroscopy identified no segregation during solution-annealing treatment. Avoiding the embrittling zones by controlled cooling led to a high cryogenic toughness in a solution-annealed condition.

Polarimetry With Phased Array Antennas: Theoretical Framework and Definitions

NASA Astrophysics Data System (ADS)

Warnick, Karl F.; Ivashina, Marianna V.; Wijnholds, Stefan J.; Maaskant, Rob

2012-01-01

For phased array receivers, the accuracy with which the polarization state of a received signal can be measured depends on the antenna configuration, array calibration process, and beamforming algorithms. A signal and noise model for a dual-polarized array is developed and related to standard polarimetric antenna figures of merit, and the ideal polarimetrically calibrated, maximum-sensitivity beamforming solution for a dual-polarized phased array feed is derived. A practical polarimetric beamformer solution that does not require exact knowledge of the array polarimetric response is shown to be equivalent to the optimal solution in the sense that when the practical beamformers are calibrated, the optimal solution is obtained. To provide a rough initial polarimetric calibration for the practical beamformer solution, an approximate single-source polarimetric calibration method is developed. The modeled instrumental polarization error for a dipole phased array feed with the practical beamformer solution and single-source polarimetric calibration was -10 dB or lower over the array field of view for elements with alignments perturbed by random rotations with 5 degree standard deviation.

Nested sparse grid collocation method with delay and transformation for subsurface flow and transport problems

NASA Astrophysics Data System (ADS)

Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi

2017-06-01

In numerical modeling of subsurface flow and transport problems, formation properties may not be deterministically characterized, which leads to uncertainty in simulation results. In this study, we propose a sparse grid collocation method, which adopts nested quadrature rules with delay and transformation to quantify the uncertainty of model solutions. We show that the nested Kronrod-Patterson-Hermite quadrature is more efficient than the unnested Gauss-Hermite quadrature. We compare the convergence rates of various quadrature rules including the domain truncation and domain mapping approaches. To further improve accuracy and efficiency, we present a delayed process in selecting quadrature nodes and a transformed process for approximating unsmooth or discontinuous solutions. The proposed method is tested by an analytical function and in one-dimensional single-phase and two-phase flow problems with different spatial variances and correlation lengths. An additional example is given to demonstrate its applicability to three-dimensional black-oil models. It is found from these examples that the proposed method provides a promising approach for obtaining satisfactory estimation of the solution statistics and is much more efficient than the Monte-Carlo simulations.

Renewable energy in electric utility capacity planning: a decomposition approach with application to a Mexican utility

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

Staschus, K.

1985-01-01

In this dissertation, efficient algorithms for electric-utility capacity expansion planning with renewable energy are developed. The algorithms include a deterministic phase that quickly finds a near-optimal expansion plan using derating and a linearized approximation to the time-dependent availability of nondispatchable energy sources. A probabilistic second phase needs comparatively few computer-time consuming probabilistic simulation iterations to modify this solution towards the optimal expansion plan. For the deterministic first phase, two algorithms, based on a Lagrangian Dual decomposition and a Generalized Benders Decomposition, are developed. The probabilistic second phase uses a Generalized Benders Decomposition approach. Extensive computational tests of the algorithms aremore » reported. Among the deterministic algorithms, the one based on Lagrangian Duality proves fastest. The two-phase approach is shown to save up to 80% in computing time as compared to a purely probabilistic algorithm. The algorithms are applied to determine the optimal expansion plan for the Tijuana-Mexicali subsystem of the Mexican electric utility system. A strong recommendation to push conservation programs in the desert city of Mexicali results from this implementation.« less

Strong shock implosion, approximate solution

NASA Astrophysics Data System (ADS)

Fujimoto, Y.; Mishkin, E. A.; Alejaldre, C.

1983-01-01

The self-similar, center-bound motion of a strong spherical, or cylindrical, shock wave moving through an ideal gas with a constant, γ= cp/ cv, is considered and a linearized, approximate solution is derived. An X, Y phase plane of the self-similar solution is defined and the representative curved of the system behind the shock front is replaced by a straight line connecting the mappings of the shock front with that of its tail. The reduced pressure P(ξ), density R(ξ) and velocity U1(ξ) are found in closed, quite accurate, form. Comparison with numerically obtained results, for γ= {5}/{3} and γ= {7}/{5}, is shown.

VAVUQ, Python and Matlab freeware for Verification and Validation, Uncertainty Quantification

NASA Astrophysics Data System (ADS)

Courtney, J. E.; Zamani, K.; Bombardelli, F. A.; Fleenor, W. E.

2015-12-01

A package of scripts is presented for automated Verification and Validation (V&V) and Uncertainty Quantification (UQ) for engineering codes that approximate Partial Differential Equations (PDFs). The code post-processes model results to produce V&V and UQ information. This information can be used to assess model performance. Automated information on code performance can allow for a systematic methodology to assess the quality of model approximations. The software implements common and accepted code verification schemes. The software uses the Method of Manufactured Solutions (MMS), the Method of Exact Solution (MES), Cross-Code Verification, and Richardson Extrapolation (RE) for solution (calculation) verification. It also includes common statistical measures that can be used for model skill assessment. Complete RE can be conducted for complex geometries by implementing high-order non-oscillating numerical interpolation schemes within the software. Model approximation uncertainty is quantified by calculating lower and upper bounds of numerical error from the RE results. The software is also able to calculate the Grid Convergence Index (GCI), and to handle adaptive meshes and models that implement mixed order schemes. Four examples are provided to demonstrate the use of the software for code and solution verification, model validation and uncertainty quantification. The software is used for code verification of a mixed-order compact difference heat transport solver; the solution verification of a 2D shallow-water-wave solver for tidal flow modeling in estuaries; the model validation of a two-phase flow computation in a hydraulic jump compared to experimental data; and numerical uncertainty quantification for 3D CFD modeling of the flow patterns in a Gust erosion chamber.

Solidification and microstructures of binary ice-I/hydrate eutectic aggregates

USGS Publications Warehouse

McCarthy, C.; Cooper, R.F.; Kirby, S.H.; Rieck, K.D.; Stern, L.A.

2007-01-01

The microstructures of two-phase binary aggregates of ice-I + salt-hydrate, prepared by eutectic solidification, have been characterized by cryogenic scanning electron microscopy (CSEM). The specific binary systems studied were H2O-Na2SO4, H2O-MgSO4, H2O-NaCl, and H2O-H2SO4; these were selected based on their potential application to the study of tectonics on the Jovian moon Europa. Homogeneous liquid solutions of eutectic compositions were undercooled modestly (??T - 1-5 ??C); similarly cooled crystalline seeds of the same composition were added to circumvent the thermodynamic barrier to nucleation and to control eutectic growth under (approximately) isothermal conditions. CSEM revealed classic eutectic solidification microstructures with the hydrate phase forming continuous lamellae, discontinuous lamellae, or forming the matrix around rods of ice-I, depending on the volume fractions of the phases and their entropy of dissolving and forming a homogeneous aqueous solution. We quantify aspects of the solidification behavior and microstructures for each system and, with these data articulate anticipated effects of the microstructure on the mechanical responses of the materials.

Low-density homogeneous symmetric nuclear matter: Disclosing dinucleons in coexisting phases

NASA Astrophysics Data System (ADS)

Arellano, Hugo F.; Delaroche, Jean-Paul

2015-01-01

The effect of in-medium dinucleon bound states on self-consistent single-particle fields in Brueckner, Bethe and Goldstone theory is investigated in symmetric nuclear matter at zero temperature. To this end, dinucleon bound state occurences in the 1 S 0 and 3 SD 1 channels are explicitly accounted for --within the continuous choice for the auxiliary fields-- while imposing self-consistency in Brueckner-Hartree-Fock approximation calculations. Searches are carried out at Fermi momenta in the range fm-1, using the Argonne bare nucleon-nucleon potential without resorting to the effective-mass approximation. As a result, two distinct solutions meeting the self-consistency requirement are found with overlapping domains in the interval 0.130 fm-1 0.285 fm-1, corresponding to mass densities between and g cm-3. Effective masses as high as three times the nucleon mass are found in the coexistence domain. The emergence of superfluidity in relationship with BCS pairing gap solutions is discussed.

Comparison of approximate solutions to the phonon Boltzmann transport equation with the relaxation time approximation: Spherical harmonics expansions and the discrete ordinates method

NASA Astrophysics Data System (ADS)

Christenson, J. G.; Austin, R. A.; Phillips, R. J.

2018-05-01

The phonon Boltzmann transport equation is used to analyze model problems in one and two spatial dimensions, under transient and steady-state conditions. New, explicit solutions are obtained by using the P1 and P3 approximations, based on expansions in spherical harmonics, and are compared with solutions from the discrete ordinates method. For steady-state energy transfer, it is shown that analytic expressions derived using the P1 and P3 approximations agree quantitatively with the discrete ordinates method, in some cases for large Knudsen numbers, and always for Knudsen numbers less than unity. However, for time-dependent energy transfer, the PN solutions differ qualitatively from converged solutions obtained by the discrete ordinates method. Although they correctly capture the wave-like behavior of energy transfer at short times, the P1 and P3 approximations rely on one or two wave velocities, respectively, yielding abrupt, step-changes in temperature profiles that are absent when the angular dependence of the phonon velocities is captured more completely. It is shown that, with the gray approximation, the P1 approximation is formally equivalent to the so-called "hyperbolic heat equation." Overall, these results support the use of the PN approximation to find solutions to the phonon Boltzmann transport equation for steady-state conditions. Such solutions can be useful in the design and analysis of devices that involve heat transfer at nanometer length scales, where continuum-scale approaches become inaccurate.

Overview of the relevant CFD work at Thiokol Corporation

NASA Technical Reports Server (NTRS)

Chwalowski, Pawel; Loh, Hai-Tien

1992-01-01

An in-house developed proprietary advanced computational fluid dynamics code called SHARP (Trademark) is a primary tool for many flow simulations and design analyses. The SHARP code is a time dependent, two dimensional (2-D) axisymmetric numerical solution technique for the compressible Navier-Stokes equations. The solution technique in SHARP uses a vectorizable implicit, second order accurate in time and space, finite volume scheme based on an upwind flux-difference splitting of a Roe-type approximated Riemann solver, Van Leer's flux vector splitting, and a fourth order artificial dissipation scheme with a preconditioning to accelerate the flow solution. Turbulence is simulated by an algebraic model, and ultimately the kappa-epsilon model. Some other capabilities of the code are 2-D two-phase Lagrangian particle tracking and cell blockages. Extensive development and testing has been conducted on the 3-D version of the code with flow, combustion, and turbulence interactions. The emphasis here is on the specific applications of SHARP in Solid Rocket Motor design. Information is given in viewgraph form.

Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents

DOE PAGES

Zheng, Zhong; Christov, Ivan  C.; Stone, Howard  A.

2014-05-01

We report experimental, theoretical and numerical results on the effects of horizontal heterogeneities on the propagation of viscous gravity currents. We use two geometries to highlight these effects: (a) a horizontal channel (or crack) whose gap thickness varies as a power-law function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have power-law variations. We demonstrate that two types of self-similar behaviours emerge as a result of horizontal heterogeneity: (a) a first-kind self-similar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (a point of zero permeability); (b)more » a second-kind self-similar solution is found using a phase-plane analysis for viscous gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of self-similar intermediate asymptotics, are compared with experimental results and numerical solutions of the governing partial differential equation developed under the lubrication approximation. All three results are found to be in good agreement.« less

Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle scattering in a random medium.

PubMed

Yura, H T; Thrane, L; Andersen, P E

2000-12-01

Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens-Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s > 1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens-Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.

Sparse approximation problem: how rapid simulated annealing succeeds and fails

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Kabashima, Yoshiyuki

2016-03-01

Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an overcomplete basis is termed the sparse approximation. In this paper, we apply simulated annealing, a metaheuristic algorithm for general optimization problems, to sparse approximation in the situation where the given data have a planted sparse representation and noise is present. The result in the noiseless case shows that our simulated annealing works well in a reasonable parameter region: the planted solution is found fairly rapidly. This is true even in the case where a common relaxation of the sparse approximation problem, the G-relaxation, is ineffective. On the other hand, when the dimensionality of the data is close to the number of non-zero components, another metastable state emerges, and our algorithm fails to find the planted solution. This phenomenon is associated with a first-order phase transition. In the case of very strong noise, it is no longer meaningful to search for the planted solution. In this situation, our algorithm determines a solution with close-to-minimum distortion fairly quickly.

On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice

NASA Astrophysics Data System (ADS)

Penati, T.; Sansottera, M.; Paleari, S.; Koukouloyannis, V.; Kevrekidis, P. G.

2018-05-01

We consider a one-dimensional discrete nonlinear Schrödinger (dNLS) model featuring interactions beyond nearest neighbors. We are interested in the existence (or nonexistence) of phase-shift discrete solitons, which correspond to four-site vortex solutions in the standard two-dimensional dNLS model (square lattice), of which this is a simpler variant. Due to the specific choice of lengths of the inter-site interactions, the vortex configurations considered present a degeneracy which causes the standard continuation techniques to be non-applicable. In the present one-dimensional case, the existence of a conserved quantity for the soliton profile (the so-called density current), together with a perturbative construction, leads to the nonexistence of any phase-shift discrete soliton which is at least C2 with respect to the small coupling ɛ, in the limit of vanishing ɛ. If we assume the solution to be only C0 in the same limit of ɛ, nonexistence is instead proved by studying the bifurcation equation of a Lyapunov-Schmidt reduction, expanded to suitably high orders. Specifically, we produce a nonexistence criterion whose efficiency we reveal in the cases of partial and full degeneracy of approximate solutions obtained via a leading order expansion.

Coherence solution for bidirectional reflectance distributions of surfaces with wavelength-scale statistics.

PubMed

Hoover, Brian G; Gamiz, Victor L

2006-02-01

The scalar bidirectional reflectance distribution function (BRDF) due to a perfectly conducting surface with roughness and autocorrelation width comparable with the illumination wavelength is derived from coherence theory on the assumption of a random reflective phase screen and an expansion valid for large effective roughness. A general quadratic expansion of the two-dimensional isotropic surface autocorrelation function near the origin yields representative Cauchy and Gaussian BRDF solutions and an intermediate general solution as the sum of an incoherent component and a nonspecular coherent component proportional to an integral of the plasma dispersion function in the complex plane. Plots illustrate agreement of the derived general solution with original bistatic BRDF data due to a machined aluminum surface, and comparisons are drawn with previously published data in the examination of variations with incident angle, roughness, illumination wavelength, and autocorrelation coefficients in the bistatic and monostatic geometries. The general quadratic autocorrelation expansion provides a BRDF solution that smoothly interpolates between the well-known results of the linear and parabolic approximations.

Metastability Gap in the Phase Diagram of Monoclonal IgG Antibody.

PubMed

Rowe, Jacob B; Cancel, Rachel A; Evangelous, Tyler D; Flynn, Rhiannon P; Pechenov, Sergei; Subramony, J Anand; Zhang, Jifeng; Wang, Ying

2017-10-17

Crystallization of IgG antibodies has important applications in the fields of structural biology, biotechnology, and biopharmaceutics. However, a rational approach to crystallize antibodies is still lacking. In this work, we report a method to estimate the solubility of antibodies at various temperatures. We experimentally determined the full phase diagram of an IgG antibody. Using the full diagram, we examined the metastability gaps, i.e., the distance between the crystal solubility line and the liquid-liquid coexistence curve, of IgG antibodies. By comparing our results to the partial phase diagrams of other IgGs reported in literature, we found that IgG antibodies have similar metastability gaps. Thereby, we present an equation with two phenomenological parameters to predict the approximate location of the solubility line of IgG antibodies with respect to their liquid-liquid coexistence curves. We have previously shown that the coexistence curve of an antibody solution can be readily determined by the polyethylene glycol-induced liquid-liquid phase separation method. Combining the polyethylene glycol-induced liquid-liquid phase separation measurements and the phenomenological equation in this article, we provide a general and practical means to predict the thermodynamic conditions for crystallizing IgG antibodies in the solution environments of interest. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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

Heating-frequency-dependent thermal conductivity: An analytical solution from diffusive to ballistic regime and its relevance to phonon scattering measurements

NASA Astrophysics Data System (ADS)

Yang, Fan; Dames, Chris

2015-04-01

The heating-frequency dependence of the apparent thermal conductivity in a semi-infinite body with periodic planar surface heating is explained by an analytical solution to the Boltzmann transport equation. This solution is obtained using a two-flux model and gray mean free time approximation and verified numerically with a lattice Boltzmann method and numerical results from the literature. Extending the gray solution to the nongray regime leads to an integral transform and accumulation-function representation of the phonon scattering spectrum, where the natural variable is mean free time rather than mean free path, as often used in previous work. The derivation leads to an approximate cutoff conduction similar in spirit to that of Koh and Cahill [Phys. Rev. B 76, 075207 (2007), 10.1103/PhysRevB.76.075207] except that the most appropriate criterion involves the heater frequency rather than thermal diffusion length. The nongray calculations are consistent with Koh and Cahill's experimental observation that the apparent thermal conductivity shows a stronger heater-frequency dependence in a SiGe alloy than in natural Si. Finally these results are demonstrated using a virtual experiment, which fits the phase lag between surface temperature and heat flux to obtain the apparent thermal conductivity and accumulation function.

Translation of waves along quantum vortex filaments in the low-temperature two-dimensional local induction approximation

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

Van Gorder, Robert A., E-mail: Robert.VanGorder@maths.ox.ac.uk

2015-09-15

In a recent paper, we give a study of the purely rotational motion of general stationary states in the two-dimensional local induction approximation (2D-LIA) governing superfluid turbulence in the low-temperature limit [B. Svistunov, “Superfluid turbulence in the low-temperature limit,” Phys. Rev. B 52, 3647 (1995)]. Such results demonstrated that variety of stationary configurations are possible from vortex filaments exhibiting purely rotational motion in addition to commonly discussed configurations such as helical or planar states. However, the filaments (or, more properly, waves along these filaments) can also exhibit translational motion along the axis of orientation. In contrast to the study onmore » vortex configurations for purely rotational stationary states, the present paper considers non-stationary states which exhibit a combination of rotation and translational motions. These solutions can essentially be described as waves or disturbances which ride along straight vortex filament lines. As expected from our previous work, there are a number of types of structures that can be obtained under the 2D-LIA. We focus on non-stationary states, as stationary states exhibiting translation will essentially take the form of solutions studied in [R. A. Van Gorder, “General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation,” Phys. Fluids 26, 065105 (2014)], with the difference being translation along the reference axis, so that qualitative appearance of the solution geometry will be the same (even if there are quantitative differences). We discuss a wide variety of general properties of these non-stationary solutions and derive cases in which they reduce to known stationary states. We obtain various routes to Kelvin waves along vortex filaments and demonstrate that if the phase and amplitude of a disturbance both propagate with the same wave speed, then Kelvin waves will result. We also consider the self-similar solutions to the model and demonstrate that these types of solutions can model vortex kinks that gradually smooth and radiate Kelvin waves as time increases. Such solutions qualitatively agree with what one might expect from post-reconnection events.« less

Towards a unification of the hierarchical reference theory and the self-consistent Ornstein-Zernike approximation.

PubMed

Reiner, A; Høye, J S

2005-12-01

The hierarchical reference theory and the self-consistent Ornstein-Zernike approximation are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as phase coexistence and the equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. As a first step towards this goal, we consider the problem of combining the lowest order gamma expansion result for the incorporation of a Fourier component of the interaction with the requirement of consistency between internal and free energies, leaving aside the compressibility relation. For simplicity, we restrict ourselves to a simplified lattice gas that is expected to display the same qualitative behavior as more elaborate models. It turns out that the analytically tractable mean spherical approximation is a solution to this problem, as are several of its generalizations. Analysis of the characteristic equations shows the potential for a practical scheme and yields necessary conditions that any closure to the Ornstein-Zernike relation must fulfill for the consistency problem to be well posed and to have a unique differentiable solution. These criteria are expected to remain valid for more general discrete and continuous systems, even if consistency with the compressibility route is also enforced where possible explicit solutions will require numerical evaluations.

Perovskite phase thin films and method of making

DOEpatents

Boyle, Timothy J.; Rodriguez, Mark A.

2000-01-01

The present invention comprises perovskite-phase thin films, of the general formula A.sub.x B.sub.y O.sub.3 on a substrate, wherein A is selected from beryllium, magnesium, calcium, strontium, and barium or a combination thereof; B is selected from niobium and tantalum or a combination thereof; and x and y are mole fractions between approximately 0.8 and 1.2. More particularly, A is strontium or barium or a combination thereof and B is niobium or tantalum or a combination thereof. Also provided is a method of making a perovskite-phase thin film, comprising combining at least one element-A-containing compound, wherein A is selected from beryllium, magnesium, calcium, strontium or barium, with at least one element-B-containing compound, wherein B niobium or tantalum, to form a solution; adding a solvent to said solution to form another solution; spin-coating the solution onto a substrate to form a thin film; and heating the film to form the perovskite-phase thin film.

Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

NASA Astrophysics Data System (ADS)

Huang, C.-S.; Yang, S.-Y.; Yeh, H.-D.

2015-03-01

An aquifer consisting of a skin zone and a formation zone is considered as a two-zone aquifer. Existing solutions for the problem of constant-flux pumping (CFP) in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathematical model including two steady-state flow equations with different hydraulic parameters for the skin and formation zones. A partially penetrating well may be treated as the Neumann condition with a known flux along the screened part and zero flux along the unscreened part. The aquifer domain is finite with an outer circle boundary treated as the Dirichlet condition. The steady-state drawdown solution of the model is derived by the finite Fourier cosine transform. Then, an approximate transient solution is developed by replacing the radius of the boundary in the steady-state solution with an analytical expression for a dimensionless time-dependent radius of influence. The approximate solution is capable of predicting good temporal drawdown distributions over the whole pumping period except at the early stage. A quantitative criterion for the validity of neglecting the vertical flow component due to a partially penetrating well is also provided. Conventional models considering radial flow without the vertical component for the CFP have good accuracy if satisfying the criterion.

Atomic density functional and diagram of structures in the phase field crystal model

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

Ankudinov, V. E., E-mail: vladimir@ankudinov.org; Galenko, P. K.; Kropotin, N. V.

2016-02-15

The phase field crystal model provides a continual description of the atomic density over the diffusion time of reactions. We consider a homogeneous structure (liquid) and a perfect periodic crystal, which are constructed from the one-mode approximation of the phase field crystal model. A diagram of 2D structures is constructed from the analytic solutions of the model using atomic density functionals. The diagram predicts equilibrium atomic configurations for transitions from the metastable state and includes the domains of existence of homogeneous, triangular, and striped structures corresponding to a liquid, a body-centered cubic crystal, and a longitudinal cross section of cylindricalmore » tubes. The method developed here is employed for constructing the diagram for the homogeneous liquid phase and the body-centered iron lattice. The expression for the free energy is derived analytically from density functional theory. The specific features of approximating the phase field crystal model are compared with the approximations and conclusions of the weak crystallization and 2D melting theories.« less

Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

NASA Astrophysics Data System (ADS)

Huang, C.-S.; Yang, S.-Y.; Yeh, H.-D.

2015-06-01

An aquifer consisting of a skin zone and a formation zone is considered as a two-zone aquifer. Existing solutions for the problem of constant-flux pumping in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathematical model describing steady-state radial and vertical flows in a two-zone aquifer. Hydraulic parameters in these two zones can be different but are assumed homogeneous in each zone. A partially penetrating well may be treated as the Neumann condition with a known flux along the screened part and zero flux along the unscreened part. The aquifer domain is finite with an outer circle boundary treated as the Dirichlet condition. The steady-state drawdown solution of the model is derived by the finite Fourier cosine transform. Then, an approximate transient solution is developed by replacing the radius of the aquifer domain in the steady-state solution with an analytical expression for a dimensionless time-dependent radius of influence. The approximate solution is capable of predicting good temporal drawdown distributions over the whole pumping period except at the early stage. A quantitative criterion for the validity of neglecting the vertical flow due to a partially penetrating well is also provided. Conventional models considering radial flow without the vertical component for the constant-flux pumping have good accuracy if satisfying the criterion.

An algorithm for the numerical solution of linear differential games

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

Polovinkin, E S; Ivanov, G E; Balashov, M V

2001-10-31

A numerical algorithm for the construction of stable Krasovskii bridges, Pontryagin alternating sets, and also of piecewise program strategies solving two-person linear differential (pursuit or evasion) games on a fixed time interval is developed on the basis of a general theory. The aim of the first player (the pursuer) is to hit a prescribed target (terminal) set by the phase vector of the control system at the prescribed time. The aim of the second player (the evader) is the opposite. A description of numerical algorithms used in the solution of differential games of the type under consideration is presented andmore » estimates of the errors resulting from the approximation of the game sets by polyhedra are presented.« less

Radiative transfer in falling snow: A two-stream approximation

NASA Astrophysics Data System (ADS)

Koh, Gary

1989-04-01

Light transmission measurements through falling snow have produced results unexplainable by single scattering arguments. A two-stream approximation to radiative transfer is used to derive an analytical expression that describes the effects of multiple scattering as a function of the snow optical depth and the snow asymmetry parameter. The approximate solution is simple and it may be as accurate as the exact solution for describing the transmission measurements within the limits of experimental uncertainties.

Solute segregation and deviation from bulk thermodynamics at nanoscale crystalline defects.

PubMed

Titus, Michael S; Rhein, Robert K; Wells, Peter B; Dodge, Philip C; Viswanathan, Gopal Babu; Mills, Michael J; Van der Ven, Anton; Pollock, Tresa M

2016-12-01

It has long been known that solute segregation at crystalline defects can have profound effects on material properties. Nevertheless, quantifying the extent of solute segregation at nanoscale defects has proven challenging due to experimental limitations. A combined experimental and first-principles approach has been used to study solute segregation at extended intermetallic phases ranging from 4 to 35 atomic layers in thickness. Chemical mapping by both atom probe tomography and high-resolution scanning transmission electron microscopy demonstrates a markedly different composition for the 4-atomic-layer-thick phase, where segregation has occurred, compared to the approximately 35-atomic-layer-thick bulk phase of the same crystal structure. First-principles predictions of bulk free energies in conjunction with direct atomistic simulations of the intermetallic structure and chemistry demonstrate the breakdown of bulk thermodynamics at nanometer dimensions and highlight the importance of symmetry breaking due to the proximity of interfaces in determining equilibrium properties.

Solute segregation and deviation from bulk thermodynamics at nanoscale crystalline defects

PubMed Central

Titus, Michael S.; Rhein, Robert K.; Wells, Peter B.; Dodge, Philip C.; Viswanathan, Gopal Babu; Mills, Michael J.; Van der Ven, Anton; Pollock, Tresa M.

2016-01-01

It has long been known that solute segregation at crystalline defects can have profound effects on material properties. Nevertheless, quantifying the extent of solute segregation at nanoscale defects has proven challenging due to experimental limitations. A combined experimental and first-principles approach has been used to study solute segregation at extended intermetallic phases ranging from 4 to 35 atomic layers in thickness. Chemical mapping by both atom probe tomography and high-resolution scanning transmission electron microscopy demonstrates a markedly different composition for the 4–atomic-layer–thick phase, where segregation has occurred, compared to the approximately 35–atomic-layer–thick bulk phase of the same crystal structure. First-principles predictions of bulk free energies in conjunction with direct atomistic simulations of the intermetallic structure and chemistry demonstrate the breakdown of bulk thermodynamics at nanometer dimensions and highlight the importance of symmetry breaking due to the proximity of interfaces in determining equilibrium properties. PMID:28028543

Two-phase flow research using the DC-9/KC-135 apparatus

NASA Technical Reports Server (NTRS)

McQuillen, John B.; Neumann, Eric S.; Shoemaker, J. Michael

1996-01-01

Low-gravity gas-liquid flow research can be conducted aboard the NASA Lewis Research Center DC-9 or the Johnson Space Center KC-135. Air and water solutions serve as the test liquids in cylindrical test sections with constant or variable inner diameters of approximately 2.54 cm and lengths of up to 3.0 m. Superficial velocities range from 0.1 to 1.1 m/sec for liquids and from 0.1 to 25 m/sec for air. Flow rate, differential pressure, void fraction, film thickness, wall shear stress, and acceleration data are measured and recorded at data rates of up to 1000 Hz throughout the 20-sec duration of the experiment. Flow is visualized with a high-speed video system. In addition, the apparatus has a heat-transfer capability whereby sensible heat is transferred between the test-section wall and a subcooled liquid phase so that the heat-transfer characteristics of gas-liquid two-phase flows can be determined.

Effects of Frequency Spreads on Beam Breakup Instabilities in Linear Accelerators

DTIC Science & Technology

1989-05-11

i - 1)A/(N - 1), i = 1, ....N. In keeping with the above model [ cf . Eq. (4)], we assume that there is an equal probability (1/N) for each of these...solution (5), which contains two approximations to (10) and (11) [ cf ., N 4 - limit, and then asymptotic analysis], could accurately model the numerical...that the transition time Tl = 0(1) is the time when the phase mixing factor A0 t is roughly balanced by the BBU exponentiation factoro 1.64W I / 3 [ cf

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Thermodynamic nonequilibrium phase change behavior and thermal properties of biological solutions for cryobiology applications.

PubMed

Han, Bumsoo; Bischof, John C

2004-04-01

Understanding the phase change behavior of biomaterials during freezing/thawing including their thermal properties at low temperatures is essential to design and improve cryobiology applications such as cryopreservation and cryosurgery. However, knowledge of phase change behavior and thermal properties of various biomaterials is still incomplete, especially at cryogenic temperatures (< or = -40 degrees C). Moreover, in these applications, chemicals are often added to improve their outcome, which can result in significant variation in the phase change behavior and thermal properties from those of the original biomaterials. These chemical additives include cryoprotective agents (CPAs), antifreeze protein (AFP), or cryosurgical adjuvants like sodium chloride (NaCl). In the present study, phase change behavior and thermal properties of saline solutions--either water-NaCl or phosphate buffered saline (PBS)--with various chemical additives were investigated. The chemical additives studied are glycerol and raffinose as CPAs, an AFP (Type III, molecular weight = 6500), and NaCl as a cryosurgical adjuvant. The phase change behavior was investigated using a differential scanning calorimeter (DSC) and a cryomicroscope. The specific and latent heat of these solutions were also measured with the DSC. The saline solutions have two distinct phase changes--water/ice and eutectic phase changes. During freezing, eutectic solidification of both water-NaCl and PBS are significantly supercooled below their thermodynamic equilibrium eutectic temperatures. However, their melting temperatures are close to thermodynamic equilibrium during thawing. These eutectic phase changes disappear when even a small amount (0.1 M glycerol) of CPA was added, but they are still observed after the addition of an AFP. The specific heats of these solutions are close to that of ice at very low temperatures (< or = -100 degrees C) regardless of the additives, but they increase between -100 degrees C and -30 degrees C with the addition of CPAs. The amount of latent heat, which is evaluated with sample weight, generally decreases with the addition of the additives, but can be normalized to approximately 300 J/g based on the weight of water which participates in the phase change. This illustrates that thermal properties, especially latent heat, of a biomaterial should be evaluated based on the understanding of its phase change behavior. The results of the present study are discussed in the context of the implications for cryobiology applications.

Potentials of mean force for biomolecular simulations: Theory and test on alanine dipeptide

NASA Astrophysics Data System (ADS)

Pellegrini, Matteo; Grønbech-Jensen, Niels; Doniach, Sebastian

1996-06-01

We describe a technique for generating potentials of mean force (PMF) between solutes in an aqueous solution. We first generate solute-solvent correlation functions (CF) using Monte Carlo (MC) simulations in which we place a single atom solute in a periodic boundary box containing a few hundred water molecules. We then make use of the Kirkwood superposition approximation, where the 3-body correlation function is approximated as the product of 2-body CFs, to describe the mean water density around two solutes. Computing the force generated on the solutes by this average water density allows us to compute potentials of mean force between the two solutes. For charged solutes an additional approximation involving dielectric screening is made, by setting the dielectric constant of water to ɛ=80. These potentials account, in an approximate manner, for the average effect of water on the atoms. Following the work of Pettitt and Karplus [Chem. Phys. Lett. 121, 194 (1985)], we approximate the n-body potential of mean force as a sum of the pairwise potentials of mean force. This allows us to run simulations of biomolecules without introducing explicit water, hence gaining several orders of magnitude in efficiency with respect to standard molecular dynamics techniques. We demonstrate the validity of this technique by first comparing the PMFs for methane-methane and sodium-chloride generated with this procedure, with those calculated with a standard Monte Carlo simulation with explicit water. We then compare the results of the free energy profiles between the equilibria of alanine dipeptide generated by the two methods.

Fractionation of aquatic natural organic matter upon sorption to goethite and kaolinite

USGS Publications Warehouse

Meier, M.; Namjesnik-Dejanovic, K.; Maurice, P.A.; Chin, Y.-P.; Aiken, G.R.

1999-01-01

Natural organic matter (NOM) consists of a complex mixture of organic molecules; previous studies have suggested that preferential sorption of higher molecular weight, more hydrophobic, and more aromatic components may lead to fractionation of the NOM pool upon passage through porous media. Our work expands upon previous studies by quantifying the change in solution-phase weight average molecular weight (M(w)) upon sorption of bulk (rather than isolated) surface water NOM from the Suwannee River (SR) and the Great Dismal Swamp (GDS) to goethite and kaolinite at different sorption densities and at pH 4, 22??C. High pressure size exclusion chromatography (HPSEC) was used to quantify changes in M(w) upon sorption, and molar absorptivities at ?? = 280 nm were used to approximate changes in solution NOM aromaticity. Two SR water samples were used, with M(w) = 2320 and 2200 Da; a single GDS sample was used, with M(w) = 1890 Da. The SR NOM was slightly more hydrophobic and aromatic. These differences were reflected in greater sorption of SR NOM than GDS NOM. Both surface water NOMs showed a much greater affinity for goethite than for kaolinite. HPSEC analysis of the NOM remaining in solution after 24 h reaction time with geothite revealed that the largest changes in solution phase M(w)s (decreases by 900-1700 Da) occurred at relatively low equilibrium sorbate concentrations (approximately 5-20 mg C 1-1); the decrease in solution M(w) suggested that reactive surface sites were occupied disproportionately by large and intermediate size NOM moieties. At higher equilibrium NOM concentrations (>20 mg C 1-1), as percent adsorption decreased, M(w) in solution was similar to original samples. A smaller decrease in solution NOM M(w) (300-500 Da at 10-20 mg C 1-1 ~ 100 Da at > 20 mg) also occurred upon sorption to kaolinite. Overall, our results showed that factors (as related to NOM composition, clay mineral surface properties, and position along the sorption isotherm) which promote a higher percent sorption lead to the most pronounced decreases in solution M(w).

Phase retrieval in annulus sector domain by non-iterative methods

NASA Astrophysics Data System (ADS)

Wang, Xiao; Mao, Heng; Zhao, Da-zun

2008-03-01

Phase retrieval could be achieved by solving the intensity transport equation (ITE) under the paraxial approximation. For the case of uniform illumination, Neumann boundary condition is involved and it makes the solving process more complicated. The primary mirror is usually designed segmented in the telescope with large aperture, and the shape of a segmented piece is often like an annulus sector. Accordingly, It is necessary to analyze the phase retrieval in the annulus sector domain. Two non-iterative methods are considered for recovering the phase. The matrix method is based on the decomposition of the solution into a series of orthogonalized polynomials, while the frequency filtering method depends on the inverse computation process of ITE. By the simulation, it is found that both methods can eliminate the effect of Neumann boundary condition, save a lot of computation time and recover the distorted phase well. The wavefront error (WFE) RMS can be less than 0.05 wavelength, even when some noise is added.

Phase behavior of blends of linear and branched polyethylenes in the molten and solid states by small-angle neutron scattering

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

Alamo, R.G.; Mandelkern, L.; Londono, J.D.

1994-01-17

The state of mixing in blends of high-density polyethylene (HDPE) and low-density polyethylene (LDPE) in the liquid and solid state has been examined by small-angle neutron scattering (SANS) in conjunction with deuterium labeling. In the melt, SANS results indicate that HDPE/LDPE mixtures from a single-phase solution for all concentrations, including blends containing high volume fractions ([phi] > 0.5) of branched polymer, for which multiphase melts have previously been suggested. Proper accounting for isotope effects is essential to avoid artifacts, because the H/D interaction parameter is sufficiently large ([sub [chi]HD] [approximately] 4 [times] 10[sup [minus]4]) to cause phase separation in themore » amorphous state for molecular weights (MW) >150,000. In the solid state, after slow cooling from the melt ([approximately]0.75 C/min), the HDPE/LDPE system shows extensive segregation into separate domains [approximately]100--300 [angstrom] in size. Both the shape and magnitude of the absolute scattering cross section are consistent with the conclusion that the components are extensively segregated into separate lamellae. Two-peak melting curves obtained for such mixtures support the SANS interpretation, and the segregation of components in the solid state is therefore a consequence of crystallization mechanisms rather than incompatibility in the liquid state.« less

Preconcentration of aqueous dyes through phase-transfer liquid-phase microextraction with a room-temperature ionic liquid.

PubMed

Chen, Hsiu-Liang; Chang, Shuo-Kai; Lee, Chia-Ying; Chuang, Li-Lin; Wei, Guor-Tzo

2012-09-12

In this study, we employed the room-temperature ionic liquid [bmim][PF(6)] as both ion-pair agent and an extractant in the phase-transfer liquid-phase microextraction (PTLPME) of aqueous dyes. In the PTLPME method, a dye solution was added to the extraction solution, comprising a small amount of [bmim][PF(6)] in a relatively large amount of CH(2)Cl(2), which serves as the disperser solvent to an extraction solution. Following extraction, CH(2)Cl(2) was evaporated from the extractant, resulting in the extracted dyes being concentrated in a small volume of the ionic liquid phase to increase the enrichment factor. The enrichment factors of for the dye Methylene Blue, Neutral Red, and Methyl Red were approximately 500, 550 and 400, respectively; their detection limits were 0.014, 0.43, and 0.02 μg L(-1), respectively, with relative standard deviations of 4.72%, 4.20%, and 6.10%, respectively. Copyright © 2012 Elsevier B.V. All rights reserved.

Numerical Simulation of a Seaway with Breaking

NASA Astrophysics Data System (ADS)

Dommermuth, Douglas; O'Shea, Thomas; Brucker, Kyle; Wyatt, Donald

2012-11-01

The focus of this presentation is to describe the recent efforts to simulate a fully non-linear seaway with breaking by using a high-order spectral (HOS) solution of the free-surface boundary value problem to drive a three-dimensional Volume of Fluid (VOF) solution. Historically, the two main types of simulations to simulate free-surface flows are the boundary integral equations method (BIEM) and high-order spectral (HOS) methods. BIEM calculations fail at the point at which the surface impacts upon itself, if not sooner, and HOS methods can only simulate a single valued free-surface. Both also employ a single-phase approximation in which the effects of the air on the water are neglected. Due to these limitations they are unable to simulate breaking waves and air entrainment. The Volume of Fluid (VOF) method on the other hand is suitable for modeling breaking waves and air entrainment. However it is computationally intractable to generate a realistic non-linear sea-state. Here, we use the HOS solution to quickly drive, or nudge, the VOF solution into a non-linear state. The computational strategies, mathematical formulation, and numerical implementation will be discussed. The results of the VOF simulation of a seaway with breaking will also be presented, and compared to the single phase, single valued HOS results.

Efficient Semiparametric Inference Under Two-Phase Sampling, With Applications to Genetic Association Studies.

PubMed

Tao, Ran; Zeng, Donglin; Lin, Dan-Yu

2017-01-01

In modern epidemiological and clinical studies, the covariates of interest may involve genome sequencing, biomarker assay, or medical imaging and thus are prohibitively expensive to measure on a large number of subjects. A cost-effective solution is the two-phase design, under which the outcome and inexpensive covariates are observed for all subjects during the first phase and that information is used to select subjects for measurements of expensive covariates during the second phase. For example, subjects with extreme values of quantitative traits were selected for whole-exome sequencing in the National Heart, Lung, and Blood Institute (NHLBI) Exome Sequencing Project (ESP). Herein, we consider general two-phase designs, where the outcome can be continuous or discrete, and inexpensive covariates can be continuous and correlated with expensive covariates. We propose a semiparametric approach to regression analysis by approximating the conditional density functions of expensive covariates given inexpensive covariates with B-spline sieves. We devise a computationally efficient and numerically stable EM-algorithm to maximize the sieve likelihood. In addition, we establish the consistency, asymptotic normality, and asymptotic efficiency of the estimators. Furthermore, we demonstrate the superiority of the proposed methods over existing ones through extensive simulation studies. Finally, we present applications to the aforementioned NHLBI ESP.

Synchronization of two homodromy rotors installed on a double vibro-body in a coupling vibration system.

PubMed

Fang, Pan; Hou, Yongjun; Nan, Yanghai

2015-01-01

A new mechanism is proposed to implement synchronization of the two unbalanced rotors in a vibration system, which consists of a double vibro-body, two induction motors and spring foundations. The coupling relationship between the vibro-bodies is ascertained with the Laplace transformation method for the dynamics equation of the system obtained with the Lagrange's equation. An analytical approach, the average method of modified small parameters, is employed to study the synchronization characteristics between the two unbalanced rotors, which is converted into that of existence and the stability of zero solutions for the non-dimensional differential equations of the angular velocity disturbance parameters. By assuming the disturbance parameters that infinitely approach to zero, the synchronization condition for the two rotors is obtained. It indicated that the absolute value of the residual torque between the two motors should be equal to or less than the maximum of their coupling torques. Meanwhile, the stability criterion of synchronization is derived with the Routh-Hurwitz method, and the region of the stable phase difference is confirmed. At last, computer simulations are preformed to verify the correctness of the approximate solution of the theoretical computation for the stable phase difference between the two unbalanced rotors, and the results of theoretical computation is in accordance with that of computer simulations. To sum up, only the parameters of the vibration system satisfy the synchronization condition and the stability criterion of the synchronization, the two unbalanced rotors can implement the synchronization operation.

Synchronization of Two Homodromy Rotors Installed on a Double Vibro-Body in a Coupling Vibration System

PubMed Central

Fang, Pan; Hou, Yongjun; Nan, Yanghai

2015-01-01

A new mechanism is proposed to implement synchronization of the two unbalanced rotors in a vibration system, which consists of a double vibro-body, two induction motors and spring foundations. The coupling relationship between the vibro-bodies is ascertained with the Laplace transformation method for the dynamics equation of the system obtained with the Lagrange’s equation. An analytical approach, the average method of modified small parameters, is employed to study the synchronization characteristics between the two unbalanced rotors, which is converted into that of existence and the stability of zero solutions for the non-dimensional differential equations of the angular velocity disturbance parameters. By assuming the disturbance parameters that infinitely approach to zero, the synchronization condition for the two rotors is obtained. It indicated that the absolute value of the residual torque between the two motors should be equal to or less than the maximum of their coupling torques. Meanwhile, the stability criterion of synchronization is derived with the Routh-Hurwitz method, and the region of the stable phase difference is confirmed. At last, computer simulations are preformed to verify the correctness of the approximate solution of the theoretical computation for the stable phase difference between the two unbalanced rotors, and the results of theoretical computation is in accordance with that of computer simulations. To sum up, only the parameters of the vibration system satisfy the synchronization condition and the stability criterion of the synchronization, the two unbalanced rotors can implement the synchronization operation. PMID:25993472

A phase space approach to wave propagation with dispersion.

PubMed

Ben-Benjamin, Jonathan S; Cohen, Leon; Loughlin, Patrick J

2015-08-01

A phase space approximation method for linear dispersive wave propagation with arbitrary initial conditions is developed. The results expand on a previous approximation in terms of the Wigner distribution of a single mode. In contrast to this previously considered single-mode case, the approximation presented here is for the full wave and is obtained by a different approach. This solution requires one to obtain (i) the initial modal functions from the given initial wave, and (ii) the initial cross-Wigner distribution between different modal functions. The full wave is the sum of modal functions. The approximation is obtained for general linear wave equations by transforming the equations to phase space, and then solving in the new domain. It is shown that each modal function of the wave satisfies a Schrödinger-type equation where the equivalent "Hamiltonian" operator is the dispersion relation corresponding to the mode and where the wavenumber is replaced by the wavenumber operator. Application to the beam equation is considered to illustrate the approach.

Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect.

PubMed

Bliokh, K Yu; Bliokh, Yu P

2004-08-01

We present a modification of the geometrical optics method, which allows one to properly separate the complex amplitude and the phase of the wave solution. Appling this modification to a smoothly inhomogeneous isotropic medium, we show that in the first geometrical optics approximation the medium is weakly anisotropic. The refractive index, being dependent on the direction of the wave vector, contains the correction, which is proportional to the Berry geometric phase. Two independent eigenmodes of right-hand and left-hand circular polarizations exist in the medium. Their group velocities and phase velocities differ. The difference in the group velocities results in the shift of the rays of different polarizations (the optical Magnus effect). The difference in the phase velocities causes an increase of the Berry phase along with the interference of two modes leading to the familiar Rytov law about the rotation of the polarization plane of a wave. The theory developed suggests that both the optical Magnus effect and the Berry phase are accompanying nonlocal topological effects. In this paper the Hamilton ray equations giving a unified description for both of these phenomena have been derived and also a novel splitting effect for a ray of noncircular polarization has been predicted. Specific examples are also discussed.

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

Broda, Jill Terese

The neutron flux across the nuclear reactor core is of interest to reactor designers and others. The diffusion equation, an integro-differential equation in space and energy, is commonly used to determine the flux level. However, the solution of a simplified version of this equation when automated is very time consuming. Since the flux level changes with time, in general, this calculation must be made repeatedly. Therefore solution techniques that speed the calculation while maintaining accuracy are desirable. One factor that contributes to the solution time is the spatial flux shape approximation used. It is common practice to use the samemore » order flux shape approximation in each energy group even though this method may not be the most efficient. The one-dimensional, two-energy group diffusion equation was solved, for the node average flux and core k-effective, using two sets of spatial shape approximations for each of three reactor types. A fourth-order approximation in both energy groups forms the first set of approximations used. The second set used combines a second-order approximation with a fourth-order approximation in energy group two. Comparison of the results from the two approximation sets show that the use of a different order spatial flux shape approximation results in considerable loss in accuracy for the pressurized water reactor modeled. However, the loss in accuracy is small for the heavy water and graphite reactors modeled. The use of different order approximations in each energy group produces mixed results. Further investigation into the accuracy and computing time is required before any quantitative advantage of the use of the second-order approximation in energy group one and the fourth-order approximation in energy group two can be determined.« less

Structural incorporation of MgCl2 into ice VII at room temperature

NASA Astrophysics Data System (ADS)

Watanabe, Mao; Komatsu, Kazuki; Noritake, Fumiya; Kagi, Hiroyuki

2017-05-01

Raman spectra and X-ray diffraction patterns were obtained from 1:100 and 1:200 \\text{MgCl}2:\\text{H}2\\text{O} solutions (in molar ratio) at pressures up to 6 GPa using diamond anvil cells (DACs) and compared with those of pure water. The O-H stretching band from ice VII crystallized from the 1:200 solution was approximately 10 cm-1 higher than that of pure ice VII. The phase boundaries between ice VII and VIII crystallized from the MgCl2 solutions at 4 GPa were 2 K lower than those of pure ice VII and VIII. These observations indicate that ice VII incorporates MgCl2 into its structure. The unit cell volumes of ice VII crystallized from pure water and the two solutions coincided with each other within the experimental error, and salt incorporation was not detectable from the cell volume. Possible configurations of ion substitution and excess volume of ice VIII were simulated on the basis of density functional theory (DFT) calculations.

Structure and anomalous solubility for hard spheres in an associating lattice gas model.

PubMed

Szortyka, Marcia M; Girardi, Mauricio; Henriques, Vera B; Barbosa, Marcia C

2012-08-14

In this paper we investigate the solubility of a hard-sphere gas in a solvent modeled as an associating lattice gas. The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated both through Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and is shown to exhibit a minimum as a function of temperature. The line of minimum solubility (TmS) coincides with the line of maximum density (TMD) for different solvent chemical potentials, in accordance with the literature on continuous realistic models and on the "cavity" picture.

