Optimum element density studies for finite-element thermal analysis of hypersonic aircraft structures

NASA Technical Reports Server (NTRS)

Ko, William L.; Olona, Timothy; Muramoto, Kyle M.

1990-01-01

Different finite element models previously set up for thermal analysis of the space shuttle orbiter structure are discussed and their shortcomings identified. Element density criteria are established for the finite element thermal modelings of space shuttle orbiter-type large, hypersonic aircraft structures. These criteria are based on rigorous studies on solution accuracies using different finite element models having different element densities set up for one cell of the orbiter wing. Also, a method for optimization of the transient thermal analysis computer central processing unit (CPU) time is discussed. Based on the newly established element density criteria, the orbiter wing midspan segment was modeled for the examination of thermal analysis solution accuracies and the extent of computation CPU time requirements. The results showed that the distributions of the structural temperatures and the thermal stresses obtained from this wing segment model were satisfactory and the computation CPU time was at the acceptable level. The studies offered the hope that modeling the large, hypersonic aircraft structures using high-density elements for transient thermal analysis is possible if a CPU optimization technique was used.

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

PubMed

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

2015-08-07

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

Salty popcorn in a homogeneous low-dimensional toy model of holographic QCD

NASA Astrophysics Data System (ADS)

Elliot-Ripley, Matthew

2017-04-01

Recently, a homogeneous ansatz has been used to study cold dense nuclear matter in the Sakai-Sugimoto model of holographic QCD. To justify this homogeneous approximation we here investigate a homogeneous ansatz within a low-dimensional toy version of Sakai-Sugimoto to study finite baryon density configurations and compare it to full numerical solutions. We find the ansatz corresponds to enforcing a dyon salt arrangement in which the soliton solutions are split into half-soliton layers. Within this ansatz we find analogues of the proposed baryonic popcorn transitions, in which solutions split into multiple layers in the holographic direction. The homogeneous results are found to qualitatively match the full numerical solutions, lending confidence to the homogeneous approximations of the full Sakai-Sugimoto model. In addition, we find exact compact solutions in the high density, flat space limit which demonstrate the existence of further popcorn transitions to three layers and beyond.

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

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

2005-01-01

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

A potential model for sodium chloride solutions based on the TIP4P/2005 water model

NASA Astrophysics Data System (ADS)

Benavides, A. L.; Portillo, M. A.; Chamorro, V. C.; Espinosa, J. R.; Abascal, J. L. F.; Vega, C.

2017-09-01

Despite considerable efforts over more than two decades, our knowledge of the interactions in electrolyte solutions is not yet satisfactory. Not even one of the most simple and important aqueous solutions, NaCl(aq), escapes this assertion. A requisite for the development of a force field for any water solution is the availability of a good model for water. Despite the fact that TIP4P/2005 seems to fulfill the requirement, little work has been devoted to build a force field based on TIP4P/2005. In this work, we try to fill this gap for NaCl(aq). After unsuccessful attempts to produce accurate predictions for a wide range of properties using unity ionic charges, we decided to follow recent suggestions indicating that the charges should