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.

Correlation Energies from the Two-Component Random Phase Approximation.

PubMed

Kühn, Michael

2014-02-11

The correlation energy within the two-component random phase approximation accounting for spin-orbit effects is derived. The resulting plasmon equation is rewritten-analogously to the scalar relativistic case-in terms of the trace of two Hermitian matrices for (Kramers-restricted) closed-shell systems and then represented as an integral over imaginary frequency using the resolution of the identity approximation. The final expression is implemented in the TURBOMOLE program suite. The code is applied to the computation of equilibrium distances and vibrational frequencies of heavy diatomic molecules. The efficiency is demonstrated by calculation of the relative energies of the Oh-, D4h-, and C5v-symmetric isomers of Pb6. Results within the random phase approximation are obtained based on two-component Kohn-Sham reference-state calculations, using effective-core potentials. These values are finally compared to other two-component and scalar relativistic methods, as well as experimental data.

Electromagnetic fields radiated from a lightning return stroke - Application of an exact solution to Maxwell's equations

NASA Technical Reports Server (NTRS)

Le Vine, D. M.; Meneghini, R.

1978-01-01

A solution is presented for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense; no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additional attribute of being specified in closed form in terms of elementary functions. This solution is discussed from the point of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compared with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

NASA Technical Reports Server (NTRS)

Siegel, R.; Spuckler, C. M.

1994-01-01

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Automatic Cell Segmentation Using a Shape-Classification Model in Immunohistochemically Stained Cytological Images

NASA Astrophysics Data System (ADS)

Shah, Shishir

This paper presents a segmentation method for detecting cells in immunohistochemically stained cytological images. A two-phase approach to segmentation is used where an unsupervised clustering approach coupled with cluster merging based on a fitness function is used as the first phase to obtain a first approximation of the cell locations. A joint segmentation-classification approach incorporating ellipse as a shape model is used as the second phase to detect the final cell contour. The segmentation model estimates a multivariate density function of low-level image features from training samples and uses it as a measure of how likely each image pixel is to be a cell. This estimate is constrained by the zero level set, which is obtained as a solution to an implicit representation of an ellipse. Results of segmentation are presented and compared to ground truth measurements.

Phase change in liquid face seals

NASA Technical Reports Server (NTRS)

Hughes, W. F.; Winowich, N. S.; Birchak, M. J.; Kennedy, W. C.

1978-01-01

A study is made of boiling (or phase change) in liquid face seals. An appropriate model is set up and approximate solutions obtained. Some practical illustrative examples are given. Major conclusions are that (1) boiling may occur more often than has been suspected particularly when the sealed liquid is near saturation conditions, (2) the temperature variation in a seal clearance region may not be very great and the main reason for boiling is the flashing which occurs as the pressure decreases through the seal clearance, and (3) there are two separate values of the parameter film-thickness/angular-velocity-squared (and associated radii where phase change takes place) which provide the same separating force under a given set of operating conditions. For a given speed seal face excursions about the larger spacing are stable, but excursions about the smaller spacing are unstable, leading to a growth to the larger spacing or a catastrophic collapse.

Project H - A Complete Spaceport Hydrogen Solution

NASA Technical Reports Server (NTRS)

Notardonato, William

2011-01-01

This slide presentation reviews Project H, and its importance in the development of Kennedy Space Center (KSC) as a Spaceport capable of multiple launches. It is known that current KSC cryogenic technology results in only approximately 55 % of purchased hydrogen being used. The rest is lost at various points in the process: transfer from transporting vehicle to tank, storage tank boil off, and from the tank to the intended propulsion tanks. Project H's goals would be to have local hydrogen production and liquifaction capability, and to increase the efficiency of hydrogen operations to greater than 80 %. The project envisions two phases: Phase 1 will build a smaller scale demonstration system, and phase 2 will build a full scale spaceport system. This initial project has proposed ideas for local hydrogen production, gaseous distribution, integrated refrigeration and storage, and high efficiency transfer lines that merit further investigation.

Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry

NASA Astrophysics Data System (ADS)

Besse, Nicolas; Coulette, David

2016-08-01

Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov-Poisson and Vlasov-Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, "Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry" (submitted)] and were found to be surprisingly close to those for the original gyrokinetic-Vlasov equations. The purpose of the present paper is to make these new ideas accessible to two readerships: applied mathematicians and plasma physicists.

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

Experimental study of phase equilibria and thermodynamic optimization of the Fe-Zn-O system

NASA Astrophysics Data System (ADS)

Degterov, Sergei A.; Pelton, Arthur D.; Jak, Evgueni; Hayes, Peter C.

2001-08-01

The Fe-Zn-O phase diagram in air was studied over the temperature range from 900 °C to 1500 °C. The compositions of the phases in quenched samples were obtained by electron probe X-ray microanalysis (EPMA). This experimental technique is not affected by zinc losses resulting from vaporization of zinc at high temperatures. The model for the spinel solid solution was developed within the framework of the compound-energy formalism (CEF). The choice of parameters of the CEF and the sequence of their optimization can have a major influence on the predictions in multicomponent phases. These choices can only be made rationally by reference to the specific model being represented in the CEF. This is discussed for the case of the two-sublattice spinel model. In the limiting case, the proposed model reduces to the model by O’Neill and Navrotsky for spinels. When the CEF is used in combination with the equation of Hillert and Jarl to describe the magnetic contribution to thermodynamic functions of a solution, it is necessary to assign certain values of magnetic properties to all pseudocomponents and to magnetic interaction parameters to obtain the most reasonable approximation of the magnetic properties of a solution. It was shown how this can be done based on very limited experimental data. The same equations can be used when the Murnaghan or the Birch-Murnaghan equation is combined with the CEF to describe the pressure dependence of thermodynamic functions. The polynomial model was used to describe the properties of wustite and zincite, and the modified quasichemical model was used for the liquid slag. All thermodynamic and phase-equilibria data on the Fe-O and Fe-Zn-O systems were critically evaluated, and parameters of the models were optimized to give a self-consistent set of thermodynamic functions of the phases in these systems. All experimental data are reproduced within experimental error limits. These include the thermodynamic properties of phases (such as specific heat, heat content, entropy, enthalpy, and Gibbs energy); the cation distribution between octahedral and tetrahedral sites in spinel; the oxygen partial pressure over single-phase, two-phase, and three-phase regions; the phase boundaries (liquidus, solidus, and subsolidus); and the tie-lines.

Modelling Assisted Design and Synthesis of Highly Porous Materials for Chemical Adsorbents

DTIC Science & Technology

2010-10-01

two phases of crystal, a monoclinic phase within the solution, and after removal from solution a trigonal phase is obtained. The single crystal...days. Single crystal X-ray data showed there existed a monoclinic phase within the solution that, upon removal from solution, rapidly converted to a... monoclinic to trigonal upon desolvation, as the new peak which has emerged matches the simulated PXRD of the trigonal phase. Also, as the sample is

Linking photochemistry in the gas and solution phase: S-H bond fission in p-methylthiophenol following UV photoexcitation.

PubMed

Oliver, Thomas A A; Zhang, Yuyuan; Ashfold, Michael N R; Bradforth, Stephen E

2011-01-01

Gas-phase H (Rydberg) atom photofragment translational spectroscopy and solution-phase femtosecond-pump dispersed-probe transient absorption techniques are applied to explore the excited state dynamics of p-methylthiophenol connecting the short time reactive dynamics in the two phases. The molecule is excited at a range of UV wavelengths from 286 to 193 nm. The experiments clearly demonstrate that photoexcitation results in S-H bond fission--both in the gas phase and in ethanol solution-and that the resulting p-methythiophenoxyl radical fragments are formed with significant vibrational excitation. In the gas phase, the recoil anisotropy of the H atom and the vibrational energy disposal in the p-MePhS radical products formed at the longer excitation wavelengths reveal the operation of two excited state dissociation mechanisms. The prompt excited state dissociation motif appears to map into the condensed phase also. In both phases, radicals are produced in both their ground and first excited electronic states; characteristic signatures for both sets of radical products are already apparent in the condensed phase studies after 50 fs. No evidence is seen for either solute ionisation or proton coupled electron transfer--two alternate mechanisms that have been proposed for similar heteroaromatics in solution. Therefore, at least for prompt S-H bond fissions, the direct observation of the dissociation process in solution confirms that the gas phase photofragmentation studies indeed provide important insights into the early time dynamics that transfer to the condensed phase.

Tuning the phase diagram of colloid-polymer mixtures via Yukawa interactions

NASA Astrophysics Data System (ADS)

González García, Álvaro; Tuinier, Remco

2016-12-01

Theory that predicts the phase behavior of interacting Yukawa spheres in a solution containing nonadsorbing polymer is presented. Our approach accounts for multiple overlap of depletion zones. It is found that additional Yukawa interactions beyond hard core interactions strongly affect the location and presence of coexistence regions and phase states. The theoretical phase diagrams are compared with Monte Carlo simulations. The agreement between the two approaches supports the validity of the theoretical approximations made and confirms that, by choosing the parameters of the interaction potentials, tuning of the binodals is possible. The critical end point characterizes the phase diagram topology. It is demonstrated how an additional Yukawa interaction shifts this point with respect to the hard sphere case. Provided a certain depletant-to-colloid size ratio for which a stable colloidal gas-liquid phase coexistence takes place for hard spheres, added direct interactions turn this into a metastable gas-liquid equilibrium. The opposite case, the induction of a stable gas-liquid coexistence where only fluid-solid was present for hard spheres, is also reported.

Bidirectional plant canopy reflection models derived from the radiation transfer equation

NASA Technical Reports Server (NTRS)

Beeth, D. R.

1975-01-01

A collection of bidirectional canopy reflection models was obtained from the solution of the radiation transfer equation for a horizontally homogeneous canopy. A phase function is derived for a collection of bidirectionally reflecting and transmitting planar elements characterized geometrically by slope and azimuth density functions. Two approaches to solving the radiation transfer equation for the canopy are presented. One approach factors the radiation transfer equation into a solvable set of three first-order linear differential equations by assuming that the radiation field within the canopy can be initially approximated by three components: uniformly diffuse downwelling, uniformly diffuse upwelling, and attenuated specular. The solution to these equations, which can be iterated to any degree of accuracy, was used to obtain overall canopy reflection from the formal solution to the radiation transfer equation. A programable solution to canopy overall bidirectional reflection is given for this approach. The special example of Lambertian leaves with constant leaf bidirectional reflection and scattering functions is considered, and a programmable solution for this example is given. The other approach to solving the radiation transfer equation, a generalized Chandrasekhar technique, is presented in the appendix.

Stratospheric sulfuric acid fraction and mass estimate for the 1982 volcanic eruption of El Chichon

NASA Technical Reports Server (NTRS)

Hofmann, D. J.; Rosen, J. M.

1983-01-01

The stratospheric sulfuric acid fraction and mass for the 1982 volcanic eruptions of El Chichon are investigated using data from balloon soundings at Laramie (41 deg N) and in southern Texas (27-29 deg N). The total stratospheric mass of these eruptions is estimated to be approximately 8 Tg about 6.5 months after the eruption with possibly as much as 20 Tg in the stratosphere about 45 days after the eruption. Observations of the aerosol in Texas revealed two primary layers, both highly volatile at 150 C. Aerosol in the upper layer at about 25 km was composed of an approximately 80 percent H2SO4 solution while the lower layer at approximately 18 km was composed of a 60-65 percent H2SO4 solution aerosol. It is calculated that an H2SO4 vapor concentration of at least 3 x 10 to the 7th molecules/cu cm is needed to sustain the large droplets in the upper layer. An early bi-modal nature in the size distribution indicates droplet nucleation from the gas phase during the first 3 months, while the similarity of the large particle profiles 2 months apart shows continued particle growth 6.5 months after the explosion.

Approximate analytical solutions to the double-stance dynamics of the lossy spring-loaded inverted pendulum.

PubMed

Shahbazi, Mohammad; Saranlı, Uluç; Babuška, Robert; Lopes, Gabriel A D

2016-12-05

This paper introduces approximate time-domain solutions to the otherwise non-integrable double-stance dynamics of the 'bipedal' spring-loaded inverted pendulum (B-SLIP) in the presence of non-negligible damping. We first introduce an auxiliary system whose behavior under certain conditions is approximately equivalent to the B-SLIP in double-stance. Then, we derive approximate solutions to the dynamics of the new system following two different methods: (i) updated-momentum approach that can deal with both the lossy and lossless B-SLIP models, and (ii) perturbation-based approach following which we only derive a solution to the lossless case. The prediction performance of each method is characterized via a comprehensive numerical analysis. The derived representations are computationally very efficient compared to numerical integrations, and, hence, are suitable for online planning, increasing the autonomy of walking robots. Two application examples of walking gait control are presented. The proposed solutions can serve as instrumental tools in various fields such as control in legged robotics and human motion understanding in biomechanics.

Second-order numerical solution of time-dependent, first-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Shah, Patricia L.; Hardin, Jay

1995-01-01

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

The convergence rate of approximate solutions for nonlinear scalar conservation laws

NASA Technical Reports Server (NTRS)

Nessyahu, Haim; Tadmor, Eitan

1991-01-01

The convergence rate is discussed of approximate solutions for the nonlinear scalar conservation law. The linear convergence theory is extended into a weak regime. The extension is based on the usual two ingredients of stability and consistency. On the one hand, the counterexamples show that one must strengthen the linearized L(sup 2)-stability requirement. It is assumed that the approximate solutions are Lip(sup +)-stable in the sense that they satisfy a one-sided Lipschitz condition, in agreement with Oleinik's E-condition for the entropy solution. On the other hand, the lack of smoothness requires to weaken the consistency requirement, which is measured in the Lip'-(semi)norm. It is proved for Lip(sup +)-stable approximate solutions, that their Lip'convergence rate to the entropy solution is of the same order as their Lip'-consistency. The Lip'-convergence rate is then converted into stronger L(sup p) convergence rate estimates.

Global multiresolution models of surface wave propagation: comparing equivalently regularized Born and ray theoretical solutions

NASA Astrophysics Data System (ADS)

Boschi, Lapo

2006-10-01

I invert a large set of teleseismic phase-anomaly observations, to derive tomographic maps of fundamental-mode surface wave phase velocity, first via ray theory, then accounting for finite-frequency effects through scattering theory, in the far-field approximation and neglecting mode coupling. I make use of a multiple-resolution pixel parametrization which, in the assumption of sufficient data coverage, should be adequate to represent strongly oscillatory Fréchet kernels. The parametrization is finer over North America, a region particularly well covered by the data. For each surface-wave mode where phase-anomaly observations are available, I derive a wide spectrum of plausible, differently damped solutions; I then conduct a trade-off analysis, and select as optimal solution model the one associated with the point of maximum curvature on the trade-off curve. I repeat this exercise in both theoretical frameworks, to find that selected scattering and ray theoretical phase-velocity maps are coincident in pattern, and differ only slightly in amplitude.

High-yield production of graphene by liquid-phase exfoliation of graphite.

PubMed

Hernandez, Yenny; Nicolosi, Valeria; Lotya, Mustafa; Blighe, Fiona M; Sun, Zhenyu; De, Sukanta; McGovern, I T; Holland, Brendan; Byrne, Michele; Gun'Ko, Yurii K; Boland, John J; Niraj, Peter; Duesberg, Georg; Krishnamurthy, Satheesh; Goodhue, Robbie; Hutchison, John; Scardaci, Vittorio; Ferrari, Andrea C; Coleman, Jonathan N

2008-09-01

Fully exploiting the properties of graphene will require a method for the mass production of this remarkable material. Two main routes are possible: large-scale growth or large-scale exfoliation. Here, we demonstrate graphene dispersions with concentrations up to approximately 0.01 mg ml(-1), produced by dispersion and exfoliation of graphite in organic solvents such as N-methyl-pyrrolidone. This is possible because the energy required to exfoliate graphene is balanced by the solvent-graphene interaction for solvents whose surface energies match that of graphene. We confirm the presence of individual graphene sheets by Raman spectroscopy, transmission electron microscopy and electron diffraction. Our method results in a monolayer yield of approximately 1 wt%, which could potentially be improved to 7-12 wt% with further processing. The absence of defects or oxides is confirmed by X-ray photoelectron, infrared and Raman spectroscopies. We are able to produce semi-transparent conducting films and conducting composites. Solution processing of graphene opens up a range of potential large-area applications, from device and sensor fabrication to liquid-phase chemistry.

The frequency-dependent response of single aerosol particles to vapour phase oscillations and its application in measuring diffusion coefficients

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

Preston, Thomas C.; Davies, James F.; Wilson, Kevin R.

A new method for measuring diffusion in the condensed phase of single aerosol particles is proposed and demonstrated. The technique is based on the frequency-dependent response of a binary particle to oscillations in the vapour phase of one of its chemical components. Here, we discuss how this physical situation allows for what would typically be a non-linear boundary value problem to be approximately reduced to a linear boundary value problem. For the case of aqueous aerosol particles, we investigate the accuracy of the closed-form analytical solution to this linear problem through a comparison with the numerical solution of the fullmore » problem. Then, using experimentally measured whispering gallery modes to track the frequency-dependent response of aqueous particles to relative humidity oscillations, we determine diffusion coefficients as a function of water activity. The measured diffusion coefficients are compared to previously reported values found using the two common experiments: (i) the analysis of the sorption/desorption of water from a particle after a step-wise change to the surrounding relative humidity and (ii) the isotopic exchange of water between a particle and the vapour phase. The technique presented here has two main strengths: first, when compared to the sorption/desorption experiment, it does not require the numerical evaluation of a boundary value problem during the fitting process as a closed-form expression is available. Second, when compared to the isotope exchange experiment, it does not require the use of labeled molecules. Therefore, the frequency-dependent experiment retains the advantages of these two commonly used methods but does not suffer from their drawbacks.« less

The frequency-dependent response of single aerosol particles to vapour phase oscillations and its application in measuring diffusion coefficients

DOE PAGES

Preston, Thomas C.; Davies, James F.; Wilson, Kevin R.

2017-01-13

A new method for measuring diffusion in the condensed phase of single aerosol particles is proposed and demonstrated. The technique is based on the frequency-dependent response of a binary particle to oscillations in the vapour phase of one of its chemical components. Here, we discuss how this physical situation allows for what would typically be a non-linear boundary value problem to be approximately reduced to a linear boundary value problem. For the case of aqueous aerosol particles, we investigate the accuracy of the closed-form analytical solution to this linear problem through a comparison with the numerical solution of the fullmore » problem. Then, using experimentally measured whispering gallery modes to track the frequency-dependent response of aqueous particles to relative humidity oscillations, we determine diffusion coefficients as a function of water activity. The measured diffusion coefficients are compared to previously reported values found using the two common experiments: (i) the analysis of the sorption/desorption of water from a particle after a step-wise change to the surrounding relative humidity and (ii) the isotopic exchange of water between a particle and the vapour phase. The technique presented here has two main strengths: first, when compared to the sorption/desorption experiment, it does not require the numerical evaluation of a boundary value problem during the fitting process as a closed-form expression is available. Second, when compared to the isotope exchange experiment, it does not require the use of labeled molecules. Therefore, the frequency-dependent experiment retains the advantages of these two commonly used methods but does not suffer from their drawbacks.« less

Modeling Healthcare Processes Using Commitments: An Empirical Evaluation.

PubMed

Telang, Pankaj R; Kalia, Anup K; Singh, Munindar P

2015-01-01

The two primary objectives of this paper are: (a) to demonstrate how Comma, a business modeling methodology based on commitments, can be applied in healthcare process modeling, and (b) to evaluate the effectiveness of such an approach in producing healthcare process models. We apply the Comma approach on a breast cancer diagnosis process adapted from an HHS committee report, and presents the results of an empirical study that compares Comma with a traditional approach based on the HL7 Messaging Standard (Traditional-HL7). Our empirical study involved 47 subjects, and two phases. In the first phase, we partitioned the subjects into two approximately equal groups. We gave each group the same requirements based on a process scenario for breast cancer diagnosis. Members of one group first applied Traditional-HL7 and then Comma whereas members of the second group first applied Comma and then Traditional-HL7-each on the above-mentioned requirements. Thus, each subject produced two models, each model being a set of UML Sequence Diagrams. In the second phase, we repartitioned the subjects into two groups with approximately equal distributions from both original groups. We developed exemplar Traditional-HL7 and Comma models; we gave one repartitioned group our Traditional-HL7 model and the other repartitioned group our Comma model. We provided the same changed set of requirements to all subjects and asked them to modify the provided exemplar model to satisfy the new requirements. We assessed solutions produced by subjects in both phases with respect to measures of flexibility, time, difficulty, objective quality, and subjective quality. Our study found that Comma is superior to Traditional-HL7 in flexibility and objective quality as validated via Student's t-test to the 10% level of significance. Comma is a promising new approach for modeling healthcare processes. Further gains could be made through improved tooling and enhanced training of modeling personnel.

Modeling Healthcare Processes Using Commitments: An Empirical Evaluation

PubMed Central

2015-01-01

The two primary objectives of this paper are: (a) to demonstrate how Comma, a business modeling methodology based on commitments, can be applied in healthcare process modeling, and (b) to evaluate the effectiveness of such an approach in producing healthcare process models. We apply the Comma approach on a breast cancer diagnosis process adapted from an HHS committee report, and presents the results of an empirical study that compares Comma with a traditional approach based on the HL7 Messaging Standard (Traditional-HL7). Our empirical study involved 47 subjects, and two phases. In the first phase, we partitioned the subjects into two approximately equal groups. We gave each group the same requirements based on a process scenario for breast cancer diagnosis. Members of one group first applied Traditional-HL7 and then Comma whereas members of the second group first applied Comma and then Traditional-HL7—each on the above-mentioned requirements. Thus, each subject produced two models, each model being a set of UML Sequence Diagrams. In the second phase, we repartitioned the subjects into two groups with approximately equal distributions from both original groups. We developed exemplar Traditional-HL7 and Comma models; we gave one repartitioned group our Traditional-HL7 model and the other repartitioned group our Comma model. We provided the same changed set of requirements to all subjects and asked them to modify the provided exemplar model to satisfy the new requirements. We assessed solutions produced by subjects in both phases with respect to measures of flexibility, time, difficulty, objective quality, and subjective quality. Our study found that Comma is superior to Traditional-HL7 in flexibility and objective quality as validated via Student’s t-test to the 10% level of significance. Comma is a promising new approach for modeling healthcare processes. Further gains could be made through improved tooling and enhanced training of modeling personnel. PMID:26539985

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

Scrutinization of thermal radiation, viscous dissipation and Joule heating effects on Marangoni convective two-phase flow of Casson fluid with fluid-particle suspension

NASA Astrophysics Data System (ADS)

Mahanthesh, B.; Gireesha, B. J.

2018-03-01

The impact of Marangoni convection on dusty Casson fluid boundary layer flow with Joule heating and viscous dissipation aspects is addressed. The surface tension is assumed to vary linearly with temperature. Physical aspects of magnetohydrodynamics and thermal radiation are also accounted. The governing problem is modelled under boundary layer approximations for fluid phase and dust particle phase and then Runge-Kutta-Fehlberg method based numeric solutions are established. The momentum and heat transport mechanisms are focused on the result of distinct governing parameters. The Nusselt number is also calculated. It is established that the rate of heat transfer can be enhanced by suspending dust particles in the base fluid. The temperature field of fluid phase and temperature of dust phase are quite reverse for thermal dust parameter. The radiative heat, viscous dissipation and Joule heating aspects are constructive for thermal fields of fluid and dust phases. The velocity of dusty Casson fluid dominates the velocity of dusty fluid while this trend is opposite in the case of temperature. Moreover qualitative behaviour of fluid phase and dust phase temperature/velocity are similar.

Stability of Dirac Liquids with Strong Coulomb Interaction.

PubMed

Tupitsyn, Igor S; Prokof'ev, Nikolay V

2017-01-13

We develop and apply the diagrammatic Monte Carlo technique to address the problem of the stability of the Dirac liquid state (in a graphene-type system) against the strong long-range part of the Coulomb interaction. So far, all attempts to deal with this problem in the field-theoretical framework were limited either to perturbative or random phase approximation and functional renormalization group treatments, with diametrically opposite conclusions. Our calculations aim at the approximation-free solution with controlled accuracy by computing vertex corrections from higher-order skeleton diagrams and establishing the renormalization group flow of the effective Coulomb coupling constant. We unambiguously show that with increasing the system size L (up to ln(L)∼40), the coupling constant always flows towards zero; i.e., the two-dimensional Dirac liquid is an asymptotically free T=0 state with divergent Fermi velocity.

The passage of an infinite swept airfoil through an oblique gust. [approximate solution for aerodynamic response

NASA Technical Reports Server (NTRS)

Adamczyk, J. L.

1974-01-01

An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

Simulations of phase space distributions of storm time proton ring current

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Lyons, Larry R.; Schulz, Michael

1994-01-01

We use results of guiding-center simulations of ion transport to map phase space densities of the stormtime proton ring current. We model a storm as a sequence of substorm-associated enhancements in the convection electric field. Our pre-storm phase space distribution is an analytical solution to a steady-state transport model in which quiet-time radial diffusion balances charge exchange. This pre-storm phase space spectra at L approximately 2 to 4 reproduce many of the features found in observed quiet-time spectra. Using results from simulations of ion transport during model storms having main phases of 3, 6, and 12 hr, we map phase space distributions from the pre-storm distribution in accordance with Liouville's theorem. We find stormtime enhancements in the phase space densities at energies E approximately 30-160 keV for L approximately 2.5 to 4. These enhancements agree well with the observed stormtime ring current. For storms with shorter main phases (approximately 3 hr), the enhancements are caused mainly by the trapping of ions injected from open night side trajectories, and diffusive transport of higher-energy (greater than or approximately 160 keV) ions contributes little to the stormtime ring current. However, the stormtime ring current is augmented also by the diffusive transport of higher-energy ions (E greater than or approximately 160 keV) durinng stroms having longer main phases (greater than or approximately 6 hr). In order to account for the increase in Dst associated with the formation of the stormtime ring current, we estimate the enhancement in particle-energy content that results from stormtime ion transport in the equatorial magnetosphere. We find that transport alone cannot account for the entire increase in absolute value of Dst typical of a major storm. However, we can account for the entire increase in absolute value of Dst by realistically increasing the stormtime outer boundary value of the phase space density relative to the quiet-time value. We compute the magnetic field produced by the ring current itself and find that radial profiles of the magnetic field depression resemble those obtained from observational data.

Cyclic stress effect on stress corrosion cracking of duplex stainless steel in chloride and caustic solutions

NASA Astrophysics Data System (ADS)

Yang, Di

Duplex stainless steel (DSS) is a dual-phase material with approximately equal volume amount of austenite and ferrite. It has both great mechanical properties (good ductility and high tensile/fatigue strength) and excellent corrosion resistance due to the mixture of the two phases. Cyclic loadings with high stress level and low frequency are experienced by many structures. However, the existing study on corrosion fatigue (CF) study of various metallic materials has mainly concentrated on relatively high frequency range. No systematic study has been done to understand the ultra-low frequency (˜10-5 Hz) cyclic loading effect on stress corrosion cracking (SCC) of DSSs. In this study, the ultra-low frequency cyclic loading effect on SCC of DSS 2205 was studied in acidified sodium chloride and caustic white liquor (WL) solutions. The research work focused on the environmental effect on SCC of DSS 2205, the cyclic stress effect on strain accumulation behavior of DSS 2205, and the combined environmental and cyclic stress effect on the stress corrosion crack initiation of DSS 2205 in the above environments. Potentiodynamic polarization tests were performed to investigate the electrochemical behavior of DSS 2205 in acidic NaCl solution. Series of slow strain rate tests (SSRTs) at different applied potential values were conducted to reveal the optimum applied potential value for SCC to happen. Room temperature static and cyclic creep tests were performed in air to illustrate the strain accumulation effect of cyclic stresses. Test results showed that cyclic loading could enhance strain accumulation in DSS 2205 compared to static loading. Moreover, the strain accumulation behavior of DSS 2205 was found to be controlled by the two phases of DSS 2205 with different crystal structures. The B.C.C. ferrite phase enhanced strain accumulation due to extensive cross-slips of the dislocations, whereas the F.C.C. austenite phase resisted strain accumulation due to cyclic strain hardening. Cyclic SSRTs were performed under the conditions that SCC occurs in sodium chloride and WL solutions. Test results show that cyclic stress facilitated crack initiations in DSS 2205. Stress corrosion cracks initiated from the intermetallic precipitates in acidic chloride environment, and the cracks initiated from austenite phase in WL environment. Cold-working has been found to retard the crack initiations induced by cyclic stresses.

Kinetics of binary nucleation of vapors in size and composition space.

PubMed

Fisenko, Sergey P; Wilemski, Gerald

2004-11-01

We reformulate the kinetic description of binary nucleation in the gas phase using two natural independent variables: the total number of molecules g and the molar composition x of the cluster. The resulting kinetic equation can be viewed as a two-dimensional Fokker-Planck equation describing the simultaneous Brownian motion of the clusters in size and composition space. Explicit expressions for the Brownian diffusion coefficients in cluster size and composition space are obtained. For characterization of binary nucleation in gases three criteria are established. These criteria establish the relative importance of the rate processes in cluster size and composition space for different gas phase conditions and types of liquid mixtures. The equilibrium distribution function of the clusters is determined in terms of the variables g and x. We obtain an approximate analytical solution for the steady-state binary nucleation rate that has the correct limit in the transition to unary nucleation. To further illustrate our description, the nonequilibrium steady-state cluster concentrations are found by numerically solving the reformulated kinetic equation. For the reformulated transient problem, the relaxation or induction time for binary nucleation was calculated using Galerkin's method. This relaxation time is affected by processes in both size and composition space, but the contributions from each process can be separated only approximately.

Cesium and strontium extraction using a mixed extractant solvent including crown ether and calixarene extractants

DOEpatents

Meikrantz, David H.; Todd, Terry A.; Riddle, Catherine L.; Law, Jack D.; Peterman, Dean R.; Mincher, Bruce J.; McGrath, Christopher A.; Baker, John D.

2007-11-06

A mixed extractant solvent including calix[4]arene-bis-(tert-octylbenzo)-crown-6 ("BOBCalixC6"), 4',4',(5')-di-(t-butyldicyclo-hexano)-18-crown-6 ("DtBu18C6"), and at least one modifier dissolved in a diluent. The mixed extractant solvent may be used to remove cesium and strontium from an acidic solution. The DtBu18C6 may be present from approximately 0.01 M to approximately 0.4M, such as from approximately 0.086 M to approximately 0.108 M. The modifier may be 1-(2,2,3,3-tetrafluoropropoxy)-3-(4-sec-butylphenoxy)-2-propanol ("Cs-7SB") and may be present from approximately 0.01M to approximately 0.8M. In one embodiment, the mixed extractant solvent includes approximately 0.15M DtBu18C6, approximately 0.007M BOBCalixC6, and approximately 0.75M Cs-7SB modifier dissolved in an isoparaffinic hydrocarbon diluent. The mixed extractant solvent may form an organic phase in an extraction system that also includes an aqueous phase. Methods of extracting cesium and strontium as well as strontium alone are also disclosed.

Numerical Simulations of Crystal Growth of an Alloy Under Microgravity Conditions

NASA Technical Reports Server (NTRS)

Simpson, James E.; deGroh, Henry C., III; Garimella, Suresh V.; Abbaschian, Reza

1999-01-01

The directional solidification of a dilute binary alloy (Bi-1.0 at.%Sn)is investigated. Results are obtained at a gravity level of I pg. Computations are performed in two dimensions with a fixed, non-uniform grid. The simulation involves a solution of the species concentration equation (modified to account for solute rejection at the interface) and energy equation (modified to account for phase-change) for both the solid and liquid phases, in addition to the constitutive equations for describing convective flow in the melt. The effects of conductive heat transfer in the ampoule and in a capillary tube in the sample are included. To gauge the effects of including this growth capillary tube in the apparatus, simulations both with and without the capillary tube are presented and compared. Fully transient simulations have been performed; no simplifying steady-state approximations are used, however, the influence of solute on the melting temperature at the interface is not included. Both thermal and solutal convective cells are seen to form. Convective velocities are significantly damped inside the capillary, causing less segregation due to convection. As solidification proceeds beyond the capillary tube, longitudinal segregation arises as a result of the change in cross-sectional area of solidifying material. The magnitudes of the velocities in this cell increase significantly once the solid/liquid front passes beyond the end of the capillary tube; this causes a corresponding increase in the level of radial solute segregation in the solidified material.

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

NASA Astrophysics Data System (ADS)

Cummings, Patrick

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

Research on properties of an infrared imaging diffractive element

NASA Astrophysics Data System (ADS)

Rachoń, M.; Wegrzyńska, K.; Doch, M.; Kołodziejczyk, A.; Siemion, A.; Suszek, J.; Kakarenko, K.; Sypek, M.

2014-09-01

Novel thermovision imaging systems having high efficiency require very sophisticated optical components. This paper describes the diffractive optical elements which are designed for the wavelengths between 8 and 14 μm for the application in the FLIR cameras. In the current paper the authors present phase only diffractive elements manufactured in the etched gallium arsenide. Due to the simplicity of the manufacturing process only binary phase elements were designed and manufactured. Such solution exhibits huge chromatic aberration. Moreover, the performance of such elements is rather poor, which is caused by two factors. The first one is the limited diffraction efficiency (c.a. 40%) of binary phase structures. The second problem lies in the Fresnel losses coming from the reflection from the two surfaces (around 50%). Performance of this structures is limited and the imaging contrast is poor. However, such structures can be used for relatively cheap practical testing of the new ideas. For example this solution is sufficient for point spread function (PSF) measurements. Different diffractive elements were compared. The first one was the equivalent of the lens designed on the basis of the paraxial approximation. For the second designing process, the non-paraxial approach was used. It was due to the fact that f/# was equal to 1. For the non-paraxial designing the focal spot is smaller and better focused. Moreover, binary phase structures suffer from huge chromatic aberrations. Finally, it is presented that non-paraxially designed optical element imaging with extended depth of focus (light-sword) can suppress chromatic aberration and therefore it creates the image not only in the image plane.

Convective fluid flows in a horizontal channel with evaporation: analytical and experimental investigations

NASA Astrophysics Data System (ADS)

Lyulin, Y. V.; Rezanova, E. V.

2017-11-01

Heat- and mass transfer processes in a two-layer system of the liquid and gas are studied with respect to evaporation at interface. The stationary convective flows of two immiscible viscous incompressible fluids filling an infinite channel and being under action of the transverse gravitation field are studied analytically. Mathematical modeling of the flows is carried out with the help of the Navier-Stokes equations in Boussinesq approximation. The Dufour and Soret effects are taken into consideration in the gas-vapor phase. In the two-dimensional case the exact solutions of special type are constructed under condition of a given specific gas flow rate. Comparison of the analytical results with results of the physical experiments with the “liquid-gas” system like “ethanol-air” are presented.

Tube radial distribution phenomenon with a two-phase separation solution of a fluorocarbon and hydrocarbon organic solvent mixture in a capillary tube and metal compounds separation.

PubMed

Kitaguchi, Koichi; Hanamura, Naoya; Murata, Masaharu; Hashimoto, Masahiko; Tsukagoshi, Kazuhiko

2014-01-01

A fluorocarbon and hydrocarbon organic solvent mixture is known as a temperature-induced phase-separation solution. When a mixed solution of tetradecafluorohexane as a fluorocarbon organic solvent and hexane as a hydrocarbon organic solvent (e.g., 71:29 volume ratio) was delivered in a capillary tube that was controlled at 10°C, the tube radial distribution phenomenon (TRDP) of the solvents was clearly observed through fluorescence images of the dye, perylene, dissolved in the mixed solution. The homogeneous mixed solution (single phase) changed to a heterogeneous solution (two phases) with inner tetradecafluorohexane and outer hexane phases in the tube under laminar flow conditions, generating the dynamic liquid-liquid interface. We also tried to apply TRDP to a separation technique for metal compounds. A model analyte mixture, copper(II) and hematin, was separated through the capillary tube, and detected with a chemiluminescence detector in this order within 4 min.

Propagation of waves from an arbitrary shaped surface-A generalization of the Fresnel diffraction integral

NASA Astrophysics Data System (ADS)

Feshchenko, R. M.; Vinogradov, A. V.; Artyukov, I. A.

2018-04-01

Using the method of Laplace transform the field amplitude in the paraxial approximation is found in the two-dimensional free space using initial values of the amplitude specified on an arbitrary shaped monotonic curve. The obtained amplitude depends on one a priori unknown function, which can be found from a Volterra first kind integral equation. In a special case of field amplitude specified on a concave parabolic curve the exact solution is derived. Both solutions can be used to study the light propagation from arbitrary surfaces including grazing incidence X-ray mirrors. They can find applications in the analysis of coherent imaging problems of X-ray optics, in phase retrieval algorithms as well as in inverse problems in the cases when the initial field amplitude is sought on a curved surface.

Interaction of finite-amplitude sound with air-filled porous materials

NASA Technical Reports Server (NTRS)

Nelson, D. A.

1985-01-01

The propagation of high intensity sound waves through an air-filled porus material was studied. The material is assumed: (1) to be rigid, incompressible, and homogeneous, and (2) to be adequately described by two properties: resistivity r and porosity. The resulting wave equation is still nonlinear, however, because of the u sgn(u) term in the resistivity. The equation is solved in the frequency domain as an infinite set of coupled inhomogeneous Helmholtz equations, one for each harmonic. An approximate but analytical solution leads to predictions of excess attenuation, saturation, and phase speed reduction for the fundamental component. A more general numerical solution is used to calculate the propagation curves for the higher harmonics. The u sgn(u) nonlinearity produces a cubic distortion pattern; when the input signal is a pure tone, only odd harmonic distortion products are generated.

Two types of phase diagrams for two-species Bose-Einstein condensates and the combined effect of the parameters

NASA Astrophysics Data System (ADS)

Li, Z. B.; Liu, Y. M.; Yao, D. X.; Bao, C. G.

2017-07-01

Under the Thomas-Fermi approximation, an approach is proposed to solve the coupled Gross-Pitaevskii equations (CGP) for the two-species Bose-Einstein condensate analytically. The essence of this approach is to find out the building blocks to build the solution. By introducing the weighted strengths, relatively simpler analytical solutions have been obtained. A number of formulae have been deduced to relate the parameters when the system is experimentally tuned at various status. These formulae demonstrate the combined effect of the parameters, and are useful for the evaluation of their magnitudes. The whole parameter space is divided into zones, where each supports a specific phase. All the boundaries separating these zones have analytical expressions. Based on the division, the phase diagrams against any set of parameters can be plotted. In addition, by introducing a model for the asymmetric states, the total energies of the lowest symmetric and asymmetric states have been compared. Thereby, in which case the former will be replaced by the latter has been evaluated. The CGP can be written in a matrix form. For repulsive inter-species interaction V AB , when the parameters vary and cross over the singular point of the matrix, a specific state transition will happen and the total energy of the lowest symmetric state will increase remarkably. This provides an excellent opportunity for the lowest asymmetric state to emerge as the ground state. For attractive V AB , when the parameters tend to a singular point, the system will tend to collapse. The effects caused by the singular points have been particularly studied.

Optimal rendezvous in the neighborhood of a circular orbit

NASA Technical Reports Server (NTRS)

Jones, J. B.

1975-01-01

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

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

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

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

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.

RAPID CONCENTRATION OF VIRUSES FROM WATER - PHASE I

EPA Science Inventory

In the United States, several high profile outbreaks of waterborne illness during the past 15 years have highlighted the need for solutions to drinking water contamination.  Several recent studies suggest that approximately 20 percent of the surface and ground source waters...

Simulation results for a multirate mass transfer modell for immiscible displacement of two fluids in highly heterogeneous porous media

NASA Astrophysics Data System (ADS)

Tecklenburg, Jan; Neuweiler, Insa; Dentz, Marco; Carrera, Jesus; Geiger, Sebastian

2013-04-01

Flow processes in geotechnical applications do often take place in highly heterogeneous porous media, such as fractured rock. Since, in this type of media, classical modelling approaches are problematic, flow and transport is often modelled using multi-continua approaches. From such approaches, multirate mass transfer models (mrmt) can be derived to describe the flow and transport in the "fast" or mobile zone of the medium. The porous media is then modeled with one mobile zone and multiple immobile zones, where the immobile zones are connected to the mobile zone by single rate mass transfer. We proceed from a mrmt model for immiscible displacement of two fluids, where the Buckley-Leverett equation is expanded by a sink-source-term which is nonlocal in time. This sink-source-term models exchange with an immobile zone with mass transfer driven by capillary diffusion. This nonlinear diffusive mass transfer can be approximated for particular imbibition or drainage cases by a linear process. We present a numerical scheme for this model together with simulation results for a single fracture test case. We solve the mrmt model with the finite volume method and explicit time integration. The sink-source-term is transformed to multiple single rate mass transfer processes, as shown by Carrera et. al. (1998), to make it local in time. With numerical simulations we studied immiscible displacement in a single fracture test case. To do this we calculated the flow parameters using information about the geometry and the integral solution for two phase flow by McWorther and Sunnada (1990). Comparision to the results of the full two dimensional two phase flow model by Flemisch et. al. (2011) show good similarities of the saturation breakthrough curves. Carrera, J., Sanchez-Vila, X., Benet, I., Medina, A., Galarza, G., and Guimera, J.: On matrix diffusion: formulations, solution methods and qualitative effects, Hydrogeology Journal, 6, 178-190, 1998. Flemisch, B., Darcis, M., Erbertseder, K., Faigle, B., Lauser, A. et al.: Dumux: Dune for multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media, Advances in Water Resources, 34, 1102-1112, 2011. McWhorter, D. B., and Sunada, D. K.: Exact integral solutions for two-phase flow, Water Resources Research, 26(3), 399-413, 1990.

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.

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.

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

NASA Astrophysics Data System (ADS)

Haitjema, Henk M.

1985-10-01

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

Determination of the quaternary phase diagram of the water-ethylene glycol-sucrose-NaCl system and a comparison between two theoretical methods for synthetic phase diagrams

PubMed Central

Han, Xu; Liu, Yang; Critser, John K.

2010-01-01

Characterization of the thermodynamic properties of multi-solute aqueous solutions is of critical importance for biological and biochemical research. For example, the phase diagrams of aqueous systems, containing salts, saccharides, and plasma membrane permeating solutes, are indispensible in the field of cryobiology and pharmacology. However, only a few ternary phase diagrams are currently available for these systems. In this study, an auto-sampler differential scanning calorimeter (DSC) was used to determine the quaternary phase diagram of the water-ethylene glycol-sucrose-NaCl system. To improve the accuracy of melting point measurement, a “mass redemption” method was also applied for the DSC technique. Base on the analyses of these experimental data, a comparison was made between the two practical approaches to generate phase diagrams of multi-solute solutions from those of single-solute solutions: the summation of cubic polynomial melting point equations versus the use of osmotic virial equations with cross coefficients. The calculated values of the model standard deviations suggested that both methods are satisfactory for characterizing this quaternary system. PMID:20447385

Composition design for Laves phase-related body-centered cubic-V solid solution alloys with large hydrogen storage capacities.

PubMed

Wang, H B; Wang, Q; Dong, C; Yuan, L; Xu, F; Sun, L X

2008-03-19

This paper analyzes the characteristics of alloy compositions with large hydrogen storage capacities in Laves phase-related body-centered cubic (bcc) solid solution alloy systems using the cluster line approach. Since a dense-packed icosahedral cluster A(6)B(7) characterizes the local structure of AB(2) Laves phases, in an A-B-C ternary system, such as Ti-Cr (Mn, Fe)-V, where A-B forms AB(2) Laves phases while A-C and B-C tend to form solid solutions, a cluster line A(6)B(7)-C is constructed by linking A(6)B(7) to C. The alloy compositions with large hydrogen storage capacities are generally located near this line and are approximately expressed with the cluster-plus-glue-atom model. The cluster line alloys (Ti(6)Cr(7))(100-x)V(x) (x = 2.5-70 at.%) exhibit different structures and hence different hydrogen storage capacities with increasing V content. The alloys (Ti(6)Cr(7))(95)V(5) and Ti(30)Cr(40)V(30) with bcc solid solution structure satisfy the cluster-plus-glue-atom model.

Exploiting the dynamics of S-phase tracers in developing brain: interkinetic nuclear migration for cells entering versus leaving the S-phase

NASA Technical Reports Server (NTRS)

Hayes, N. L.; Nowakowski, R. S.

2000-01-01

Two S-phase markers for in vivo studies of cell proliferation in the developing central nervous system, tritiated thymidine ((3)H-TdR) and bromodeoxyuridine (BUdR), were compared using double-labeling techniques in the developing mouse cortex at embryonic day 14 (E14). The labeling efficiencies and detectability of the two tracers were approximately equivalent, and there was no evidence of significant tracer interactions that depend on order of administration. For both tracers, the loading time needed to label an S-phase cell to detectability is estimated at <0.2 h shortly after the injection of the label, but, as the concentration of the label falls, it increases to approximately 0.65 h after about 30 min. Thereafter, cells that enter the S-phase continue to become detectably labeled for approximately 5-6 h. The approximate equivalence of these two tracers was exploited to observe directly the numbers and positions of nuclei entering (labeled with the second tracer only) and leaving (labeled with the first tracer only) the S-phase. As expected, the numbers of nuclei entering and leaving the S-phase both increased as the interval between the two injections lengthened. Also, nuclei leaving the S-phase rapidly move towards the ventricular surface during G2, but, unexpectedly, the distribution of the entering nuclei does not differ significantly from the distribution of the nuclei in the S-phase. This indicates that: (1) the extent and rate of abventricular nuclear movement during G1 is variable, such that not all nuclei traverse the entire width of the ventricular zone, and (2) interkinetic nuclear movements are minimal during S-phase. Copyright 2000 S. Karger AG, Basel.

Stresses due to Relative Sliding between Particles Surrounded by an Electrolyte Solution with Application to Lithium-Ion Batteries

NASA Astrophysics Data System (ADS)

Zhang, Cong; Conlisk, A. T.

2013-11-01

Mechanical stresses in the solid phase of the electrodes within lithium-ion batteries have been the subject of much work recently with the emphasis on the stresses induced by lithium insertion to or extraction from the active solid material. The particles within lithium-ion battery electrodes can undergo relative motion with relative velocities of different magnitudes and directions. One mode of the relative motion, resembling the slider bearing motion, manifests itself as two particles sliding relative to each other within an electrolyte solution. The electrolyte solution within the narrow pores between the particles is the medium through which the particles interact with each other. The effect of the electrolyte solution is not conventionally considered. The relative motion of the particles induces significant pressures. The primary objective of this work is to develop a model based on the lubrication approximation to investigate the magnitude and direction of the stresses induced by this sliding motion. Other applications in the biomedical field are also discussed. Supported by DOE Graduate Automotive Technology Education (GATE) and OSU Center for Automotive Research.

Approximate solution to the Callan-Giddings-Harvey-Strominger field equations for two-dimensional evaporating black holes

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

Ori, Amos

2010-11-15

Callan, Giddings, Harvey, and Strominger (CGHS) previously introduced a two-dimensional semiclassical model of gravity coupled to a dilaton and to matter fields. Their model yields a system of field equations which may describe the formation of a black hole in gravitational collapse as well as its subsequent evaporation. Here we present an approximate analytical solution to the semiclassical CGHS field equations. This solution is constructed using the recently introduced formalism of flux-conserving hyperbolic systems. We also explore the asymptotic behavior at the horizon of the evaporating black hole.

Kinetic studies on phosphorus sorption by selected soil amendments for septic tank effluent renovation.

PubMed

Cheung, K C; Venkitachalam, T H

2006-01-01

A systematic kinetic study of phosphorus (P) sorption by various materials in the soil infiltration system of septic tanks was undertaken by following the time course of P sorption by sorbents in contact with various P solutions over periods up to 360 days. Uptake of P seemed to consist of two distinct stages. Initial uptake was very rapid and this phase was completed in 4 days or less. A slower removal stage followed for some materials over many months. Phosphorus sorption during the fast reaction stage appeared to be associated with the soluble Ca content of the materials. The fast reaction of calcareous materials accounted for the bulk (>70%) of the total P removed. Merribrook loamy sand exhibited the highest proportion of P sorption during the slow phase. It should be noted, however, that for solution P concentrations in the range found in typical effluents (approximately 20 mg L(-1)) the fast reaction phase seemed to be responsible for virtually all P removed. None of the six kinetic formulae examined possessed the sophistication and detail needed to portray accurately the time course of P sorption for all the sorbents investigated. The Elovich equation and the kinetic modification of the Freundlich isotherm expression appeared to provide a reasonable fit of the experimental data.

A Three-Phase Microgrid Restoration Model Considering Unbalanced Operation of Distributed Generation

DOE PAGES

Wang, Zeyu; Wang, Jianhui; Chen, Chen

2016-12-07

Recent severe outages highlight the urgency of improving grid resiliency in the U.S. Microgrid formation schemes are proposed to restore critical loads after outages occur. Most distribution networks have unbalanced configurations that are not represented in sufficient detail by single-phase models. This study provides a microgrid formation plan that adopts a three-phase network model to represent unbalanced distribution networks. The problem formulation has a quadratic objective function with mixed-integer linear constraints. The three-phase network model enables us to examine the three-phase power outputs of distributed generators (DGs), preventing unbalanced operation that might trip DGs. Because the DG unbalanced operation constraintmore » is non-convex, an iterative process is presented that checks whether the unbalanced operation limits for DGs are satisfied after each iteration of optimization. We also develop a relatively conservative linear approximation on the unbalanced operation constraint to handle larger networks. Compared with the iterative solution process, the conservative linear approximation is able to accelerate the solution process at the cost of sacrificing optimality to a limited extent. Simulation in the IEEE 34 node and IEEE 123 test feeders indicate that the proposed method yields more practical microgrid formations results. In addition, this paper explores the coordinated operation of DGs and energy storage (ES) installations. The unbalanced three-phase outputs of ESs combined with the relatively balanced outputs of DGs could supply unbalanced loads. In conclusion, the case study also validates the DG-ES coordination.« less

A Three-Phase Microgrid Restoration Model Considering Unbalanced Operation of Distributed Generation

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

Wang, Zeyu; Wang, Jianhui; Chen, Chen

Recent severe outages highlight the urgency of improving grid resiliency in the U.S. Microgrid formation schemes are proposed to restore critical loads after outages occur. Most distribution networks have unbalanced configurations that are not represented in sufficient detail by single-phase models. This study provides a microgrid formation plan that adopts a three-phase network model to represent unbalanced distribution networks. The problem formulation has a quadratic objective function with mixed-integer linear constraints. The three-phase network model enables us to examine the three-phase power outputs of distributed generators (DGs), preventing unbalanced operation that might trip DGs. Because the DG unbalanced operation constraintmore » is non-convex, an iterative process is presented that checks whether the unbalanced operation limits for DGs are satisfied after each iteration of optimization. We also develop a relatively conservative linear approximation on the unbalanced operation constraint to handle larger networks. Compared with the iterative solution process, the conservative linear approximation is able to accelerate the solution process at the cost of sacrificing optimality to a limited extent. Simulation in the IEEE 34 node and IEEE 123 test feeders indicate that the proposed method yields more practical microgrid formations results. In addition, this paper explores the coordinated operation of DGs and energy storage (ES) installations. The unbalanced three-phase outputs of ESs combined with the relatively balanced outputs of DGs could supply unbalanced loads. In conclusion, the case study also validates the DG-ES coordination.« less

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

Molecular dynamics simulation study of hydrogen bonding in aqueous poly(ethylene oxide) solutions.

PubMed

Smith, G D; Bedrov, D; Borodin, O

2000-12-25

A molecular dynamics simulation study of hydrogen bonding in poly(ethylene oxide) (PEO)/water solutions was performed. PEO-water and water-water hydrogen bonding manifested complex dependence on both composition and temperature. Strong water clustering in concentrated solutions was seen. Saturation of hydrogen bonding at w(p) approximately equal to 0.5 and a dramatic decrease in PEO-water hydrogen bonding with increasing temperature, consistent with experimentally observed closed-loop phase behavior, were observed. Little tendency toward intermolecular bridging of PEO chains by water molecules was seen.

Aircraft Range Optimization Using Singular Perturbations

NASA Technical Reports Server (NTRS)

Oconnor, Joseph Taffe

1973-01-01

An approximate analytic solution is developed for the problem of maximizing the range of an aircraft for a fixed end state. The problem is formulated as a singular perturbation and solved by matched inner and outer asymptotic expansions and the minimum principle of Pontryagin. Cruise in the stratosphere, and on transition to and from cruise at constant Mach number are discussed. The state vector includes altitude, flight path angle, and mass. Specific fuel consumption becomes a linear function of power approximating that of the cruise values. Cruise represents the outer solution; altitude and flight path angle are constants, and only mass changes. Transitions between cruise and the specified initial and final conditions correspond to the inner solutions. The mass is constant and altitude and velocity vary. A solution is developed which is valid for cruise but which is not for the initial and final conditions. Transforming of the independent variable near the initial and final conditions result in solutions which are valid for the two inner solutions but not for cruise. The inner solutions can not be obtained without simplifying the state equations. The singular perturbation approach overcomes this difficulty. A quadratic approximation of the state equations is made. The resulting problem is solved analytically, and the two inner solutions are matched to the outer solution.

The stability of two-phase flow over a swept-wing

NASA Technical Reports Server (NTRS)

Coward, Adrian; Hall, Philip

1994-01-01

We use numerical and asymptotic techniques to study the stability of a two-phase air/water flow above a flat porous plate. This flow is a model of the boundary layer which forms on a yawed cylinder and can be used as a useful approximation to the air flow over swept wings during heavy rainfall. We show that the interface between the water and air layers can significantly destabilize the flow, leading to traveling wave disturbances which move along the attachment line. This instability occurs for lower Reynolds numbers than in the case of the absence of a water layer. We also investigate the instability of inviscid stationary modes. We calculate the effective wavenumber and orientation of the stationary disturbance when the fluids have identical physical properties. Using perturbation methods we obtain corrections due to a small stratification in viscosity, thus quantifying the interfacial effects. Our analytical results are in agreement with the numerical solution which we obtain for arbitrary fluid properties.

Multitemperature compaction model of a magma melt in the asthenosphere: A numerical approach

NASA Astrophysics Data System (ADS)

Pak, V. V.

2007-09-01

A numerical compaction model of a fluid in a viscous skeleton is developed with regard for a phase transition. The temperatures of phases are different. The solution is found by the method of asymptotic expansion relative to the incompressible variant, which removes a number of computational problems related to the weak compressibility of the skeleton. For each approximation, the problem is solved by the finite element method. The process of 2-D compaction of a magmatic melt in the asthenosphere under a fault zone is examined for one-and two-temperature cases. The magmatic flow concentrates in this region due to a lower pore pressure. Higher temperature magma entering from lower levels causes a local heating of the skeleton and intense melting of its fusible component. In the two-temperature model, a magma concentration anomaly develops under the fault zone. The fundamental limitations substantially complicating the corresponding calculations within the framework of a one-temperature model are pointed out and the necessity of applying a multitemperature variant is substantiated.

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.

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

NASA Technical Reports Server (NTRS)

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

1987-01-01

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

Equilibrium fractionation of H and O isotopes in water from path integral molecular dynamics

NASA Astrophysics Data System (ADS)

Pinilla, Carlos; Blanchard, Marc; Balan, Etienne; Ferlat, Guillaume; Vuilleumier, Rodolphe; Mauri, Francesco

2014-06-01

The equilibrium fractionation factor between two phases is of importance for the understanding of many planetary and environmental processes. Although thermodynamic equilibrium can be achieved between minerals at high temperature, many natural processes involve reactions between liquids or aqueous solutions and solids. For crystals, the fractionation factor α can be theoretically determined using a statistical thermodynamic approach based on the vibrational properties of the phases. These calculations are mostly performed in the harmonic approximation, using empirical or ab-initio force fields. In the case of aperiodic and dynamic systems such as liquids or solutions, similar calculations can be done using finite-size molecular clusters or snapshots obtained from molecular dynamics (MD) runs. It is however difficult to assess the effect of these approximate models on the isotopic fractionation properties. In this work we present a systematic study of the calculation of the D/H and 18O/16O equilibrium fractionation factors in water for the liquid/vapour and ice/vapour phases using several levels of theory within the simulations. Namely, we use a thermodynamic integration approach based on Path Integral MD calculations (PIMD) and an empirical potential model of water. Compared with standard MD, PIMD takes into account quantum effects in the thermodynamic modeling of systems and the exact fractionation factor for a given potential can be obtained. We compare these exact results with those of modeling strategies usually used, which involve the mapping of the quantum system on its harmonic counterpart. The results show the importance of including configurational disorder for the estimation of isotope fractionation in liquid phases. In addition, the convergence of the fractionation factor as a function of parameters such as the size of the simulated system and multiple isotope substitution is analyzed, showing that isotope fractionation is essentially a local effect in the investigated system.

OPTRAN- OPTIMAL LOW THRUST ORBIT TRANSFERS

NASA Technical Reports Server (NTRS)

Breakwell, J. V.

1994-01-01

OPTRAN is a collection of programs that solve the problem of optimal low thrust orbit transfers between non-coplanar circular orbits for spacecraft with chemical propulsion systems. The programs are set up to find Hohmann-type solutions, with burns near the perigee and apogee of the transfer orbit. They will solve both fairly long burn-arc transfers and "divided-burn" transfers. Program modeling includes a spherical earth gravity model and propulsion system models for either constant thrust or constant acceleration. The solutions obtained are optimal with respect to fuel use: i.e., final mass of the spacecraft is maximized with respect to the controls. The controls are the direction of thrust and the thrust on/off times. Two basic types of programs are provided in OPTRAN. The first type is for "exact solution" which results in complete, exact tkme-histories. The exact spacecraft position, velocity, and optimal thrust direction are given throughout the maneuver, as are the optimal thrust switch points, the transfer time, and the fuel costs. Exact solution programs are provided in two versions for non-coplanar transfers and in a fast version for coplanar transfers. The second basic type is for "approximate solutions" which results in approximate information on the transfer time and fuel costs. The approximate solution is used to estimate initial conditions for the exact solution. It can be used in divided-burn transfers to find the best number of burns with respect to time. The approximate solution is useful by itself in relatively efficient, short burn-arc transfers. These programs are written in FORTRAN 77 for batch execution and have been implemented on a DEC VAX series computer with the largest program having a central memory requirement of approximately 54K of 8 bit bytes. The OPTRAN program were developed in 1983.

Absolute phase estimation: adaptive local denoising and global unwrapping.

PubMed

Bioucas-Dias, Jose; Katkovnik, Vladimir; Astola, Jaakko; Egiazarian, Karen

2008-10-10

The paper attacks absolute phase estimation with a two-step approach: the first step applies an adaptive local denoising scheme to the modulo-2 pi noisy phase; the second step applies a robust phase unwrapping algorithm to the denoised modulo-2 pi phase obtained in the first step. The adaptive local modulo-2 pi phase denoising is a new algorithm based on local polynomial approximations. The zero-order and the first-order approximations of the phase are calculated in sliding windows of varying size. The zero-order approximation is used for pointwise adaptive window size selection, whereas the first-order approximation is used to filter the phase in the obtained windows. For phase unwrapping, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [IEEE Trans. Image Process.16, 698 (2007)] to the denoised wrapped phase. Simulations give evidence that the proposed algorithm yields state-of-the-art performance, enabling strong noise attenuation while preserving image details. (c) 2008 Optical Society of America

An Investigation into Solution Verification for CFD-DEM

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

Fullmer, William D.; Musser, Jordan

This report presents the study of the convergence behavior of the computational fluid dynamicsdiscrete element method (CFD-DEM) method, specifically National Energy Technology Laboratory’s (NETL) open source MFiX code (MFiX-DEM) with a diffusion based particle-tocontinuum filtering scheme. In particular, this study focused on determining if the numerical method had a solution in the high-resolution limit where the grid size is smaller than the particle size. To address this uncertainty, fixed particle beds of two primary configurations were studied: i) fictitious beds where the particles are seeded with a random particle generator, and ii) instantaneous snapshots from a transient simulation of anmore » experimentally relevant problem. Both problems considered a uniform inlet boundary and a pressure outflow. The CFD grid was refined from a few particle diameters down to 1/6 th of a particle diameter. The pressure drop between two vertical elevations, averaged across the bed cross-section was considered as the system response quantity of interest. A least-squares regression method was used to extrapolate the grid-dependent results to an approximate “grid-free” solution in the limit of infinite resolution. The results show that the diffusion based scheme does yield a converging solution. However, the convergence is more complicated than encountered in simpler, single-phase flow problems showing strong oscillations and, at times, oscillations superimposed on top of globally non-monotonic behavior. The challenging convergence behavior highlights the importance of using at least four grid resolutions in solution verification problems so that (over-determined) regression-based extrapolation methods may be applied to approximate the grid-free solution. The grid-free solution is very important in solution verification and VVUQ exercise in general as the difference between it and the reference solution largely determines the numerical uncertainty. By testing different randomized particle configurations of the same general problem (for the fictitious case) or different instances of freezing a transient simulation, the numerical uncertainties appeared to be on the same order of magnitude as ensemble or time averaging uncertainties. By testing different drag laws, almost all cases studied show that model form uncertainty in this one, very important closure relation was larger than the numerical uncertainty, at least with a reasonable CFD grid, roughly five particle diameters. In this study, the diffusion width (filtering length scale) was mostly set at a constant of six particle diameters. A few exploratory tests were performed to show that similar convergence behavior was observed for diffusion widths greater than approximately two particle diameters. However, this subject was not investigated in great detail because determining an appropriate filter size is really a validation question which must be determined by comparison to experimental or highly accurate numerical data. Future studies are being considered targeting solution verification of transient simulations as well as validation of the filter size with direct numerical simulation data.« less

Solution of the two-dimensional spectral factorization problem

NASA Technical Reports Server (NTRS)

Lawton, W. M.

1985-01-01

An approximation theorem is proven which solves a classic problem in two-dimensional (2-D) filter theory. The theorem shows that any continuous two-dimensional spectrum can be uniformly approximated by the squared modulus of a recursively stable finite trigonometric polynomial supported on a nonsymmetric half-plane.

A discrete fracture model for two-phase flow in fractured porous media

NASA Astrophysics Data System (ADS)

Gläser, Dennis; Helmig, Rainer; Flemisch, Bernd; Class, Holger

2017-12-01

A discrete fracture model on the basis of a cell-centered finite volume scheme with multi-point flux approximation (MPFA) is presented. The fractures are included in a d-dimensional computational domain as (d - 1)-dimensional entities living on the element facets, which requires the grid to have the element facets aligned with the fracture geometries. However, the approach overcomes the problem of small cells inside the fractures when compared to equi-dimensional models. The system of equations considered is solved on both the matrix and the fracture domain, where on the prior the fractures are treated as interior boundaries and on the latter the exchange term between fracture and matrix appears as an additional source/sink. This exchange term is represented by the matrix-fracture fluxes, computed as functions of the unknowns in both domains by applying adequate modifications to the MPFA scheme. The method is applicable to both low-permeable as well as highly conductive fractures. The quality of the results obtained by the discrete fracture model is studied by comparison to an equi-dimensional discretization on a simple geometry for both single- and two-phase flow. For the case of two-phase flow in a highly conductive fracture, good agreement in the solution and in the matrix-fracture transfer fluxes could be observed, while for a low-permeable fracture the discrepancies were more pronounced. The method is then applied two-phase flow through a realistic fracture network in two and three dimensions.

Many-body Green’s function theory for electron-phonon interactions: Ground state properties of the Holstein dimer

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

Säkkinen, Niko; Leeuwen, Robert van; Peng, Yang

2015-12-21

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is stronglymore » correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.« less

Spectrum Evolution of Accelerating or Slowing down Soliton at its Propagation in a Medium with Gold Nanorods

NASA Astrophysics Data System (ADS)

Trofimov, Vyacheslav A.; Lysak, Tatiana M.

2018-04-01

We investigate both numerically and analytically the spectrum evolution of a novel type soliton - nonlinear chirped accelerating or decelerating soliton - at a femtosecond pulse propagation in a medium containing noble nanoparticles. In our consideration, we take into account one- or two-photon absorption of laser radiation by nanorods, and time-dependent nanorod aspect ratio changing due to their melting or reshaping because of laser energy absorption. The chirped solitons are formed due to the trapping of laser radiation by the nanorods reshaping fronts, if a positive or negative phase-amplitude grating is induced by laser radiation. Accelerating or slowing down chirped soliton formation is accompanied by the soliton spectrum blue or red shift. To prove our numerical results, we derived the approximate analytical law for the spectrum maximum intensity evolution along the propagation coordinate, based on earlier developed approximate analytical solutions for accelerating and decelerating solitons.

Optimal rendezvous in the neighborhood of a circular orbit

NASA Technical Reports Server (NTRS)

Jones, J. B.

1976-01-01

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

Early-Time Solution of the Horizontal Unconfined Aquifer in the Buildup Phase

NASA Astrophysics Data System (ADS)

Gravanis, Elias; Akylas, Evangelos

2017-10-01

We derive the early-time solution of the Boussinesq equation for the horizontal unconfined aquifer in the buildup phase under constant recharge and zero inflow. The solution is expressed as a power series of a suitable similarity variable, which is constructed so that to satisfy the boundary conditions at both ends of the aquifer, that is, it is a polynomial approximation of the exact solution. The series turns out to be asymptotic and it is regularized by resummation techniques that are used to define divergent series. The outflow rate in this regime is linear in time, and the (dimensionless) coefficient is calculated to eight significant figures. The local error of the series is quantified by its deviation from satisfying the self-similar Boussinesq equation at every point. The local error turns out to be everywhere positive, hence, so is the integrated error, which in turn quantifies the degree of convergence of the series to the exact solution.

Direct computation of stochastic flow in reservoirs with uncertain parameters

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

Dainton, M.P.; Nichols, N.K.; Goldwater, M.H.

1997-01-15

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point andmore » to the field convariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data. 14 refs., 14 figs., 3 tabs.« less

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Comparison of simplified models in the prediction of two phase flow in pipelines

NASA Astrophysics Data System (ADS)

Jerez-Carrizales, M.; Jaramillo, J. E.; Fuentes, D.

2014-06-01

Prediction of two phase flow in pipelines is a common task in engineering. It is a complex phenomenon and many models have been developed to find an approximate solution to the problem. Some old models, such as the Hagedorn & Brown (HB) model, have been highlighted by many authors to give very good performance. Furthermore, many modifications have been applied to this method to improve its predictions. In this work two simplified models which are based on empiricism (HB and Mukherjee and Brill, MB) are considered. One mechanistic model which is based on the physics of the phenomenon (AN) and it still needs some correlations called closure relations is also used. Moreover, a drift flux model defined in steady state that is flow pattern dependent (HK model) is implemented. The implementation of these methods was tested using published data in the scientific literature for vertical upward flows. Furthermore, a comparison of the predictive performance of the four models is done against a well from Campo Escuela Colorado. Difference among four models is smaller than difference with experimental data from the well in Campo Escuela Colorado.

Model of chiral spin liquids with Abelian and non-Abelian topological phases

NASA Astrophysics Data System (ADS)

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; Tsvelik, A. M.

2017-12-01

We present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, the Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.

Phase transition solutions in geometrically constrained magnetic domain wall models

NASA Astrophysics Data System (ADS)

Chen, Shouxin; Yang, Yisong

2010-02-01

Recent work on magnetic phase transition in nanoscale systems indicates that new physical phenomena, in particular, the Bloch wall width narrowing, arise as a consequence of geometrical confinement of magnetization and leads to the introduction of geometrically constrained domain wall models. In this paper, we present a systematic mathematical analysis on the existence of the solutions of the basic governing equations in such domain wall models. We show that, when the cross section of the geometric constriction is a simple step function, the solutions may be obtained by minimizing the domain wall energy over the constriction and solving the Bogomol'nyi equation outside the constriction. When the cross section and potential density are both even, we establish the existence of an odd domain wall solution realizing the phase transition process between two adjacent domain phases. When the cross section satisfies a certain integrability condition, we prove that a domain wall solution always exists which links two arbitrarily designated domain phases.

On the Stefan Problem with Volumetric Energy Generation

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

John Crepeau; Ali Siahpush; Blaine Spotten

2009-11-01

This paper presents results of solid-liquid phase change, driven by volumetric energy generation, in a vertical cylinder. We show excellent agreement between a quasi-static, approximate analytical solution valid for Stefan numbers less than one, and a computational model solved using the CFD code FLUENT®. A computational study also shows the effect that the volumetric energy generation has on both the mushy zone thickness and convection in the melt during phase change.

An interaction algorithm for prediction of mean and fluctuating velocities in two-dimensional aerodynamic wake flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1980-01-01

A theoretical analysis is presented yielding sets of partial differential equations for determination of turbulent aerodynamic flowfields in the vicinity of an airfoil trailing edge. A four phase interaction algorithm is derived to complete the analysis. Following input, the first computational phase is an elementary viscous corrected two dimensional potential flow solution yielding an estimate of the inviscid-flow induced pressure distribution. Phase C involves solution of the turbulent two dimensional boundary layer equations over the trailing edge, with transition to a two dimensional parabolic Navier-Stokes equation system describing the near-wake merging of the upper and lower surface boundary layers. An iteration provides refinement of the potential flow induced pressure coupling to the viscous flow solutions. The final phase is a complete two dimensional Navier-Stokes analysis of the wake flow in the vicinity of a blunt-bases airfoil. A finite element numerical algorithm is presented which is applicable to solution of all partial differential equation sets of inviscid-viscous aerodynamic interaction algorithm. Numerical results are discussed.

Ultrafast excited-state relaxation of a binuclear Ag(i) phosphine complex in gas phase and solution.

PubMed

Kruppa, S V; Bäppler, F; Klopper, W; Walg, S P; Thiel, W R; Diller, R; Riehn, C

2017-08-30

The binuclear complex [Ag 2 (dcpm) 2 ](PF 6 ) 2 (dcpm = bis(dicyclohexylphosphino)methane) exhibits a structure with a close silver-silver contact mediated by the bridging ligand and thus a weak argentophilic interaction. Upon electronic excitation this cooperative effect is strongly increased and determines the optical and luminescence properties of the compound. We have studied here the ultrafast electronic dynamics in parallel in gas phase by transient photodissociation and in solution by transient absorption. In particular, we report the diverse photofragmentation pathways of isolated [Ag 2 (dcpm) 2 ] 2+ in an ion trap and its gas phase UV photodissociation spectrum. By pump-probe fragmentation action spectroscopy (λ ex = 260 nm) in the gas phase, we have obtained fragment-specific transients which exhibit a common ultrafast multiexponential decay. This is fitted to four time constants (0.6/5.8/100/>1000 ps), highlighting complex intrinsic photophysical processes. Remarkably, multiexponential dynamics (0.9/8.5/73/604 ps) are as well found for the relaxation dynamics in acetonitrile solution. Ab initio calculations at the level of approximate coupled-cluster singles-doubles (CC2) theory of ground and electronically excited states of the reduced model system [Ag 2 (dmpm) 2 ] 2+ (dmpm = bis(dimethylphosphino)methane) indicate a shortening of the Ag-Ag distance upon excitation by 0.3-0.4 Å. In C 2 geometry two close-lying singlet states S 1 ( 1 MC(dσ*-pπ), 1 B, 4.13 eV) and S 2 ( 1 MC(dσ*-pσ), 1 A, 4.45 eV) are found. The nearly dark S 1 state has not been reported so far. The excitation of the S 2 state carries a large oscillator strength for the calculated vertical transition (266 nm). Two related triplets are calculated at T 1 (3.87 eV) and T 2 (3.90 eV). From these findings we suggest possible relaxation pathways with the two short time constants ascribed to ISC/IVR and propose from the obtained similar values in gas phase that the fast solution dynamics is dominated by intramolecular processes. A further relaxation by IC/IVR in the triplet manifold is likely to account for the observed intermediate time constants. For the acetonitrile relaxation dynamics additional modifications are invoked based on solvent-induced shifts of the energy levels and the possible formation of solvent and counterion exciplexes on a longer timescale.

METHOD OF INHIBITING CORROSION IN URANYL SULFATE SOLUTIONS

DOEpatents

Bohlmann, E.G.; Griess, J.C. Jr.

1960-08-23

A method is given for treating a uranyl sulfate solution to inhibit the corrosiveness of the solution and elevate the phase separation temperature of the solution. Lithium sulfate is added to the solution in an amount ranging from 0.25 to 1.3 times the uranyl sulfate concentration. The corrosiveness of the solution with respect to stainless steel is substantially decreased by this means. This treatment also serves to raise the phase separation temperature of the solution (above 250 deg C), at which time the uranyl sulfate solution separates into two liquid phases of unequal uranium concentration and thus becomes unsuitable as nuclear reactor fuel.

Recovery of hydrogen iodide

DOEpatents

Norman, John H.

1983-01-01

A method of extraction of HI from an aqueous solution of HI and I.sub.2. HBr is added to create a two-phase liquid mixture wherein a dry phase consists essentially of HBr, I and HI and is in equilibrium with a wet phase having a far greater HBr:HI ratio. Using a countercurrent extractor, two solutions can be obtained: a dry HBr--HI--I.sub.2 solution and a wet essentially HBr solution. The dry and wet phases are easily separable, and HI is recovered from the dry phase, after first separating I.sub.2, as by distillation. Alternatively, the HI-HBr liquid mixture is treated to catalytically decompose the HI. HBr is recovered from the wet phase by suitable treatment, including high-pressure distillation, to produce an H.sub.2 O--HBr azeotrope that is not more than 25 mole percent HBr. The azeotrope may be returned for use in an earlier step in the overall process which results in the production of the aqueous solution of HI and I.sub.2 without major detriment because of the presence of HBr.

Recovery of hydrogen iodide

DOEpatents

Norman, J.H.

1983-08-02

A method is described for extraction of HI from an aqueous solution of HI and I[sub 2]. HBr is added to create a two-phase liquid mixture wherein a dry phase consists essentially of HBr, I and HI and is in equilibrium with a wet phase having a far greater HBr:HI ratio. Using a countercurrent extractor, two solutions can be obtained: a dry HBr--HI--I[sub 2] solution and a wet essentially HBr solution. The dry and wet phases are easily separable, and HI is recovered from the dry phase, after first separating I[sub 2], as by distillation. Alternatively, the HI-HBr liquid mixture is treated to catalytically decompose the HI. HBr is recovered from the wet phase by suitable treatment, including high-pressure distillation, to produce an H[sub 2]O--HBr azeotrope that is not more than 25 mole percent HBr. The azeotrope may be returned for use in an earlier step in the overall process which results in the production of the aqueous solution of HI and I[sub 2] without major detriment because of the presence of HBr. 1 fig.

Analysis of models for two solution crystal growth problems

NASA Technical Reports Server (NTRS)

Fehribach, Joseph D.; Rosenberger, Franz

1989-01-01

Two diffusive solution crystal growth models are considered which are characterized by two phases separated by an interface, a lack of convective mixing in either phase, and the presence of diffusion components differing widely in diffusivity. The first model describes precipitant-driven solution crystal growth and the second model describes a hanging drop evaporation problem. It is shown that for certain proteins sharp concentration gradients may develop in the drop during evaporation, while under the same conditions the concentrations of other proteins remain uniform.

Two-phase framework for near-optimal multi-target Lambert rendezvous

NASA Astrophysics Data System (ADS)

Bang, Jun; Ahn, Jaemyung

2018-03-01

This paper proposes a two-phase framework to obtain a near-optimal solution of multi-target Lambert rendezvous problem. The objective of the problem is to determine the minimum-cost rendezvous sequence and trajectories to visit a given set of targets within a maximum mission duration. The first phase solves a series of single-target rendezvous problems for all departure-arrival object pairs to generate the elementary solutions, which provides candidate rendezvous trajectories. The second phase formulates a variant of traveling salesman problem (TSP) using the elementary solutions prepared in the first phase and determines the final rendezvous sequence and trajectories of the multi-target rendezvous problem. The validity of the proposed optimization framework is demonstrated through an asteroid exploration case study.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

CFD Study of Turbo-Ramjet Interactions in Hypersonic Airbreathing Propulsion System

NASA Technical Reports Server (NTRS)

Chang, Ing; Hunter, Louis G.

1996-01-01

Advanced airbreathing propulsion systems used in Mach 4-6 mission scenarios, usually involve turbo-ramjet configurations. As the engines transition from turbojet to ramjet, there is an operational envelope where both engines operate simultaneously. In the first phase of our study, an over/under nozzle configuration was analyzed. The two plumes from the turbojet and ramjet interact at the end of a common 2-D cowl, where they both reach an approximate Mach 3.0 condition and then jointly expand to Mach 3.6 at the common nozzle exit plane. For the problem analyzed, the turbojet engine operates at a higher nozzle pressure ratio than the ramjet, causes the turbojet plume overpowers the ramjet plume, deflecting it approximately 12 degrees downward and in turn the turbojet plume is deflected 6 degrees upward. In the process, shocks were formed at the deflections and a shear layer formed at the confluence of the two jets. This particular case was experimentally tested and the data were used to compare with a computational fluid dynamics (CFD) study using the PARC2D code. The CFD results were in good agreement with both static pressure distributions on the cowl separator and on nozzle walls. The thrust coefficients were also in reasonable agreement. In addition, inviscid relationships were developed around the confluence point, where the two exhaust jets meet, and these results compared favorably with the CFD results. In the second phase of our study, a 3-D CFD solution was generated to compare with the 2-D solution. The major difference between the 2-D and 3-D solutions was the interaction of the shock waves, generated by the plume interactions, on the sidewall. When a shock wave interacts with a sidewall and sidewall boundary layer, it is called a glancing shock sidewall interaction. These interactions entrain boundary layer flow down the shockline into a vortical flow pattern. The 3-D plots show the streamlines being entrained down the shockline. The pressure of the flow also decreases slightly as the sidewall is approached. Other difference between the 2-D and 3-D solutions were a lowering of the nozzle thrust coefficient value from 0.9850 (2-D) to 0.9807 (3-D), where the experimental value was 0.9790. In the third phase of our study, a different turbo-ramjet configuration was analyzed. The confluence of a supersonic turbojet and a subsonic ramjet in the turbine based combined-cycle (TBCC) propulsion system was studied by a 2-D CFD code. In the analysis, Mach 1.4 primary turbojet was mixed with the subsonic ramjet secondary flow in an ejector mode operation. Reasonable agreements were obtained with the supplied I-D TBCC solutions. For low downstream backpressure, the Fabri choke condition (Break-Point condition) was observed in the secondary flow within mixing zone. For sufficient high downstream backpressure, the Fabri choke no longer exist, the ramjet flow was reduced and the ejector flow became backpressure dependent. Highly non-uniform flow at ejector exit were observed, indicated that for smooth downstream combustion, the mixing of the two streams probably required some physical devices.

Continual approach at T=0 in the mean field theory of incommensurate magnetic states in the frustrated Heisenberg ferromagnet with an easy axis anisotropy

NASA Astrophysics Data System (ADS)

Martynov, S. N.; Tugarinov, V. I.; Martynov, A. S.

2017-10-01

The algorithm of approximate solution was developed for the differential equation describing the anharmonical change of the spin orientation angle in the model of ferromagnet with the exchange competition between nearest and next nearest magnetic neighbors and the easy axis exchange anisotropy. The equation was obtained from the collinearity constraint on the discrete lattice. In the low anharmonicity approximation the equation is resulted to an autonomous form and is integrated in quadratures. The obvious dependence of the angle velocity and second derivative of angle from angle and initial condition was derived by expanding the first integral of the equation in the Taylor series in vicinity of initial condition. The ground state of the soliton solutions was calculated by a numerical minimization of the energy integral. The evaluation of the used approximation was made for a triple point of the phase diagram.

Application of thermodynamics to silicate crystalline solutions

NASA Technical Reports Server (NTRS)

Saxena, S. K.

1972-01-01

A review of thermodynamic relations is presented, describing Guggenheim's regular solution models, the simple mixture, the zeroth approximation, and the quasi-chemical model. The possibilities of retrieving useful thermodynamic quantities from phase equilibrium studies are discussed. Such quantities include the activity-composition relations and the free energy of mixing in crystalline solutions. Theory and results of the study of partitioning of elements in coexisting minerals are briefly reviewed. A thermodynamic study of the intercrystalline and intracrystalline ion exchange relations gives useful information on the thermodynamic behavior of the crystalline solutions involved. Such information is necessary for the solution of most petrogenic problems and for geothermometry. Thermodynamic quantities for tungstates (CaWO4-SrWO4) are calculated.

In vitro CPC retention and VSC adsorption by IPM oil droplets: possible mechanisms of action of a two phase mouthwash.

PubMed

Sterer, N; Slutzky, H; Kohavi, D; Matalon, S

2013-09-01

Two phase oil-water mouthwash has been previously shown to efficiently bind oral microorganisms, relying on their cell surface hydrophobicity. The aim of the present in vitro study was to test the cetylpyridinium chloride (CPC) retention and volatile sulfide compounds (VSCs) adsorption abilities of the oil droplets created by mixing of a two phase oil-water solution. VSC adsorption was assayed using a salivary incubation assay and garlic powder solutions, and demonstrated using microscopic sulfide assay. CPC retention was assayed by kinetic and endpoint measurement of Streptococcus salivarius outgrowth using microplate (ELISA) reader. Results showed that the isopropyl myristate (IPM) oil droplets in the two phase solutions were able to adsorb 68-80% of VSCs. CPC at a concentration of 0.05% was most affectively retained by the oil droplets showing a significantly increase in residual antibacterial activity against Streptococcus salivarius. These results taken together, suggests that VSC adsorption and CPC retention by IPM oil droplets may be two additional mechanisms in the activity of the two phase mouthwash formulation.

eLISA Telescope In-field Pointing and Scattered Light Study

NASA Astrophysics Data System (ADS)

Livas, J.; Sankar, S.; West, G.; Seals, L.; Howard, J.; Fitzsimons, E.

2017-05-01

The orbital motion of the three spacecraft that make up the eLISA Observatory constellation causes long-arm line of sight variations of approximately ± one degree over the course of a year. The baseline solution is to package the telescope, the optical bench, and the gravitational reference sensor (GRS) into an optical assembly at each end of the measurement arm, and then to articulate the assembly. An optical phase reference is exchanged between the moving optical benches with a single mode optical fiber (“backlink” fiber). An alternative solution, referred to as in-field pointing, embeds a steering mirror into the optical design, fixing the optical benches and eliminating the backlink fiber, but requiring the additional complication of a two-stage optical design for the telescope. We examine the impact of an in-field pointing design on the scattered light performance.

Dispersion analysis and measurement of circular cylindrical wedge-like acoustic waveguides.

PubMed

Yu, Tai-Ho

2015-09-01

This study investigated the propagation of flexural waves along the outer edge of a circular cylindrical wedge, the phase velocities, and the corresponding mode displacements. Thus far, only approximate solutions have been derived because the corresponding boundary-value problems are complex. In this study, dispersion curves were determined using the bi-dimensional finite element method and derived through the separation of variables and the Hamilton principle. Modal displacement calculations clarified that the maximal deformations appeared at the outer edge of the wedge tip. Numerical examples indicated how distinct thin-film materials deposited on the outer surface of the circular cylindrical wedge influenced the dispersion curves. Additionally, dispersion curves were measured using a laser-induced guided wave, a knife-edge measurement scheme, and a two-dimensional fast Fourier transform method. Both the numerical and experimental results correlated closely, thus validating the numerical solution. Copyright © 2015 Elsevier B.V. All rights reserved.

Calculation of Gallium-metal-Arsenic phase diagrams

NASA Technical Reports Server (NTRS)

Scofield, J. D.; Davison, J. E.; Ray, A. E.; Smith, S. R.

1991-01-01

Electrical contacts and metallization to GaAs solar cells must survive at high temperatures for several minutes under specific mission scenarios. The determination of which metallizations or alloy systems that are able to withstand extreme thermal excursions with minimum degradation to solar cell performance can be predicted by properly calculated temperature constitution phase diagrams. A method for calculating a ternary diagram and its three constituent binary phase diagrams is briefly outlined and ternary phase diagrams for three Ga-As-X alloy systems are presented. Free energy functions of the liquid and solid phase are approximated by the regular solution theory. Phase diagrams calculated using this method are presented for the Ga-As-Ge and Ga-As-Ag systems.

Solubilisation of poorly water-soluble drugs during in vitro lipolysis of medium- and long-chain triacylglycerols.

PubMed

Christensen, Janne Ørskov; Schultz, Kirsten; Mollgaard, Birgitte; Kristensen, Henning Gjelstrup; Mullertz, Anette

2004-11-01

The partitioning of poorly soluble drugs into an aqueous micellar phase was exploited using an in vitro lipid digestion model, simulating the events taking place during digestion of acylglycerols in the duodenum. The aqueous micellar phase was isolated after ultracentrifugation of samples obtained at different degrees of triacylglycerol hydrolysis. Flupentixol, 1'-[4-[1-(4-fluorophenyl)-1-H-indol-3-yl]-1-butyl]spiro[iso-benzofuran-1(3H), 4' piperidine] (LU 28-179) and probucol were studied. The effect of the alkyl chain length of the triacylglycerol was studied using a medium-chain triacylglycerol (MCT) and a long-chain triacylglycerol (LCT), respectively. In general, an oil solution was used as the lipid source in the model. Samples were analysed in regard to micellar size, lipid composition and drug concentration. During lipolysis, the content of lipolytic products in the aqueous micellar phase increased. The micellar size (R(H) approximately 3 nm) only increased when long-chain lipolytic products were incorporated in the mixed micelles (R(H) approximately 7.8 nm). Flupentixol was quickly transferred to the mixed micelles due to high solubility in this phase (100% released). A tendency towards higher solubilisation of LU 28-179, when it was administered in the LCT (approximately 24% released) compared to when it was administered in the MCT (approximately 15% released) at 70% hydrolysis, and a lagphase was observed. There was no difference in the solubilisation of probucol using MCT or LCT ( approximately 20% released), respectively. Differences in the physicochemical properties of the drugs resulted in differences in their distribution between the phases arising during lipolysis.

Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry

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

Besse, Nicolas, E-mail: Nicolas.Besse@oca.eu; Institut Jean Lamour, UMR CNRS/UL 7198, Université de Lorraine, BP 70239 54506 Vandoeuvre-lès-Nancy Cedex; Coulette, David, E-mail: David.Coulette@ipcms.unistra.fr

2016-08-15

Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov–Poisson and Vlasov–Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to themore » VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, “Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry” (submitted)] and were found to be surprisingly close to those for the original gyrokinetic-Vlasov equations. The purpose of the present paper is to make these new ideas accessible to two readerships: applied mathematicians and plasma physicists.« less

Analytic reconstruction of magnetic resonance imaging signal obtained from a periodic encoding field.

PubMed

Rybicki, F J; Hrovat, M I; Patz, S

2000-09-01

We have proposed a two-dimensional PERiodic-Linear (PERL) magnetic encoding field geometry B(x,y) = g(y)y cos(q(x)x) and a magnetic resonance imaging pulse sequence which incorporates two fields to image a two-dimensional spin density: a standard linear gradient in the x dimension, and the PERL field. Because of its periodicity, the PERL field produces a signal where the phase of the two dimensions is functionally different. The x dimension is encoded linearly, but the y dimension appears as the argument of a sinusoidal phase term. Thus, the time-domain signal and image spin density are not related by a two-dimensional Fourier transform. They are related by a one-dimensional Fourier transform in the x dimension and a new Bessel function integral transform (the PERL transform) in the y dimension. The inverse of the PERL transform provides a reconstruction algorithm for the y dimension of the spin density from the signal space. To date, the inverse transform has been computed numerically by a Bessel function expansion over its basis functions. This numerical solution used a finite sum to approximate an infinite summation and thus introduced a truncation error. This work analytically determines the basis functions for the PERL transform and incorporates them into the reconstruction algorithm. The improved algorithm is demonstrated by (1) direct comparison between the numerically and analytically computed basis functions, and (2) reconstruction of a known spin density. The new solution for the basis functions also lends proof of the system function for the PERL transform under specific conditions.

Simulation of angular-resolved RABBITT measurements in noble-gas atoms

NASA Astrophysics Data System (ADS)

Bray, Alexander W.; Naseem, Faiza; Kheifets, Anatoli S.

2018-06-01

We simulate angular-resolved RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) measurements on valence shells of noble-gas atoms (Ne, Ar, Kr, and Xe). Our nonperturbative numerical simulation is based on solution of the time-dependent Schrödinger equation (TDSE) for a target atom driven by an ionizing XUV and dressing IR fields. From these simulations we extract the angular-dependent magnitude and phase of the RABBITT oscillations and deduce the corresponding angular anisotropy β parameter and Wigner time delay τW for the single XUV photon absorption that initiates the RABBITT process. Said β and τW parameters are compared with calculations in the random-phase approximation with exchange (RPAE), which includes intershell correlation. This comparison is used to test various effective potentials employed in the one-electron TDSE. In lighter atoms (Ne and Ar), several effective potentials are found to provide accurate simulations of RABBITT measurements for a wide range of photon energies up to 100 eV above the valence-shell threshold. In heavier atoms (Kr and Xe), the onset of strong correlation with the d shell restricts the validity of the single active electron approximation to several tens of eV above the valence-shell threshold.

Standard Reference Materials (SRMs) for the Calibration and Validation of Analytical Methods for PCBs (as Aroclor Mixtures)

PubMed Central

Poster, Dianne L.; Schantz, Michele M.; Leigh, Stefan D.; Wise, Stephen A.

2004-01-01

Six Standard Reference Materials (SRMs®) have been prepared by the National Institute of Standards and Technology (NIST) for the determination of PCBs as different Aroclor mixtures in methanol. Six additional SRMs of the same Aroclors in transformer oil have also been prepared. Specifically, solutions of Aroclors 1016, 1232, 1242, 1254, and 1260 have been gravimetrically prepared (individually) in methanol and transformer oil, mixed, and transferred to amber glass ampoules in approximately 1.2 mL aliquots. Gas chromatography with electron capture detection (GC-ECD) has been used to verify the gravimetric data for each solution and transformer oil SRM. Liquid chromatography was used for the isolation of the Aroclors from the transformer oil SRMs prior to GC-ECD analysis. Separate calibration solutions and oils were prepared with Aroclor levels similar to those in each methanol solution and transformer oil SRM and were processed alongside the samples. The GC-ECD response of each Aroclor was monitored relative to internal standards that were added to the complex mixtures for quantification. The gravimetric concentrations of Aroclors 1242 and 1254 in methanol were also examined by the same method of analysis (GC-ECD) using several different sources of Aroclors and two different capillary GC columns: a 5 % phenyl methylpolysiloxane phase and a relatively non-polar phase. The preparation of the materials, the gas chromatographic results, and the certified concentration values for each Aroclor SRM are described in this paper. PMID:27366608

Conformational equilibria of alkanes in aqueous solution: relationship to water structure near hydrophobic solutes.

PubMed Central

Ashbaugh, H S; Garde, S; Hummer, G; Kaler, E W; Paulaitis, M E

1999-01-01

Conformational free energies of butane, pentane, and hexane in water are calculated from molecular simulations with explicit waters and from a simple molecular theory in which the local hydration structure is estimated based on a proximity approximation. This proximity approximation uses only the two nearest carbon atoms on the alkane to predict the local water density at a given point in space. Conformational free energies of hydration are subsequently calculated using a free energy perturbation method. Quantitative agreement is found between the free energies obtained from simulations and theory. Moreover, free energy calculations using this proximity approximation are approximately four orders of magnitude faster than those based on explicit water simulations. Our results demonstrate the accuracy and utility of the proximity approximation for predicting water structure as the basis for a quantitative description of n-alkane conformational equilibria in water. In addition, the proximity approximation provides a molecular foundation for extending predictions of water structure and hydration thermodynamic properties of simple hydrophobic solutes to larger clusters or assemblies of hydrophobic solutes. PMID:10423414

Perturbation solutions of combustion instability problems

NASA Technical Reports Server (NTRS)

Googerdy, A.; Peddieson, J., Jr.; Ventrice, M.

1979-01-01

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

Field-induced refractive index variation in the dark conglomerate phase for polarization-independent switchable liquid crystal lenses.

PubMed

Milton, H E; Nagaraj, M; Kaur, S; Jones, J C; Morgan, P B; Gleeson, H F

2014-11-01

Liquid crystal lenses are an emerging technology that can provide variable focal power in response to applied voltage. Many designs for liquid-crystal-based lenses are polarization dependent, so that 50% of light is not focused as required, making polarization-independent technologies very attractive. Recently, the dark conglomerate (DC) phase, which is an optically isotropic liquid crystalline state, has been shown to exhibit a large change in refractive index in response to an applied electric field (Δn=0.04). This paper describes computational modeling of the electrostatic solutions for two different types of 100 μm diameter liquid crystal lenses, which include the DC phase, demonstrating that it shows great potential for efficient isotropic optical switching in lenses. A feature of the field dependence of the refractive index change in the DC phase is that it is approximately linear in a certain range, leading to the prediction of excellent optical quality for driving fields in this regime. Interestingly, a simulated microlens is shown to exhibit two modes of operation: a positive lens based upon a uniform bulk change in refractive index at high voltages, and a negative lens resulting from the induction of a gradient index effect at intermediate voltages.

Density functional theory of gas-liquid phase separation in dilute binary mixtures

NASA Astrophysics Data System (ADS)

Okamoto, Ryuichi; Onuki, Akira

2016-06-01

We examine statics and dynamics of phase-separated states of dilute binary mixtures using density functional theory. In our systems, the difference of the solvation chemical potential between liquid and gas Δ {μ\\text{s}} (the Gibbs energy of transfer) is considerably larger than the thermal energy {{k}\\text{B}}T for each solute particle and the attractive interaction among the solute particles is weaker than that among the solvent particles. In these conditions, the saturated vapor pressure increases by {{k}\\text{B}}Tn2\\ell\\exp ≤ft(Δ {μ\\text{s}}/{{k}\\text{B}}T\\right) , where n2\\ell is the solute density added in liquid. For \\exp ≤ft(Δ {μ\\text{s}}/{{k}\\text{B}}T\\right)\\gg 1 , phase separation is induced at low solute densities in liquid and the new phase remains in gaseous states, even when the liquid pressure is outside the coexistence curve of the solvent. This explains the widely observed formation of stable nanobubbles in ambient water with a dissolved gas. We calculate the density and stress profiles across planar and spherical interfaces, where the surface tension decreases with increasing interfacial solute adsorption. We realize stable solute-rich bubbles with radius about 30 nm, which minimize the free energy functional. We then study dynamics around such a bubble after a decompression of the surrounding liquid, where the bubble undergoes a damped oscillation. In addition, we present some exact and approximate expressions for the surface tension and the interfacial stress tensor.

Accuracy & Computational Considerations for Wide--Angle One--way Seismic Propagators and Multiple Scattering by Invariant Embedding

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2004-12-01

Pseudodifferential operators (PSDOs) yield in principle exact one--way seismic wave equations, which are attractive both conceptually and for their promise of computational efficiency. The one--way operators can be extended to include multiple--scattering effects, again in principle exactly. In practice approximations must be made and, as an example, the variable--wavespeed Helmholtz equation for scalar waves in two space dimensions is here factorized to give the one--way wave equation. This simple case permits clear identification of a sequence of physically reasonable approximations to be used when the mathematically exact PSDO one--way equation is implemented on a computer. As intuition suggests, these approximations hinge on the medium gradients in the direction transverse to the main propagation direction. A key point is that narrow--angle approximations are to be avoided in the interests of accuracy. Another key consideration stems from the fact that the so--called ``standard--ordering'' PSDO indicates how lateral interpolation of the velocity structure can significantly reduce computational costs associated with the Fourier or plane--wave synthesis lying at the heart of the calculations. The decision on whether a slow or a fast Fourier transform code should be used rests upon how many lateral model parameters are truly distinct. A third important point is that the PSDO theory shows what approximations are necessary in order to generate an exponential one--way propagator for the laterally varying case, representing the intuitive extension of classical integral--transform solutions for a laterally homogeneous medium. This exponential propagator suggests the use of larger discrete step sizes, and it can also be used to approach phase--screen like approximations (though the latter are not the main interest here). Numerical comparisons with finite--difference solutions will be presented in order to assess the approximations being made and to gain an understanding of computation time differences. The ideas described extend to the three--dimensional, generally anisotropic case and to multiple scattering by invariant embedding.

Stability of exact solutions describing two-layer flows with evaporation at the interface

NASA Astrophysics Data System (ADS)

Bekezhanova, V. B.; Goncharova, O. N.

2016-12-01

A new exact solution of the equations of free convection has been constructed in the framework of the Oberbeck-Boussinesq approximation of the Navier-Stokes equations. The solution describes the joint flow of an evaporating viscous heat-conducting liquid and gas-vapor mixture in a horizontal channel. In the gas phase the Dufour and Soret effects are taken into account. The consideration of the exact solution allows one to describe different classes of flows depending on the values of the problem parameters and boundary conditions for the vapor concentration. A classification of solutions and results of the solution analysis are presented. The effects of the external disturbing influences (of the liquid flow rates and longitudinal gradients of temperature on the channel walls) on the stability characteristics have been numerically studied for the system HFE7100-nitrogen in the common case, when the longitudinal temperature gradients on the boundaries of the channel are not equal. In the system both monotonic and oscillatory modes can be formed, which damp or grow depending on the values of the initial perturbations, flow rates and temperature gradients. Hydrodynamic perturbations are most dangerous under large gas flow rates. The increasing oscillatory perturbations are developed due to the thermocapillary effect under large longitudinal gradients of temperature. The typical forms of the disturbances are shown.

Structurally integrated organic light emitting device-based sensors for gas phase and dissolved oxygen.

PubMed

Shinar, Ruth; Zhou, Zhaoqun; Choudhury, Bhaskar; Shinar, Joseph

2006-05-24

A compact photoluminescence (PL)-based O2 sensor utilizing an organic light emitting device (OLED) as the light source is described. The sensor device is structurally integrated. That is, the sensing element and the light source, both typically thin films that are fabricated on separate glass substrates, are attached back-to-back. The sensing elements are based on the oxygen-sensitive dyes Pt- or Pd-octaethylporphyrin (PtOEP or PdOEP, respectively), which are embedded in a polystyrene (PS) matrix, or dissolved in solution. Their performance is compared to that of a sensing element based on tris(4,7-diphenyl-l,10-phenanthroline) Ru II (Ru(dpp)) embedded in a sol-gel film. A green OLED light source, based on tris(8-hydroxy quinoline Al (Alq3), was used to excite the porphyrin dyes; a blue OLED, based on 4,4'-bis(2,2'-diphenylviny1)-1,1'-biphenyl, was used to excite the Ru(dpp)-based sensing element. The O2 level was monitored in the gas phase and in water, ethanol, and toluene solutions by measuring changes in the PL lifetime tau of the O2-sensitive dyes. The sensor performance was evaluated in terms of the detection sensitivity, dynamic range, gas flow rate, and temperature effect, including the temperature dependence of tau in pure Ar and O2 atmospheres. The dependence of the sensitivity on the preparation procedure of the sensing film and on the PS and dye concentrations in the sensing element, whether a solid matrix or solution, were also evaluated. Typical values of the detection sensitivity in the gas phase, S(g) identical with tau(0% O2)/tau(100% O2), at 23 degrees C, were approximately 35 to approximately 50 for the [Alq3 OLED[/[PtOEP dye] pair; S(g) exceeded 200 for the Alq3/PdOEP sensor. For dissolved oxygen (DO) in water and ethanol, S(DO) (defined as the ratio of tau in de-oxygenated and oxygen-saturated solutions) was approximately 9.5 and approximately 11, respectively, using the PtOEP-based film sensor. The oxygen level in toluene was measured with PtOEP dissolved directly in the solution. That sensor exhibited a high sensitivity, but a limited dynamic range. Effects of aggregation of dye molecules, sensing film porosity, and the use of the OLED-based sensor arrays for O2 and multianalyte detection are also discussed.

An approximate formula for recalescence in binary eutectic alloys

NASA Technical Reports Server (NTRS)

Ohsaka, K.; Trinh, E. H.

1993-01-01

In alloys, solidification takes place along various paths which may be ascertained via phase diagrams; while there would be no single formula applicable to all alloys, an approximate formula for a specific solidification path would be useful in estimating the fraction of the solid formed during recalescence. A formulation is here presented of recalescence in binary eutectic alloys. This formula is applied to Ag-Cu alloys which are of interest in containerless solidification, due to their formation of supersaturated solutions.

Accelerated formation of cubic phases in phosphatidylethanolamine dispersions.

PubMed Central

Tenchov, B; Koynova, R; Rapp, G

1998-01-01

By means of x-ray diffraction we show that several sodium salts and the disaccharides sucrose and trehalose strongly accelerate the formation of cubic phases in phosphatidylethanolamine (PE) dispersions upon temperature cycling through the lamellar liquid crystalline-inverted hexagonal (Lalpha-HII) phase transition. Ethylene glycol does not have such an effect. The degree of acceleration increases with the solute concentration. Such an acceleration has been observed for dielaidoyl PE (DEPE), dihexadecyl PE, and dipalmitoyl PE. It was investigated in detail for DEPE dispersions. For DEPE (10 wt% of lipid) aqueous dispersions at 1 M solute concentration, 10-50 temperature cycles typically result in complete conversion of the Lalpha phase into cubic phase. Most efficient is temperature cycling executed by laser flash T-jumps. In that case the conversion completes within 10-15 cycles. However, the cubic phases produced by laser T-jumps are less ordered in comparison to the rather regular cubic structures produced by linear, uniform temperature cycling at 10 degrees C/min. Temperature cycles at scan rates of 1-3 degrees C/min also induce the rapid formation of cubic phases. All solutes used induce the formation of Im3m (Q229) cubic phase in 10 wt% DEPE dispersions. The initial Im3m phases appearing during the first temperature cycles have larger lattice parameters that relax to smaller values with continuation of the cycling after the disappearance of the Lalpha phase. A cooperative Im3m --> Pn3m transition takes place at approximately 85 degrees C and transforms the Im3m phase into a mixture of coexisting Pn3m (Q224) and Im3m phases. The Im3m/Pn3m lattice parameter ratio is 1. 28, as could be expected from a representation of the Im3m and Pn3m phases with the primitive and diamond infinite periodic minimal surfaces, respectively. At higher DEPE contents ( approximately 30 wt%), cubic phase formation is hindered after 20-30 temperature cycles. The conversion does not go through, but reaches a stage with coexisting Ia3d (Q230) and Lalpha phases. Upon heating, the Ia3d phase cooperatively transforms into a mixture of, presumably, Im3m and Pn3m phases at about the temperature of the Lalpha-HII transition. This transformation is readily reversible with the temperature. The lattice parameters of the DEPE cubic phases are temperature-insensitive in the Lalpha temperature range and decrease with the temperature in the range of the HII phase. PMID:9675186

Cell separations and the demixing of aqueous two phase polymer solutions in microgravity

NASA Technical Reports Server (NTRS)

Brooks, Donald E.; Bamberger, Stephan; Harris, J. M.; Van Alstine, James M.

1991-01-01

Partition in phase separated aqueous polymer solutions is a cell separation procedure thought to be adversely influenced by gravity. In preparation for performing cell partitioning experiments in space, and to provide general information concerning the demixing of immiscible liquids in low gravity, a series of phase separated aqueous polymer solutions have been flown on two shuttle flights. Fluorocarbon oil and water emulsions were also flown on the second flight. The aqueous polymer emulsions, which in one g demix largely by sedimentation and convection due to the density differences between the phases, demixed more slowly than on the ground and the final disposition of the phases was determined by the wetting of the container wall by the phases. The demixing behavior and kinetics were influenced by the phase volume ratio, physical properties of the systems and chamber wall interaction. The average domain size increased linearly with time as the systems demixed.

Structure and phase transitions of asphaltenes in solutions

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

Tar, M.M. de; Sheu, E.Y.; Storm, D.A.

The authors investigated the rheological properties of two vacuum resid fractions in a series of solvents. The authors measured the viscosity as a function of concentration and temperature respectively. In this study, two aspects were focused: (1) the concentration dependence of viscosity for the pentane soluble fractions in a series of n-alkane solvents for study of the particle structure, and (2) the temperature dependence of viscosity of the heptane insoluble fraction in toluene at various concentrations for the study of the phase transitions. From their results it was found that all the systems studied are Newtonian. The results for (1)more » show that the particles are approximately spherical and as the carbon number of the n-alkane solvent increases, the quality of the solvent increases, thereby increasing the particle solvation. This result is consistent with that reported in a recent paper by Ali and Saleem. Also, the particles were found to behave similarly to colloidal particles. As for (2), a glass-like transition was observed at 50% concentration (0.31 volume fraction) with glass transition temperature at about 254 K, while no structural or phase transitions were observed for concentrations below 50%.« less

Phase separation in solution of worm-like micelles: a dilute ? spin-vector model

NASA Astrophysics Data System (ADS)

Panizza, Pascal; Cristobal, Galder; Curély, Jacques

1998-12-01

We show how the dilute 0953-8984/10/50/006/img2 spin vector model introduced originally by Wheeler and co-workers for describing the polymerization phenomenon in solutions of liquid sulphur and of living polymers may be conveniently adapted for studying phase separation in systems containing long flexible micelles. We draw an isomorphism between the coupling constant appearing in the exchange Hamiltonian and the surfactant energies in the micellar problem. We solve this problem within the mean-field approximation and compare the main results we have obtained with respect to polymer theory and previous theories of phase separation in micellar solutions. We show that the attractive interaction term 0953-8984/10/50/006/img3 between monomers renormalizes the aggregation energy and subsequently the corresponding size distribution. Under these conditions, we observe that the general aspect of the phase diagram in the 0953-8984/10/50/006/img4 plane (where 0953-8984/10/50/006/img5 is the surfactant concentration) is different from previous results. The spinodal line shows a re-entrant behaviour and, at low concentrations, we point out the possibility of specific nucleation phenomena related to the existence of a metastable transition line between a region composed of spherical micelles and another one corresponding to a dilute solution of long flexible micelles.

Numerical solution of 2D-vector tomography problem using the method of approximate inverse

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

Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna

2016-08-10

We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.

Femtosecond/picosecond time-resolved fluorescence study of hydrophilic polymer fine particles.

PubMed

Nanjo, Daisuke; Hosoi, Haruko; Fujino, Tatsuya; Tahara, Tahei; Korenaga, Takashi

2007-03-22

Femtosecond/picosecond time-resolved fluorescence study of hydrophilic polymer fine particles (polyacrylamide, PAAm) was reported. Ultrafast fluorescence dynamics of polymer/water solution was monitored using a fluorescent probe molecule (C153). In the femtosecond time-resolved fluorescence measurement at 480 nm, slowly decay components having lifetimes of tau(1) approximately 53 ps and tau(2) approximately 5 ns were observed in addition to rapid fluorescence decay. Picosecond time-resolved fluorescence spectra of C153/PAAm/H2O solution were also measured. In the time-resolved fluorescence spectra of C153/PAAm/H2O, a peak shift from 490 to 515 nm was measured, which can be assigned to the solvation dynamics of polymer fine particles. The fluorescence peak shift was related to the solvation response function and two time constants were determined (tau(3) approximately 50 ps and tau(4) approximately 467 ps). Therefore, the tau(1) component observed in the femtosecond time-resolved fluorescence measurement was assigned to the solvation dynamics that was observed only in the presence of polymer fine particles. Rotational diffusion measurements were also carried out on the basis of the picosecond time-resolved fluorescence spectra. In the C153/PAAm/H2O solution, anisotropy decay having two different time constants was also derived (tau(6) approximately 76 ps and tau(7) approximately 676 ps), indicating the presence of two different microscopic molecular environments around the polymer surface. Using the Stokes-Einstein-Debye (SED) equation, microscopic viscosity around the polymer surface was evaluated. For the area that gave a rotational diffusion time of tau(6) approximately 76 ps, the calculated viscosity is approximately 1.1 cP and for tau(7) approximately 676 ps, it is approximately 10 cP. The calculated viscosity values clearly revealed that there are two different molecular environments around the polyacrylamide fine particles.

Scaling behavior of nonisothermal phase separation.

PubMed

Rüllmann, Max; Alig, Ingo

2004-04-22

The phase separation process in a critical mixture of polydimethylsiloxane and polyethylmethylsiloxane (PDMS/PEMS, a system with an upper critical solution temperature) was investigated by time-resolved light scattering during continuous quenches from the one-phase into the two-phase region. Continuous quenches were realized by cooling ramps with different cooling rates kappa. Phase separation kinetics is studied by means of the temporal evolution of the scattering vector qm and the intensity Im at the scattering peak. The curves qm(t) for different cooling rates can be shifted onto a single mastercurve. The curves Im(t) show similar behavior. As shift factors, a characteristic length Lc and a characteristic time tc are introduced. Both characteristic quantities depend on the cooling rate through power laws: Lc approximately kappa(-delta) and tc approximately kappa(-rho). Scaling behavior in isothermal critical demixing is well known. There the temporal evolutions of qm and Im for different quench depths DeltaT can be scaled with the correlation length xi and the interdiffusion coefficient D, both depending on DeltaT through critical power laws. We show in this paper that the cooling rate scaling in nonisothermal demixing is a consequence of the quench depth scaling in the isothermal case. The exponents delta and rho are related to the critical exponents nu and nu* of xi and D, respectively. The structure growth during nonisothermal demixing can be described with a semiempirical model based on the hydrodynamic coarsening mechanism well known in the isothermal case. In very late stages of nonisothermal phase separation a secondary scattering maximum appears. This is due to secondary demixing. We explain the onset of secondary demixing by a competition between interdiffusion and coarsening. (c) 2004 American Institute of Physics

Modeling boundary measurements of scattered light using the corrected diffusion approximation

PubMed Central

Lehtikangas, Ossi; Tarvainen, Tanja; Kim, Arnold D.

2012-01-01

We study the modeling and simulation of steady-state measurements of light scattered by a turbid medium taken at the boundary. In particular, we implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation. PMID:22435102

Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory

NASA Astrophysics Data System (ADS)

Helbing, Dirk

1993-03-01

In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is developed. Three kinds of social pair interactions are distinguished: Avoidance processes, compromising processes, and imitative processes. Computational results are presented for a special case of imitative processes: the competition of two equivalent strategies. They show a phase transition that describes the self-organization of a behavioral convention. This phase transition is further analyzed by examining the equations for the most probable behavioral distribution, which are Boltzmann-like equations. Special cases of Boltzmann-like equations do not obey the H-theorem and have oscillatory or even chaotic solutions. A suitable Taylor approximation leads to the so-called game dynamical equations (also known as selection-mutation equations in the theory of evolution).

Asymptotic theory of intermediate- and high-degree solar acoustic oscillations

NASA Technical Reports Server (NTRS)

Brodsky, M.; Vorontsov, S. V.

1993-01-01

A second-order asymptotic approximation is developed for adiabatic nonradial p-modes of a spherically symmetric star. The exact solutions of adiabatic oscillations are assumed in the outermost layers, where the asymptotic description becomes invalid, which results in a eigenfrequency equation with model-dependent surface phase shift. For lower degree modes, the phase shift is a function of frequency alone; for high-degree modes, its dependence on the degree is explicitly taken into account.

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

Weinstein, Marvin; /SLAC

It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for themore » behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will turn to tunneling problems and show that the instanton can also be though of in the same way. I will do this for the classic problem of a double well potential in the extreme limit when the splitting between the two lowest levels is extremely small and the tunneling rate from one well to another is also very small.« less

Numerical methods for stiff systems of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Flaherty, J. E.; Omalley, R. E., Jr.

1983-01-01

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

PubMed

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary

PubMed Central

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations. PMID:27031232

Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

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

Dasgupta, C.; Pandit, R.

The two-dimensional, q-state (q > 4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model asmore » a testing ground for these theories are discussed.« less

Stable finite element approximations of two-phase flow with soluble surfactant

NASA Astrophysics Data System (ADS)

Barrett, John W.; Garcke, Harald; Nürnberg, Robert

2015-09-01

A parametric finite element approximation of incompressible two-phase flow with soluble surfactants is presented. The Navier-Stokes equations are coupled to bulk and surfaces PDEs for the surfactant concentrations. At the interface adsorption, desorption and stress balances involving curvature effects and Marangoni forces have to be considered. A parametric finite element approximation for the advection of the interface, which maintains good mesh properties, is coupled to the evolving surface finite element method, which is used to discretize the surface PDE for the interface surfactant concentration. The resulting system is solved together with standard finite element approximations of the Navier-Stokes equations and of the bulk parabolic PDE for the surfactant concentration. Semidiscrete and fully discrete approximations are analyzed with respect to stability, conservation and existence/uniqueness issues. The approach is validated for simple test cases and for complex scenarios, including colliding drops in a shear flow, which are computed in two and three space dimensions.

Constructing analytic solutions on the Tricomi equation

NASA Astrophysics Data System (ADS)

Ghiasi, Emran Khoshrouye; Saleh, Reza

2018-04-01

In this paper, homotopy analysis method (HAM) and variational iteration method (VIM) are utilized to derive the approximate solutions of the Tricomi equation. Afterwards, the HAM is optimized to accelerate the convergence of the series solution by minimizing its square residual error at any order of the approximation. It is found that effect of the optimal values of auxiliary parameter on the convergence of the series solution is not negligible. Furthermore, the present results are found to agree well with those obtained through a closed-form equation available in the literature. To conclude, it is seen that the two are effective to achieve the solution of the partial differential equations.

Role of small-norm components in extended random-phase approximation

NASA Astrophysics Data System (ADS)

Tohyama, Mitsuru

2017-09-01

The role of the small-norm amplitudes in extended random-phase approximation (RPA) theories such as the particle-particle and hole-hole components of one-body amplitudes and the two-body amplitudes other than two-particle/two-hole components are investigated for the one-dimensional Hubbard model using an extended RPA derived from the time-dependent density matrix theory. It is found that these amplitudes cannot be neglected in strongly interacting regions where the effects of ground-state correlations are significant.

Multi-phase arrival tracking using tetrahedral cells within a 3D layered titled transversely isotropic anisotropic model involving undulating topography and irregular interfaces

NASA Astrophysics Data System (ADS)

Li, Xing-Wang; Bai, Chao-Ying; Yue, Xiao-Peng; Greenhalgh, Stewart

2018-02-01

To overcome a major problem in current ray tracing methods, which are only capable of tracing first arrivals, and occasionally primary reflections (or mode conversions) in regular cell models, we extend in this paper the multistage triangular shortest-path method (SPM) into 3D titled transversely isotropic (TTI) anisotropic media. The proposed method is capable of tracking multi-phase arrivals composed of any kind of combinations of transmissions, mode conversions and reflections. In model parameterization, five elastic parameters, plus two angles defining the titled axis of symmetry of TTI media are sampled at the primary nodes of the tetrahedral cell, and velocity value at secondary node positions are linked by a tri-linear velocity interpolation function to the primary node velocity value of that of a tetrahedral cell, from which the group velocities of the three wave modes (qP, qSV and qSH) are computed. The multistage triangular SPM is used to track multi-phase arrivals. The uniform anisotropic test indicates that the numerical solution agrees well with the analytic solution, thus verifying the accuracy of the methodology. Several simulations and comparison results for heterogeneous models show that the proposed algorithm is able to efficiently and accurately approximate undulating surface topography and irregular subsurface velocity discontinuities. It is suitable for any combination of multi-phase arrival tracking in arbitrary tilt angle TTI media and can accommodate any magnitude of anisotropy.

Modifications Of Discrete Ordinate Method For Computations With High Scattering Anisotropy: Comparative Analysis

NASA Technical Reports Server (NTRS)

Korkin, Sergey V.; Lyapustin, Alexei I.; Rozanov, Vladimir V.

2012-01-01

A numerical accuracy analysis of the radiative transfer equation (RTE) solution based on separation of the diffuse light field into anisotropic and smooth parts is presented. The analysis uses three different algorithms based on the discrete ordinate method (DOM). Two methods, DOMAS and DOM2+, that do not use the truncation of the phase function, are compared against the TMS-method. DOMAS and DOM2+ use the Small-Angle Modification of RTE and the single scattering term, respectively, as an anisotropic part. The TMS method uses Delta-M method for truncation of the phase function along with the single scattering correction. For reference, a standard discrete ordinate method, DOM, is also included in analysis. The obtained results for cases with high scattering anisotropy show that at low number of streams (16, 32) only DOMAS provides an accurate solution in the aureole area. Outside of the aureole, the convergence and accuracy of DOMAS, and TMS is found to be approximately similar: DOMAS was found more accurate in cases with coarse aerosol and liquid water cloud models, except low optical depth, while the TMS showed better results in case of ice cloud.

Two-level schemes for the advection equation

NASA Astrophysics Data System (ADS)

Vabishchevich, Petr N.

2018-06-01

The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (divergent) and non-conservative (characteristic) forms. The advection operator is skew-symmetric. Standard finite element approximations in space are used. The standard explicit two-level scheme for the advection equation is absolutely unstable. New conditionally stable regularized schemes are constructed, on the basis of the general theory of stability (well-posedness) of operator-difference schemes, the stability conditions of the explicit Lax-Wendroff scheme are established. Unconditionally stable and conservative schemes are implicit schemes of the second (Crank-Nicolson scheme) and fourth order. The conditionally stable implicit Lax-Wendroff scheme is constructed. The accuracy of the investigated explicit and implicit two-level schemes for an approximate solution of the advection equation is illustrated by the numerical results of a model two-dimensional problem.

Fully- and weakly-nonlinear biperiodic traveling waves in shallow water

NASA Astrophysics Data System (ADS)

Hirakawa, Tomoaki; Okamura, Makoto

2018-04-01

We directly calculate fully nonlinear traveling waves that are periodic in two independent horizontal directions (biperiodic) in shallow water. Based on the Riemann theta function, we also calculate exact periodic solutions to the Kadomtsev-Petviashvili (KP) equation, which can be obtained by assuming weakly-nonlinear, weakly-dispersive, weakly-two-dimensional waves. To clarify how the accuracy of the biperiodic KP solution is affected when some of the KP approximations are not satisfied, we compare the fully- and weakly-nonlinear periodic traveling waves of various wave amplitudes, wave depths, and interaction angles. As the interaction angle θ decreases, the wave frequency and the maximum wave height of the biperiodic KP solution both increase, and the central peak sharpens and grows beyond the height of the corresponding direct numerical solutions, indicating that the biperiodic KP solution cannot qualitatively model direct numerical solutions for θ ≲ 45^\\circ . To remedy the weak two-dimensionality approximation, we apply the correction of Yeh et al (2010 Eur. Phys. J. Spec. Top. 185 97-111) to the biperiodic KP solution, which substantially improves the solution accuracy and results in wave profiles that are indistinguishable from most other cases.

Analytical solutions for combined close-contact and natural convection melting in horizontal cylindrical heat storage capsule

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

Saitoh, T.S.; Hoshi, A.

1998-07-01

Melting and solidification of a phase change material (PCM) in a capsule is of practical importance in latent heat thermal energy storage (LHTES) systems which are considered to be very promising to reduce a peak demand of electricity in the summer season and carbon dioxide (CO{sub 2}) emissions. Two melting modes are involved in melting of capsules. One is close-contact melting between the solid bulk and the capsule wall, and another is natural convection melting in the liquid region. Close-contact melting processes for a single enclosure have been solved using several numerical methods (e.g., Saitoh and Kato (1994)). In additionmore » close-contact melting heat transfer characteristics including melt flow in the liquid film under inner wall temperature distribution were analyzed and simple approximate equations were already presented by Saitoh and Hoshi (1997). The effects of Stefan number and variable temperature profile etc. were clarified in detail. And the melting velocity of the solid bulk under various conditions was also studied theoretically. In addition the effects of variable inner wall temperature on molten mass fraction were investigated. The present paper reports analytical solutions for combined close-contact and natural convection melting in horizontal cylindrical capsule. Moreover, natural convection melting in the liquid region were analyzed in this report. The upper interface shape of the solid bulk is approximated by a circular arc throughout the melting process. For the sake of verification, close-contact melting heat-transfer characteristics including natural convection in the liquid region were studied experimentally. Apparent shift of upper solid-liquid interface is good agreement with the experiment. The present simple approximate solutions will be useful to facilitate designing of the practical capsule bed LHTES systems.« less

Permeation of protons, potassium ions, and small polar molecules through phospholipid bilayers as a function of membrane thickness.

PubMed Central

Paula, S; Volkov, A G; Van Hoek, A N; Haines, T H; Deamer, D W

1996-01-01

Two mechanisms have been proposed to account for solute permeation of lipid bilayers. Partitioning into the hydrophobic phase of the bilayer, followed by diffusion, is accepted by many for the permeation of water and other small neutral solutes, but transient pores have also been proposed to account for both water and ionic solute permeation. These two mechanisms make distinctively different predictions about the permeability coefficient as a function of bilayer thickness. Whereas the solubility-diffusion mechanism predicts only a modest variation related to bilayer thickness, the pore model predicts an exponential relationship. To test these models, we measured the permeability of phospholipid bilayers to protons, potassium ions, water, urea, and glycerol. Bilayers were prepared as liposomes, and thickness was varied systematically by using unsaturated lipids with chain lengths ranging from 14 to 24 carbon atoms. The permeability coefficient of water and neutral polar solutes displayed a modest dependence on bilayer thickness, with an approximately linear fivefold decrease as the carbon number varied from 14 to 24 atoms. In contrast, the permeability to protons and potassium ions decreased sharply by two orders of magnitude between 14 and 18 carbon atoms, and leveled off, when the chain length was further extended to 24 carbon atoms. The results for water and the neutral permeating solutes are best explained by the solubility-diffusion mechanism. The results for protons and potassium ions in shorter-chain lipids are consistent with the transient pore model, but better fit the theoretical line predicted by the solubility-diffusion model at longer chain lengths. PMID:8770210

Permeation of protons, potassium ions, and small polar molecules through phospholipid bilayers as a function of membrane thickness

NASA Technical Reports Server (NTRS)

Paula, S.; Volkov, A. G.; Van Hoek, A. N.; Haines, T. H.; Deamer, D. W.

1996-01-01

Two mechanisms have been proposed to account for solute permeation of lipid bilayers. Partitioning into the hydrophobic phase of the bilayer, followed by diffusion, is accepted by many for the permeation of water and other small neutral solutes, but transient pores have also been proposed to account for both water and ionic solute permeation. These two mechanisms make distinctively different predictions about the permeability coefficient as a function of bilayer thickness. Whereas the solubility-diffusion mechanism predicts only a modest variation related to bilayer thickness, the pore model predicts an exponential relationship. To test these models, we measured the permeability of phospholipid bilayers to protons, potassium ions, water, urea, and glycerol. Bilayers were prepared as liposomes, and thickness was varied systematically by using unsaturated lipids with chain lengths ranging from 14 to 24 carbon atoms. The permeability coefficient of water and neutral polar solutes displayed a modest dependence on bilayer thickness, with an approximately linear fivefold decrease as the carbon number varied from 14 to 24 atoms. In contrast, the permeability to protons and potassium ions decreased sharply by two orders of magnitude between 14 and 18 carbon atoms, and leveled off, when the chain length was further extended to 24 carbon atoms. The results for water and the neutral permeating solutes are best explained by the solubility-diffusion mechanism. The results for protons and potassium ions in shorter-chain lipids are consistent with the transient pore model, but better fit the theoretical line predicted by the solubility-diffusion model at longer chain lengths.

The Binary Temperature-Composition Phase Diagram

ERIC Educational Resources Information Center

Sanders, Philip C.; Reeves, James H.; Messina, Michael

2006-01-01

The equations for the liquid and gas lines in the binary temperature-composition phase diagram are derived by approximating that delta(H)[subscript vap] of the two liquids are equal. It is shown that within this approximation, the resulting equations are not too difficult to present in an undergraduate physical chemistry lecture.

Enhanced Remediation of Toluene in the Vadose Zone via a Nitrate-Rich Nutrient Solution: Field Study

NASA Astrophysics Data System (ADS)

Tindall, J. A.; Friedel, M. J.

2003-12-01

The objective of this study was to test the effectiveness of nitrate-rich nutrient solutions and hydrogen peroxide (H202) to enhance in-situ microbial remediation of toluene. Three sand filled plots (2 m2 surface area and 1.5 meters deep) were tested in three phases (each phase lasting approximately 2 weeks). During each phase, toluene (21.6 mol as an emulsion in 50L of water) was applied uniformly via sprinkler irrigation. Passive remediation was allowed to occur during the first (control) phase. A nutrient solution (modified Hoagland), concentrated in 40L of water, was tested during the second phase. The final phase involved addition of 230 moles of H202 in 50L of water to increase the available oxygen needed for aerobic biodegradation. During the first phase, toluene concentrations in soil gas were reduced from 120 ppm to 25 ppm in 14 days. After the addition of nutrients during the second phase, concentrations were reduced from 90 ppm to about 8 ppm within 14 days, and for the third phase (H202), toluene concentrations were about 1 ppm after only five days. Initial results suggest that this method could be an effective means of remediating a contaminated site, directly after a BTEX spill, without the intrusiveness and high cost of other abatement technologies such as bioventing and soil vapor extraction. However, further tests need to be completed to determine the effect of each of the BTEX components.

Part 2: A field study of enhanced remediation of Toluene in the vadose zone using a nutrient solution

USGS Publications Warehouse

Tindall, J.A.; Weeks, E.P.; Friedel, M.

2005-01-01

The objective of this study was to test the effectiveness of a nitrate-rich nutrient solution and hydrogen peroxide (H2O2) to enhance in-situ microbial remediation of toluene in the unsaturated zone. Three sand-filled plots were tested in three phases (each phase lasting approximately 2 weeks). During the control phase, toluene was applied uniformly via sprinkler irrigation. Passive remediation was allowed to occur during this phase. A modified Hoagland nutrient solution, concentrated in 150 L of water, was tested during the second phase. The final phase involved addition of 230 moles of H2O2 in 150 L of water to increase the available oxygen needed for aerobic biodegradation. During the first phase, measured toluene concentrations in soil gas were reduced from 120 ppm to 25 ppm in 14 days. After the addition of nutrients during the second phase, concentrations were reduced from 90 ppm to about 8 ppm within 14 days, and for the third phase (H 2O2), toluene concentrations were about 1 ppm after only 5 days. Initial results suggest that this method could be an effective means of remediating a contaminated site, directly after a BTEX spill, without the intrusiveness and high cost of other abatement technologies such as bioventing or soil-vapor extraction. However, further tests need to be completed to determine the effect of each of the BTEX components. ?? Springer 2005.

Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks.

PubMed

Mehraeen, Shahab; Dierks, Travis; Jagannathan, S; Crow, Mariesa L

2013-12-01

In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach.

Two phase microstructure for Ag-Ni nanowires

NASA Astrophysics Data System (ADS)

Srivastava, Chandan; Rai, Rajesh Kumar

2013-03-01

In the present study, electrodeposition technique was used to produce Ag-Ni nanowires. Ag-Ni system shows extremely high bulk immiscibility. Nanowire morphology was achieved by employing an anodic alumina membrane having pores of ˜200 nm diameter. Microstructure of as-deposited wire was composed of nano-sized solid solution structured Ag-Ni nanoparticles embedded in a matrix of pure Ag phase. It is proposed that the two phase microstructure resulted from an initial formation of solid solution structured nanoparticles in the alumina template pore followed by nucleation of pure Ag phase over the particles which eventually grew to form the matrix phase.

Permeability Sensitivity Functions and Rapid Simulation of Hydraulic-Testing Measurements Using Perturbation Theory

NASA Astrophysics Data System (ADS)

Escobar Gómez, J. D.; Torres-Verdín, C.

2018-03-01

Single-well pressure-diffusion simulators enable improved quantitative understanding of hydraulic-testing measurements in the presence of arbitrary spatial variations of rock properties. Simulators of this type implement robust numerical algorithms which are often computationally expensive, thereby making the solution of the forward modeling problem onerous and inefficient. We introduce a time-domain perturbation theory for anisotropic permeable media to efficiently and accurately approximate the transient pressure response of spatially complex aquifers. Although theoretically valid for any spatially dependent rock/fluid property, our single-phase flow study emphasizes arbitrary spatial variations of permeability and anisotropy, which constitute key objectives of hydraulic-testing operations. Contrary to time-honored techniques, the perturbation method invokes pressure-flow deconvolution to compute the background medium's permeability sensitivity function (PSF) with a single numerical simulation run. Subsequently, the first-order term of the perturbed solution is obtained by solving an integral equation that weighs the spatial variations of permeability with the spatial-dependent and time-dependent PSF. Finally, discrete convolution transforms the constant-flow approximation to arbitrary multirate conditions. Multidimensional numerical simulation studies for a wide range of single-well field conditions indicate that perturbed solutions can be computed in less than a few CPU seconds with relative errors in pressure of <5%, corresponding to perturbations in background permeability of up to two orders of magnitude. Our work confirms that the proposed joint perturbation-convolution (JPC) method is an efficient alternative to analytical and numerical solutions for accurate modeling of pressure-diffusion phenomena induced by Neumann or Dirichlet boundary conditions.

Time-Parallel Solutions to Ordinary Differential Equations on GPUs with a New Functional Optimization Approach Related to the Sobolev Gradient Method

DTIC Science & Technology

2012-10-01

black and approximations in cyan and magenta. The second ODE is the pendulum equation, given by: This ODE was also implemented using Crank...The drawback of approaches like the one proposed can be observed with a very simple example. Suppose vector is found by applying 4 linear...public release; distribution unlimited Figure 2. A phase space plot of the Pendulum example. Fine solution (black) contains 32768 time steps

Large Torque Variations in Two Soft Gamma Repeaters

NASA Technical Reports Server (NTRS)

Woods, Peter M.; Kouveliotou, Chryssa; Gogus, Ersin; Finger, Mark H.; Swank, Jean; Markwardt, Craig B.; Hurley, Kevin; vanderKlis, Michiel

2002-01-01

We have monitored the pulse frequencies of the two soft gamma repeaters SGR 1806-20 and SGR 1900+14 through the beginning of year 2001 using primarily Rossi X-Ray Timing Explorer Proportional Counter Array observations. In both sources, we observe large changes in the spin-down torque up to a factor of approximately 4, which persist for several months. Using long-baseline phase-connected timing solutions as well as the overall frequency histories, we construct torque noise power spectra for each SGR (Soft Gamma Repeater). The power spectrum of each source is very red (power-law slope is approximately -3.5). The torque noise power levels are consistent with some accreting systems on timescales of approximately 1 yr, yet the full power spectrum is much steeper in frequency than any known accreting source. To the best of our knowledge, torque noise power spectra with a comparably steep frequency dependence have been seen only in young, glitching radio pulsars (e.g., Vela). The observed changes in spin-down rate do not correlate with burst activity; therefore, the physical mechanisms behind each phenomenon are also likely unrelated. Within the context of the magnetar model, seismic activity can not account for both the bursts and the long-term torque changes unless the seismically active regions are decoupled from one another.

Metaheuristic optimisation methods for approximate solving of singular boundary value problems

NASA Astrophysics Data System (ADS)

Sadollah, Ali; Yadav, Neha; Gao, Kaizhou; Su, Rong

2017-07-01

This paper presents a novel approximation technique based on metaheuristics and weighted residual function (WRF) for tackling singular boundary value problems (BVPs) arising in engineering and science. With the aid of certain fundamental concepts of mathematics, Fourier series expansion, and metaheuristic optimisation algorithms, singular BVPs can be approximated as an optimisation problem with boundary conditions as constraints. The target is to minimise the WRF (i.e. error function) constructed in approximation of BVPs. The scheme involves generational distance metric for quality evaluation of the approximate solutions against exact solutions (i.e. error evaluator metric). Four test problems including two linear and two non-linear singular BVPs are considered in this paper to check the efficiency and accuracy of the proposed algorithm. The optimisation task is performed using three different optimisers including the particle swarm optimisation, the water cycle algorithm, and the harmony search algorithm. Optimisation results obtained show that the suggested technique can be successfully applied for approximate solving of singular BVPs.

Model reduction method using variable-separation for stochastic saddle point problems

NASA Astrophysics Data System (ADS)

Jiang, Lijian; Li, Qiuqi

2018-02-01

In this paper, we consider a variable-separation (VS) method to solve the stochastic saddle point (SSP) problems. The VS method is applied to obtain the solution in tensor product structure for stochastic partial differential equations (SPDEs) in a mixed formulation. The aim of such a technique is to construct a reduced basis approximation of the solution of the SSP problems. The VS method attempts to get a low rank separated representation of the solution for SSP in a systematic enrichment manner. No iteration is performed at each enrichment step. In order to satisfy the inf-sup condition in the mixed formulation, we enrich the separated terms for the primal system variable at each enrichment step. For the SSP problems by regularization or penalty, we propose a more efficient variable-separation (VS) method, i.e., the variable-separation by penalty method. This can avoid further enrichment of the separated terms in the original mixed formulation. The computation of the variable-separation method decomposes into offline phase and online phase. Sparse low rank tensor approximation method is used to significantly improve the online computation efficiency when the number of separated terms is large. For the applications of SSP problems, we present three numerical examples to illustrate the performance of the proposed methods.

NMR signal analysis to characterize solid, aqueous, and lipid phases in baked cakes.

PubMed

Le Grand, F; Cambert, M; Mariette, F

2007-12-26

Proton mobility was studied in molecular fractions of some model systems and of cake using a 1H nuclear magnetic resonance (NMR) relaxation technique. For cake, five spin-spin relaxation times (T2) were obtained from transverse relaxation curves: T2 (1) approximately 20 micros, T2 (2) approximately 0.2 ms, T2 (3) approximately 3 ms, T2 (4) approximately 50 ms, and T2 (2) approximately 165 ms. The faster component was attributed to the solid phase, components 2 and 3 were associated with the aqueous phase, and the two slowest components were linked to the lipid phase. After cooking, the crust contained more fat but less water than the center part of the cake. The amount of gelatinized starch was lower in the crust, and water was more mobile due to less interaction with macromolecules. This preliminary study revealed different effects of storage on the center and crust.

Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Singhal, A. K.; Tam, L. T.

1984-01-01

The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.

Model of chiral spin liquids with Abelian and non-Abelian topological phases

DOE PAGES

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; ...

2017-12-15

In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less

Model of chiral spin liquids with Abelian and non-Abelian topological phases

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

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio

In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less

Thermodynamically self-consistent theory for the Blume-Capel model.

PubMed

Grollau, S; Kierlik, E; Rosinberg, M L; Tarjus, G

2001-04-01

We use a self-consistent Ornstein-Zernike approximation to study the Blume-Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partial differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundaries in a nonzero magnetic field. In particular, the coordinates of the tricritical point are in very good agreement with the best estimates from simulation or series expansion. Numerical and analytical analysis strongly suggest that the theory predicts a universal Ising-like critical behavior along the lambda line and the wing critical lines, and a tricritical behavior governed by mean-field exponents.

Quantifying uncertainty in stable isotope mixing models

DOE PAGES

Davis, Paul; Syme, James; Heikoop, Jeffrey; ...

2015-05-19

Mixing models are powerful tools for identifying biogeochemical sources and determining mixing fractions in a sample. However, identification of actual source contributors is often not simple, and source compositions typically vary or even overlap, significantly increasing model uncertainty in calculated mixing fractions. This study compares three probabilistic methods, SIAR [ Parnell et al., 2010] a pure Monte Carlo technique (PMC), and Stable Isotope Reference Source (SIRS) mixing model, a new technique that estimates mixing in systems with more than three sources and/or uncertain source compositions. In this paper, we use nitrate stable isotope examples (δ 15N and δ 18O) butmore » all methods tested are applicable to other tracers. In Phase I of a three-phase blind test, we compared methods for a set of six-source nitrate problems. PMC was unable to find solutions for two of the target water samples. The Bayesian method, SIAR, experienced anchoring problems, and SIRS calculated mixing fractions that most closely approximated the known mixing fractions. For that reason, SIRS was the only approach used in the next phase of testing. In Phase II, the problem was broadened where any subset of the six sources could be a possible solution to the mixing problem. Results showed a high rate of Type I errors where solutions included sources that were not contributing to the sample. In Phase III some sources were eliminated based on assumed site knowledge and assumed nitrate concentrations, substantially reduced mixing fraction uncertainties and lowered the Type I error rate. These results demonstrate that valuable insights into stable isotope mixing problems result from probabilistic mixing model approaches like SIRS. The results also emphasize the importance of identifying a minimal set of potential sources and quantifying uncertainties in source isotopic composition as well as demonstrating the value of additional information in reducing the uncertainty in calculated mixing fractions.« less

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.

Correlation energy functional within the GW -RPA: Exact forms, approximate forms, and challenges

NASA Astrophysics Data System (ADS)

Ismail-Beigi, Sohrab

2010-05-01

In principle, the Luttinger-Ward Green’s-function formalism allows one to compute simultaneously the total energy and the quasiparticle band structure of a many-body electronic system from first principles. We present approximate and exact expressions for the correlation energy within the GW -random-phase approximation that are more amenable to computation and allow for developing efficient approximations to the self-energy operator and correlation energy. The exact form is a sum over differences between plasmon and interband energies. The approximate forms are based on summing over screened interband transitions. We also demonstrate that blind extremization of such functionals leads to unphysical results: imposing physical constraints on the allowed solutions (Green’s functions) is necessary. Finally, we present some relevant numerical results for atomic systems.

Strong solutions and instability for the fitness gradient system in evolutionary games between two populations

NASA Astrophysics Data System (ADS)

Xu, Qiuju; Belmonte, Andrew; deForest, Russ; Liu, Chun; Tan, Zhong

2017-04-01

In this paper, we study a fitness gradient system for two populations interacting via a symmetric game. The population dynamics are governed by a conservation law, with a spatial migration flux determined by the fitness. By applying the Galerkin method, we establish the existence, regularity and uniqueness of global solutions to an approximate system, which retains most of the interesting mathematical properties of the original fitness gradient system. Furthermore, we show that a Turing instability occurs for equilibrium states of the fitness gradient system, and its approximations.

Analysis of dynamic system response to product random processes

NASA Technical Reports Server (NTRS)

Sidwell, K.

1978-01-01

The response of dynamic systems to the product of two independent Gaussian random processes is developed by use of the Fokker-Planck and associated moment equations. The development is applied to the amplitude modulated process which is used to model atmospheric turbulence in aeronautical applications. The exact solution for the system response is compared with the solution obtained by the quasi-steady approximation which omits the dynamic properties of the random amplitude modulation. The quasi-steady approximation is valid as a limiting case of the exact solution for the dynamic response of linear systems to amplitude modulated processes. In the nonlimiting case the quasi-steady approximation can be invalid for dynamic systems with low damping.

On the dynamics of approximating schemes for dissipative nonlinear equations

NASA Technical Reports Server (NTRS)

Jones, Donald A.

1993-01-01

Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.

Cultivation and energy efficient harvesting of microalgae using thermoreversible sol-gel transition

PubMed Central

Estime, Bendy; Ren, Dacheng; Sureshkumar, Radhakrishna

2017-01-01

Microalgae represent a promising source of renewable biomass for the production of biofuels and valuable chemicals. However, energy efficient cultivation and harvesting technologies are necessary to improve economic viability. A Tris-Acetate-Phosphate-Pluronic (TAPP) medium that undergoes a thermoreversible sol-gel transition is developed to efficiently culture and harvest microalgae without affecting the productivity as compared to that in traditional culture in a well-mixed suspension. After seeding microalgae in the TAPP medium in a solution phase at 15 °C, the temperature is increased by 7 °C to induce gelation. Within the gel, microalgae are observed to grow in large clusters rather than as isolated cells. The settling velocity of the microalgal clusters is approximately ten times larger than that of individual cells cultured in typical solution media. Such clusters are easily harvested gravimetrically by decreasing the temperature to bring the medium to a solution phase. PMID:28102313

Padé approximant for normal stress differences in large-amplitude oscillatory shear flow

NASA Astrophysics Data System (ADS)

Poungthong, P.; Saengow, C.; Giacomin, A. J.; Kolitawong, C.; Merger, D.; Wilhelm, M.

2018-04-01

Analytical solutions for the normal stress differences in large-amplitude oscillatory shear flow (LAOS), for continuum or molecular models, normally take the inexact form of the first few terms of a series expansion in the shear rate amplitude. Here, we improve the accuracy of these truncated expansions by replacing them with rational functions called Padé approximants. The recent advent of exact solutions in LAOS presents an opportunity to identify accurate and useful Padé approximants. For this identification, we replace the truncated expansion for the corotational Jeffreys fluid with its Padé approximants for the normal stress differences. We uncover the most accurate and useful approximant, the [3,4] approximant, and then test its accuracy against the exact solution [C. Saengow and A. J. Giacomin, "Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow," Phys. Fluids 29, 121601 (2017)]. We use Ewoldt grids to show the stunning accuracy of our [3,4] approximant in LAOS. We quantify this accuracy with an objective function and then map it onto the Pipkin space. Our two applications illustrate how to use our new approximant reliably. For this, we use the Spriggs relations to generalize our best approximant to multimode, and then, we compare with measurements on molten high-density polyethylene and on dissolved polyisobutylene in isobutylene oligomer.

Crystallographic features of the approximant H (Mn7Si2V) phase in the Mn-Si-V alloy system

NASA Astrophysics Data System (ADS)

Nakayama, Kei; Komatsuzaki, Takumi; Koyama, Yasumasa

2018-07-01

The intermetallic compound H (Mn7Si2V) phase in the Mn-Si-V alloy system can be regarded as an approximant phase of the dodecagonal quasicrystal as one of the two-dimensional quasicrystals. To understand the features of the approximant H phase, in this study, the crystallographic features of both the H phase and the (σ → H) reaction in Mn-Si-V alloy samples were investigated, mainly by transmission electron microscopy. It was found that, in the H phase, there were characteristic structural disorders with respect to an array of a dodecagonal structural unit consisting of 19 dodecagonal atomic columns. Concretely, penetrated structural units consisting of two dodecagonal structural units were presumed to be typical of such disorders. An interesting feature of the (σ → H) reaction was that regions with a rectangular arrangement of penetrated structural units (RAPU) first appeared in the σ matrix as the initial state, and H regions were then nucleated in contact with RAPU regions. The subsequent conversion of RAPU regions into H regions eventually resulted in the formation of the approximant H state as the final state. Furthermore, atomic positions in both the H structure and the dodecagonal quasicrystal were examined using a simple plane-wave model with 12 plane waves.

Revisiting the time until fixation of a neutral mutant in a finite population - A coalescent theory approach.

PubMed

Greenbaum, Gili

2015-09-07

Evaluation of the time scale of the fixation of neutral mutations is crucial to the theoretical understanding of the role of neutral mutations in evolution. Diffusion approximations of the Wright-Fisher model are most often used to derive analytic formulations of genetic drift, as well as for the time scales of the fixation of neutral mutations. These approximations require a set of assumptions, most notably that genetic drift is a stochastic process in a continuous allele-frequency space, an assumption appropriate for large populations. Here equivalent approximations are derived using a coalescent theory approach which relies on a different set of assumptions than the diffusion approach, and adopts a discrete allele-frequency space. Solutions for the mean and variance of the time to fixation of a neutral mutation derived from the two approaches converge for large populations but slightly differ for small populations. A Markov chain analysis of the Wright-Fisher model for small populations is used to evaluate the solutions obtained, showing that both the mean and the variance are better approximated by the coalescent approach. The coalescence approximation represents a tighter upper-bound for the mean time to fixation than the diffusion approximation, while the diffusion approximation and coalescence approximation form an upper and lower bound, respectively, for the variance. The converging solutions and the small deviations of the two approaches strongly validate the use of diffusion approximations, but suggest that coalescent theory can provide more accurate approximations for small populations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Atomic structure solution of the complex quasicrystal approximant Al77Rh15Ru8 from electron diffraction data.

PubMed

Samuha, Shmuel; Mugnaioli, Enrico; Grushko, Benjamin; Kolb, Ute; Meshi, Louisa

2014-12-01

The crystal structure of the novel Al77Rh15Ru8 phase (which is an approximant of decagonal quasicrystals) was determined using modern direct methods (MDM) applied to automated electron diffraction tomography (ADT) data. The Al77Rh15Ru8 E-phase is orthorhombic [Pbma, a = 23.40 (5), b = 16.20 (4) and c = 20.00 (5) Å] and has one of the most complicated intermetallic structures solved solely by electron diffraction methods. Its structural model consists of 78 unique atomic positions in the unit cell (19 Rh/Ru and 59 Al). Precession electron diffraction (PED) patterns and high-resolution electron microscopy (HRTEM) images were used for the validation of the proposed atomic model. The structure of the E-phase is described using hierarchical packing of polyhedra and a single type of tiling in the form of a parallelogram. Based on this description, the structure of the E-phase is compared with that of the ε6-phase formed in Al-Rh-Ru at close compositions.

Comparative density functional study of the complexes [UO2(CO3)3]4- and [(UO2)3(CO3)6]6- in aqueous solution.

PubMed

Schlosser, Florian; Moskaleva, Lyudmila V; Kremleva, Alena; Krüger, Sven; Rösch, Notker

2010-06-28

With a relativistic all-electron density functional method, we studied two anionic uranium(VI) carbonate complexes that are important for uranium speciation and transport in aqueous medium, the mononuclear tris(carbonato) complex [UO(2)(CO(3))(3)](4-) and the trinuclear hexa(carbonato) complex [(UO(2))(3)(CO(3))(6)](6-). Focusing on the structures in solution, we applied for the first time a full solvation treatment to these complexes. We approximated short-range effects by explicit aqua ligands and described long-range electrostatic interactions via a polarizable continuum model. Structures and vibrational frequencies of "gas-phase" models with explicit aqua ligands agree best with experiment. This is accidental because the continuum model of the solvent to some extent overestimates the electrostatic interactions of these highly anionic systems with the bulk solvent. The calculated free energy change when three mono-nuclear complexes associate to the trinuclear complex, agrees well with experiment and supports the formation of the latter species upon acidification of a uranyl carbonate solution.

Comparison of 2-Octanol and Tributyl Phosphate in Recovery of Tungsten from Sulfuric-Phosphoric Acid Leach Solution of Scheelite

NASA Astrophysics Data System (ADS)

Liao, Yulong; Zhao, Zhongwei

2018-04-01

Tungsten was recovered from sulfuric-phosphoric acid leach solution of scheelite using 2-octanol and tributyl phosphate (TBP). Approximately 76% of the tungsten and less than 6.2% of the iron were extracted when using 70% 2-octanol, showing good selectivity for tungsten over iron; the tungsten extraction could not be significantly enhanced using a three-stage countercurrent simulation test. Moreover, more than 99.2% of the W and 91.0% of the Fe were extracted when using 70% TBP, showing poor selectivity, but after pretreating the leach solution with iron powder, less than 5.5% of the Fe was extracted. The loaded phases were stripped using deionized water and ammonia solution. The maximum stripping rate of tungsten from loaded 2-octanol was 45.6% when using water, compared with only 13.1% from loaded TBP. Tungsten was efficiently stripped from loaded phases using ammonia solution without formation of Fe(OH)3 precipitate. Finally, a flow sheet for recovery of tungsten with TBP is proposed.

Phase Shift Interferometer and Growth Set Up to Step Pattern Formation During Growth From Solutions. Influence of the Oscillatory solution Flow on Stability

NASA Technical Reports Server (NTRS)

Chernov, Alex A.; Booth, N. A.; Vekilov, P. G.; Murray, B. T.; McFadden, G. B.

2000-01-01

We have assembled an experimental setup based on Michelson interferometry with the growing crystal surface as one of the reflective surfaces. The crystallization part of the device allows optical monitoring of a face of a crystal growing at temperature stable within 0.05 C in a flow of solution of controlled direction and speed. The reference arm of the interferometer contains a liquid crystal element that allows controlled shifts of the phase of the interferograms. We employ an image-processing algorithm, which combines five images with a pi/2 phase difference between each pair of images. The images are transferred to a computer by a camera capable of capturing 60 frames per second. The device allows data collection on surface morphology and kinetics during the face layers growth over a relatively large area (approximately 4 sq. mm) in situ and in real time during growth. The estimated depth resolution of the phase shifting interferometry is approximately 50 Angstroms. The data will be analyzed in order to reveal and monitor step bunching during the growth process. The crystal chosen as a model for study in this work is KH2PO4 (KDP). This optically non-linear material is widely used in frequency doubling applications. There have been a number of studies of the kinetics of KDP crystallization that can serve as a benchmark for our investigations. However, so far, systematic quantitative characteristics of step interaction and bunching are missing. We intend to present our first quantitative results on the onset, initial stages and development of instabilities in moving step trains on vicinal crystal surfaces at varying supersaturation, flow rate, and flow direction. Behavior of a vicinal face growing from solution flowing normal to the steps and periodically changing its direction in time was considered theoretically. It was found that this oscillating flow reduces both stabilization and destabilization effects resulted from the unidirectional solution flow directed up the step stream and down the step stream. This reduction of stabilization and destabilization comes from effective mixing which entangles the phase shifts between the spatially periodic interface perturbation and the concentration wave induced by this perturbation. Numerical results and simplified mixing criterion will be discussed.

Two-Phase Flow and Compaction Within and Outside a Sphere under Pure Shear

NASA Astrophysics Data System (ADS)

Hier-Majumder, S.

2017-12-01

This work presents a framework for building analytical solutions for coupled flow in two interacting multiphase domains. The coupled system consists of a multiphase sphere embedded in a multiphase substrate. Each of these domains consist of an interconnected load bearing matrix phase and an inviscid interstitial fluid phase. This work outlines techniques for building analytical solutions for velocity, pressure, and compaction within each domain, subject to boundary conditions of continuity of matrix velocity and normal traction at the interface between the two domains. The solutions indicate that the flow is strongly dependent on the ratio of shear viscosities between the matrix phase in the sphere and the matrix phase in the substrate. When deformed under a pure shear deformation, the magnitude of flow within the sphere rapidly decreases with an increase in this ratio until it reaches a value of 40, after which, the velocity within the sphere becomes relatively insensitive to the increase in the viscosity contrast.

Analytic approximations to the modon dispersion relation. [in oceanography

NASA Technical Reports Server (NTRS)

Boyd, J. P.

1981-01-01

Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.

Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe

2013-01-01

This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

Dissociation of biomolecules in liquid environments during fast heavy-ion irradiation

NASA Astrophysics Data System (ADS)

Nomura, Shinji; Tsuchida, Hidetsugu; Kajiwara, Akihiro; Yoshida, Shintaro; Majima, Takuya; Saito, Manabu

2017-12-01

The effect of aqueous environment on fast heavy-ion radiation damage of biomolecules was studied by comparative experiments using liquid- and gas-phase amino acid targets. Three types of amino acids with different chemical structures were used: glycine, proline, and hydroxyproline. Ion-induced reaction products were analyzed by time-of-flight secondary-ion mass spectrometry. The results showed that fragments from the amino acids resulting from the C—Cα bond cleavage were the major products for both types of targets. For liquid-phase targets, specific products originating from chemical reactions in solutions were observed. Interestingly, multiple dissociated atomic fragments were negligible for the liquid-phase targets. We found that the ratio of multifragment to total fragment ion yields was approximately half of that for gas-phase targets. This finding agreed with the results of other studies on biomolecular cluster targets. It is concluded that the suppression of molecular multifragmentation is caused by the energy dispersion to numerous water molecules surrounding the biomolecular solutes.

Ammonium Removal from Aqueous Solutions by Clinoptilolite: Determination of Isotherm and Thermodynamic Parameters and Comparison of Kinetics by the Double Exponential Model and Conventional Kinetic Models

PubMed Central

Tosun, İsmail

2012-01-01

The adsorption isotherm, the adsorption kinetics, and the thermodynamic parameters of ammonium removal from aqueous solution by using clinoptilolite in aqueous solution was investigated in this study. Experimental data obtained from batch equilibrium tests have been analyzed by four two-parameter (Freundlich, Langmuir, Tempkin and Dubinin-Radushkevich (D-R)) and four three-parameter (Redlich-Peterson (R-P), Sips, Toth and Khan) isotherm models. D-R and R-P isotherms were the models that best fitted to experimental data over the other two- and three-parameter models applied. The adsorption energy (E) from the D-R isotherm was found to be approximately 7 kJ/mol for the ammonium-clinoptilolite system, thereby indicating that ammonium is adsorbed on clinoptilolite by physisorption. Kinetic parameters were determined by analyzing the nth-order kinetic model, the modified second-order model and the double exponential model, and each model resulted in a coefficient of determination (R2) of above 0.989 with an average relative error lower than 5%. A Double Exponential Model (DEM) showed that the adsorption process develops in two stages as rapid and slow phase. Changes in standard free energy (∆G°), enthalpy (∆H°) and entropy (∆S°) of ammonium-clinoptilolite system were estimated by using the thermodynamic equilibrium coefficients. PMID:22690177

Ammonium removal from aqueous solutions by clinoptilolite: determination of isotherm and thermodynamic parameters and comparison of kinetics by the double exponential model and conventional kinetic models.

PubMed

Tosun, Ismail

2012-03-01

The adsorption isotherm, the adsorption kinetics, and the thermodynamic parameters of ammonium removal from aqueous solution by using clinoptilolite in aqueous solution was investigated in this study. Experimental data obtained from batch equilibrium tests have been analyzed by four two-parameter (Freundlich, Langmuir, Tempkin and Dubinin-Radushkevich (D-R)) and four three-parameter (Redlich-Peterson (R-P), Sips, Toth and Khan) isotherm models. D-R and R-P isotherms were the models that best fitted to experimental data over the other two- and three-parameter models applied. The adsorption energy (E) from the D-R isotherm was found to be approximately 7 kJ/mol for the ammonium-clinoptilolite system, thereby indicating that ammonium is adsorbed on clinoptilolite by physisorption. Kinetic parameters were determined by analyzing the nth-order kinetic model, the modified second-order model and the double exponential model, and each model resulted in a coefficient of determination (R(2)) of above 0.989 with an average relative error lower than 5%. A Double Exponential Model (DEM) showed that the adsorption process develops in two stages as rapid and slow phase. Changes in standard free energy (∆G°), enthalpy (∆H°) and entropy (∆S°) of ammonium-clinoptilolite system were estimated by using the thermodynamic equilibrium coefficients.

An HLLC Riemann solver for resistive relativistic magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Miranda-Aranguren, S.; Aloy, M. A.; Rembiasz, T.

2018-05-01

We present a new approximate Riemann solver for the augmented system of equations of resistive relativistic magnetohydrodynamics that belongs to the family of Harten-Lax-van Leer contact wave (HLLC) solvers. In HLLC solvers, the solution is approximated by two constant states flanked by two shocks separated by a contact wave. The accuracy of the new approximate solver is calibrated through 1D and 2D test problems.

Generalized gradient algorithm for trajectory optimization

NASA Technical Reports Server (NTRS)

Zhao, Yiyuan; Bryson, A. E.; Slattery, R.

1990-01-01

The generalized gradient algorithm presented and verified as a basis for the solution of trajectory optimization problems improves the performance index while reducing path equality constraints, and terminal equality constraints. The algorithm is conveniently divided into two phases, of which the first, 'feasibility' phase yields a solution satisfying both path and terminal constraints, while the second, 'optimization' phase uses the results of the first phase as initial guesses.

Thermodynamic integration based on classical atomistic simulations to determine the Gibbs energy of condensed phases: Calculation of the aluminum-zirconium system

NASA Astrophysics Data System (ADS)

Harvey, J.-P.; Gheribi, A. E.; Chartrand, P.

2012-12-01

In this work, an in silico procedure to generate a fully coherent set of thermodynamic properties obtained from classical molecular dynamics (MD) and Monte Carlo (MC) simulations is proposed. The procedure is applied to the Al-Zr system because of its importance in the development of high strength Al-Li alloys and of bulk metallic glasses. Cohesive energies of the studied condensed phases of the Al-Zr system (the liquid phase, the fcc solid solution, and various orthorhombic stoichiometric compounds) are calculated using the modified embedded atom model (MEAM) in the second-nearest-neighbor formalism (2NN). The Al-Zr MEAM-2NN potential is parameterized in this work using ab initio and experimental data found in the literature for the AlZr3-L12 structure, while its predictive ability is confirmed for several other solid structures and for the liquid phase. The thermodynamic integration (TI) method is implemented in a general MC algorithm in order to evaluate the absolute Gibbs energy of the liquid and the fcc solutions. The entropy of mixing calculated from the TI method, combined to the enthalpy of mixing and the heat capacity data generated from MD/MC simulations performed in the isobaric-isothermal/canonical (NPT/NVT) ensembles are used to parameterize the Gibbs energy function of all the condensed phases in the Al-rich side of the Al-Zr system in a CALculation of PHAse Diagrams (CALPHAD) approach. The modified quasichemical model in the pair approximation (MQMPA) and the cluster variation method (CVM) in the tetrahedron approximation are used to define the Gibbs energy of the liquid and the fcc solid solution respectively for their entire range of composition. Thermodynamic and structural data generated from our MD/MC simulations are used as input data to parameterize these thermodynamic models. A detailed analysis of the validity and transferability of the Al-Zr MEAM-2NN potential is presented throughout our work by comparing the predicted properties obtained from this formalism with available ab initio and experimental data for both liquid and solid phases.

An exact solution of a simplified two-phase plume model. [for solid propellant rocket

NASA Technical Reports Server (NTRS)

Wang, S.-Y.; Roberts, B. B.

1974-01-01

An exact solution of a simplified two-phase, gas-particle, rocket exhaust plume model is presented. It may be used to make the upper-bound estimation of the heat flux and pressure loads due to particle impingement on the objects existing in the rocket exhaust plume. By including the correction factors to be determined experimentally, the present technique will provide realistic data concerning the heat and aerodynamic loads on these objects for design purposes. Excellent agreement in trend between the best available computer solution and the present exact solution is shown.

The Pendulum Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2002-01-01

We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…

Unified Approximations: A New Approach for Monoprotic Weak Acid-Base Equilibria

ERIC Educational Resources Information Center

Pardue, Harry; Odeh, Ihab N.; Tesfai, Teweldemedhin M.

2004-01-01

The unified approximations reduce the conceptual complexity by combining solutions for a relatively large number of different situations into just two similar sets of processes. Processes used to solve problems by either the unified or classical approximations require similar degrees of understanding of the underlying chemical processes.

Potential of mean force between two hydrophobic solutes in water.

PubMed

Southall, Noel T; Dill, Ken A

2002-12-10

We study the potential of mean force between two nonpolar solutes in the Mercedes Benz model of water. Using NPT Monte Carlo simulations, we find that the solute size determines the relative preference of two solute molecules to come into contact ('contact minimum') or to be separated by a single layer of water ('solvent-separated minimum'). Larger solutes more strongly prefer the contacting state, while smaller solutes have more tendency to become solvent-separated, particularly in cold water. The thermal driving forces oscillate with solute separation. Contacts are stabilized by entropy, whereas solvent-separated solute pairing is stabilized by enthalpy. The free energy of interaction for small solutes is well-approximated by scaled-particle theory. Copyright 2002 Elsevier Science B.V.

The microscopic structure of an exactly solvable model binary solution that exhibits two closed loops in the phase diagram.

PubMed

Lungu, Radu P; Huckaby, Dale A

2008-07-21

An exactly solvable lattice model describing a binary solution is considered where rodlike molecules of types AA and BB cover the links of a honeycomb lattice, the neighboring molecular ends having three-body and orientation-dependent bonding interactions. At phase coexistence of AA-rich and BB-rich phases, the average fraction of each type of triangle of neighboring molecular ends is calculated exactly. The fractions of the different types of triangles are then used to deduce the local microscopic structure of the coexisting phases for a case of the model that contains two closed loops in the phase diagram.

In vitro corrosion study by EIS of a nickel-free stainless steel for orthopaedic applications.

PubMed

Rondelli, G; Torricelli, P; Fini, M; Giardino, R

2005-03-01

The electrochemical impedance spectroscopy (EIS) technique was used for the study of the electrochemical behaviour of Ni-free austenitic stainless steel for orthopaedic applications. Experiments were carried out using four different test solutions: (i) phosphate-buffered saline (PBS), (ii) minimum essential medium (MEM), (iii) MEM + 10% fetal calf serum (FCS), (iv) MEM + 10% fetal calf serum + L929 fibroblast cell line (Cell). Bode-phase spectra showed the presence of two maxima and were fitted with an equivalent circuit characterized by two parallel combinations (Resistance, Constant Phase Element). The (R(1), CPE(1)) branch was assigned to the inner compact passive film and the (R(2), CPE(2)) branch to the external porous film. The resistance of the inner film R(1), here directly related to the material's uniform corrosion resistance, raised with the immersion time and increased in the following order: PBS

Determination of the Residence Time of Food Particles During Aseptic Sterilization

NASA Technical Reports Server (NTRS)

Carl, J. R.; Arndt, G. D.; Nguyen, T. X.

1994-01-01

The paper describes a non-invasive method to measure the time an individual particle takes to move through a length of stainless steel pipe. The food product is in two phase flow (liquids and solids) and passes through a pipe with pressures of approximately 60 psig and temperatures of 270-285 F. The proposed problem solution is based on the detection of transitory amplitude and/or phase changes in a microwave transmission path caused by the passage of the particles of interest. The particles are enhanced in some way, as will be discussed later, such that they will provide transitory changes that are distinctive enough not to be mistaken for normal variations in the received signal (caused by the non-homogeneous nature of the medium). Two detectors (transmission paths across the pipe) will be required and place at a known separation. A minimum transit time calculation is made from which the maximum velocity can be determined. This provides the minimum residence time. Also average velocity and statistical variations can be computed so that the amount of 'over-cooking' can be determined.

An Unusual Salt Effect in an Interfacial Nucleophilic Substitution Reaction.

PubMed

Li, Shuheng; Mrksich, Milan

2018-06-12

This paper reports a kinetic characterization of the interfacial reaction of N-methylpyrrolidine with a self-assembled monolayer presenting an iodoalkyl group. SAMDI (self-assembled monolayers for matrix-assisted laser desorption/ionization) mass spectrometry was used to determine the extent of reaction for monolayers that were treated with a range of concentrations of the nucleophile for a range of times. These data revealed a second-order rate constant for the reaction that was approximately 100-fold greater than that for the analogous solution-phase reaction. However, addition of sodium iodide to the reaction mixture resulted in a 7-fold decrease in the reaction rate. Addition of bromide and chloride salts also gave slower rate constants for the reaction, but only at 100- and 1000-fold higher concentrations than was observed with iodide, respectively. The corresponding solution-phase reactions, by contrast, had rate constants that were unaffected by the concentration of halide salts. This work provides a well-characterized example illustrating the extent to which the kinetics and properties of an interfacial reaction can depart substantially from their better-understood solution-phase counterparts.

High Frequency Acoustic Propagation using Level Set Methods

DTIC Science & Technology

2007-01-01

solution of the high frequency approximation to the wave equation. Traditional solutions to the Eikonal equation in high frequency acoustics are...the Eikonal equation derived from the high frequency approximation to the wave equation, ucuH ∇±=∇ )(),( xx , with the nonnegative function c(x...For simplicity, we only consider the case ucuH ∇+=∇ )(),( xx . Two difficulties must be addressed when solving the Eikonal equation in a fixed

High-Order Central WENO Schemes for Multi-Dimensional Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)

2002-01-01

We present new third- and fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme that is based on a genuinely two-dimensional Central WENO reconstruction, and another scheme that is based on a simpler dimension-by-dimension reconstruction. The simpler dimension-by-dimension variant is then extended to a multi-dimensional fifth-order scheme. Our numerical examples in one, two and three space dimensions verify the expected order of accuracy of the schemes.

The ice VII-ice X phase transition with implications for planetary interiors

NASA Astrophysics Data System (ADS)

Aarestad, B.; Frank, M. R.; Scott, H.; Bricker, M.; Prakapenka, V.

2008-12-01

A significant amount of research on the high pressure polymorphs of H2O have detailed the lattice structure and density of these phases, namely ice VI, ice VII, and ice X. These high pressure ices are noteworthy as they may comprise a considerable part of the interior of large icy planets and satellites. However, there is a dearth of data on how the incorporation of an impurity, charged or non-charged, affects the ice VII-ice X transition. This study examined the ice VII-ice X transition that occurs at approximately 62 GPa with a pure system and two select impure systems. Solutions of pure H2O, 1.6 mole percent NaCl in H2O, and 1.60 mole percent CH3OH in H2O were compressed in a diamond anvil cell (DAC). The experiments were performed at the GSECARS 13-BM-D beam line at the Advanced Photon Source at Argonne National Laboratory. Powder diffraction data of the ice samples were collected using monochromatic X-ray radiation, 0.2755 Å, and a MAR 345 online imaging system at intervals of approximately 2 GPa up to ~71.5, ~74.5, and ~68 GPa, respectively. Analyses of the data provided volume-pressure relations (at 298 K) which were used to detail the ice VII-ice X phase transition. The pressure of the phase transition, based upon an interpretation of the X-ray diffraction data, was found to vary as a function of the impurity type. Thus, the depth of the ice VII-ice X phase transition within an ice-rich planetary body can be influenced by trace-level impurities.

A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems

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

Bertola, Marco, E-mail: Marco.Bertola@concordia.ca; Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec H3C 3J7; SISSA/ISAS, via Bonomea 265, Trieste

2015-06-15

Two-phase solutions of focusing NLS equation are classically constructed out of an appropriate Riemann surface of genus two and expressed in terms of the corresponding theta-function. We show here that in a certain limiting regime, such solutions reduce to some elementary ones called “Solitons on unstable condensate.” This degeneration turns out to be conveniently studied by means of basic tools from the theory of Riemann-Hilbert problems. In particular, no acquaintance with Riemann surfaces and theta-function is required for such analysis.

Solitary solutions including spatially localized chaos and their interactions in two-dimensional Kolmogorov flow.

PubMed

Hiruta, Yoshiki; Toh, Sadayoshi

2015-12-01

Two-dimensional Kolmogorov flow in wide periodic boxes is numerically investigated. It is shown that the total flow rate in the direction perpendicular to the force controls the characteristics of the flow, especially the existence of spatially localized solitary solutions such as traveling waves, periodic solutions, and chaotic solutions, which can behave as elementary components of the flow. We propose a procedure to construct approximate solutions consisting of solitary solutions. It is confirmed by direct numerical simulations that these solutions are stable and represent interactions between elementary components such as collisions, coexistence, and collapse of chaos.

A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

PubMed

Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

2016-01-01

This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

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

NASA Technical Reports Server (NTRS)

Spreiter, John R; Alksne, Alberta Y

1957-01-01

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

A three-dimensional multiphase flow model for assesing NAPL contamination in porous and fractured media, 1. Formulation

NASA Astrophysics Data System (ADS)

Huyakorn, P. S.; Panday, S.; Wu, Y. S.

1994-06-01

A three-dimensional, three-phase numerical model is presented for stimulating the movement on non-aqueous-phase liquids (NAPL's) through porous and fractured media. The model is designed for practical application to a wide variety of contamination and remediation scenarios involving light or dense NAPL's in heterogeneous subsurface systems. The model formulation is first derived for three-phase flow of water, NAPL and air (or vapor) in porous media. The formulation is then extended to handle fractured systems using the dual-porosity and discrete-fracture modeling approaches The model accommodates a wide variety of boundary conditions, including withdrawal and injection well conditions which are treated rigorously using fully implicit schemes. The three-phase of formulation collapses to its simpler forms when air-phase dynamics are neglected, capillary effects are neglected, or two-phase-air-liquid, liquid-liquid systems with one or two active phases are considered. A Galerkin procedure with upstream weighting of fluid mobilities, storage matrix lumping, and fully implicit treatment of nonlinear coefficients and well conditions is used. A variety of nodal connectivity schemes leading to finite-difference, finite-element and hybrid spatial approximations in three dimensions are incorporated in the formulation. Selection of primary variables and evaluation of the terms of the Jacobian matrix for the Newton-Raphson linearized equations is discussed. The various nodal lattice options, and their significance to the computational time and memory requirements with regards to the block-Orthomin solution scheme are noted. Aggressive time-stepping schemes and under-relaxation formulas implemented in the code further alleviate the computational burden.

Charging of Proteins in Native Mass Spectrometry

DOE PAGES

Susa, Anna C.; Xia, Zijie; Tang, Henry Y. H.; ...

2016-10-12

Factors that influence the charging of protein ions formed by electrospray ionization from aqueous solutions in which proteins have native structures and function were investigated. Protein ions ranging in molecular weight from 12.3 to 79.7 kDa and pI values from 5.4 to 9.6 were formed from different solutions and reacted with volatile bases of gas-phase basicities higher than that of ammonia in the cell of a Fourier-transform ion cyclotron resonance mass spectrometer. The charge-state distribution of cytochrome c ions formed from aqueous ammonium or potassium acetate is the same. Moreover, ions formed from these two solutions do not undergo protonmore » transfer to 2-fluoropyridine, which is 8 kcal/mol more basic than ammonia. These results provide compelling evidence that proton transfer between ammonia and protein ions does not limit protein ion charge in native electrospray ionization. Both circular dichroism and ion mobility measurements indicate that there are differences in conformations of proteins in pure water and aqueous ammonium acetate, and these differences can account for the difference in the extent of charging and proton-transfer reactivities of protein ions formed from these solutions. The extent of proton transfer of the protein ions with higher gas-phase basicity bases trends with how closely the protein ions are charged to the value predicted by the Rayleigh limit for spherical water droplets approximately the same size as the proteins. These results indicate that droplet charge limits protein ion charge in native mass spectrometry and are consistent with these ions being formed by the charged residue mechanism.« less

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

Susa, Anna C.; Xia, Zijie; Tang, Henry Y. H.

Factors that influence the charging of protein ions formed by electrospray ionization from aqueous solutions in which proteins have native structures and function were investigated. Protein ions ranging in molecular weight from 12.3 to 79.7 kDa and pI values from 5.4 to 9.6 were formed from different solutions and reacted with volatile bases of gas-phase basicities higher than that of ammonia in the cell of a Fourier-transform ion cyclotron resonance mass spectrometer. The charge-state distribution of cytochrome c ions formed from aqueous ammonium or potassium acetate is the same. Moreover, ions formed from these two solutions do not undergo protonmore » transfer to 2-fluoropyridine, which is 8 kcal/mol more basic than ammonia. These results provide compelling evidence that proton transfer between ammonia and protein ions does not limit protein ion charge in native electrospray ionization. Both circular dichroism and ion mobility measurements indicate that there are differences in conformations of proteins in pure water and aqueous ammonium acetate, and these differences can account for the difference in the extent of charging and proton-transfer reactivities of protein ions formed from these solutions. The extent of proton transfer of the protein ions with higher gas-phase basicity bases trends with how closely the protein ions are charged to the value predicted by the Rayleigh limit for spherical water droplets approximately the same size as the proteins. These results indicate that droplet charge limits protein ion charge in native mass spectrometry and are consistent with these ions being formed by the charged residue mechanism.« less

Charging of Proteins in Native Mass Spectrometry

NASA Astrophysics Data System (ADS)

Susa, Anna C.; Xia, Zijie; Tang, Henry Y. H.; Tainer, John A.; Williams, Evan R.

2017-02-01

Factors that influence the charging of protein ions formed by electrospray ionization from aqueous solutions in which proteins have native structures and function were investigated. Protein ions ranging in molecular weight from 12.3 to 79.7 kDa and pI values from 5.4 to 9.6 were formed from different solutions and reacted with volatile bases of gas-phase basicities higher than that of ammonia in the cell of a Fourier-transform ion cyclotron resonance mass spectrometer. The charge-state distribution of cytochrome c ions formed from aqueous ammonium or potassium acetate is the same. Moreover, ions formed from these two solutions do not undergo proton transfer to 2-fluoropyridine, which is 8 kcal/mol more basic than ammonia. These results provide compelling evidence that proton transfer between ammonia and protein ions does not limit protein ion charge in native electrospray ionization. Both circular dichroism and ion mobility measurements indicate that there are differences in conformations of proteins in pure water and aqueous ammonium acetate, and these differences can account for the difference in the extent of charging and proton-transfer reactivities of protein ions formed from these solutions. The extent of proton transfer of the protein ions with higher gas-phase basicity bases trends with how closely the protein ions are charged to the value predicted by the Rayleigh limit for spherical water droplets approximately the same size as the proteins. These results indicate that droplet charge limits protein ion charge in native mass spectrometry and are consistent with these ions being formed by the charged residue mechanism.

Single scattering solution for radiative transfer through Rayleigh and aerosol atmosphere

NASA Technical Reports Server (NTRS)

Otterman, J.

1977-01-01

A solution is presented to the radiative transfer of the solar irradiation through a turbid atmosphere, based on the single-scattering approximation, i.e., an assumption that a photon that underwent scattering either leaves the top of the atmosphere or strikes the surface. The solution depends on a special idealization of the scattering phase function of the aerosols. The equations developed are subsequently applied to analyze quantitatively the enhancement of the surface irradiation and the enhancement of the scattered radiant emittance as seen from above the atmosphere, caused by the surface reflectance and atmospheric back scattering. An order of magnitude error analysis is presented.

Approximate analytical solutions in the analysis of thin elastic plates

NASA Astrophysics Data System (ADS)

Goloskokov, Dmitriy P.; Matrosov, Alexander V.

2018-05-01

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

A homogenization approach for the effective drained viscoelastic properties of 2D porous media and an application for cortical bone.

PubMed

Nguyen, Sy-Tuan; Vu, Mai-Ba; Vu, Minh-Ngoc; To, Quy-Dong

2018-02-01

Closed-form solutions for the effective rheological properties of a 2D viscoelastic drained porous medium made of a Generalized Maxwell viscoelastic matrix and pore inclusions are developed and applied for cortical bone. The in-plane (transverse) effective viscoelastic bulk and shear moduli of the Generalized Maxwell rheology of the homogenized medium are expressed as functions of the porosity and the viscoelastic properties of the solid phase. When deriving these functions, the classical inverse Laplace-Carson transformation technique is avoided, due to its complexity, by considering the short and long term approximations. The approximated results are validated against exact solutions obtained from the inverse Laplace-Carson transform for a simple configuration when the later is available. An application for cortical bone with assumption of circular pore in the transverse plane shows that the proposed approximation fit very well with experimental data. Copyright © 2017 Elsevier Ltd. All rights reserved.

Hafnia-rich mixed oxide ceramics of the system HfO2-ZrO2-TiO2 for heaters and heat exchangers in electrothermal thrusters: The effects of titania on selected electrical and mechanical properties of Hafnia-rich mixed oxides in the system Hafnia-Zirconia-Titania, volume 1

NASA Technical Reports Server (NTRS)

Staszak, Paul Russell; Wirtz, G. P.; Berg, M.; Brown, S. D.

1988-01-01

A study of the effects of titania on selected properties of hafnia-rich mixed oxides in the system hafnia-zirconia-titania (HZT) was made in the region 5 to 20 mol percent titania. The studied properties included electrical conductivity, thermal expansion, and fracture strength and toughness. The effects of titania on the properties were studied for the reduced state as well as the oxidized state of the sintered mixed oxides. X-ray analysis showed that the materials were not always single phase. The oxidized compositions went from being monoclinic solid solutions at low titania additions to having three phases (two monoclinic and a titanate phase) at high additions of titania. The reduced compositions showed an increasing cubic phase presence mixed with the monoclinic phase as titania was added. The electrical conductivity increased with temperature at approximately 0.1 mhos/cm at 1700 C for all compositions. The thermal expansion coefficient decreased with increasing titania as did the monoclinic to tetragonal transformation temperature. The fracture strength of the oxidized bars tended to decrease with the addition of titania owing to the presence of the second phase titania. The fracture strength of the reduced bars exhibited a minimum corresponding to a two-phase region of monoclinic and cubic phases. When the second phases were suppressed, the titania tended to increase the fracture strength slightly in both the oxidized and reduced states. The fracture toughness followed similar trends.

Gaseous Viscous Peeling of Linearly Elastic Substrates

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2017-11-01

We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the governing nonlinear evolution equation describes the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility, characteristic to gaseous microflows. Several physical limits allow simplification of the evolution equation and enable solution by self-similarity. During the peeling process the flow-field transitions between the different limits and the respective approximate solutions. The sequence of limits occurring during the propagation dynamics can be related to the thickness of the prewetting layer of the configuration at rest, yielding an approximate description of the entire peeling dynamics. The results are validated by numerical solutions of the evolution equation. Israel Science Foundation 818/13.

Phase equilibrium of methane and nitrogen at low temperatures - Application to Titan

NASA Technical Reports Server (NTRS)

Kouvaris, Louis C.; Flasar, F. M.

1991-01-01

Since the vapor phase composition of Titan's methane-nitrogen lower atmosphere is uniquely determined as a function of the Gibbs phase rule, these data are presently computed via integration of the Gibbs-Duhem equation. The thermodynamic consistency of published measurements and calculations of the vapor phase composition is then examined, and the saturated mole fraction of gaseous methane is computed as a function of altitude up to the 700-mbar level. The mole fraction is found to lie approximately halfway between that computed from Raoult's law, for a gas in equilibrium with an ideal solution of liquid nitrogen and methane, and that for a gas in equilibrium with pure liquid methane.

Synthesis of Pt 3Y and Other Early–Late Intermetallic Nanoparticles by Way of a Molten Reducing Agent

DOE PAGES

Kanady, Jacob S.; Leidinger, Peter; Haas, Andreas; ...

2017-03-29

Early–late intermetallic phases have garnered increased attention recently for their catalytic properties. To achieve the high surface areas needed for industrially relevant applications, these phases must be synthesized as nanoparticles in a scalable fashion. Herein, Pt 3Y—targeted as a prototypical example of an early–late intermetallic—has been synthesized as nanoparticles approximately 5–20 nm in diameter via a solution process and characterized by XRD, TEM, EDS, and XPS. The key development is the use of a molten borohydride (MEt 3BH, M = Na, K) as both the reducing agent and reaction medium. Readily available halide precursors of the two metals are used.more » Accordingly, no organic ligands are necessary, as the resulting halide salt byproduct prevents sintering, which further permits dispersion of the nanoscale intermetallic onto a support. The versatility of this approach was validated by the synthesis of other intermetallic phases such as Pt 3Sc, Pt 3Lu, Pt 2Na, and Au 2Y.« less

Synthesis of Pt 3Y and Other Early–Late Intermetallic Nanoparticles by Way of a Molten Reducing Agent

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

Kanady, Jacob S.; Leidinger, Peter; Haas, Andreas

Early–late intermetallic phases have garnered increased attention recently for their catalytic properties. To achieve the high surface areas needed for industrially relevant applications, these phases must be synthesized as nanoparticles in a scalable fashion. Herein, Pt 3Y—targeted as a prototypical example of an early–late intermetallic—has been synthesized as nanoparticles approximately 5–20 nm in diameter via a solution process and characterized by XRD, TEM, EDS, and XPS. The key development is the use of a molten borohydride (MEt 3BH, M = Na, K) as both the reducing agent and reaction medium. Readily available halide precursors of the two metals are used.more » Accordingly, no organic ligands are necessary, as the resulting halide salt byproduct prevents sintering, which further permits dispersion of the nanoscale intermetallic onto a support. The versatility of this approach was validated by the synthesis of other intermetallic phases such as Pt 3Sc, Pt 3Lu, Pt 2Na, and Au 2Y.« less

Size response of an SMPS-APS system to commercial multi-walled carbon nanotubes

NASA Astrophysics Data System (ADS)

Lee, Seung-Bok; Lee, Jun-Hyun; Bae, Gwi-Nam

2010-02-01

Carbon nanotubes (CNTs) are representative-engineered nanomaterials with unique properties. The safe production of CNTs urgently requires reliable tools to assess inhalation exposure. In this study, on-line aerosol instruments were employed to detect the release of multi-walled CNTs (MWCNTs) in workplace environments. The size responses of aerosol instruments consisting of both a scanning mobility particle sizer (SMPS) and an aerodynamic particle sizer (APS) were examined using five types of commercial MWCNTs. A MWCNT solution and powder were aerosolized using atomizing and shaking methods, respectively. Regardless of the phase and purity, the aerosolized MWCNTs showed consistent size distributions with both SMPS and APS. The SMPS and APS measurements revealed a dominant broad peak at approximately 200-400 nm and a distinct narrow peak at approximately 2 μm, respectively. Comparing with field application of the two aerosol instruments, the APS response could be a fingerprint of the MWCNTs in a real workplace environment. A modification of the atomizing method is recommended for the long-term inhalation toxicity studies.

Accurate approximation of in-ecliptic trajectories for E-sail with constant pitch angle

NASA Astrophysics Data System (ADS)

Huo, Mingying; Mengali, Giovanni; Quarta, Alessandro A.

2018-05-01

Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.

Dual-phase Cr-Ta alloys for structural applications

DOEpatents

Liu, Chain T.; Brady, Michael P.; Zhu, Jiahong; Tortorelli, Peter F.

2001-01-01

Dual phase alloys of chromium containing 2 to 11 atomic percent tantalum with minor amounts of Mo, Cr, Ti, Y, La, Cr, Si and Ge are disclosed. These alloys contain two phases including Laves phase and Cr-rich solid solution in either eutectic structures or dispersed Laves phase particles in the Cr-rich solid solution matrix. The alloys have superior mechanical properties at high temperature and good oxidation resistance when heated to above 1000.degree. C. in air.

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

DOE PAGES

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

2017-01-05

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

Possible mechanism to enhance spin-fluctuation-mediated superconductivity in two-dimensional organic conductor

NASA Astrophysics Data System (ADS)

Nonoyama, Yoshito; Maekawa, Yukiko; Kobayashi, Akito; Suzumura, Yoshikazu; Yamada, Jun-ichi

2008-10-01

Mechanisms of superconductivity in quasi-two-dimensional organic conductors have been investigated using an extended Hubbard model by using the transfer energies between BDA-TTP molecules for β-(BDA-TTP)2I3 based on the X-ray experiment data and the extended Hückel calculation. We obtain several mean-field solutions with charge orderings which may represent short-range orderings or low-energy fluctuations in the low-dimensional electronic system. In the pressure-temperature phase diagram, a charge ordered metal state almost degenerates with a normal metal state between an insulating phase with charge ordering and the normal metal phase. Using the random phase approximation (RPA) and the linearized gap equation, the transition temperature of the superconducting state is estimated for the charge-ordered metal state and the normal metal state. It is found that transition temperature of the superconductivity induced by spin fluctuations in the charge-ordered metal state is much higher than that of the normal metal state and that the superconductivity in the charge-ordered metal state is the gapless d-wave. This suggests that the short range charge ordering may also contribute to an enhancement of spin-fluctuation-mediated superconductivity. The difference in the superconducting states between β-(BDA-TTP)2I3 and β-(BDA-TTP)2SbF6 are briefly discussed.

Raman spectroscopic studies on single supersaturated droplets of sodium and magnesium acetate.

PubMed

Wang, Liang-Yu; Zhang, Yun-Hong; Zhao, Li-Jun

2005-02-03

Raman spectroscopy was used to study structural changes, in particular, the formation of contact-ion pairs in supersaturated aqueous NaCH(3)COO and Mg(CH(3)COO)(2) droplets at ambient temperatures. The single droplets levitated in an electrodynamic balance (EDB), lost water, and became supersaturated when the relative humidity (RH) decreased. For NaCH(3)COO droplet the water-to-solute molar ratio (WSR) was 3.87 without solidification when water molecules were not enough to fill in the first hydration layer of Na(+), in favor of the formation of contact-ion pairs. However, the symmetric stretching vibration band (nu(3) mode) of free -COO(-) constantly appeared at 1416 cm(-1), and no spectroscopic information related to monodentate, bidentate, or bridge bidentate contact-ion pairs was observed due to the weak interactions between the Na(+) and acetate ion. On the other hand, the band of methyl deformation blue shifted from 1352 to 1370 cm(-1) (at RH = 34.2%, WSR = 2.43), corresponding to the solidification process of a novel metastable phase in the highly supersaturated solutions. With further decreasing RH, a small amount of supersaturated solution still existed and was proposed to be hermetically covered by the metastable phase of the particle. In contrast, the interaction between Mg(2+) and acetate ion is much stronger. When WSR decreased from 21.67 to 2.58 for the Mg(CH(3)COO)(2) droplet, the band of C-C-symmetric stretching (nu(4) mode) had a blue shift from 936 to 947 cm(-1). The intensity of the two new shoulders (approximately 1456 and approximately 1443 cm(-1)) of the nu(3) band of free -COO(-) at 1420 cm(-1) increased with the decrease of WSR. These changes were attributed to the formation of contact-ion pairs with bidentate structures. In particular, the small frequency difference between the shoulder at approximately 1443 cm(-1) and the nu(3) band of the free -COO(-) group (approximately 1420 cm(-1)) was proposed to be related to the formation of a chain structure based on the contact-ion pairs of bridge bidentate. The continuous formation of various contact-ion pairs started at higher WSR value (WSR = 15.5) greatly reduced the hygroscopic properties of Mg(CH(3)COO)(2) droplet, so that the WSR of Mg(CH(3)COO)(2) droplets was even lower than that of NaCH(3)COO in the RH range of 40-60%.

Energy-saving method for technogenic waste processing

PubMed Central

Dikhanbaev, Bayandy; Dikhanbaev, Aristan Bayandievich

2017-01-01

Dumps of a mining-metallurgical complex of post-Soviet Republics have accumulated a huge amount of technogenic waste products. Out of them, Kazakhstan alone has preserved about 20 billion tons. In the field of technogenic waste treatment, there is still no technical solution that leads it to be a profitable process. Recent global trends prompted scientists to focus on developing energy-saving and a highly efficient melting unit that can significantly reduce specific fuel consumption. This paper reports, the development of a new technological method—smelt layer of inversion phase. The introducing method is characterized by a combination of ideal stirring and ideal displacement regimes. Using the method of affine modelling, recalculation of pilot plant’s test results on industrial sample has been obtained. Experiments show that in comparison with bubbling and boiling layers of smelt, the degree of zinc recovery increases in the layer of inversion phase. That indicates the reduction of the possibility of new formation of zinc silicates and ferrites from recombined molecules of ZnO, SiO2, and Fe2O3. Calculations show that in industrial samples of the pilot plant, the consumption of natural gas has reduced approximately by two times in comparison with fuming-furnace. The specific fuel consumption has reduced by approximately four times in comparison with Waelz-kiln. PMID:29281646

Liquid-vapor phase equilibria and the thermodynamic properties of 2-methylpropanol- n-alkyl propanoate solutions

NASA Astrophysics Data System (ADS)

Suntsov, Yu. K.; Goryunov, V. A.; Chuikov, A. M.; Meshcheryakov, A. V.

2016-08-01

The boiling points of solutions of five binary systems are measured via ebulliometry in the pressure range of 2.05-103.3 kPa. Equilibrium vapor phase compositions, the values of the excess Gibbs energies, enthalpies, and entropies of solution of these systems are calculated. Patterns in the changes of phase equilibria and thermodynamic properties of solutions are established, depending on the compositions and temperatures of the systems. Liquid-vapor equilibria in the systems are described using the equations of Wilson and the NRTL (Non-Random Two-Liquid Model).

Interdiffusion and Intrinsic Diffusion in the Mg-Al System

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

Brennan, Sarah; Bermudez, Katrina; Sohn, Yong Ho

2012-01-01

Solid-to-solid diffusion couples were assembled and annealed to examine the diffusion between pure Mg (99.96%) and Al (99.999%). Diffusion anneals were carried out at 300 , 350 , and 400 C for 720, 360, and 240 hours, respectively. Optical and scanning electron microscopes were utilized to identify the formation of the intermetallic phases, -Al12Mg17 and -Al3Mg2 and absence of the -phase in the diffusion couples. Thicknesses of the -Al12Mg17 and -Al3Mg2 phases were measured and the parabolic growth constants were calculated to determine the activation energies for the growth, 165 and 86 KJ/mole, respectively. Concentration profiles were determined with electronmore » microprobe analysis using pure elemental standards. Composition-dependent interdiffusion coefficients in Mg-solid solution, -Al12Mg17 and - Al3Mg2 and Al-solid solutions were calculated based on the Boltzmann-Matano analysis. Average effective interdiffusion coefficients for each phase were also calculated, and the magnitude was the highest for the -Al3Mg2 phase, followed by -Al12Mg17, Al-solid solution and Mg-solid solution. Intrinsic diffusion coefficients based on Huemann s analysis (e.g., marker plane) were determined for the ~38 at.% Mg in the -Al3Mg2 phase. Activation energies and the pre-exponential factors for the inter- and intrinsic diffusion coefficients were calculated for the temperature range examined. The -Al3Mg2 phase was found to have the lowest activation energies for growth and interdiffusion among all four phases studied. At the marker location in the -Al3Mg2 phase, the intrinsic diffusion of Al was found to be faster than that of Mg. Extrapolations of the impurity diffusion coefficients in the terminal solid solutions were made and compared to the available self- and impurity diffusion data from literature. Thermodynamic factor, tracer diffusion coefficients and atomic mobilities at the marker plane composition were approximated using available literature values of Mg activity in the -Al3Mg2 phase.« less

Recent advances in two-phase flow numerics

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

Mahaffy, J.H.; Macian, R.

1997-07-01

The authors review three topics in the broad field of numerical methods that may be of interest to individuals modeling two-phase flow in nuclear power plants. The first topic is iterative solution of linear equations created during the solution of finite volume equations. The second is numerical tracking of macroscopic liquid interfaces. The final area surveyed is the use of higher spatial difference techniques.

Quantum noise of a Bose-Einstein condensate in an optical cavity, correlations, and entanglement

NASA Astrophysics Data System (ADS)

Szirmai, G.; Nagy, D.; Domokos, P.

2010-04-01

A Bose-Einstein condensate of ultracold atoms inside the field of a laser-driven optical cavity exhibits dispersive optical bistability. We describe this system by using mean-field approximation and by analyzing the correlation functions of the linearized quantum fluctuations around the mean-field solution. The entanglement and the statistics of the atom-field quadratures are given in the stationary state. It is shown that the mean-field solution, that is, the Bose-Einstein condensate, is robust against entanglement generation for most of the phase diagram.

An approximate analysis of the diffusing flow in a self-controlled heat pipe.

NASA Technical Reports Server (NTRS)

Somogyi, D.; Yen, H. H.

1973-01-01

Constant-density two-dimensional axisymmetric equations are presented for the diffusing flow of a class of self-controlled heat pipes. The analysis is restricted to the vapor space. Condensation of the vapor is related to its mass fraction at the wall by the gas kinetic formula. The Karman-Pohlhausen integral method is applied to obtain approximate solutions. Solutions are presented for a water heat pipe with neon control gas.

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter.

PubMed

Kulkarni, Rishikesh; Rastogi, Pramod

2018-02-01

A noise-robust phase unwrapping algorithm is proposed based on state space analysis and polynomial phase approximation using wrapped phase measurement. The true phase is approximated as a two-dimensional first order polynomial function within a small sized window around each pixel. The estimates of polynomial coefficients provide the measurement of phase and local fringe frequencies. A state space representation of spatial phase evolution and the wrapped phase measurement is considered with the state vector consisting of polynomial coefficients as its elements. Instead of using the traditional nonlinear Kalman filter for the purpose of state estimation, we propose to use the linear Kalman filter operating directly with the wrapped phase measurement. The adaptive window width is selected at each pixel based on the local fringe density to strike a balance between the computation time and the noise robustness. In order to retrieve the unwrapped phase, either a line-scanning approach or a quality guided strategy of pixel selection is used depending on the underlying continuous or discontinuous phase distribution, respectively. Simulation and experimental results are provided to demonstrate the applicability of the proposed method.

Reconciling phase diffusion and Hartree-Fock approximation in condensate systems

NASA Astrophysics Data System (ADS)

Giorgi, Gian Luca; de Pasquale, Ferdinando

2012-01-01

Despite the weakly interacting regime, the physics of Bose-Einstein condensates is widely affected by particle-particle interactions. They determine quantum phase diffusion, which is known to be the main cause of loss of coherence. Studying a simple model of two interacting Bose systems, we show how to predict the appearance of phase diffusion beyond the Bogoliubov approximation, providing a self-consistent treatment in the framework of a generalized Hartree-Fock-Bogoliubov perturbation theory.

Study on a Multi-Frequency Homotopy Analysis Method for Period-Doubling Solutions of Nonlinear Systems

NASA Astrophysics Data System (ADS)

Fu, H. X.; Qian, Y. H.

In this paper, a modification of homotopy analysis method (HAM) is applied to study the two-degree-of-freedom coupled Duffing system. Firstly, the process of calculating the two-degree-of-freedom coupled Duffing system is presented. Secondly, the single periodic solutions and double periodic solutions are obtained by solving the constructed nonlinear algebraic equations. Finally, comparing the periodic solutions obtained by the multi-frequency homotopy analysis method (MFHAM) and the fourth-order Runge-Kutta method, it is found that the approximate solution agrees well with the numerical solution.

Supercooling of aqueous dimethylsulfoxide solution at normal and high pressures: Evidence for the coexistence of phase-separated aqueous dimethylsulfoxide solutions of different water structures

NASA Astrophysics Data System (ADS)

Kanno, H.; Kajiwara, K.; Miyata, K.

2010-05-01

Supercooling behavior of aqueous dimethylsulfoxide (DMSO) solution was investigated as a function of DMSO concentration and at high pressures. A linear relationship was observed for TH (homogeneous ice nucleation temperature) and Tm (melting temperature) for the supercooling of aqueous DMSO solution at normal pressure. Analysis of the DTA (differential thermal analysis) traces for homogeneous ice crystallization in the bottom region of the TH curve for a DMSO solution of R =20 (R: moles of water/moles of DMSO) at high pressures supported the contention that the second critical point (SCP) of liquid water should exist at Pc2=˜200 MPa and at Tc2<-100 °C (Pc2: pressure of SCP, Tc2: temperature of SCP). The presence of two TH peaks for DMSO solutions (R =15, 12, and 10) suggests that phase separation occurs in aqueous DMSO solution (R ≤15) at high pressures and low temperatures (<-90 °C). The pressure dependence of the two TH curves for DMSO solutions of R =10 and 12 indicates that the two phase-separated components in the DMSO solution of R =10 have different liquid water structures [LDL-like and HDL-like structures (LDL: low-density liquid water, HDL: high-density liquid water)] in the pressure range of 120-230 MPa.

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

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.

Interaction and charge transfer between dielectric spheres: Exact and approximate analytical solutions.

PubMed

Lindén, Fredrik; Cederquist, Henrik; Zettergren, Henning

2016-11-21

We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.

On the acceleration of charged particles at relativistic shock fronts

NASA Technical Reports Server (NTRS)

Kirk, J. G.; Schneider, P.

1987-01-01

The diffusive acceleration of highly relativistic particles at a shock is reconsidered. Using the same physical assumptions as Blandford and Ostriker (1978), but dropping the restriction to nonrelativistic shock velocities, the authors find approximate solutions of the particle kinetic equation by generalizing the diffusion approximation to higher order terms in the anisotropy of the particle distribution. The general solution of the transport equation on either side of the shock is constructed, which involves the solution of an eigenvalue problem. By matching the two solutions at the shock, the spectral index of the resulting power law is found by taking into account a sufficiently large number of eigenfunctions. Low-order truncation corresponds to the standard diffusion approximation and to a somewhat more general method described by Peacock (1981). In addition to the energy spectrum, the method yields the angular distribution of the particles and its spatial dependence.

A comparison between state-specific and linear-response formalisms for the calculation of vertical electronic transition energy in solution with the CCSD-PCM method.

PubMed

Caricato, Marco

2013-07-28

The calculation of vertical electronic transition energies of molecular systems in solution with accurate quantum mechanical methods requires the use of approximate and yet reliable models to describe the effect of the solvent on the electronic structure of the solute. The polarizable continuum model (PCM) of solvation represents a computationally efficient way to describe this effect, especially when combined with coupled cluster (CC) methods. Two formalisms are available to compute transition energies within the PCM framework: State-Specific (SS) and Linear-Response (LR). The former provides a more complete account of the solute-solvent polarization in the excited states, while the latter is computationally very efficient (i.e., comparable to gas phase) and transition properties are well defined. In this work, I review the theory for the two formalisms within CC theory with a focus on their computational requirements, and present the first implementation of the LR-PCM formalism with the coupled cluster singles and doubles method (CCSD). Transition energies computed with LR- and SS-CCSD-PCM are presented, as well as a comparison between solvation models in the LR approach. The numerical results show that the two formalisms provide different absolute values of transition energy, but similar relative solvatochromic shifts (from nonpolar to polar solvents). The LR formalism may then be used to explore the solvent effect on multiple states and evaluate transition probabilities, while the SS formalism may be used to refine the description of specific states and for the exploration of excited state potential energy surfaces of solvated systems.

A self-adapting system for the automated detection of inter-ictal epileptiform discharges.

PubMed

Lodder, Shaun S; van Putten, Michel J A M

2014-01-01

Scalp EEG remains the standard clinical procedure for the diagnosis of epilepsy. Manual detection of inter-ictal epileptiform discharges (IEDs) is slow and cumbersome, and few automated methods are used to assist in practice. This is mostly due to low sensitivities, high false positive rates, or a lack of trust in the automated method. In this study we aim to find a solution that will make computer assisted detection more efficient than conventional methods, while preserving the detection certainty of a manual search. Our solution consists of two phases. First, a detection phase finds all events similar to epileptiform activity by using a large database of template waveforms. Individual template detections are combined to form "IED nominations", each with a corresponding certainty value based on the reliability of their contributing templates. The second phase uses the ten nominations with highest certainty and presents them to the reviewer one by one for confirmation. Confirmations are used to update certainty values of the remaining nominations, and another iteration is performed where ten nominations with the highest certainty are presented. This continues until the reviewer is satisfied with what has been seen. Reviewer feedback is also used to update template accuracies globally and improve future detections. Using the described method and fifteen evaluation EEGs (241 IEDs), one third of all inter-ictal events were shown after one iteration, half after two iterations, and 74%, 90%, and 95% after 5, 10 and 15 iterations respectively. Reviewing fifteen iterations for the 20-30 min recordings 1 took approximately 5 min. The proposed method shows a practical approach for combining automated detection with visual searching for inter-ictal epileptiform activity. Further evaluation is needed to verify its clinical feasibility and measure the added value it presents.

Kinetics of phase separation and coarsening in dilute surfactant pentaethylene glycol monododecyl ether solutions

NASA Astrophysics Data System (ADS)

Tanaka, S.; Kubo, Y.; Yokoyama, Y.; Toda, A.; Taguchi, K.; Kajioka, H.

2011-12-01

We investigated the phase separation phenomena in dilute surfactant pentaethylene glycol monodedecyl ether (C12E5) solutions focusing on the growth law of separated domains. The solutions confined between two glass plates were found to exhibit the phase inversion, characteristic of the viscoelastic phase separation; the majority phase (water-rich phase) nucleated as droplets and the minority phase (micelle-rich phase) formed a network temporarily, then they collapsed into an usual sea-island pattern where minority phase formed islands. We found from the real-space microscopic imaging that the dynamic scaling hypothesis did not hold throughout the coarsening process. The power law growth of the domains with the exponent close to 1/3 was observed even though the coarsening was induced mainly by hydrodynamic flow, which was explained by Darcy's law of laminar flow.

Gas-phase and solution-phase polymerization of epoxides by Cr(salen) complexes: evidence for a dinuclear cationic mechanism.

PubMed

Schön, Eva; Zhang, Xiangyang; Zhou, Zhiping; Chisholm, Malcolm H; Chen, Peter

2004-11-15

The gas-phase reactions of a series of mass-selected mononuclear and dinuclear Cr(salen) complexes with propylene oxide suggest that the enhanced reactivity of the dinuclear complexes in gas-phase and in solution may derive from a dicationic mechanism in which the alkoxide chain is mu(2)-coordinated to two Lewis acidic metal centers. The double coordination is proposed to suppress backbiting, and hence chain-transfer in the gas-phase homopolymerization of epoxides.

Determination of anionic surfactants during wastewater recycling process by ion pair chromatography with suppressed conductivity detection

NASA Technical Reports Server (NTRS)

Levine, L. H.; Judkins, J. E.; Garland, J. L.; Sager, J. C. (Principal Investigator)

2000-01-01

A direct approach utilizing ion pairing reversed-phase chromatography coupled with suppressed conductivity detection was developed to monitor biodegradation of anionic surfactants during wastewater recycling through hydroponic plant growth systems and fixed-film bioreactors. Samples of hydroponic nutrient solution and bioreactor effluent with high concentrations (up to 120 mS electrical conductance) of inorganic ions can be analyzed without pretreatment or interference. The presence of non-ionic surfactants did not significantly affect the analysis. Dynamic linear ranges for tested surfactants [Igepon TC-42, ammonium lauryl sulfate, sodium laureth sulfate and sodium alkyl (C10-C16) ether sulfate] were 2 to approximately 500, 1 to approximately 500, 2.5 to approximately 550 and 3.0 to approximately 630 microg/ml, respectively.

Modeling two-phase flow in PEM fuel cell channels

NASA Astrophysics Data System (ADS)

Wang, Yun; Basu, Suman; Wang, Chao-Yang

2008-05-01

This paper is concerned with the simultaneous flow of liquid water and gaseous reactants in mini-channels of a proton exchange membrane (PEM) fuel cell. Envisaging the mini-channels as structured and ordered porous media, we develop a continuum model of two-phase channel flow based on two-phase Darcy's law and the M2 formalism, which allow estimate of the parameters key to fuel cell operation such as overall pressure drop and liquid saturation profiles along the axial flow direction. Analytical solutions of liquid water saturation and species concentrations along the channel are derived to explore the dependences of these physical variables vital to cell performance on operating parameters such as flow stoichiometric ratio and relative humility. The two-phase channel model is further implemented for three-dimensional numerical simulations of two-phase, multi-component transport in a single fuel-cell channel. Three issues critical to optimizing channel design and mitigating channel flooding in PEM fuel cells are fully discussed: liquid water buildup towards the fuel cell outlet, saturation spike in the vicinity of flow cross-sectional heterogeneity, and two-phase pressure drop. Both the two-phase model and analytical solutions presented in this paper may be applicable to more general two-phase flow phenomena through mini- and micro-channels.

Multifrequency InSAR height reconstruction through maximum likelihood estimation of local planes parameters.

PubMed

Pascazio, Vito; Schirinzi, Gilda

2002-01-01

In this paper, a technique that is able to reconstruct highly sloped and discontinuous terrain height profiles, starting from multifrequency wrapped phase acquired by interferometric synthetic aperture radar (SAR) systems, is presented. We propose an innovative unwrapping method, based on a maximum likelihood estimation technique, which uses multifrequency independent phase data, obtained by filtering the interferometric SAR raw data pair through nonoverlapping band-pass filters, and approximating the unknown surface by means of local planes. Since the method does not exploit the phase gradient, it assures the uniqueness of the solution, even in the case of highly sloped or piecewise continuous elevation patterns with strong discontinuities.

Solution-phase electronegativity scale: insight into the chemical behaviors of metal ions in solution.

PubMed

Li, Keyan; Li, Min; Xue, Dongfeng

2012-04-26

By incorporating the solvent effect into the Born effective radius, we have proposed an electronegativity scale of metal ions in aqueous solution with the most common oxidation states and hydration coordination numbers in terms of the effective ionic electrostatic potential. It is found that the metal ions in aqueous solution are poorer electron acceptors compared to those in the gas phase. This solution-phase electronegativity scale shows its efficiency in predicting some important properties of metal ions in aqueous solution such as the aqueous acidities of the metal ions, the stability constants of metal complexes, and the solubility product constants of the metal hydroxides. We have elaborated that the standard reduction potential and the solution-phase electronegativity are two different quantities for describing the processes of metal ions in aqueous solution to soak up electrons with different final states. This work provides a new insight into the chemical behaviors of the metal ions in aqueous solution, indicating a potential application of this electronegativity scale to the design of solution reactions.

Generation of net sediment transport by velocity skewness in oscillatory sheet flow

NASA Astrophysics Data System (ADS)

Chen, Xin; Li, Yong; Chen, Genfa; Wang, Fujun; Tang, Xuelin

2018-01-01

This study utilizes a qualitative approach and a two-phase numerical model to investigate net sediment transport caused by velocity skewness beneath oscillatory sheet flow and current. The qualitative approach is derived based on the pseudo-laminar approximation of boundary layer velocity and exponential approximation of concentration. The two-phase model can obtain well the instantaneous erosion depth, sediment flux, boundary layer thickness, and sediment transport rate. It can especially illustrate the difference between positive and negative flow stages caused by velocity skewness, which is considerably important in determining the net boundary layer flow and sediment transport direction. The two-phase model also explains the effect of sediment diameter and phase-lag to sediment transport by comparing the instantaneous-type formulas to better illustrate velocity skewness effect. In previous studies about sheet flow transport in pure velocity-skewed flows, net sediment transport is only attributed to the phase-lag effect. In the present study with the qualitative approach and two-phase model, phase-lag effect is shown important but not sufficient for the net sediment transport beneath pure velocity-skewed flow and current, while the asymmetric wave boundary layer development between positive and negative flow stages also contributes to the sediment transport.

Temperature dependences of the time of electron-electron interactions in two-dimensional heterojunction

NASA Astrophysics Data System (ADS)

Bukhenskyy, K. V.; Dubois, A. B.; Kucheryavyy, S. I.; Mashnina, S. N.; Safoshkin, A. S.; Baukov, A. A.; Shchigorev, E. Yu

2017-12-01

The article discusses the joint solution of the Schrödinger and Poisson equations for two-dimensional semiconductor heterojunction. The application of a triangular potential of well approximation for the calculation of the electron-electron interaction is offered in the paper. The influence of the parameters of the selected approximation was analyzed.

Layered double hydroxide stability. 2. Formation of Cr(III)-containing layered double hydroxides directly from solution

NASA Technical Reports Server (NTRS)

Boclair, J. W.; Braterman, P. S.; Jiang, J.; Lou, S.; Yarberry, F.

1999-01-01

Solutions containing divalent metal [M(II) = Mg2+, Zn2+, Co2+, Ni2+, Mn2+] chlorides and CrCl3 6H2O were titrated with NaOH to yield, for M(II) = Zn, Co, and Ni, hydrotalcite-like layered double hydroxides (LDHs), [[M(II)]1-z[Cr(III)]z(OH)2][Cl]z yH2O, in a single step, without intermediate formation of chromium hydroxide. Analysis of the resultant titration curves yields solubility constants for these compounds. These are in the order Zn < Ni approximately Co, with a clear preference for formation of the phase with z = 1/3. With Mg2+ as chloride, titration gives a mixture of Cr(OH)3 and Mg(OH)2, but the metal sulfates give Mg2Cr(OH)6 1/2(SO4) by a two-step process. Titrimetric and spectroscopic evidence suggests short-range cation order in the one-step LDH systems.

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

PubMed

Chao, Fa-An; Byrd, R Andrew

2017-04-01

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

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

Karamatskos, E. T.; Stockhofe, J.; Kevrekidis, P. G.

In this study, we consider a binary repulsive Bose-Einstein condensate in a harmonic trap in one spatial dimension and investigate particular solutions consisting of two dark-bright solitons. There are two different stationary solutions characterized by the phase difference in the bright component, in-phase and out-of-phase states. We show that above a critical particle number in the bright component, a symmetry-breaking bifurcation of the pitchfork type occurs that leads to a new asymmetric solution whereas the parental branch, i.e., the out-of-phase state, becomes unstable. These three different states support different small amplitude oscillations, characterized by an almost stationary density of themore » dark component and a tunneling of the bright component between the two dark solitons. Within a suitable effective double-well picture, these can be understood as the characteristic features of a bosonic Josephson junction (BJJ), and we show within a two-mode approach that all characteristic features of the BJJ phase space are recovered. For larger deviations from the stationary states, the simplifying double-well description breaks down due to the feedback of the bright component onto the dark one, causing the solitons to move. In this regime we observe intricate anharmonic and aperiodic dynamics, exhibiting remnants of the BJJ phase space.« less

Stability and tunneling dynamics of a dark-bright soliton pair in a harmonic trap

DOE PAGES

Karamatskos, E. T.; Stockhofe, J.; Kevrekidis, P. G.; ...

2015-04-30

In this study, we consider a binary repulsive Bose-Einstein condensate in a harmonic trap in one spatial dimension and investigate particular solutions consisting of two dark-bright solitons. There are two different stationary solutions characterized by the phase difference in the bright component, in-phase and out-of-phase states. We show that above a critical particle number in the bright component, a symmetry-breaking bifurcation of the pitchfork type occurs that leads to a new asymmetric solution whereas the parental branch, i.e., the out-of-phase state, becomes unstable. These three different states support different small amplitude oscillations, characterized by an almost stationary density of themore » dark component and a tunneling of the bright component between the two dark solitons. Within a suitable effective double-well picture, these can be understood as the characteristic features of a bosonic Josephson junction (BJJ), and we show within a two-mode approach that all characteristic features of the BJJ phase space are recovered. For larger deviations from the stationary states, the simplifying double-well description breaks down due to the feedback of the bright component onto the dark one, causing the solitons to move. In this regime we observe intricate anharmonic and aperiodic dynamics, exhibiting remnants of the BJJ phase space.« less

On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

NASA Astrophysics Data System (ADS)

BOERTJENS, G. J.; VAN HORSSEN, W. T.

2000-08-01

In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

Solving fractional optimal control problems within a Chebyshev-Legendre operational technique

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Ezz-Eldien, S. S.; Doha, E. H.; Abdelkawy, M. A.; Baleanu, D.

2017-06-01

In this manuscript, we report a new operational technique for approximating the numerical solution of fractional optimal control (FOC) problems. The operational matrix of the Caputo fractional derivative of the orthonormal Chebyshev polynomial and the Legendre-Gauss quadrature formula are used, and then the Lagrange multiplier scheme is employed for reducing such problems into those consisting of systems of easily solvable algebraic equations. We compare the approximate solutions achieved using our approach with the exact solutions and with those presented in other techniques and we show the accuracy and applicability of the new numerical approach, through two numerical examples.

Landau-Zener extension of the Tavis-Cummings model: Structure of the solution

DOE PAGES

Sun, Chen; Sinitsyn, Nikolai A.

2016-09-07

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of an arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well-known special functions. In this form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. Furthermore, we also reveal connection between DTCM and q-deformed binomial statistics.

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Control and measurement of the phase behavior of aqueous solutions using microfluidics

PubMed Central

Shim, Jung-uk; Cristobal, Galder; Link, Darren R.; Thorsen, Todd; Jia, Yanwei; Piattelli, Katie; Fraden, Seth

2008-01-01

A microfluidic device denoted the Phase Chip has been designed to measure and manipulate the phase diagram of multi-component fluid mixtures. The Phase Chip exploits the permeation of water through poly(dimethylsiloxane) (PDMS) in order to controllably vary the concentration of solutes in aqueous nanoliter volume microdrops stored in wells. The permeation of water in the Phase Chip is modeled using the diffusion equation and good agreement between experiment and theory is obtained. The Phase Chip operates by first creating drops of the water/solute mixture whose composition varies sequentially. Next, drops are transported down channels and guided into storage wells using surface tension forces. Finally, the solute concentration of each stored drop is simultaneously varied and measured. Two applications of the Phase Chip are presented. First, the phase diagram of a polymer/salt mixture is measured on-chip and validated off-chip and second, protein crystallization rates are enhanced through the manipulation of the kinetics of nucleation and growth. PMID:17580868

Coupled discrete element and finite volume solution of two classical soil mechanics problems

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

Chen, Feng; Drumm, Eric; Guiochon, Georges A

One dimensional solutions for the classic critical upward seepage gradient/quick condition and the time rate of consolidation problems are obtained using coupled routines for the finite volume method (FVM) and discrete element method (DEM), and the results compared with the analytical solutions. The two phase flow in a system composed of fluid and solid is simulated with the fluid phase modeled by solving the averaged Navier-Stokes equation using the FVM and the solid phase is modeled using the DEM. A framework is described for the coupling of two open source computer codes: YADE-OpenDEM for the discrete element method and OpenFOAMmore » for the computational fluid dynamics. The particle-fluid interaction is quantified using a semi-empirical relationship proposed by Ergun [12]. The two classical verification problems are used to explore issues encountered when using coupled flow DEM codes, namely, the appropriate time step size for both the fluid and mechanical solution processes, the choice of the viscous damping coefficient, and the number of solid particles per finite fluid volume.« less

Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta

NASA Technical Reports Server (NTRS)

Cockrell, C. R.

1989-01-01

Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.

Hydration of copper(II): new insights from density functional theory and the COSMO solvation model.

PubMed

Bryantsev, Vyacheslav S; Diallo, Mamadou S; van Duin, Adri C T; Goddard, William A

2008-09-25

The hydrated structure of the Cu(II) ion has been a subject of ongoing debate in the literature. In this article, we use density functional theory (B3LYP) and the COSMO continuum solvent model to characterize the structure and stability of [Cu(H2O)n](2+) clusters as a function of coordination number (4, 5, and 6) and cluster size (n = 4-18). We find that the most thermodynamically favored Cu(II) complexes in the gas phase have a very open four-coordinate structure. They are formed from a stable square-planar [Cu(H2O)8](2+) core stabilized by an unpaired electron in the Cu(II) ion d(x(2)-y(2)) orbital. This is consistent with cluster geometries suggested by recent mass-spectrometric experiments. In the aqueous phase, we find that the more compact five-coordinate square-pyramidal geometry is more stable than either the four-coordinate or six-coordinate clusters in agreement with recent combined EXAFS and XANES studies of aqueous solutions of Cu(II). However, a small energetic difference (approximately 1.4 kcal/mol) between the five- and six-coordinate models with two full hydration shells around the metal ion suggests that both forms may coexist in solution.

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.

An algorithm for calculating minimum Euclidean distance between two geographic features

NASA Astrophysics Data System (ADS)

Peuquet, Donna J.

1992-09-01

An efficient algorithm is presented for determining the shortest Euclidean distance between two features of arbitrary shape that are represented in quadtree form. These features may be disjoint point sets, lines, or polygons. It is assumed that the features do not overlap. Features also may be intertwined and polygons may be complex (i.e. have holes). Utilizing a spatial divide-and-conquer approach inherent in the quadtree data model, the basic rationale is to narrow-in on portions of each feature quickly that are on a facing edge relative to the other feature, and to minimize the number of point-to-point Euclidean distance calculations that must be performed. Besides offering an efficient, grid-based alternative solution, another unique and useful aspect of the current algorithm is that is can be used for rapidly calculating distance approximations at coarser levels of resolution. The overall process can be viewed as a top-down parallel search. Using one list of leafcode addresses for each of the two features as input, the algorithm is implemented by successively dividing these lists into four sublists for each descendant quadrant. The algorithm consists of two primary phases. The first determines facing adjacent quadrant pairs where part or all of the two features are separated between the two quadrants, respectively. The second phase then determines the closest pixel-level subquadrant pairs within each facing quadrant pair at the lowest level. The key element of the second phase is a quick estimate distance heuristic for further elimination of locations that are not as near as neighboring locations.

Topics in elementary particle physics

NASA Astrophysics Data System (ADS)

Jin, Xiang

The author of this thesis discusses two topics in elementary particle physics: n-ary algebras and their applications to M-theory (Part I), and functional evolution and Renormalization Group flows (Part II). In part I, Lie algebra is extended to four different n-ary algebraic structure: generalized Lie algebra, Filippov algebra, Nambu algebra and Nambu-Poisson tensor; though there are still many other n-ary algebras. A natural property of Generalized Lie algebras — the Bremner identity, is studied, and proved with a totally different method from its original version. We extend Bremner identity to n-bracket cases, where n is an arbitrary odd integer. Filippov algebras do not focus on associativity, and are defined by the Fundamental identity. We add associativity to Filippov algebras, and give examples of how to construct Filippov algebras from su(2), bosonic oscillator, Virasoro algebra. We try to include fermionic charges into the ternary Virasoro-Witt algebra, but the attempt fails because fermionic charges keep generating new charges that make the algebra not closed. We also study the Bremner identity restriction on Nambu algebras and Nambu-Poisson tensors. So far, the only example 3-algebra being used in physics is the BLG model with 3-algebra A4, describing two M2-branes interactions. Its extension with Nambu algebra, BLG-NB model, is believed to describe infinite M2-branes condensation. Also, there is another propose for M2-brane interactions, the ABJM model, which is constructed by ordinary Lie algebra. We compare the symmetry properties between them, and discuss the possible approaches to include these three models into a grand unification theory. In Part II, we give an approximate solution for Schroeder's equations, based on series and conjugation methods. We use the logistic map as an example, and demonstrate that this approximate solution converges to known analytical solutions around the fixed point, around which the approximate solution is constructed. Although the closed-form solutions for Schroeder's equations can not always be approached analytically, by fitting the approximation solutions, one can still obtain closed-form solutions sometimes. Based on Schroeder's theory, approximate solutions for trajectories, velocities and potentials can also be constructed. The approximate solution is significantly useful to calculate the beta function in renormalization group trajectory. By "wrapping" the series solutions with the conjugations from different inverse functions, we generate different branches of the trajectory, and construct a counterexample for a folk theorem about limited cycles.

Two degree-of-freedom flutter solution for a personal computer

NASA Technical Reports Server (NTRS)

Turnock, D. L.

1985-01-01

A computer programmed flutter solution has been written in the BASIC language for a personal computer. The program is for two degree-of-freedom bending torsion flutter applications and utilizes two dimensional Theodorsen aerodynamics. The aerodynamics were modified to include approximations for Mach number (compressibility) effects and aspect ratio (finite span) effects. Input options, user instructions, program listing, and a test case application are included.

Large Torque Variations in Two Soft Gamma Repeaters

NASA Technical Reports Server (NTRS)

Woods, Peter M.; Kouveliotou, Chryssa; Gogus, Ersin; Finger, Mark H.; Swank, Jean; Markwardt, Craig B.; Hurley, Kevin; vanderKlis, Michiel; Six, N. Frank (Technical Monitor)

2001-01-01

We have monitored the pulse frequencies of the two soft gamma repeaters SGR 1806-20 and SGR 1900+14 through the beginning of year 2001 using primarily Rossi X-ray Timing Explorer Proportional Counter Array observations. In both sources, we observe large changes in the spin-down torque up to a factor of approximately 4, which persist for several months. Using long baseline phase-connected timing solutions as well as the overall frequency histories, we construct torque noise power spectra for each SGR. The power spectrum of each source is very red (power-law slope approximately -3.5). These power spectra are consistent in normalization with some accreting systems, yet much steeper in slope than any known accreting source. To the best of our knowledge, torque noise power spectra with a comparably steep frequency dependence have only been seen in young, glitching radio pulsars (e.g. Vela). The observed changes in spin-down rate do not correlate with burst activity, therefore, the physical mechanisms behind each phenomenon are also likely unrelated. Within the context of the magnetar model, seismic activity cannot account for both the bursts and the long-term torque changes unless the seismically active regions are decoupled from one another.

On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.; Maccamy, R. C.

1993-01-01

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

QRAP: A numerical code for projected (Q)uasiparticle (RA)ndom (P)hase approximation

NASA Astrophysics Data System (ADS)

Samana, A. R.; Krmpotić, F.; Bertulani, C. A.

2010-06-01

A computer code for quasiparticle random phase approximation - QRPA and projected quasiparticle random phase approximation - PQRPA models of nuclear structure is explained in details. The residual interaction is approximated by a simple δ-force. An important application of the code consists in evaluating nuclear matrix elements involved in neutrino-nucleus reactions. As an example, cross sections for 56Fe and 12C are calculated and the code output is explained. The application to other nuclei and the description of other nuclear and weak decay processes are also discussed. Program summaryTitle of program: QRAP ( Quasiparticle RAndom Phase approximation) Computers: The code has been created on a PC, but also runs on UNIX or LINUX machines Operating systems: WINDOWS or UNIX Program language used: Fortran-77 Memory required to execute with typical data: 16 Mbytes of RAM memory and 2 MB of hard disk space No. of lines in distributed program, including test data, etc.: ˜ 8000 No. of bytes in distributed program, including test data, etc.: ˜ 256 kB Distribution format: tar.gz Nature of physical problem: The program calculates neutrino- and antineutrino-nucleus cross sections as a function of the incident neutrino energy, and muon capture rates, using the QRPA or PQRPA as nuclear structure models. Method of solution: The QRPA, or PQRPA, equations are solved in a self-consistent way for even-even nuclei. The nuclear matrix elements for the neutrino-nucleus interaction are treated as the beta inverse reaction of odd-odd nuclei as function of the transfer momentum. Typical running time: ≈ 5 min on a 3 GHz processor for Data set 1.

A new, double-inversion mechanism of the F- + CH3Cl SN2 reaction in aqueous solution.

PubMed

Liu, Peng; Wang, Dunyou; Xu, Yulong

2016-11-23

Atomic-level, bimolecular nucleophilic substitution reaction mechanisms have been studied mostly in the gas phase, but the gas-phase results cannot be expected to reliably describe condensed-phase chemistry. As a novel, double-inversion mechanism has just been found for the F - + CH 3 Cl S N 2 reaction in the gas phase [Nat. Commun., 2015, 6, 5972], here, using multi-level quantum mechanics methods combined with the molecular mechanics method, we discovered a new, double-inversion mechanism for this reaction in aqueous solution. However, the structures of the stationary points along the reaction path show significant differences from those in the gas phase due to the strong influence of solvent and solute interactions, especially due to the hydrogen bonds formed between the solute and the solvent. More importantly, the relationship between the two double-inversion transition states is not clear in the gas phase, but, here we revealed a novel intermediate complex serving as a "connecting link" between the two transition states of the abstraction-induced inversion and the Walden-inversion mechanisms. A detailed reaction path was constructed to show the atomic-level evolution of this novel double reaction mechanism in aqueous solution. The potentials of mean force were calculated and the obtained Walden-inversion barrier height agrees well with the available experimental value.

Charge-regulation phase transition on surface lattices of titratable sites adjacent to electrolyte solutions: An analog of the Ising antiferromagnet in a magnetic field

PubMed Central

Shore, Joel D.; Thurston, George M.

2018-01-01

We report a charge-patterning phase transition on two-dimensional square lattices of titratable sites, here regarded as protonation sites, placed in a low-dielectric medium just below the planar interface between this medium and a salt solution. We calculate the work-of-charging matrix of the lattice with use of a linear Debye-Hückel model, as input to a grand-canonical partition function for the distribution of occupancy patterns. For a large range of parameter values, this model exhibits an approximate inverse cubic power-law decrease of the voltage produced by an individual charge, as a function of its in-lattice separation from neighboring titratable sites. Thus, the charge coupling voltage biases the local probabilities of proton binding as a function of the occupancy of sites for many neighbors beyond the nearest ones. We find that even in the presence of these longer-range interactions, the site couplings give rise to a phase transition in which the site occupancies exhibit an alternating, checkerboard pattern that is an analog of antiferromagnetic ordering. The overall strength W of this canonical charge coupling voltage, per unit charge, is a function of the Debye length, the charge depth, the Bjerrum length, and the dielectric coefficients of the medium and the solvent. The alternating occupancy transition occurs above a curve of thermodynamic critical points in the (pH-pK,W) plane, the curve representing a charge-regulation analog of variation of the Néel temperature of an Ising antiferromagnet as a function of an applied, uniform magnetic field. The analog of a uniform magnetic field in the antiferromagnet problem is a combination of pH-pK and W, and 1/W is the analog of the temperature in the antiferromagnet problem. We use Monte Carlo simulations to study the occupancy patterns of the titratable sites, including interactions out to the 37th nearest-neighbor category (a distance of 74 lattice constants), first validating simulations through comparison with exact and approximate results for the nearest-neighbor case. We then use the simulations to map the charge-patterning phase boundary in the (pH-pK,W) plane. The physical parameters that determine W provide a framework for identifying and designing real surfaces that could exhibit charge-patterning phase transitions. PMID:26764648

Charge-regulation phase transition on surface lattices of titratable sites adjacent to electrolyte solutions: An analog of the Ising antiferromagnet in a magnetic field.

PubMed

Shore, Joel D; Thurston, George M

2015-12-01

We report a charge-patterning phase transition on two-dimensional square lattices of titratable sites, here regarded as protonation sites, placed in a low-dielectric medium just below the planar interface between this medium and a salt solution. We calculate the work-of-charging matrix of the lattice with use of a linear Debye-Hückel model, as input to a grand-canonical partition function for the distribution of occupancy patterns. For a large range of parameter values, this model exhibits an approximate inverse cubic power-law decrease of the voltage produced by an individual charge, as a function of its in-lattice separation from neighboring titratable sites. Thus, the charge coupling voltage biases the local probabilities of proton binding as a function of the occupancy of sites for many neighbors beyond the nearest ones. We find that even in the presence of these longer-range interactions, the site couplings give rise to a phase transition in which the site occupancies exhibit an alternating, checkerboard pattern that is an analog of antiferromagnetic ordering. The overall strength W of this canonical charge coupling voltage, per unit charge, is a function of the Debye length, the charge depth, the Bjerrum length, and the dielectric coefficients of the medium and the solvent. The alternating occupancy transition occurs above a curve of thermodynamic critical points in the (pH-pK,W) plane, the curve representing a charge-regulation analog of variation of the Néel temperature of an Ising antiferromagnet as a function of an applied, uniform magnetic field. The analog of a uniform magnetic field in the antiferromagnet problem is a combination of pH-pK and W, and 1/W is the analog of the temperature in the antiferromagnet problem. We use Monte Carlo simulations to study the occupancy patterns of the titratable sites, including interactions out to the 37th nearest-neighbor category (a distance of √74 lattice constants), first validating simulations through comparison with exact and approximate results for the nearest-neighbor case. We then use the simulations to map the charge-patterning phase boundary in the (pH-pK,W) plane. The physical parameters that determine W provide a framework for identifying and designing real surfaces that could exhibit charge-patterning phase transitions.

Charge-regulation phase transition on surface lattices of titratable sites adjacent to electrolyte solutions: An analog of the Ising antiferromagnet in a magnetic field

NASA Astrophysics Data System (ADS)

Shore, Joel D.; Thurston, George M.

2015-12-01

We report a charge-patterning phase transition on two-dimensional square lattices of titratable sites, here regarded as protonation sites, placed in a low-dielectric medium just below the planar interface between this medium and a salt solution. We calculate the work-of-charging matrix of the lattice with use of a linear Debye-Hückel model, as input to a grand-canonical partition function for the distribution of occupancy patterns. For a large range of parameter values, this model exhibits an approximate inverse cubic power-law decrease of the voltage produced by an individual charge, as a function of its in-lattice separation from neighboring titratable sites. Thus, the charge coupling voltage biases the local probabilities of proton binding as a function of the occupancy of sites for many neighbors beyond the nearest ones. We find that even in the presence of these longer-range interactions, the site couplings give rise to a phase transition in which the site occupancies exhibit an alternating, checkerboard pattern that is an analog of antiferromagnetic ordering. The overall strength W of this canonical charge coupling voltage, per unit charge, is a function of the Debye length, the charge depth, the Bjerrum length, and the dielectric coefficients of the medium and the solvent. The alternating occupancy transition occurs above a curve of thermodynamic critical points in the (p H-p K ,W ) plane, the curve representing a charge-regulation analog of variation of the Néel temperature of an Ising antiferromagnet as a function of an applied, uniform magnetic field. The analog of a uniform magnetic field in the antiferromagnet problem is a combination of p H-p K and W , and 1 /W is the analog of the temperature in the antiferromagnet problem. We use Monte Carlo simulations to study the occupancy patterns of the titratable sites, including interactions out to the 37th nearest-neighbor category (a distance of √{74 } lattice constants), first validating simulations through comparison with exact and approximate results for the nearest-neighbor case. We then use the simulations to map the charge-patterning phase boundary in the (p H-p K ,W ) plane. The physical parameters that determine W provide a framework for identifying and designing real surfaces that could exhibit charge-patterning phase transitions.

Results of Copper-Silver Rail Materials Tests

DTIC Science & Technology

2006-05-01

dislocation-dense grain structure. An annealing, recrystallization , and re-straining model is proposed to predict the bandwidth within which the...darker phase is the copper-rich solid solution, while the lighter regions are the eutectic structure consisting of both copper-rich and silver-rich solid...solutions. The eutectic phase ribbons consist of finer copper and silver filaments [1], [5]. The two phases are inhomogeneously deformed during the

Approximation and Numerical Analysis of Nonlinear Equations of Evolution.

DTIC Science & Technology

1980-01-31

dominant convective terms, or Stefan type problems such as the flow of fluids through porous media or the melting and freezing of ice. Such problems...means of formulating time-dependent Stefan problems was initiated. Classes of problems considered here include the one-phase and two-phase Stefan ...some new numerical methods were 2 developed for two dimensional, two-phase Stefan problems with time dependent boundary conditions. A variety of example

Ca-Rich Carbonate Melts: A Regular-Solution Model, with Applications to Carbonatite Magma + Vapor Equilibria and Carbonate Lavas on Venus

NASA Technical Reports Server (NTRS)

Treiman, Allan H.

1995-01-01

A thermochemical model of the activities of species in carbonate-rich melts would be useful in quantifying chemical equilibria between carbonatite magmas and vapors and in extrapolating liquidus equilibria to unexplored PTX. A regular-solution model of Ca-rich carbonate melts is developed here, using the fact that they are ionic liquids, and can be treated (to a first approximation) as interpenetrating regular solutions of cations and of anions. Thermochemical data on systems of alkali metal cations with carbonate and other anions are drawn from the literature; data on systems with alkaline earth (and other) cations and carbonate (and other) anions are derived here from liquidus phase equilibria. The model is validated in that all available data (at 1 kbar) are consistent with single values for the melting temperature and heat of fusion for calcite, and all liquidi are consistent with the liquids acting as regular solutions. At 1 kbar, the metastable congruent melting temperature of calcite (CaCO3) is inferred to be 1596 K, with (Delta)bar-H(sub fus)(calcite) = 31.5 +/- 1 kJ/mol. Regular solution interaction parameters (W) for Ca(2+) and alkali metal cations are in the range -3 to -12 kJ/sq mol; W for Ca(2+)-Ba(2+) is approximately -11 kJ/sq mol; W for Ca(2+)-Mg(2+) is approximately -40 kJ/sq mol, and W for Ca(2+)-La(3+) is approximately +85 kJ/sq mol. Solutions of carbonate and most anions (including OH(-), F(-), and SO4(2-)) are nearly ideal, with W between 0(ideal) and -2.5 kJ/sq mol. The interaction of carbonate and phosphate ions is strongly nonideal, which is consistent with the suggestion of carbonate-phosphate liquid immiscibility. Interaction of carbonate and sulfide ions is also nonideal and suggestive of carbonate-sulfide liquid immiscibility. Solution of H2O, for all but the most H2O-rich compositions, can be modeled as a disproportionation to hydronium (H3O(+)) and hydroxyl (OH(-)) ions with W for Ca(2+)-H3O(+) (approximately) equals 33 kJ/sq mol. The regular-solution model of carbonate melts can be applied to problems of carbonatite magma + vapor equilibria and of extrapolating liquidus equilibria to unstudied systems. Calculations on one carbonatite (the Husereau dike, Oka complex, Quebec, Canada) show that the anion solution of its magma contained an OH mole fraction of (approximately) 0.07, although the vapor in equilibrium with the magma had P(H2O) = 8.5 x P(CO2). F in carbonatite systems is calculated to be strongly partitioned into the magma (as F(-)) relative to coexisting vapor. In the Husereau carbonatite magma, the anion solution contained an F(-) mole fraction of (approximately) 6 x 10(exp -5).

Statistical mechanics of light elements at high pressure. VI - Liquid-state calculations with Thomas-Fermi-Dirac theory

NASA Technical Reports Server (NTRS)

Macfarlane, J. J.

1984-01-01

A model free energy is developed for hydrogen-helium mixtures based on solid-state Thomas-Fermi-Dirac calculations at pressures relevant to the interiors of giant planets. Using a model potential similar to that for a two-component plasma, effective charges for the nuclei (which are in general smaller than the actual charges because of screening effects) are parameterized, being constrained by calculations at a number of densities, compositions, and lattice structures. These model potentials are then used to compute the equilibrium properties of H-He fluids using a charged hard-sphere model. The results find critical temperatures of about 0 K, 500 K, and 1500 K, for pressures of 10, 100, and 1000 Mbar, respectively. These phase separation temperatures are considerably lower (approximately 6,000-10,000 K) than those found from calculations using free electron perturbation theory, and suggest that H-He solutions should be stable against phase separation in the metallic zones of Jupiter and Saturn.

Effective spring stiffness for a periodic array of interacting coplanar penny-shaped cracks at an interface between two dissimilar isotropic materials

PubMed Central

Lekesiz, Huseyin; Katsube, Noriko; Rokhlin, Stanislav I.; Seghi, Robert R.

2013-01-01

An effective spring stiffness approximation is proposed for a hexagonal array of coplanar penny shaped cracks located at the interface between two dissimilar solids. The approximation is based on the factorization of the solution on the material dissimilarity factor, the crack interaction factor and the effective spring stiffness solution for non-interacting cracks in a homogeneous material. Such factorization is exact and was validated for 2D collinear cracks between two dissimilar solids. The crack interaction factor is obtained using a recently developed model for stress intensity factors for an array of coplanar penny shaped cracks in a homogeneous material; also the material dissimilarity function recently obtained for non-interacting penny shaped crack at the interface between two dissimilar materials is employed. The obtained solution is useful for an assessment by ultrasonic measurements of the interface stiffness in bonded structures for monitoring the interfacial microdamage growth due to mechanical loading and environmental factors. PMID:27175036

Effective spring stiffness for a periodic array of interacting coplanar penny-shaped cracks at an interface between two dissimilar isotropic materials.

PubMed

Lekesiz, Huseyin; Katsube, Noriko; Rokhlin, Stanislav I; Seghi, Robert R

2013-08-15

An effective spring stiffness approximation is proposed for a hexagonal array of coplanar penny shaped cracks located at the interface between two dissimilar solids. The approximation is based on the factorization of the solution on the material dissimilarity factor, the crack interaction factor and the effective spring stiffness solution for non-interacting cracks in a homogeneous material. Such factorization is exact and was validated for 2D collinear cracks between two dissimilar solids. The crack interaction factor is obtained using a recently developed model for stress intensity factors for an array of coplanar penny shaped cracks in a homogeneous material; also the material dissimilarity function recently obtained for non-interacting penny shaped crack at the interface between two dissimilar materials is employed. The obtained solution is useful for an assessment by ultrasonic measurements of the interface stiffness in bonded structures for monitoring the interfacial microdamage growth due to mechanical loading and environmental factors.

Development of "ultrasound-assisted dynamic extraction" and its combination with CCC and CPC for simultaneous extraction and isolation of phytochemicals.

PubMed

Zhang, Yuchi; Liu, Chunming; Li, Jing; Qi, Yanjuan; Li, Yuchun; Li, Sainan

2015-09-01

A new method for the extraction of medicinal herbs termed ultrasonic-assisted dynamic extraction (UADE) was designed and evaluated. This technique was coupled with counter-current chromatography (CCC) and centrifugal partition chromatography (CPC) and then applied to the continuous extraction and online isolation of chemical constituents from Paeonia lactiflora Pall (white peony) roots. The mechanical parameters, including the pitch and diameter of the shaft, were optimized by means of mathematical modeling. Furthermore, the configuration and mechanism of online UADE coupled with CCC and CPC were elaborated. The stationary phases of the two-phase solvent systems from CCC and CPC were utilized as the UADE solution. The extraction solution was pumped into the sample loop and then introduced into the CCC column; the target compounds were eluted with the lower aqueous phase of the two-phase solvent system. During the CCC separation, the extraction solution was continuously fed in the sample loop by turning the ten-port valve; the extraction solution was then pumped into the CPC column and eluted by the mobile phase of the two-phase solvent system mentioned above. When the first cycle of the UADE/CCC/CPC was completed, the second cycle experiment could be carried out, and so on. Four target compounds (albiflorin, benzoylpaeoniflorin, paeoniflorin, and galloylpaeoniflorin) with purities above 94.96% were successfully extracted and isolated online using the two-phase solvent system comprising ethyl acetate-n-butanol-ethanol-water (1:3.5:2:4.5, v/v/v/v). Compared with conventional extraction methods, the instrumental setup of the present method offers the advantages of automation and systematic extraction and isolation of natural products. Crown Copyright © 2015. Published by Elsevier B.V. All rights reserved.

Epitaxial BiFeO3 thin films fabricated by chemical solution deposition

NASA Astrophysics Data System (ADS)

Singh, S. K.; Kim, Y. K.; Funakubo, H.; Ishiwara, H.

2006-04-01

Epitaxial BiFeO3 (BFO) thin films were fabricated on (001)-, (110)-, and (111)-oriented single-crystal SrRuO3(SRO )/SrTiO3(STO) structures by chemical solution deposition. X-ray diffraction indicates the formation of an epitaxial single-phase perovskite structure and pole figure measurement confirms the cube-on-cube epitaxial relationship of BFO ‖SRO‖STO. Chemical-solution-deposited BFO films have a rhombohedral structure with lattice parameter of 0.395nm, which is the same structure as that of a bulk single crystal. The remanent polarization of approximately 50μC/cm2 was observed in BFO (001) thin films at 80K.

Reentrant behaviors in the phase diagram of spin-1 planar ferromagnet with single-ion anisotropy

NASA Astrophysics Data System (ADS)

Rabuffo, I.; De Cesare, L.; Caramico D'Auria, A.; Mercaldo, M. T.

2018-05-01

We used the two-time Green function framework to investigate the role played by the easy-axis single-ion anisotropy on the phase diagram of (d > 2)-dimensional spin-1planar ferromagnets, which exhibit a magnetic field induced quantum phase transition. We tackled the problem using two different kind of approximations: the Anderson-Callen decoupling scheme and the Devlin approach. In the latter scheme, the exchange anisotropy terms in the equations of motion are treated at the Tyablikov decoupling level while the crystal field anisotropy contribution is handled exactly. The emerging key result is a reentrant structure of the phase diagram close to the quantum critical point, for certain values of the single-ion anisotropy parameter. We compare the results obtained within the two approximation schemes. In particular, we recover the same qualitative behavior. We show the phase diagram, close to the field-induced quantum critical point and the behavior of the susceptibility for different values of the single-ion anisotropy parameter, enhancing the differences between the two different scenarios (i.e. with and without reentrant behavior).

Two-dimensional Anderson-Hubbard model in the DMFT + {Sigma} approximation

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

Kuchinskii, E. Z., E-mail: kuchinsk@iep.uran.ru; Kuleeva, N. A.; Nekrasov, I. A.

The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + {Sigma} approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular 'bare' density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The 'correlated metal,' Mott insulator, and correlated Anderson insulator phases are identified from the evolution ofmore » the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.« less

Frequency mode excitations in two-dimensional Hindmarsh-Rose neural networks

NASA Astrophysics Data System (ADS)

Tabi, Conrad Bertrand; Etémé, Armand Sylvin; Mohamadou, Alidou

2017-05-01

In this work, we explicitly show the existence of two frequency regimes in a two-dimensional Hindmarsh-Rose neural network. Each of the regimes, through the semi-discrete approximation, is shown to be described by a two-dimensional complex Ginzburg-Landau equation. The modulational instability phenomenon for the two regimes is studied, with consideration given to the coupling intensities among neighboring neurons. Analytical solutions are also investigated, along with their propagation in the two frequency regimes. These waves, depending on the coupling strength, are identified as breathers, impulses and trains of soliton-like structures. Although the waves in two regimes appear in some common regions of parameters, some phase differences are noticed and the global dynamics of the system is highly influenced by the values of the coupling terms. For some values of such parameters, the high-frequency regime displays modulated trains of waves, while the low-frequency dynamics keeps the original asymmetric character of action potentials. We argue that in a wide range of pathological situations, strong interactions among neurons can be responsible for some pathological states, including schizophrenia and epilepsy.

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

NASA Astrophysics Data System (ADS)

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

2008-02-01

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

Analysis of physics-based preconditioning for single-phase subchannel equations

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

Hansel, J. E.; Ragusa, J. C.; Allu, S.

2013-07-01

The (single-phase) subchannel approximations are used throughout nuclear engineering to provide an efficient flow simulation because the computational burden is much smaller than for computational fluid dynamics (CFD) simulations, and empirical relations have been developed and validated to provide accurate solutions in appropriate flow regimes. Here, the subchannel equations have been recast in a residual form suitable for a multi-physics framework. The Eigen spectrum of the Jacobian matrix, along with several potential physics-based preconditioning approaches, are evaluated, and the the potential for improved convergence from preconditioning is assessed. The physics-based preconditioner options include several forms of reduced equations that decouplemore » the subchannels by neglecting crossflow, conduction, and/or both turbulent momentum and energy exchange between subchannels. Eigen-scopy analysis shows that preconditioning moves clusters of eigenvalues away from zero and toward one. A test problem is run with and without preconditioning. Without preconditioning, the solution failed to converge using GMRES, but application of any of the preconditioners allowed the solution to converge. (authors)« less

The local phase transitions of the solvent in the neighborhood of a solvophobic polymer at high pressures

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

Budkov, Yu. A., E-mail: urabudkov@rambler.ru; National Research University Higher School of Economics, Moscow; Department of Chemistry, Lomonosov Moscow State University, Moscow

2014-11-28

We investigate local phase transitions of the solvent in the neighborhood of a solvophobic polymer chain which is induced by a change of the polymer-solvent repulsion and the solvent pressure in the bulk solution. We describe the polymer in solution by the Edwards model, where the conditional partition function of the polymer chain at a fixed radius of gyration is described by a mean-field theory. The contributions of the polymer-solvent and the solvent-solvent interactions to the total free energy are described within the mean-field approximation. We obtain the total free energy of the solution as a function of the radiusmore » of gyration and the average solvent number density within the gyration volume. The resulting system of coupled equations is solved varying the polymer-solvent repulsion strength at high solvent pressure in the bulk. We show that the coil-globule (globule-coil) transition occurs accompanied by a local solvent evaporation (condensation) within the gyration volume.« less

Approximate furrow infiltration model for time-variable ponding depth

USDA-ARS?s Scientific Manuscript database

A methodology is proposed for estimating furrow infiltration under time-variable ponding depth conditions. The methodology approximates the solution to the two-dimensional Richards equation, and is a modification of a procedure that was originally proposed for computing infiltration under constant ...

Limiting cases of the small-angle scattering approximation solutions for the propagation of laser beams in anisotropic scattering media

NASA Technical Reports Server (NTRS)

Box, M. A.; Deepak, A.

1981-01-01

The propagation of photons in a medium with strongly anisotropic scattering is a problem with a considerable history. Like the propagation of electrons in metal foils, it may be solved in the small-angle scattering approximation by the use of Fourier-transform techniques. In certain limiting cases, one may even obtain analytic expressions. This paper presents some of these results in a model-independent form and also illustrates them by the use of four different phase-function models. Sample calculations are provided for comparison purposes

Measurements of the scattering of sound by a line vortex

NASA Technical Reports Server (NTRS)

Horne, W. C.

1983-01-01

This paper presents measurements of the phase and magnitude of the scattered field arising from the incidence of a monochromatic plane sound field as a steady vortex. The amplitude of the scattered field was found to vary linearly with the vortex strength, and with the incident wave amplitude and frequency as predicted by solutions based on the Born approximation. The scattered field was observed to be nonsingular in the incidence direction, and this was similar to predictions by the Parabolic Equation Method (PEM) rather than the Born approximation, which predicts singular behavior in the incidence direction.

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

Dehghani, M.H.; Research Institute for Astrophysics and Astronomy of Maragha; Khodam-Mohammadi, A.

First, we construct the Taub-NUT/bolt solutions of (2k+2)-dimensional Einstein-Maxwell gravity, when all the factor spaces of 2k-dimensional base space B have positive curvature. These solutions depend on two extra parameters, other than the mass and the NUT charge. These are electric charge q and electric potential at infinity V. We investigate the existence of Taub-NUT solutions and find that in addition to the two conditions of uncharged NUT solutions, there exist two extra conditions. These two extra conditions come from the regularity of vector potential at r=N and the fact that the horizon at r=N should be the outer horizonmore » of the NUT charged black hole. We find that the NUT solutions in 2k+2 dimensions have no curvature singularity at r=N, when the 2k-dimensional base space is chosen to be CP{sup 2k}. For bolt solutions, there exists an upper limit for the NUT parameter which decreases as the potential parameter increases. Second, we study the thermodynamics of these spacetimes. We compute temperature, entropy, charge, electric potential, action and mass of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We perform a stability analysis by computing the heat capacity, and show that the NUT solutions are not thermally stable for even k's, while there exists a stable phase for odd k's, which becomes increasingly narrow with increasing dimensionality and wide with increasing V. We also study the phase behavior of the 4 and 6 dimensional bolt solutions in canonical ensemble and find that these solutions have a stable phase, which becomes smaller as V increases.« less

Lévy walks with variable waiting time: A ballistic case

NASA Astrophysics Data System (ADS)

Kamińska, A.; Srokowski, T.

2018-06-01

The Lévy walk process for a lower interval of an excursion times distribution (α <1 ) is discussed. The particle rests between the jumps, and the waiting time is position-dependent. Two cases are considered: a rising and diminishing waiting time rate ν (x ) , which require different approximations of the master equation. The process comprises two phases of the motion: particles at rest and in flight. The density distributions for them are derived, as a solution of corresponding fractional equations. For strongly falling ν (x ) , the resting particles density assumes the α -stable form (truncated at fronts), and the process resolves itself to the Lévy flights. The diffusion is enhanced for this case but no longer ballistic, in contrast to the case for the rising ν (x ) . The analytical results are compared with Monte Carlo trajectory simulations. The results qualitatively agree with observed properties of human and animal movements.

Scalar Dissipation Modeling for Passive and Active Scalars: a priori Study Using Direct Numerical Simulation

NASA Technical Reports Server (NTRS)

Selle, L. C.; Bellan, Josette

2006-01-01

Transitional databases from Direct Numerical Simulation (DNS) of three-dimensional mixing layers for single-phase flows and two-phase flows with evaporation are analyzed and used to examine the typical hypothesis that the scalar dissipation Probability Distribution Function (PDF) may be modeled as a Gaussian. The databases encompass a single-component fuel and four multicomponent fuels, two initial Reynolds numbers (Re), two mass loadings for two-phase flows and two free-stream gas temperatures. Using the DNS calculated moments of the scalar-dissipation PDF, it is shown, consistent with existing experimental information on single-phase flows, that the Gaussian is a modest approximation of the DNS-extracted PDF, particularly poor in the range of the high scalar-dissipation values, which are significant for turbulent reaction rate modeling in non-premixed flows using flamelet models. With the same DNS calculated moments of the scalar-dissipation PDF and making a change of variables, a model of this PDF is proposed in the form of the (beta)-PDF which is shown to approximate much better the DNS-extracted PDF, particularly in the regime of the high scalar-dissipation values. Several types of statistical measures are calculated over the ensemble of the fourteen databases. For each statistical measure, the proposed (beta)-PDF model is shown to be much superior to the Gaussian in approximating the DNS-extracted PDF. Additionally, the agreement between the DNS-extracted PDF and the (beta)-PDF even improves when the comparison is performed for higher initial Re layers, whereas the comparison with the Gaussian is independent of the initial Re values. For two-phase flows, the comparison between the DNS-extracted PDF and the (beta)-PDF also improves with increasing free-stream gas temperature and mass loading. The higher fidelity approximation of the DNS-extracted PDF by the (beta)-PDF with increasing Re, gas temperature and mass loading bodes well for turbulent reaction rate modeling.

Recursive approach to the moment-based phase unwrapping method.

PubMed

Langley, Jason A; Brice, Robert G; Zhao, Qun

2010-06-01

The moment-based phase unwrapping algorithm approximates the phase map as a product of Gegenbauer polynomials, but the weight function for the Gegenbauer polynomials generates artificial singularities along the edge of the phase map. A method is presented to remove the singularities inherent to the moment-based phase unwrapping algorithm by approximating the phase map as a product of two one-dimensional Legendre polynomials and applying a recursive property of derivatives of Legendre polynomials. The proposed phase unwrapping algorithm is tested on simulated and experimental data sets. The results are then compared to those of PRELUDE 2D, a widely used phase unwrapping algorithm, and a Chebyshev-polynomial-based phase unwrapping algorithm. It was found that the proposed phase unwrapping algorithm provides results that are comparable to those obtained by using PRELUDE 2D and the Chebyshev phase unwrapping algorithm.

In situ neutron scattering study of nanoscale phase evolution in PbTe-PbS thermoelectric material

DOE PAGES

Ren, Fei; Schmidt, Robert; Keum, Jong K.; ...

2016-08-24

Introducing nanostructural second phases has been proved to be an effective approach to reduce the lattice thermal conductivity and thus enhance the figure of merit for many thermoelectric materials. Furthermore studies of the formation and evolution of these second phases are central to understanding temperature dependent material behavior, improving thermal stabilities, as well as designing new materials. We examined powder samples of PbTe-PbS thermoelectric material using in situ neutron diffraction and small angle neutron scattering (SANS) techniques from room temperature to elevated temperature up to 663 K, to explore quantitative information on the structure, weight fraction, and size of themore » second phase. Neutron diffraction data showed the as-milled powder was primarily solid solution before heat treatment. During heating, PbS second phase precipitated out of the PbTe matrix around 480 K, while re-dissolution started around 570 K. The second phase remained separated from the matrix upon cooling. Furthermore, SANS data indicated there are two populations of nanostructures. The size of the smaller nanostructure increased from initially 5 nm to approximately 25 nm after annealing at 650 K, while the size of the larger nanostructure remained unchanged. Our study demonstrated that in situ neutron techniques are effective means to obtain quantitative information to study temperature dependent nanostructural behavior of thermoelectrics and likely other high-temperature materials.« less

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

NASA Astrophysics Data System (ADS)

Zabihi, F.; Saffarian, M.

2016-07-01

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

A multi-harmonic generalized energy balance method for studying autonomous oscillations of nonlinear conservative systems

NASA Astrophysics Data System (ADS)

Balaji, Nidish Narayanaa; Krishna, I. R. Praveen; Padmanabhan, C.

2018-05-01

The Harmonic Balance Method (HBM) is a frequency-domain based approximation approach used for obtaining the steady state periodic behavior of forced dynamical systems. Intrinsically these systems are non-autonomous and the method offers many computational advantages over time-domain methods when the fundamental period of oscillation is known (generally fixed as the forcing period itself or a corresponding sub-harmonic if such behavior is expected). In the current study, a modified approach, based on He's Energy Balance Method (EBM), is applied to obtain the periodic solutions of conservative systems. It is shown that by this approach, periodic solutions of conservative systems on iso-energy manifolds in the phase space can be obtained very efficiently. The energy level provides the additional constraint on the HBM formulation, which enables the determination of the period of the solutions. The method is applied to the linear harmonic oscillator, a couple of nonlinear oscillators, the elastic pendulum and the Henon-Heiles system. The approach is used to trace the bifurcations of the periodic solutions of the last two, being 2 degree-of-freedom systems demonstrating very rich dynamical behavior. In the process, the advantages offered by the current formulation of the energy balance is brought out. A harmonic perturbation approach is used to evaluate the stability of the solutions for the bifurcation diagram.

Analysis of features of stainless steels in dissimilar welded joints in chloride inducted corrosion

NASA Astrophysics Data System (ADS)

Topolska, S.; Łabanowski, J.

2017-08-01

Stainless steels of femtic-austenitic microstructure that means the duplex Cr-Ni-Mo steels, in comparison with austenitic steel includes less expensive nickel and has much better mechanical properties with good formability and corrosion resistance, even in environments containing chloride ions. Similar share of high chromium ferrite and austenite, which is characterized by high ductility, determines that the duplex steels have good crack resistance at temperatures up to approximately -40°C. The steels containing approximately 22% Cr, 5% Ni, 3% Mo and 0.2% N crystallizes as a solid solution δ, partially transforming from the temperature of about 1200°C to 850°C into the phase α. The stable structure of considered steels, at temperatures above 850°C, is ferrite, and at lower temperatures the mixture of phase γ+α +σ. The two-phase structure α+γ the duplex steel obtains after hyperquenching at the temperature of stability of the mixture of α+γ phases, and the share of the phases depends on the hyper quenching attributes. Hyperquenching in water, with a temperature close to 1200°C, ensures the instance in the microstructure of the steel a large share of ferrite and a small share of the high chromium austenite. This causes the increase of strength properties and reducing the plasticity of the steel and its resistance ability to cracking and corrosion. Slower cooling from the mentioned temperature, for example in the air, enables the partial transformation of the a phase into the γ one (α → γ) and increasing the share of austenite in the steel structure. It leads to improvement of plasticity properties. In the paper are presented the results of investigations of heteronymous welded joints of duplex steel and austenitic one. The results include the relation between the chemical composition of steels and their weldability.

Decay of the 3D viscous liquid-gas two-phase flow model with damping

NASA Astrophysics Data System (ADS)

Zhang, Yinghui

2016-08-01

We establish the optimal Lp - L2(1 ≤ p < 6/5) time decay rates of the solution to the Cauchy problem for the 3D viscous liquid-gas two-phase flow model with damping and analyse the influences of the damping on the qualitative behaviors of solution. It is observed that the fraction effect of the damping affects the dispersion of fluids and enhances the time decay rate of solution. Our method of proof consists of Hodge decomposition technique, Lp - L2 estimates for the linearized equations, and delicate energy estimates.

OPTIMIZING THROUGH CO-EVOLUTIONARY AVALANCHES

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

S. BOETTCHER; A. PERCUS

2000-08-01

We explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problems. The method, called extremal optimization, is inspired by ''self-organized critically,'' a concept introduced to describe emergent complexity in many physical systems. In contrast to Genetic Algorithms which operate on an entire ''gene-pool'' of possible solutions, extremal optimization successively replaces extremely undesirable elements of a sub-optimal solution with new, random ones. Large fluctuations, called ''avalanches,'' ensue that efficiently explore many local optima. Drawing upon models used to simulate far-from-equilibrium dynamics, extremal optimization complements approximation methods inspired by equilibrium statistical physics, such as simulated annealing. With only onemore » adjustable parameter, its performance has proved competitive with more elaborate methods, especially near phase transitions. Those phase transitions are found in the parameter space of most optimization problems, and have recently been conjectured to be the origin of some of the hardest instances in computational complexity. We will demonstrate how extremal optimization can be implemented for a variety of combinatorial optimization problems. We believe that extremal optimization will be a useful tool in the investigation of phase transitions in combinatorial optimization problems, hence valuable in elucidating the origin of computational complexity.« less

A liquid-liquid transition in supercooled aqueous solution related to the HDA-LDA transition

NASA Astrophysics Data System (ADS)

Woutersen, Sander; Ensing, Bernd; Hilbers, Michiel; Zhao, Zuofeng; Angell, C. Austen

2018-03-01

Simulations and theory suggest that the thermodynamic anomalies of water may be related to a phase transition between two supercooled liquid states, but so far this phase transition has not been observed experimentally because of preemptive ice crystallization. We used calorimetry, infrared spectroscopy, and molecular dynamics simulations to investigate a water-rich hydrazinium trifluoroacetate solution in which the local hydrogen bond structure surrounding a water molecule resembles that in neat water at elevated pressure, but which does not crystallize upon cooling. Instead, this solution underwent a sharp, reversible phase transition between two homogeneous liquid states. The hydrogen-bond structures of these two states are similar to those established for high- and low-density amorphous (HDA and LDA) water. Such structural similarity supports theories that predict a similar sharp transition in pure water under pressure if ice crystallization could be suppressed.

Purification of lipase produced by a new source of Bacillus in submerged fermentation using an aqueous two-phase system.

PubMed

Barbosa, José Murillo P; Souza, Ranyere L; Fricks, Alini T; Zanin, Gisella Maria; Soares, Cleide Mara F; Lima, Alvaro S

2011-12-15

This work discusses the application of an aqueous two-phase system for the purification of lipases produced by Bacillus sp. ITP-001 using polyethylene glycol (PEG) and potassium phosphate. In the first step, the protein content was precipitated with ammonium sulphate (80% saturation). The enzyme remained in the aqueous solution and was dialyzed against ultra-pure water for 18 h and used to prepare an aqueous two-phase system (PEG/potassium phosphate). The use of different molecular weights of PEG to purify the lipase was investigated; the best purification factor (PF) was obtained using PEG 20,000g/mol, however PEG 8000 was used in the next tests due to lower viscosity. The influence of PEG and potassium phosphate concentrations on the enzyme purification was then studied: the highest FP was obtained with 20% of PEG and 18% of potassium phosphate. NaCl was added to increase the hydrophobicity between the phases, and also increased the purification factor. The pH value and temperature affected the enzyme partitioning, with the best purifying conditions achieved at pH 6.0 and 4°C. The molecular mass of the purified enzyme was determined to be approximately 54 kDa by SDS-PAGE. According to the results the best combination for purifying the enzyme is PEG 8000g/mol and potassium phosphate (20/18%) with 6% of NaCl at pH 6.0 and 4°C (201.53 fold). The partitioning process of lipase is governed by the entropy contribution. Copyright © 2011 Elsevier B.V. All rights reserved.

Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1+1 nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.

2014-03-01

A Jacobi-Gauss-Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge-Kutta method of fourth order, is proposed as a numerical algorithm for the approximation of solutions to nonlinear Schrödinger equations (NLSE) with initial-boundary data in 1+1 dimensions. Our procedure is implemented in two successive steps. In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N-1) nodes of the Jacobi-Gauss-Lobatto interpolation which depends upon two general Jacobi parameters. The resulting equations together with the two-point boundary conditions induce a system of 2(N-1) first-order ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve this temporal system. The proposed J-GL-C method, used in combination with the implicit Runge-Kutta method of fourth order, is employed to obtain highly accurate numerical approximations to four types of NLSE, including the attractive and repulsive NLSE and a Gross-Pitaevskii equation with space-periodic potential. The numerical results obtained by this algorithm have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively few nodes used, the absolute error in our numerical solutions is sufficiently small.

Phase Transformation Temperatures and Solute Redistribution in a Quaternary Zirconium Alloy

NASA Astrophysics Data System (ADS)

Cochrane, C.; Daymond, M. R.

2018-05-01

This study investigates the phase stability and redistribution of solute during heating and cooling of a quaternary zirconium alloy, Excel (Zr-3.2Sn-0.8Mo-0.8Nb). Time-of-flight neutron diffraction data are analyzed using a novel Vegard's law-based approach to determine the phase fractions and location of substitutional solute atoms in situ during heating from room temperature up to 1050 °C. It is seen that this alloy exhibits direct nucleation of the β Zr phase from martensite during tempering, and stable retention of the β Zr phase to high temperatures, unlike other two-phase zirconium alloys. The transformation strains resulting from the α \\leftrightarrow β transformation are shown to have a direct impact on the development of microstructure and crystallographic texture.

Molecular species forming at the α-Fe2O3 nanoparticle-aqueous solution interface.

PubMed

Ali, Hebatallah; Seidel, Robert; Pohl, Marvin N; Winter, Bernd

2018-05-21

We report on electronic structure measurements of the interface between hematite nanoparticles (6 nm diameter) and aqueous solutions. Using soft X-ray photoelectron spectroscopy from a liquid microjet we detect valence and core-level photoelectrons as well as Auger electrons from liquid water, from the nanoparticle-water interface, and from the interior of the aqueous-phase nanoparticles. Most noteworthy, the method is shown to be sufficiently sensitive for the detection of adsorbed hydroxyl species, resulting from H 2 O dissociation at the nanoparticle surface in aqueous solution. We obtain signal from surface OH from resonant, non-resonant, and from so-called partial-electron-yield X-ray absorption (PEY-XA) spectra. In addition, we report resonant photoelectron measurements at the iron 2p excitation. The respective Fe iron 2p 3/2 edge (L 3 -edge) PEY-XA spectra exhibit two main absorption peaks with their energies being sensitive to the chemical environment of the Fe 3+ ions at the nanoparticle-solution interface. This manifests in the 10 D q value which is a measure of the ligand-field strength. Furthermore, an observed intensity variation of the pre-peak, when comparing the PEY-XA spectra for different iron Auger-decay channels, can be assigned to different extents of electron delocalization. From the experimental fraction of local versus non-local autoionization signals we then find a very fast, approximately 1 fs, charge transfer time from interfacial Fe 3+ into the environment. The present study, which is complementary to ambient-pressure photoemission studies on solid-electrolyte systems, also highlights the multiple aspects of photoemission that need to be explored for a full characterization of the transition-metal-oxide nanoparticle surface in aqueous phase.

Process for production of solution-derived (Pb,La)(Nb,Sn,Zr,Ti)O{sub 3} thin films and powders

DOEpatents

Boyle, T.J.

1999-01-12

A simple and rapid process for synthesizing (Pb,La)(Nb,Sn,Zr,Ti)O{sub 3} precursor solutions and subsequent ferroelectric thin films and powders of the perovskite phase of these materials has been developed. This process offers advantages over standard methods, including: rapid solution synthesis (<10 minutes), use of commercially available materials, film production under ambient conditions, ease of lanthanum dissolution at high concentrations, and no heating requirements during solution synthesis. For lanthanum-doped ferroelectric materials, the lanthanum source can be added with total synthesis time less than 10 minutes. Films and powders are crystallized at approximately 650 C and exhibit ferroelectric properties comparable to films and powders produced by other techniques which require higher crystallization temperatures. 2 figs.

Process for production of solution-derived (Pb,La)(Nb,Sn,Zr,Ti)O.sub.3 thin films and powders

DOEpatents

Boyle, Timothy J.

1999-01-01

A simple and rapid process for synthesizing (Pb,La)(Nb,Sn,Zr,Ti)O.sub.3 precursor solutions and subsequent ferroelectric thin films and powders of the perovskite phase of these materials has been developed. This process offers advantages over standard methods, including: rapid solution synthesis (<10 minutes), use of commercially available materials, film production under ambient conditions, ease of lanthanum dissolution at high concentrations, and no heating requirements during solution synthesis. For lanthanum-doped ferroelectric materials, the lanthanum source can be added with total synthesis time less than 10 minutes. Films and powders are crystallized at approximately 650.degree. C. and exhibit ferroelectric properties comparable to films and powders produced by other techniques which require higher crystallization temperatures.

Comparison with CLPX II airborne data using DMRT model

USGS Publications Warehouse

Xu, X.; Liang, D.; Andreadis, K.M.; Tsang, L.; Josberger, E.G.

2009-01-01

In this paper, we considered a physical-based model which use numerical solution of Maxwell Equations in three-dimensional simulations and apply into Dense Media Radiative Theory (DMRT). The model is validated in two specific dataset from the second Cold Land Processes Experiment (CLPX II) at Alaska and Colorado. The data were all obtain by the Ku-band (13.95GHz) observations using airborne imaging polarimetric scatterometer (POLSCAT). Snow is a densely packed media. To take into account the collective scattering and incoherent scattering, analytical Quasi-Crystalline Approximation (QCA) and Numerical Maxwell Equation Method of 3-D simulation (NMM3D) are used to calculate the extinction coefficient and phase matrix. DMRT equations were solved by iterative solution up to 2nd order for the case of small optical thickness and full multiple scattering solution by decomposing the diffuse intensities into Fourier series was used when optical thickness exceed unity. It was shown that the model predictions agree with the field experiment not only co-polarization but also cross-polarization. For Alaska region, the input snow structure data was obtain by the in situ ground observations, while for Colorado region, we combined the VIC model to get the snow profile. ??2009 IEEE.

Validation of zero-order feedback strategies for medium range air-to-air interception in a horizontal plane

NASA Technical Reports Server (NTRS)

Shinar, J.

1982-01-01

A zero order feedback solution of a variable speed interception game between two aircraft in the horizontal plane, obtained by using the method of forced singular perturbation (FSP), is compared with the exact open loop solution. The comparison indicates that for initial distances of separation larger than eight turning radii of the evader, the accuracy of the feedback approximation is better than one percent. The result validates the zero order FSP approximation for medium range air combat analysis.

Solute Migration from the Aquifer Matrix into a Solution Conduit and the Reverse.

PubMed

Li, Guangquan; Field, Malcolm S

2016-09-01

A solution conduit has a permeable wall allowing for water exchange and solute transfer between the conduit and its surrounding aquifer matrix. In this paper, we use Laplace Transform to solve a one-dimensional equation constructed using the Euler approach to describe advective transport of solute in a conduit, a production-value problem. Both nonuniform cross-section of the conduit and nonuniform seepage at the conduit wall are considered in the solution. Physical analysis using the Lagrangian approach and a lumping method is performed to verify the solution. Two-way transfer between conduit water and matrix water is also investigated by using the solution for the production-value problem as a first-order approximation. The approximate solution agrees well with the exact solution if dimensionless travel time in the conduit is an order of magnitude smaller than unity. Our analytical solution is based on the assumption that the spatial and/or temporal heterogeneity in the wall solute flux is the dominant factor in the spreading of spring-breakthrough curves, and conduit dispersion is only a secondary mechanism. Such an approach can lead to the better understanding of water exchange and solute transfer between conduits and aquifer matrix. Euler and Lagrangian approaches are used to solve transport in conduit. Two-way transfer between conduit and matrix is investigated. The solution is applicable to transport in conduit of persisting solute from matrix. © 2016, National Ground Water Association.

Evaluation of trichloroethene recovery processes in heterogeneous aquifer cells flushed with biodegradable surfactants

NASA Astrophysics Data System (ADS)

Suchomel, Eric J.; Ramsburg, C. Andrew; Pennell, Kurt D.

2007-12-01

The ability of two biodegradable surfactants, polyoxyethylene (20) sorbitan monooleate (Tween® 80) and sodium dihexyl sulfosuccinate (Aerosol® MA), to recover a representative dense non-aqueous-phase liquid (DNAPL), trichloroethene (TCE), from heterogeneous porous media was evaluated through a combination of batch and aquifer cell experiments. An aqueous solution containing 3.3% Aerosol MA, 8% 2-propanol and 6 g/l CaCl 2 yielded a weight solubilization ratio (WSR) of 1.21 g TCE/g surfactant, with a corresponding liquid-liquid interfacial tension (IFT) of 0.19 dyn/cm. Flushing of aquifer cells containing a TCE-DNAPL source zone with approximately two pore volumes of the AMA formulation resulted in substantial (> 30%) mobilization of TCE-DNAPL. However, a TCE mass recovery of 81% was achieved when the aqueous-phase flow rate was sufficient to displace the mobile TCE-DNAPL toward the effluent well. Aqueous solutions of Tween 80 exhibited a greater capacity to solubilize TCE (WSR = 1.74 g TCE/g surfactant) and exerted markedly less reduction in IFT (10.4 dyn/cm). These data contradict an accepted empirical correlation used to estimate IFT values from solubilization capacity, and indicate a unique capacity of T80 to form concentrated TCE emulsions. Flushing of aquifer cells with less than 2.5 pore volumes of a 4% T80 solution achieved TCE mass recoveries ranging from 66 to 85%, with only slight TCE-DNAPL mobilization (< 5%) occurring when the total trapping number exceeded 2 × 10 - 5 . These findings demonstrate the ability of Tween 80 and Aerosol MA solutions to efficiently recover TCE from a heterogeneous DNAPL source zone, and the utility of the total trapping number as a design parameter for a priori prediction of DNAPL mobilization and bank angle formation when flushing with low-IFT solutions. Given their potential to stimulate microbial reductive dechlorination at low concentrations, these surfactants are well-suited for remedial action plans that couple aggressive mass removal followed by enhanced bioremediation to treat chlorinated solvent source zones.

Simulations of black-hole binaries with unequal masses or nonprecessing spins: Accuracy, physical properties, and comparison with post-Newtonian results

NASA Astrophysics Data System (ADS)

Hannam, Mark; Husa, Sascha; Ohme, Frank; Müller, Doreen; Brügmann, Bernd

2010-12-01

We present gravitational waveforms for the last orbits and merger of black-hole-binary systems along two branches of the black-hole-binary parameter space: equal-mass binaries with equal nonprecessing spins, and nonspinning unequal-mass binaries. The waveforms are calculated from numerical solutions of Einstein’s equations for black-hole binaries that complete between six and ten orbits before merger. Along the equal-mass spinning branch, the spin parameter of each black hole is χi=Si/Mi2∈[-0.85,0.85], and along the unequal-mass branch the mass ratio is q=M2/M1∈[1,4]. We discuss the construction of low-eccentricity puncture initial data for these cases, the properties of the final merged black hole, and compare the last 8-10 gravitational-wave cycles up to Mω=0.1 with the phase and amplitude predicted by standard post-Newtonian (PN) approximants. As in previous studies, we find that the phase from the 3.5PN TaylorT4 approximant is most accurate for nonspinning binaries. For equal-mass spinning binaries the 3.5PN TaylorT1 approximant (including spin terms up to only 2.5PN order) gives the most robust performance, but it is possible to treat TaylorT4 in such a way that it gives the best accuracy for spins χi>-0.75. When high-order amplitude corrections are included, the PN amplitude of the (ℓ=2,m=±2) modes is larger than the numerical relativity amplitude by between 2-4%.

The diagram of phase-field crystal structures: an influence of model parameters in a two-mode approximation

NASA Astrophysics Data System (ADS)

Ankudinov, V.; Galenko, P. K.

2017-04-01

Effect of phase-field crystal model (PFC-model) parameters on the structure diagram is analyzed. The PFC-model is taken in a two-mode approximation and the construction of structure diagram follows from the free energy minimization and Maxwell thermodynamic rule. The diagram of structure’s coexistence for three dimensional crystal structures [Body-Centered-Cubic (BCC), Face-Centered-Cubic (FCC) and homogeneous structures] are constructed. An influence of the model parameters, including the stability parameters, are discussed. A question about the structure diagram construction using the two-mode PFC-model with the application to real materials is established.

Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

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

Bonatsos, Dennis; Karampagia, S.; Casten, R. F.

2011-05-15

Using a contraction of the SU(3) algebra to the algebra of the rigid rotator in the large-boson-number limit of the interacting boson approximation (IBA) model, a line is found inside the symmetry triangle of the IBA, along which the SU(3) symmetry is preserved. The line extends from the SU(3) vertex to near the critical line of the first-order shape/phase transition separating the spherical and prolate deformed phases, and it lies within the Alhassid-Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices in the midst of chaotic regions. In addition to providing an explanation formore » the existence of the arc of regularity, the present line represents an example of an analytically determined approximate symmetry in the interior of the symmetry triangle of the IBA. The method is applicable to algebraic models possessing subalgebras amenable to contraction. This condition is equivalent to algebras in which the equilibrium ground state and its rotational band become energetically isolated from intrinsic excitations, as typified by deformed solutions to the IBA for large numbers of valence nucleons.« less

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.

Stability of smectic phases in hard-rod mixtures

NASA Astrophysics Data System (ADS)

Martínez-Ratón, Yuri; Velasco, Enrique; Mederos, Luis

2005-09-01

Using density-functional theory, we have analyzed the phase behavior of binary mixtures of hard rods of different lengths and diameters. Previous studies have shown a strong tendency of smectic phases of these mixtures to segregate and, in some circumstances, to form microsegregated phases. Our focus in the present work is on the formation of columnar phases which some studies, under some approximations, have shown to become thermodynamically stable prior to crystallization. Specifically we focus on the relative stability between smectic and columnar phases, a question not fully addressed in previous work. Our analysis is based on two complementary perspectives: on the one hand, an extended Onsager theory, which includes the full orientational degrees of freedom but with spatial and orientational correlations being treated in an approximate manner; on the other hand, we formulate a Zwanzig approximation of fundamental-measure theory on hard parallelepipeds, whereby orientations are restricted to be only along three mutually orthogonal axes, but correlations are faithfully represented. In the latter case novel, complete phase diagrams containing regions of stability of liquid-crystalline phases are calculated. Our findings indicate that the restricted-orientation approximation enhances the stability of columnar phases so as to preempt smectic order completely while, in the framework of the extended Onsager model, with full orientational degrees of freedom taken into account, columnar phases may preempt a large region of smectic stability in some mixtures, but some smectic order still persists.

Electron-transfer dynamics of photosynthetic reaction centers in thermoresponsive soft materials.

PubMed

Laible, Philip D; Kelley, Richard F; Wasielewski, Michael R; Firestone, Millicent A

2005-12-15

Poly(ethylene glycol)-grafted, lipid-based, thermoresponsive, soft nanostructures are shown to serve as scaffolding into which reconstituted integral membrane proteins, such as the bacterial photosynthetic reaction centers (RCs) can be stabilized, and their packing arrangement, and hence photophysical properties, can be controlled. The self-assembled nanostructures exist in two distinct states: a liquid-crystalline gel phase at temperatures above 21 degrees C and a non-birefringent, reduced viscosity state at lower temperatures. Characterization of the effect of protein introduction on the mesoscopic structure of the materials by 31P NMR and small-angle X-ray scattering shows that the expanded lamellar structure of the protein-free material is retained. At reduced temperatures, however, the aggregate structure is found to convert from a two-dimensional normal hexagonal structure to a three-dimensional cubic phase upon introduction of the RCs. Structural and functional characteristics of the RCs were determined by ground-state and femtosecond transient absorption spectroscopy. Time-resolved results indicate that the kinetics of primary electron transfer for the RCs in the low-viscosity cold phase of the self-assembled nanostructures are identical to those observed in a detergent-solubilized state in buffered aqueous solutions (approximately 4 ps) over a wide range of protein concentrations and experimental conditions. This is also true for RCs held within the lamellar gel phase at low protein concentrations and at short sample storage times. In contrast are kinetics from samples that are prepared with high RC concentrations and stored for several hours, which display additional kinetic components with extended electron-transfer times (approximately 10-12 ps). This observation is tentatively attributed to energy transfer between RCs that have laterally (in-plane) organized within the lipid bilayers of the lamellar gel phase prior to charge separation. These results not only demonstrate the use of soft nanostructures as a matrix in which to stabilize and organize membrane proteins but also suggest the possibility of using them to control the interactions between proteins and thus to tune their collective optical/electronic properties.

SOTXTSTREAM: Density-based self-organizing clustering of text streams.

PubMed

Bryant, Avory C; Cios, Krzysztof J

2017-01-01

A streaming data clustering algorithm is presented building upon the density-based self-organizing stream clustering algorithm SOSTREAM. Many density-based clustering algorithms are limited by their inability to identify clusters with heterogeneous density. SOSTREAM addresses this limitation through the use of local (nearest neighbor-based) density determinations. Additionally, many stream clustering algorithms use a two-phase clustering approach. In the first phase, a micro-clustering solution is maintained online, while in the second phase, the micro-clustering solution is clustered offline to produce a macro solution. By performing self-organization techniques on micro-clusters in the online phase, SOSTREAM is able to maintain a macro clustering solution in a single phase. Leveraging concepts from SOSTREAM, a new density-based self-organizing text stream clustering algorithm, SOTXTSTREAM, is presented that addresses several shortcomings of SOSTREAM. Gains in clustering performance of this new algorithm are demonstrated on several real-world text stream datasets.

An n -material thresholding method for improving integerness of solutions in topology optimization

DOE PAGES

Watts, Seth; Tortorelli, Daniel A.

2016-04-10

It is common in solving topology optimization problems to replace an integer-valued characteristic function design field with the material volume fraction field, a real-valued approximation of the design field that permits "fictitious" mixtures of materials during intermediate iterations in the optimization process. This is reasonable so long as one can interpolate properties for such materials and so long as the final design is integer valued. For this purpose, we present a method for smoothly thresholding the volume fractions of an arbitrary number of material phases which specify the design. This method is trivial for two-material design problems, for example, themore » canonical topology design problem of specifying the presence or absence of a single material within a domain, but it becomes more complex when three or more materials are used, as often occurs in material design problems. We take advantage of the similarity in properties between the volume fractions and the barycentric coordinates on a simplex to derive a thresholding, method which is applicable to an arbitrary number of materials. As we show in a sensitivity analysis, this method has smooth derivatives, allowing it to be used in gradient-based optimization algorithms. Finally, we present results, which show synergistic effects when used with Solid Isotropic Material with Penalty and Rational Approximation of Material Properties material interpolation functions, popular methods of ensuring integerness of solutions.« less

A solution procedure for behavior of thick plates on a nonlinear foundation and postbuckling behavior of long plates

NASA Technical Reports Server (NTRS)

Stein, M.; Stein, P. A.

1978-01-01

Approximate solutions for three nonlinear orthotropic plate problems are presented: (1) a thick plate attached to a pad having nonlinear material properties which, in turn, is attached to a substructure which is then deformed; (2) a long plate loaded in inplane longitudinal compression beyond its buckling load; and (3) a long plate loaded in inplane shear beyond its buckling load. For all three problems, the two dimensional plate equations are reduced to one dimensional equations in the y-direction by using a one dimensional trigonometric approximation in the x-direction. Each problem uses different trigonometric terms. Solutions are obtained using an existing algorithm for simultaneous, first order, nonlinear, ordinary differential equations subject to two point boundary conditions. Ordinary differential equations are derived to determine the variable coefficients of the trigonometric terms.

A Second-Order Phase Transition as a Limit of the First-Order Phase Transitions —Coherent Anomalies and Critical Phenomena in the Potts Models—

NASA Astrophysics Data System (ADS)

Katori, Makoto

1988-12-01

A new scheme of the coherent-anomaly method (CAM) is proposed to study critical phenomena in the models for which a mean-field description gives spurious first-order phase transition. A canonical series of mean-field-type approximations are constructed so that the spurious discontinuity should vanish asymptotically as the approximate critical temperature approachs the true value. The true value of the critical exponents β and γ are related to the coherent-anomaly exponents defined among the classical approximations. The formulation is demonstrated in the two-dimensional q-state Potts models for q{=}3 and 4. The result shows that the present method enables us to estimate the critical exponents with high accuracy by using the date of the cluster-mean-field approximations.

Exact Solution of the Two-Level System and the Einstein Solid in the Microcanonical Formalism

ERIC Educational Resources Information Center

Bertoldi, Dalia S.; Bringa, Eduardo M.; Miranda, E. N.

2011-01-01

The two-level system and the Einstein model of a crystalline solid are taught in every course of statistical mechanics and they are solved in the microcanonical formalism because the number of accessible microstates can be easily evaluated. However, their solutions are usually presented using the Stirling approximation to deal with factorials. In…

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Ductile tungsten-nickel alloy and method for making same

DOEpatents

Snyder, Jr., William B.

1976-01-01

The present invention is directed to a ductile, high-density tungsten-nickel alloy which possesses a tensile strength in the range of 100,000 to 140,000 psi and a tensile elongation of 3.1 to 16.5 percent in 1 inch at 25.degree.C. This alloy is prepared by the steps of liquid phase sintering a mixture of tungsten-0.5 to 10.0 weight percent nickel, heat treating the alloy at a temperature above the ordering temperature of approximately 970.degree.C. to stabilize the matrix phase, and thereafter rapidly quenching the alloy in a suitable liquid to maintain the matrix phase in a metastable, face-centered cubic, solid- solution of tungsten in nickel.

A semi-analytical study of positive corona discharge in wire-plane electrode configuration

NASA Astrophysics Data System (ADS)

Yanallah, K.; Pontiga, F.; Chen, J. H.

2013-08-01

Wire-to-plane positive corona discharge in air has been studied using an analytical model of two species (electrons and positive ions). The spatial distributions of electric field and charged species are obtained by integrating Gauss's law and the continuity equations of species along the Laplacian field lines. The experimental values of corona current intensity and applied voltage, together with Warburg's law, have been used to formulate the boundary condition for the electron density on the corona wire. To test the accuracy of the model, the approximate electric field distribution has been compared with the exact numerical solution obtained from a finite element analysis. A parametrical study of wire-to-plane corona discharge has then been undertaken using the approximate semi-analytical solutions. Thus, the spatial distributions of electric field and charged particles have been computed for different values of the gas pressure, wire radius and electrode separation. Also, the two dimensional distribution of ozone density has been obtained using a simplified plasma chemistry model. The approximate semi-analytical solutions can be evaluated in a negligible computational time, yet provide precise estimates of corona discharge variables.

Heat Treatment Development for a Rapidly Solidified Heat Resistant Cast Al-Si Alloy

NASA Astrophysics Data System (ADS)

Kasprzak, W.; Chen, D. L.; Shaha, S. K.

2013-07-01

Existing heat treatment standards do not properly define tempers for thin-walled castings that solidified with high solidification rates. Recently emerged casting processes such as vacuum high pressure die casting should not require long solution treatment times due to the fine microstructures arising from rapid solidification rates. The heat treatment studies involving rapidly solidified samples with secondary dendrite arm spacing between 10 and 35 μm were conducted for solution times between 30 min and 9 h and temperatures of 510 and 525 °C and for various aging parameters. The metallurgical analysis revealed that an increase in microstructure refinement could enable a reduction of solution time up to 88%. Solution treatment resulted in the dissolution of Al2Cu and Al5Mg8Si6Cu2, while Fe- and TiZrV-based phases remained partially in the microstructure. The highest strength of approximately 351 ± 9.7 and 309 ± 3.4 MPa for the UTS and YS, respectively, was achieved for a 2-step solution treatment at 510 and 525 °C in the T6 peak aging conditions, i.e., 150 °C for 100 h. The T6 temper did not yield dimensionally stable microstructure since exceeding 250 °C during in-service operation could result in phase transformation corresponding to the over-aging reaction. The microstructure refinement had a statistically stronger effect on the alloy strength than the increase in solutionizing time. Additionally, thermal analysis and dilatometer results were presented to assess the dissolution of phases during solution treatment, aging kinetics as well as dimensional stability.

Further investigations of the effect of pressure on retention in ultra-high-pressure liquid chromatography.

PubMed

Fallas, Morgane M; Neue, Uwe D; Hadley, Mark R; McCalley, David V

2010-01-15

In this study, we investigated further the large increases in retention with pressure that we observed previously in RP-LC especially for ionised solutes. These findings were initially confirmed on a conventional silica C(18) column, which gave extremely similar results to the hybrid C(18) phase originally used. Large increases in retention factor of approximately 50% for a pressure increase of 500 bar were also shown for high MW polar but neutral solutes. However, experiments with the same bases in ionised and non-ionised forms suggest that somewhat greater pressure-induced retention increases are found for ionised solutes. Retention increases with pressure were found to be considerably smaller for a C(1) column compared with a C(18) column; decreases in retention with increasing pressure were noted for ionised bases when using a bare silica column in the hydrophilic interaction chromatography (HILIC) mode. These observations are consistent with the partial loss of the solvation layer in RP-LC as the solute is forced into the hydrophobic environment of the stationary phase, and consequent reduction in the solute molar volume, while the water layer on the surface of a HILIC packing increases the hydration of a basic analyte. Finally, retention changes with pressure in RP-LC can also be observed at a mobile phase pH close to the solute pK(a), due to changes in pK(a) with pressure. However, this effect has no influence on the results of most of our studies. 2009 Elsevier B.V. All rights reserved.

Fluorescence Studies of Protein Crystal Nucleation

NASA Technical Reports Server (NTRS)

Pusey, Marc L.; Sumida, John

2000-01-01

One of the most powerful and versatile methods for studying molecules in solution is fluorescence. Crystallization typically takes place in a concentrated solution environment, whereas fluorescence typically has an upper concentration limit of approximately 1 x 10(exp -5)M, thus intrinsic fluorescence cannot be employed, but a fluorescent probe must be added to a sub population of the molecules. However the fluorescent species cannot interfere with the self-assembly process. This can be achieved with macromolecules, where fluorescent probes can be covalently attached to a sub population of molecules that are subsequently used to track the system as a whole. We are using fluorescence resonance energy transfer (FRET) to study the initial solution phase self-assembly process of tetragonal lysozyme crystal nucleation, using covalent fluorescent derivatives which crystallize in the characteristic P432121 space group. FRET studies are being carried out between cascade blue (CB-lys, donor, Ex 376 nm, Em 420 nm) and lucifer yellow (LY-lys, acceptor, Ex 425 nm, Em 520 nm) asp101 derivatives. The estimated R0 for this probe pair, the distance where 50% of the donor energy is transferred to the acceptor, is approximately 1.2 nm, compared to 2.2 nm between the side chain carboxyls of adjacent asp101's in the crystalline 43 helix. The short CB-lys lifetime (approximately 5 ns), coupled with the large average distances between the molecules ((sup 3) 50 nm) in solution, ensure that any energy transfer observed is not due to random diffusive interactions. Addition of LY-lys to CB-lys results in the appearance of a second, shorter lifetime (approximately 0.2 ns). Results from these and other ongoing studies will be discussed in conjunction with a model for how tetragonal lysozyme crystals nucleate and grow, and the relevance of that model to microgravity protein crystal growth

Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Convergence analysis of surrogate-based methods for Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Yan, Liang; Zhang, Yuan-Xiang

2017-12-01

The major challenges in the Bayesian inverse problems arise from the need for repeated evaluations of the forward model, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. Many attempts at accelerating Bayesian inference have relied on surrogates for the forward model, typically constructed through repeated forward simulations that are performed in an offline phase. Although such approaches can be quite effective at reducing computation cost, there has been little analysis of the approximation on posterior inference. In this work, we prove error bounds on the Kullback-Leibler (KL) distance between the true posterior distribution and the approximation based on surrogate models. Our rigorous error analysis show that if the forward model approximation converges at certain rate in the prior-weighted L 2 norm, then the posterior distribution generated by the approximation converges to the true posterior at least two times faster in the KL sense. The error bound on the Hellinger distance is also provided. To provide concrete examples focusing on the use of the surrogate model based methods, we present an efficient technique for constructing stochastic surrogate models to accelerate the Bayesian inference approach. The Christoffel least squares algorithms, based on generalized polynomial chaos, are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. The numerical strategy and the predicted convergence rates are then demonstrated on the nonlinear inverse problems, involving the inference of parameters appearing in partial differential equations.

Low density microcellular foams

DOEpatents

Aubert, J.H.; Clough, R.L.; Curro, J.G.; Quintana, C.A.; Russick, E.M.; Shaw, M.T.

1985-10-02

Low density, microporous polymer foams are provided by a process which comprises forming a solution of polymer and a suitable solvent followed by rapid cooling of the solution to form a phase-separated system and freeze the phase-separated system. The phase-separated system comprises a polymer phase and a solvent phase, each of which is substantially continuous within the other. The morphology of the polymer phase prior to and subsequent to freezing determine the morphology of the resultant foam. Both isotropic and anisotropic foams can be produced. If isotropic foams are produced, the polymer and solvent are tailored such that the solution spontaneously phase-separates prior to the point at which any component freezes. The morphology of the resultant polymer phase determines the morphology of the reusltant foam and the morphology of the polymer phase is retained by cooling the system at a rate sufficient to freeze one or both components of the system before a change in morphology can occur. Anisotropic foams are produced by forming a solution of polymer and solvent that will not phase separate prior to freezing of one or both components of the solution. In such a process, the solvent typically freezes before phase separation occurs. The morphology of the resultant frozen two-phase system determines the morphology of the resultant foam. The process involves subjecting the solution to essentially one-dimensional cooling. Foams having a density of less than 0.1 g/cc and a uniform cell size of less than 10 ..mu..m and a volume such that the foams have a length greater than 1 cm are provided.

Effect of alpha/gamma phase ratio on corrosion behavior of dual-phase stainless steels.

PubMed

Lim, Y J; Reyes, M; Thongthammachat, S; Sukchit, K; Panich, M; Oshida, Y

1999-01-01

Dual-phase stainless steels have been developed in order to reduce the nickel content, which is potentially responsible to an allergic reaction when these steels are used as medical or dental applications. In this study, two different dual-phase stainless steels (2205 and Z100) were electrochemically tested to evaluate their corrosion resistance in three corrosive solutions (i.e., synthetic saliva, 0.9% NaCl solution, and Ringer solution). Particularly, an attempt was made to correlate the corrosion resistance to a metallographic parameter, which is, in this study, the alpha/gamma phase ratio. It was concluded that (1) type 2205 stainless steel exhibited excellent corrosion resistance in all three corrosion media; however 2205 stainless steel decreases its corrosion resistance by increasing chloride concentration in tested electrolytes from synthetic saliva through 0.9% NaCl solution to Ringer solution. (2) X-ray diffraction analysis indicated that the alpha/gamma phase ratio of 2205 (1.735) was higher than that of Z100 (0.905). As a result, it is suggested that by increasing the alpha/gamma phase ratio the material shows more corrosion-prone behavior when being subjected to a hostile environment containing higher chloride ion concentration.

Two kissing bolts

NASA Astrophysics Data System (ADS)

Bossard, Guillaume; Katmadas, Stefanos; Turton, David

2018-02-01

The study of non-supersymmetric black hole microstates offers the potential to resolve the black hole information paradox. A system of equations was recently obtained that enables the systematic construction of non-supersymmetric smooth horizonless supergravity solutions, that are candidates to describe microstates of non-extremal black holes. Within this system we construct a family of six-dimensional supergravity solutions that feature two topologically-nontrivial three-cycles known as bolts. The two bolts touch at a single point and are supported by fluxes. We find that the fluxes on the two three-cycles can be either aligned or anti-aligned, and exhibit examples of both. We present several examples of smooth solutions, including near-extremal solutions that have an approximate AdS3 region, and far-from extremal solutions that have arbitrarily small charge compared to their mass.

Oxidizing dissolution mechanism of an irradiated MOX fuel in underwater aerated conditions at slightly acidic pH

NASA Astrophysics Data System (ADS)

Magnin, M.; Jégou, C.; Caraballo, R.; Broudic, V.; Tribet, M.; Peuget, S.; Talip, Z.

2015-07-01

The (U,Pu)O2 matrix behavior of an irradiated MIMAS-type (MIcronized MASter blend) MOX fuel, under radiolytic oxidation in aerated pure water at pH 5-5.5 was studied by combining chemical and radiochemical analyses of the alteration solution with Raman spectroscopy characterizations of the surface state. Two leaching experiments were performed on segments of irradiated fuel under different conditions: with or without an external γ irradiation field, over long periods (222 and 604 days, respectively). The gamma irradiation field was intended to be representative of the irradiation conditions for a fuel assembly in an underwater interim storage situation. The data acquired enabled an alteration mechanism to be established, characterized by uranium (UO22+) release mainly controlled by solubility of studtite over the long-term. The massive precipitation of this phase was observed for the two experiments based on high uranium oversaturation indexes of the solution and the kinetics involved depended on the irradiation conditions. External gamma irradiation accelerated the precipitation kinetics and the uranium concentrations (2.9 × 10-7 mol/l) were lower than for the non-irradiated reference experiment (1.4 × 10-5 mol/l), as the quantity of hydrogen peroxide was higher. Under slightly acidic pH conditions, the formation of an oxidized UO2+x phase was not observed on the surface and did not occur in the radiolysis dissolution mechanism of the fuel matrix. The Raman spectroscopy performed on the heterogeneous MOX fuel matrix surface, showed that the fluorite structure of the mainly UO2 phase surrounding the Pu-enriched aggregates had not been particularly impacted by any major structural change compared to the data obtained prior to leaching. For the plutonium, its behavior in solution involved a continuous release up to concentrations of approximately 3 × 10-6 mol L-1 with negligible colloid formation. This data appears to support a predominance of the +V oxidation state for plutonium in solution under highly oxidizing conditions. Furthermore, the Raman spectroscopy monitoring of the sample surface oxidation states did not point to any significant effect from the high Pu content of the aggregates (10-15%) and therefore did not indicate a better aggregate stability under radiolysis compared to the mainly UO2 matrix. This is because acidic pH conditions do not favor the development of oxidized layers on a fuel surface, with the exception of secondary phases.

Method for separating water soluble organics from a process stream by aqueous biphasic extraction

DOEpatents

Chaiko, David J.; Mego, William A.

1999-01-01

A method for separating water-miscible organic species from a process stream by aqueous biphasic extraction is provided. An aqueous biphase system is generated by contacting a process stream comprised of water, salt, and organic species with an aqueous polymer solution. The organic species transfer from the salt-rich phase to the polymer-rich phase, and the phases are separated. Next, the polymer is recovered from the loaded polymer phase by selectively extracting the polymer into an organic phase at an elevated temperature, while the organic species remain in a substantially salt-free aqueous solution. Alternatively, the polymer is recovered from the loaded polymer by a temperature induced phase separation (cloud point extraction), whereby the polymer and the organic species separate into two distinct solutions. The method for separating water-miscible organic species is applicable to the treatment of industrial wastewater streams, including the extraction and recovery of complexed metal ions from salt solutions, organic contaminants from mineral processing streams, and colorants from spent dye baths.

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

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

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

Online Solution of Two-Player Zero-Sum Games for Continuous-Time Nonlinear Systems With Completely Unknown Dynamics.

PubMed

Fu, Yue; Chai, Tianyou

2016-12-01

Regarding two-player zero-sum games of continuous-time nonlinear systems with completely unknown dynamics, this paper presents an online adaptive algorithm for learning the Nash equilibrium solution, i.e., the optimal policy pair. First, for known systems, the simultaneous policy updating algorithm (SPUA) is reviewed. A new analytical method to prove the convergence is presented. Then, based on the SPUA, without using a priori knowledge of any system dynamics, an online algorithm is proposed to simultaneously learn in real time either the minimal nonnegative solution of the Hamilton-Jacobi-Isaacs (HJI) equation or the generalized algebraic Riccati equation for linear systems as a special case, along with the optimal policy pair. The approximate solution to the HJI equation and the admissible policy pair is reexpressed by the approximation theorem. The unknown constants or weights of each are identified simultaneously by resorting to the recursive least square method. The convergence of the online algorithm to the optimal solutions is provided. A practical online algorithm is also developed. Simulation results illustrate the effectiveness of the proposed method.

Nonuniform fluids in the grand canonical ensemble

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

Percus, J.K.

1982-01-01

Nonuniform simple classical fluids are considered quite generally. The grand canonical ensemble is particularly suitable, conceptually, in the leading approximation of local thermodynamics, which figuratively divides the system into approximately uniform spatial subsystems. The procedure is reviewed by which this approach is systematically corrected for slowly varying density profiles, and a model is suggested that carries the correction into the domain of local fluctuations. The latter is assessed for substrate bounded fluids, as well as for two-phase interfaces. The peculiarities of the grand ensemble in a two-phase region stem from the inherent very large number fluctuations. A primitive model showsmore » how these are quenched in the canonical ensemble. This is taken advantage of by applying the Kac-Siegert representation of the van der Waals decomposition with petit canonical corrections, to the two-phase regime.« less

Processing of solid solution, mixed uranium/refractory metal carbides for advanced space nuclear power and propulsion systems

NASA Astrophysics Data System (ADS)

Knight, Travis Warren

Nuclear thermal propulsion (NTP) and space nuclear power are two enabling technologies for the manned exploration of space and the development of research outposts in space and on other planets such as Mars. Advanced carbide nuclear fuels have been proposed for application in space nuclear power and propulsion systems. This study examined the processing technologies and optimal parameters necessary to fabricate samples of single phase, solid solution, mixed uranium/refractory metal carbides. In particular, the pseudo-ternary carbide, UC-ZrC-NbC, system was examined with uranium metal mole fractions of 5% and 10% and corresponding uranium densities of 0.8 to 1.8 gU/cc. Efforts were directed to those methods that could produce simple geometry fuel elements or wafers such as those used to fabricate a Square Lattice Honeycomb (SLHC) fuel element and reactor core. Methods of cold uniaxial pressing, sintering by induction heating, and hot pressing by self-resistance heating were investigated. Solid solution, high density (low porosity) samples greater than 95% TD were processed by cold pressing at 150 MPa and sintering above 2600 K for times longer than 90 min. Some impurity oxide phases were noted in some samples attributed to residual gases in the furnace during processing. Also, some samples noted secondary phases of carbon and UC2 due to some hyperstoichiometric powder mixtures having carbon-to-metal ratios greater than one. In all, 33 mixed carbide samples were processed and analyzed with half bearing uranium as ternary carbides of UC-ZrC-NbC. Scanning electron microscopy, x-ray diffraction, and density measurements were used to characterize samples. Samples were processed from powders of the refractory mono-carbides and UC/UC 2 or from powders of uranium hydride (UH3), graphite, and refractory metal carbides to produce hypostoichiometric mixed carbides. Samples processed from the constituent carbide powders and sintered at temperatures above the melting point of UC showed signs of liquid phase sintering and were shown to be largely solid solutions. Pre-compaction of mixed carbide powders prior to sintering was shown to be necessary to achieve high densities. Hypostoichiometric, samples processed at 2500 K exhibited only the initial stage of sintering and solid solution formation. Based on these findings, a suggested processing methodology is proposed for producing high density, solid solution, mixed carbide fuels. Pseudo-binary, refractory carbide samples hot pressed at 3100 K and 6 MPa showed comparable densities (approximately 85% of the theoretical value) to samples processed by cold pressing and sintering at temperatures of 2800 K.

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

NASA Technical Reports Server (NTRS)

Lee, Charles H.; Cheung, Kar-Ming

2012-01-01

In this paper, we propose to solve the constrained optimization problem in two phases. The first phase uses heuristic methods such as the ant colony method, particle swarming optimization, and genetic algorithm to seek a near optimal solution among a list of feasible initial populations. The final optimal solution can be found by using the solution of the first phase as the initial condition to the SQP algorithm. We demonstrate the above problem formulation and optimization schemes with a large-scale network that includes the DSN ground stations and a number of spacecraft of deep space missions.

Quantum mechanical force fields for condensed phase molecular simulations

NASA Astrophysics Data System (ADS)

Giese, Timothy J.; York, Darrin M.

2017-09-01

Molecular simulations are powerful tools for providing atomic-level details into complex chemical and physical processes that occur in the condensed phase. For strongly interacting systems where quantum many-body effects are known to play an important role, density-functional methods are often used to provide the model with the potential energy used to drive dynamics. These methods, however, suffer from two major drawbacks. First, they are often too computationally intensive to practically apply to large systems over long time scales, limiting their scope of application. Second, there remain challenges for these models to obtain the necessary level of accuracy for weak non-bonded interactions to obtain quantitative accuracy for a wide range of condensed phase properties. Quantum mechanical force fields (QMFFs) provide a potential solution to both of these limitations. In this review, we address recent advances in the development of QMFFs for condensed phase simulations. In particular, we examine the development of QMFF models using both approximate and ab initio density-functional models, the treatment of short-ranged non-bonded and long-ranged electrostatic interactions, and stability issues in molecular dynamics calculations. Example calculations are provided for crystalline systems, liquid water, and ionic liquids. We conclude with a perspective for emerging challenges and future research directions.

Soft symmetry improvement of two particle irreducible effective actions

NASA Astrophysics Data System (ADS)

Brown, Michael J.; Whittingham, Ian B.

2017-01-01

Two particle irreducible effective actions (2PIEAs) are valuable nonperturbative techniques in quantum field theory; however, finite truncations of them violate the Ward identities (WIs) of theories with spontaneously broken symmetries. The symmetry improvement (SI) method of Pilaftsis and Teresi attempts to overcome this by imposing the WIs as constraints on the solution; however, the method suffers from the nonexistence of solutions in linear response theory and in certain truncations in equilibrium. Motivated by this, we introduce a new method called soft-symmetry improvement (SSI) which relaxes the constraint. Violations of WIs are allowed but punished in a least-squares implementation of the symmetry improvement idea. A new parameter ξ controls the strength of the constraint. The method interpolates between the unimproved (ξ →∞ ) and SI (ξ →0 ) cases, and the hope is that practically useful solutions can be found for finite ξ . We study the SSI 2PIEA for a scalar O (N ) model in the Hartree-Fock approximation. We find that the method is IR sensitive; the system must be formulated in finite volume V and temperature T =β-1 , and the V β →∞ limit must be taken carefully. Three distinct limits exist. Two are equivalent to the unimproved 2PIEA and SI 2PIEA respectively, and the third is a new limit where the WI is satisfied but the phase transition is strongly first order and solutions can fail to exist depending on ξ . Further, these limits are disconnected from each other; there is no smooth way to interpolate from one to another. These results suggest that any potential advantages of SSI methods, and indeed any application of (S)SI methods out of equilibrium, must occur in finite volume.

Equilibrium composition of interphase boundaries

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

Wynblatt, P.

1990-01-01

Two modeling approaches have been used to investigate segregation effects at interphase boundaries. The first approach is based on the nearest neighbor bond model, used in conjunction with the regular solution approximation, and is an extension of an earlier framework developed to address segregation phenomena at free surfaces. In order to model a semicoherent interphase boundary, we have employed a second modeling approach, based on Monte Carol simulation, in conjunction with the embedded atom method (EAM). The EAM is a powerful new method for describing interatomic interactions in metallic systems. It includes certain many-body interactions that depend on the localmore » environment of an atom. The Monte Carol approach has been applied to semicoherent interphase boundaries in Cu-Ag-Au alloys dilute in Au. These alloys consist of coexisting Cu-rich and Ag-rich phases, which differ in lattice constant by about 12%, such that good matching across in interface occurs when nine structural units of the Cu-rich phase are opposed to eight structural units of the Ag-rich phase. Thus far, interfaces with two different orientations have been studied: {l brace}001{r brace}-Cu//{l brace}001{r brace}-Ag, {l angle}110{r angle}-Cu//{l angle}110{r angle}-Ag; and {l brace}111{r brace}-Cu//{l brace}111{r brace}-Ag, {l angle}110{r angle}-Cu//{l angle}110{r angle}-Ag. These two interfaces will be referred to as the (001) and (111) interphase boundaries, for short. 18 refs.« less

Enhancements and limits in drug membrane transport using supersaturated solutions of poorly water soluble drugs.

PubMed

Raina, Shweta A; Zhang, Geoff G Z; Alonzo, David E; Wu, Jianwei; Zhu, Donghua; Catron, Nathaniel D; Gao, Yi; Taylor, Lynne S

2014-09-01

Amorphous solid dispersions (ASDs) give rise to supersaturated solutions (solution concentration greater than equilibrium crystalline solubility). We have recently found that supersaturating dosage forms can exhibit the phenomenon of liquid-liquid phase separation (LLPS). Thus, the high supersaturation generated by dissolving ASDs can lead to a two-phase system wherein one phase is an initially nanodimensioned and drug-rich phase and the other is a drug-lean continuous aqueous phase. Herein, the membrane transport of supersaturated solutions, at concentrations above and below the LLPS concentration has been evaluated using a side-by-side diffusion cell. Measurements of solution concentration with time in the receiver cell yield the flux, which reflects the solute thermodynamic activity in the donor cell. As the nominal concentration of solute in the donor cell increases, a linear increase in flux was observed up to the concentration where LLPS occurred. Thereafter, the flux remained essentially constant. Both nifedipine and felodipine solutions exhibit such behavior as long as crystallization is absent. This suggests that there is an upper limit in passive membrane transport that is dictated by the LLPS concentration. These results have several important implications for drug delivery, especially for poorly soluble compounds requiring enabling formulation technologies. © 2013 Wiley Periodicals, Inc. and the American Pharmacists Association.

Estimation of the sugar cane cultivated area from LANDSAT images using the two phase sampling method

NASA Technical Reports Server (NTRS)

Parada, N. D. J. (Principal Investigator); Cappelletti, C. A.; Mendonca, F. J.; Lee, D. C. L.; Shimabukuro, Y. E.

1982-01-01

A two phase sampling method and the optimal sampling segment dimensions for the estimation of sugar cane cultivated area were developed. This technique employs visual interpretations of LANDSAT images and panchromatic aerial photographs considered as the ground truth. The estimates, as a mean value of 100 simulated samples, represent 99.3% of the true value with a CV of approximately 1%; the relative efficiency of the two phase design was 157% when compared with a one phase aerial photographs sample.

Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, Diego

We study a mean field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas in the finite N and N-> infty kinetic limit (where N is the number of particles). The linear stability of equilibria in the kinetic model is studied as well as the initial value problem including Landau damping . Numerical simulations show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles and show that the N=2 limit has a family of rotating integrable solutions that provide an accurate description of the dynamics. We discuss the role of self-consistent Hamiltonian chaos in the formation of coherent structures, and discuss a mechanism of "violent" mixing caused by a self-consistent elliptic-hyperbolic bifurcation in phase space.

The unsaturated flow in porous media with dynamic capillary pressure

NASA Astrophysics Data System (ADS)

Milišić, Josipa-Pina

2018-05-01

In this paper we consider a degenerate pseudoparabolic equation for the wetting saturation of an unsaturated two-phase flow in porous media with dynamic capillary pressure-saturation relationship where the relaxation parameter depends on the saturation. Following the approach given in [13] the existence of a weak solution is proved using Galerkin approximation and regularization techniques. A priori estimates needed for passing to the limit when the regularization parameter goes to zero are obtained by using appropriate test-functions, motivated by the fact that considered PDE allows a natural generalization of the classical Kullback entropy. Finally, a special care was given in obtaining an estimate of the mixed-derivative term by combining the information from the capillary pressure with the obtained a priori estimates on the saturation.

Chemistry Division. Quarterly progress report for period ending June 30, 1949

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

Not Available

1949-09-14

Progress reports are presented for the following tasks: (1) nuclear and chemical properties of heavy elements (solution chemistry, phase rule studies); (2) nuclear and chemical properties of elements in the fission product region; (3) general nuclear chemistry; (4) radio-organic chemistry; (5) chemistry of separations processes; (6) physical chemistry and chemical physics; (7) radiation chemistry; (8) physical measurements and instrumentation; and (9) analytical chemistry. The program of the chemistry division is divided into two efforts of approximately equal weight with respect to number of personnel, chemical research, and analytical service for the Laboratory. The various research problems fall into the followingmore » classifications: (1) chemical separation processes for isolation and recovery of fissionable material, production of radioisotopes, and military applications; (2) reactor development; and (3) fundamental research.« less

Phenomenological Study of Interaction between Solar Acoustic Waves and Sunspots from Measured Scattered Wavefunctions

NASA Astrophysics Data System (ADS)

Yang, Ming-Hsu; Chou, Dean-Yi; Zhao, Hui; Liang, Zhi-Chao

2012-08-01

The solar acoustic waves around a sunspot are modified because of the interaction with the sunspot. The interaction can be viewed as that the sunspot, excited by the incident wave, generates the scattered wave, and the scattered wave is added to the incident wave to form the total wave around the sunspot. We define an interaction parameter, which could be complex, describing the interaction between the acoustic waves and the sunspot. The scattered wavefunction on the surface can be expressed as a two-dimensional integral of the product of the Green's function, the wavefunction, and the two-dimensional interaction parameter over the sunspot area for the Born approximation of different orders. We assume a simple model for the two-dimensional interaction parameter distribution: its absolute value is axisymmetric with a Gaussian distribution and its phase is a constant. The measured scattered wavefunctions of various modes for NOAAs 11084 and 11092 are fitted to the theoretical scattered wavefunctions to determine the three model parameters, magnitude, Gaussian radius, and phase, for the Born approximation of different orders. The three model parameters converge to some values at high-order Born approximations. The result of the first-order Born approximation is significantly different from the convergent value in some cases. The rate of convergence depends on the sunspot size and wavelength. It converges more rapidly for the smaller sunspot and longer wavelength. The magnitude increases with mode frequency and degree for each radial order. The Gaussian radius is insensitive to frequency and degree. The spatial range of the interaction parameter is greater than that of the continuum intensity deficit, but smaller than that of the acoustic power deficit of the sunspot. The phase versus phase speed falls into a small range. This suggests that the phase could be a function phase speed. NOAAs 11084 and 11092 have a similar magnitude and phase, although the ratio of their sizes is 0.75.

Collective phase description of oscillatory convection

NASA Astrophysics Data System (ADS)

Kawamura, Yoji; Nakao, Hiroya

2013-12-01

We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, stable time-periodic solutions to partial differential equations, representing the oscillatory convection. We derive the phase sensitivity function, which quantifies the phase response of the oscillatory convection to weak perturbations applied at each spatial point, and analyze the phase synchronization between two weakly coupled Hele-Shaw cells exhibiting oscillatory convection on the basis of the derived phase equations.

Quantum chemical approach for condensed-phase thermochemistry (V): Development of rigid-body type harmonic solvation model

NASA Astrophysics Data System (ADS)

Tarumi, Moto; Nakai, Hiromi

2018-05-01

This letter proposes an approximate treatment of the harmonic solvation model (HSM) assuming the solute to be a rigid body (RB-HSM). The HSM method can appropriately estimate the Gibbs free energy for condensed phases even where an ideal gas model used by standard quantum chemical programs fails. The RB-HSM method eliminates calculations for intra-molecular vibrations in order to reduce the computational costs. Numerical assessments indicated that the RB-HSM method can evaluate entropies and internal energies with the same accuracy as the HSM method but with lower calculation costs.

Bin packing problem solution through a deterministic weighted finite automaton

NASA Astrophysics Data System (ADS)

Zavala-Díaz, J. C.; Pérez-Ortega, J.; Martínez-Rebollar, A.; Almanza-Ortega, N. N.; Hidalgo-Reyes, M.

2016-06-01

In this article the solution of Bin Packing problem of one dimension through a weighted finite automaton is presented. Construction of the automaton and its application to solve three different instances, one synthetic data and two benchmarks are presented: N1C1W1_A.BPP belonging to data set Set_1; and BPP13.BPP belonging to hard28. The optimal solution of synthetic data is obtained. In the first benchmark the solution obtained is one more container than the ideal number of containers and in the second benchmark the solution is two more containers than the ideal solution (approximately 2.5%). The runtime in all three cases was less than one second.

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

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

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

Coherent control of molecular alignment of homonuclear diatomic molecules by analytically designed laser pulses.

PubMed

Zou, Shiyang; Sanz, Cristina; Balint-Kurti, Gabriel G

2008-09-28

We present an analytic scheme for designing laser pulses to manipulate the field-free molecular alignment of a homonuclear diatomic molecule. The scheme is based on the use of a generalized pulse-area theorem and makes use of pulses constructed around two-photon resonant frequencies. In the proposed scheme, the populations and relative phases of the rovibrational states of the molecule are independently controlled utilizing changes in the laser intensity and in the carrier-envelope phase difference, respectively. This allows us to create the correct coherent superposition of rovibrational states needed to achieve optimal molecular alignment. The validity and efficiency of the scheme are demonstrated by explicit application to the H(2) molecule. The analytically designed laser pulses are tested by exact numerical solutions of the time-dependent Schrodinger equation including laser-molecule interactions to all orders of the field strength. The design of a sequence of pulses to further enhance molecular alignment is also discussed and tested. It is found that the rotating wave approximation used in the analytic design of the laser pulses leads to small errors in the prediction of the relative phase of the rotational states. It is further shown how these errors may be easily corrected.

The Dark Matter Crisis: Falsification of the Current Standard Model of Cosmology

NASA Astrophysics Data System (ADS)

Kroupa, P.

2012-06-01

The current standard model of cosmology (SMoC) requires The Dual Dwarf Galaxy Theorem to be true according to which two types of dwarf galaxies must exist: primordial dark-matter (DM) dominated (type A) dwarf galaxies, and tidal-dwarf and ram-pressure-dwarf (type B) galaxies void of DM. Type A dwarfs surround the host approximately spherically, while type B dwarfs are typically correlated in phase-space. Type B dwarfs must exist in any cosmological theory in which galaxies interact. Only one type of dwarf galaxy is observed to exist on the baryonic Tully-Fisher plot and in the radius-mass plane. The Milky Way satellite system forms a vast phase-space-correlated structure that includes globular clusters and stellar and gaseous streams. Other galaxies also have phase-space correlated satellite systems. Therefore, The Dual Dwarf Galaxy Theorem is falsified by observation and dynamically relevant cold or warm DM cannot exist. It is shown that the SMoC is incompatible with a large set of other extragalactic observations. Other theoretical solutions to cosmological observations exist. In particular, alone the empirical mass-discrepancy-acceleration correlation constitutes convincing evidence that galactic-scale dynamics must be Milgromian. Major problems with inflationary big bang cosmologies remain unresolved.

A Discrete Approximation Framework for Hereditary Systems.

DTIC Science & Technology

1980-05-01

schemes which are included in the general framework and which may be implemented directly on high-speed computing machines are developed. A numerical...an appropriately chosen Hilbert space. We then proceed to develop general approximation schemes for the solutions to the homogeneous AEE which in turn...rich classes of these schemes . In addition, two particular families of approximation schemes included in the general framework are developed and

On the propagation of decaying planar shock and blast waves through non-uniform channels

NASA Astrophysics Data System (ADS)

Peace, J. T.; Lu, F. K.

2018-05-01

The propagation of planar decaying shock and blast waves in non-uniform channels is investigated with the use of a two-equation approximation of the generalized CCW theory. The effects of flow non-uniformity for the cases of an arbitrary strength decaying shock and blast wave in the strong shock limit are considered. Unlike the original CCW theory, the two-equation approximation takes into account the effects of initial temporal flow gradients in the flow properties behind the shock as the shock encounters an area change. A generalized order-of-magnitude analysis is carried out to analyze under which conditions the classical area-Mach (A-M) relation and two-equation approximation are valid given a time constant of decay for the flow properties behind the shock. It is shown that the two-equation approximation extends the applicability of the CCW theory to problems where flow non-uniformity behind the shock is orders of magnitude above that for appropriate use of the A-M relation. The behavior of the two-equation solution is presented for converging and diverging channels and compared against the A-M relation. It is shown that the second-order approximation and A-M relation have good agreement for converging geometries, such that the influence of flow non-uniformity behind the shock is negligible compared to the effects of changing area. Alternatively, the two-equation approximation is shown to be strongly dependent on the initial magnitude of flow non-uniformity in diverging geometries. Further, in diverging geometries, the inclusion of flow non-uniformity yields shock solutions that tend toward an acoustic wave faster than that predicted by the A-M relation.

Decay of the 3D viscous liquid-gas two-phase flow model with damping

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

Zhang, Yinghui, E-mail: zhangyinghui0910@126.com

We establish the optimal L{sup p} − L{sup 2}(1 ≤ p < 6/5) time decay rates of the solution to the Cauchy problem for the 3D viscous liquid-gas two-phase flow model with damping and analyse the influences of the damping on the qualitative behaviors of solution. It is observed that the fraction effect of the damping affects the dispersion of fluids and enhances the time decay rate of solution. Our method of proof consists of Hodge decomposition technique, L{sup p} − L{sup 2} estimates for the linearized equations, and delicate energy estimates.

Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions

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

Santillán, David; Juanes, Ruben; Cueto-Felgueroso, Luis

Propagation of fluid-driven fractures plays an important role in natural and engineering processes, including transport of magma in the lithosphere, geologic sequestration of carbon dioxide, and oil and gas recovery from low-permeability formations, among many others. The simulation of fracture propagation poses a computational challenge as a result of the complex physics of fracture and the need to capture disparate length scales. Phase field models represent fractures as a diffuse interface and enjoy the advantage that fracture nucleation, propagation, branching, or twisting can be simulated without ad hoc computational strategies like remeshing or local enrichment of the solution space. Heremore » we propose a new quasi-static phase field formulation for modeling fluid-driven fracturing in elastic media at small strains. The approach fully couples the fluid flow in the fracture (described via the Reynolds lubrication approximation) and the deformation of the surrounding medium. The flow is solved on a lower dimensionality mesh immersed in the elastic medium. This approach leads to accurate coupling of both physics. We assessed the performance of the model extensively by comparing results for the evolution of fracture length, aperture, and fracture fluid pressure against analytical solutions under different fracture propagation regimes. Thus, the excellent performance of the numerical model in all regimes builds confidence in the applicability of phase field approaches to simulate fluid-driven fracture.« less

Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions

DOE PAGES

Santillán, David; Juanes, Ruben; Cueto-Felgueroso, Luis

2017-04-20

Propagation of fluid-driven fractures plays an important role in natural and engineering processes, including transport of magma in the lithosphere, geologic sequestration of carbon dioxide, and oil and gas recovery from low-permeability formations, among many others. The simulation of fracture propagation poses a computational challenge as a result of the complex physics of fracture and the need to capture disparate length scales. Phase field models represent fractures as a diffuse interface and enjoy the advantage that fracture nucleation, propagation, branching, or twisting can be simulated without ad hoc computational strategies like remeshing or local enrichment of the solution space. Heremore » we propose a new quasi-static phase field formulation for modeling fluid-driven fracturing in elastic media at small strains. The approach fully couples the fluid flow in the fracture (described via the Reynolds lubrication approximation) and the deformation of the surrounding medium. The flow is solved on a lower dimensionality mesh immersed in the elastic medium. This approach leads to accurate coupling of both physics. We assessed the performance of the model extensively by comparing results for the evolution of fracture length, aperture, and fracture fluid pressure against analytical solutions under different fracture propagation regimes. Thus, the excellent performance of the numerical model in all regimes builds confidence in the applicability of phase field approaches to simulate fluid-driven fracture.« less

A methodology for commonality analysis, with applications to selected space station systems

NASA Technical Reports Server (NTRS)

Thomas, Lawrence Dale

1989-01-01

The application of commonality in a system represents an attempt to reduce costs by reducing the number of unique components. A formal method for conducting commonality analysis has not been established. In this dissertation, commonality analysis is characterized as a partitioning problem. The cost impacts of commonality are quantified in an objective function, and the solution is that partition which minimizes this objective function. Clustering techniques are used to approximate a solution, and sufficient conditions are developed which can be used to verify the optimality of the solution. This method for commonality analysis is general in scope. It may be applied to the various types of commonality analysis required in the conceptual, preliminary, and detail design phases of the system development cycle.

Quantum spatial propagation of squeezed light in a degenerate parametric amplifier

NASA Technical Reports Server (NTRS)

Deutsch, Ivan H.; Garrison, John C.

1992-01-01

Differential equations which describe the steady state spatial evolution of nonclassical light are established using standard quantum field theoretic techniques. A Schroedinger equation for the state vector of the optical field is derived using the quantum analog of the slowly varying envelope approximation (SVEA). The steady state solutions are those that satisfy the time independent Schroedinger equation. The resulting eigenvalue problem then leads to the spatial propagation equations. For the degenerate parametric amplifier this method shows that the squeezing parameter obey nonlinear differential equations coupled by the amplifier gain and phase mismatch. The solution to these differential equations is equivalent to one obtained from the classical three wave mixing steady state solution to the parametric amplifier with a nondepleted pump.

Dark matter and dark energy from the solution of the strong CP problem.

PubMed

Mainini, Roberto; Bonometto, Silvio A

2004-09-17

The Peccei-Quinn (PQ) solution of the strong CP problem requires the existence of axions, which are viable candidates for dark matter. If the Nambu-Goldstone potential of the PQ model is replaced by a potential V(|Phi|) admitting a tracker solution, the scalar field |Phi| can account for dark energy, while the phase of Phi yields axion dark matter. If V is a supergravity (SUGRA) potential, the model essentially depends on a single parameter, the energy scale Lambda. Once we set Lambda approximately equal to 10(10) GeV at the quark-hadron transition, |Phi| naturally passes through values suitable to solve the strong CP problem, later growing to values providing fair amounts of dark matter and dark energy.

Seasonal multiphase equilibria in the atmospheres of Titan and Pluto

NASA Astrophysics Data System (ADS)

Tan, S. P.; Kargel, J. S.

2017-12-01

At the extremely low temperatures in Titan's upper troposphere and on Pluto's surface, the atmospheres as a whole are subject to freeze into solid solutions, not pure ices. The presence of the solid phases introduces conditions with rich phase equilibria upon seasonal changes, even if the temperature undergoes only small changes. For the first time, the profile of atmospheric methane in Titan's troposphere will be reproduced complete with the solid solutions. This means that the freezing point, i.e. the altitude where the first solid phase appears, is determined. The seasonal change will also be evaluated both at the equator and the northern polar region. For Pluto, also for the first time, the seasonal solid-vapor equilibria will be evaluated. The fate of the two solid phases, the methane-rich and carbon-monoxide-rich solid solutions, will be analyzed upon temperature and pressure changes. Such investigations are enabled by the development of a molecular-based thermodynamic model for cryogenic chemical systems, referred to as CRYOCHEM, which includes solid solutions in its phase-equilibria calculations. The atmospheres of Titan and Pluto are modeled as ternary gas mixtures: nitrogen-methane-ethane and nitrogen-methane-carbon monoxide, respectively. Calculations using CRYOCHEM can provide us with compositions not only in two-phase equilibria, but also that in three-phase equilibria. Densities of all phases involved will also be calculated. For Titan, density inversion between liquid and solid phases will be identified and presented. In the inversion, the density of solid phase is less than that in the liquid phase. The method and results of this work will be useful for further investigations and modeling on the atmospheres of Titan, Pluto, and other bodies with similar conditions in the Solar System and beyond.

Fixed point theorems of GPS carrier phase ambiguity resolution and their application to massive network processing: Ambizap

NASA Astrophysics Data System (ADS)

Blewitt, Geoffrey

2008-12-01

Precise point positioning (PPP) has become popular for Global Positioning System (GPS) geodetic network analysis because for n stations, PPP has O(n) processing time, yet solutions closely approximate those of O(n3) full network analysis. Subsequent carrier phase ambiguity resolution (AR) further improves PPP precision and accuracy; however, full-network bootstrapping AR algorithms are O(n4), limiting single network solutions to n < 100. In this contribution, fixed point theorems of AR are derived and then used to develop "Ambizap," an O(n) algorithm designed to give results that closely approximate full network AR. Ambizap has been tested to n ≈ 2800 and proves to be O(n) in this range, adding only ˜50% to PPP processing time. Tests show that a 98-station network is resolved on a 3-GHz CPU in 7 min, versus 22 h using O(n4) AR methods. Ambizap features a novel network adjustment filter, producing solutions that precisely match O(n4) full network analysis. The resulting coordinates agree to ≪1 mm with current AR methods, much smaller than the ˜3-mm RMS precision of PPP alone. A 2000-station global network can be ambiguity resolved in ˜2.5 h. Together with PPP, Ambizap enables rapid, multiple reanalysis of large networks (e.g., ˜1000-station EarthScope Plate Boundary Observatory) and facilitates the addition of extra stations to an existing network solution without need to reprocess all data. To meet future needs, PPP plus Ambizap is designed to handle ˜10,000 stations per day on a 3-GHz dual-CPU desktop PC.

Galvanizing and Galvannealing Behavior of CMnSiCr Dual-Phase Steels

NASA Astrophysics Data System (ADS)

Lin, Ko-Chun; Chu, Peng-Wei; Lin, Chao-Sung; Chen, Hon-Bor

2013-06-01

Alloying elements, such as Mn, Mo, Si, and Cr, are commonly used to enhance the strength of advanced high-strength steels. Those elements also play an important role in the hot-dip galvanizing (GI) and galvannealing (GA) process. In this study, two kinds of CMnSiCr dual-phase steels were galvanized and galvannealed using a hot-dip simulator to investigate the effect of the alloying elements on the microstructure of the GI and GA coatings. The results showed that the dual-phase steels had good galvanizability because no bare spots were observed and the Fe-Zn phases were readily formed at the interface. However, the alloying reaction during the GA process was significantly hindered. XPS analysis showed that external oxidation occurred under an extremely low dew point [213 K to 203 K (-60 °C to -70 °C)] atmosphere during the annealing prior to hot dipping. However, most of the oxides were reduced during the GI process. After the GI process, the Al was present as solid solutes in the Fe-Zn phase, suggesting that the Fe-Zn phase was formed from the transformation of the Fe-Al inhibition alloy. Meanwhile, the solubility of Si in the ζ phase was extremely low. With continued GA reaction, the ζ phase transformed into the δ phase, which contained approximately 1.0 at.pct Si. The Si also diffused into the Zn layer during the GA reaction. Hence, the ζ phase did not homogeneously nucleate at the steel substrate/Zn coating interface, but was found at the area away from the interface. Therefore, the Fe-Zn phases on the CMnSiCr dual-phase steels were relatively non-uniform compared to those on interstitial-free steel.

Decay of the 3D inviscid liquid-gas two-phase flow model

NASA Astrophysics Data System (ADS)

Zhang, Yinghui

2016-06-01

We establish the optimal {Lp-L2(1 ≤ p < 6/5)} time decay rates of the solution to the Cauchy problem for the 3D inviscid liquid-gas two-phase flow model and analyze the influences of the damping on the qualitative behaviors of solution. Compared with the viscous liquid-gas two-phase flow model (Zhang and Zhu in J Differ Equ 258:2315-2338, 2015), our results imply that the friction effect of the damping is stronger than the dissipation effect of the viscosities and enhances the decay rate of the velocity. Our proof is based on Hodge decomposition technique, the {Lp-L2} estimates for the linearized equations and an elaborate energy method.

Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models.

PubMed

Azeyanagi, Tatsuo; Ferrari, Frank; Massolo, Fidel I Schaposnik

2018-02-09

We study the Schwinger-Dyson equations of a fermionic planar matrix quantum mechanics [or tensor and Sachdev-Ye-Kitaev (SYK) models] at leading melonic order. We find two solutions describing a high entropy, SYK black-hole-like phase and a low entropy one with trivial IR behavior. There is a line of first order phase transitions that terminates at a new critical point. Critical exponents are nonmean field and differ on the two sides of the transition. Interesting phenomena are also found in unstable and stable bosonic models, including Kazakov critical points and inconsistency of SYK-like solutions of the IR limit.

Versions of the collocation and least squares method for solving biharmonic equations in non-canonical domains

NASA Astrophysics Data System (ADS)

Belyaev, V. A.; Shapeev, V. P.

2017-10-01

New versions of the collocations and least squares method of high-order accuracy are proposed and implemented for the numerical solution of the boundary value problems for the biharmonic equation in non-canonical domains. The solution of the biharmonic equation is used for simulating the stress-strain state of an isotropic plate under the action of transverse load. The differential problem is projected into a space of fourth-degree polynomials by the CLS method. The boundary conditions for the approximate solution are put down exactly on the boundary of the computational domain. The versions of the CLS method are implemented on the grids which are constructed in two different ways. It is shown that the approximate solution of problems converges with high order. Thus it matches with high accuracy with the analytical solution of the test problems in the case of known solution in the numerical experiments on the convergence of the solution of various problems on a sequence of grids.

Implicitly solving phase appearance and disappearance problems using two-fluid six-equation model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-01-25

Phase appearance and disappearance issue presents serious numerical challenges in two-phase flow simulations using the two-fluid six-equation model. Numerical challenges arise from the singular equation system when one phase is absent, as well as from the discontinuity in the solution space when one phase appears or disappears. In this work, a high-resolution spatial discretization scheme on staggered grids and fully implicit methods were applied for the simulation of two-phase flow problems using the two-fluid six-equation model. A Jacobian-free Newton-Krylov (JFNK) method was used to solve the discretized nonlinear problem. An improved numerical treatment was proposed and proved to be effectivemore » to handle the numerical challenges. The treatment scheme is conceptually simple, easy to implement, and does not require explicit truncations on solutions, which is essential to conserve mass and energy. Various types of phase appearance and disappearance problems relevant to thermal-hydraulics analysis have been investigated, including a sedimentation problem, an oscillating manometer problem, a non-condensable gas injection problem, a single-phase flow with heat addition problem and a subcooled flow boiling problem. Successful simulations of these problems demonstrate the capability and robustness of the proposed numerical methods and numerical treatments. As a result, volume fraction of the absent phase can be calculated effectively as zero.« less

Convergence of discrete Aubry–Mather model in the continuous limit

NASA Astrophysics Data System (ADS)

Su, Xifeng; Thieullen, Philippe

2018-05-01

We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry–Mather–Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent and periodic in space. By Legendre transform it is equivalent to find a fixed point of some nonlinear operator, called Lax-Oleinik operator, which may be discounted or not. By discretizing in time, we are led to solve an additive eigenvalue problem involving a discrete Lax–Oleinik operator. We show how to approximate the effective Hamiltonian and some weak KAM solutions by letting the time step in the discrete model tend to zero. We also obtain a selected discrete weak KAM solution as in Davini et al (2016 Invent. Math. 206 29–55), and show that it converges to a particular solution of the cell equation. In order to unify the two settings, continuous and discrete, we develop a more general formalism of the short-range interactions.

Hybrid-dimensional modelling of two-phase flow through fractured porous media with enhanced matrix fracture transmission conditions

NASA Astrophysics Data System (ADS)

Brenner, Konstantin; Hennicker, Julian; Masson, Roland; Samier, Pierre

2018-03-01

In this work, we extend, to two-phase flow, the single-phase Darcy flow model proposed in [26], [12] in which the (d - 1)-dimensional flow in the fractures is coupled with the d-dimensional flow in the matrix. Three types of so called hybrid-dimensional two-phase Darcy flow models are proposed. They all account for fractures acting either as drains or as barriers, since they allow pressure jumps at the matrix-fracture interfaces. The models also permit to treat gravity dominated flow as well as discontinuous capillary pressure at the material interfaces. The three models differ by their transmission conditions at matrix fracture interfaces: while the first model accounts for the nonlinear two-phase Darcy flux conservations, the second and third ones are based on the linear single phase Darcy flux conservations combined with different approximations of the mobilities. We adapt the Vertex Approximate Gradient (VAG) scheme to this problem, in order to account for anisotropy and heterogeneity aspects as well as for applicability on general meshes. Several test cases are presented to compare our hybrid-dimensional models to the generic equi-dimensional model, in which fractures have the same dimension as the matrix, leading to deep insight about the quality of the proposed reduced models.

Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.

2018-05-01

A fully nonlinear model of Choi and Camassa (1999) describing one-dimensional incompressible dynamics of two non-mixing fluids in a horizontal channel, under a shallow water approximation, is considered. An equivalence transformation is presented, leading to a special dimensionless form of the system, involving a single dimensionless constant physical parameter, as opposed to five parameters present in the original model. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of physically meaningful exact closed-form solutions of the two-fluid model are derived, corresponding to periodic, solitary, and kink-type bidirectional traveling waves; specific examples are given, and properties of the exact solutions are analyzed.

Distinct hydroxy-radical-induced damage of 3'-uridine monophosphate in RNA: a theoretical study.

PubMed

Zhang, Ru bo; Eriksson, Leif A

2009-01-01

RNA strand scission and base release in 3'-uridine monophosphate (UMP), induced by OH radical addition to uracil, is studied at the DFT B3LYP/6-31+G(d,p) level in the gas phase and in solution. In particular, the mechanism of hydrogen-atom transfer subsequent to radical formation, from C2' on the sugar to the C6 site on the base, is explored. The barriers of (C2'-)H2'(a) abstraction by the C6 radical site range from 11.2 to 20.0 kcal mol(-1) in the gas phase and 14.1 to 21.0 kcal mol(-1) in aqueous solution, indicating that the local surrounding governs the hydrogen-abstraction reaction in a stereoselective way. The calculated N1-C1' (N1-glycosidic bond) and beta-phosphate bond strengths show that homolytic and heterolytic bond-breaking processes are largely favored in each case, respectively. The barrier for beta-phosphate bond rupture is approximately 3.2-4.0 kcal mol(-1) and is preferred by 8-12 kcal mol(-1) over N1-glycosidic bond cleavage in both the gas phase and solution. The beta-phosphate bond-rupture reactions are exothermal in the gas phase and solution, whereas N1-C1' bond-rupture reactions require both solvation and thermal corrections at 298 K to be energetically favored. The presence of the ribose 2'-OH group and its formation of low-barrier hydrogen bonds with oxygen atoms of the 3'-phosphate linkage are highly important for hydrogen transfer and the subsequent bond-breakage reactions.

Numerical analysis of a main crack interactions with micro-defects/inhomogeneities using two-scale generalized/extended finite element method

NASA Astrophysics Data System (ADS)

Malekan, Mohammad; Barros, Felício B.

2017-12-01

Generalized or extended finite element method (G/XFEM) models the crack by enriching functions of partition of unity type with discontinuous functions that represent well the physical behavior of the problem. However, this enrichment functions are not available for all problem types. Thus, one can use numerically-built (global-local) enrichment functions to have a better approximate procedure. This paper investigates the effects of micro-defects/inhomogeneities on a main crack behavior by modeling the micro-defects/inhomogeneities in the local problem using a two-scale G/XFEM. The global-local enrichment functions are influenced by the micro-defects/inhomogeneities from the local problem and thus change the approximate solution of the global problem with the main crack. This approach is presented in detail by solving three different linear elastic fracture mechanics problems for different cases: two plane stress and a Reissner-Mindlin plate problems. The numerical results obtained with the two-scale G/XFEM are compared with the reference solutions from the analytical, numerical solution using standard G/XFEM method and ABAQUS as well, and from the literature.

Static quadrupolar susceptibility for a Blume-Emery-Griffiths model based on the mean-field approximation

NASA Astrophysics Data System (ADS)

Pawlak, A.; Gülpınar, G.; Erdem, R.; Ağartıoğlu, M.

2015-12-01

The expressions for the dipolar and quadrupolar susceptibilities are obtained within the mean-field approximation in the Blume-Emery-Griffiths model. Temperature as well as crystal field dependences of the susceptibilities are investigated for two different phase diagram topologies which take place for K/J=3 and K/J=5.0.Their behavior near the second and first order transition points as well as multi-critical points such as tricritical, triple and critical endpoint is presented. It is found that in addition to the jumps connected with the phase transitions there are broad peaks in the quadrupolar susceptibility. It is indicated that these broad peaks lie on a prolongation of the first-order line from a triple point to a critical point ending the line of first-order transitions between two distinct paramagnetic phases. It is argued that the broad peaks are a reminiscence of very strong quadrupolar fluctuations at the critical point. The results reveal the fact that near ferromagnetic-paramagnetic phase transitions the quadrupolar susceptibility generally shows a jump whereas near the phase transition between two distinct paramagnetic phases it is an edge-like.

Causal implications of viscous damping in compressible fluid flows

PubMed

Jordan; Meyer; Puri

2000-12-01

Classically, a compressible, isothermal, viscous fluid is regarded as a mathematical continuum and its motion is governed by the linearized continuity, Navier-Stokes, and state equations. Unfortunately, solutions of this system are of a diffusive nature and hence do not satisfy causality. However, in the case of a half-space of fluid set to motion by a harmonically vibrating plate the classical equation of motion can, under suitable conditions, be approximated by the damped wave equation. Since this equation is hyperbolic, the resulting solutions satisfy causal requirements. In this work the Laplace transform and other analytical and numerical tools are used to investigate this apparent contradiction. To this end the exact solutions, as well as their special and limiting cases, are found and compared for the two models. The effects of the physical parameters on the solutions and associated quantities are also studied. It is shown that propagating wave fronts are only possible under the hyperbolic model and that the concept of phase speed has different meanings in the two formulations. In addition, discontinuities and shock waves are noted and a physical system is modeled under both formulations. Overall, it is shown that the hyperbolic form gives a more realistic description of the physical problem than does the classical theory. Lastly, a simple mechanical analog is given and connections to viscoelastic fluids are noted. In particular, the research presented here supports the notion that linear compressible, isothermal, viscous fluids can, at least in terms of causality, be better characterized as a type of viscoelastic fluid.

Successive phase transitions and kink solutions in Φ⁸, Φ¹⁰, and Φ¹² field theories

DOE PAGES

Khare, Avinash; Christov, Ivan C.; Saxena, Avadh

2014-08-27

We obtain exact solutions for kinks in Φ⁸, Φ¹⁰, and Φ¹² field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically-decaying tails and also asymmetric cases with mixed exponential-algebraic tail decay, unlike the lower-order Φ⁴ and Φ⁶ theories. Additionally, we construct distinct kinks withmore » equal energies in all three field theories considered, and we show the co-existence of up to three distinct kinks (for a Φ¹² potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the Φ¹⁰ field theory, which is a quasi-exactly solvable (QES) model akin to Φ⁶, we are also able to obtain three analytical solutions for the classical free energy as well as the probability distribution function in the thermodynamic limit.« less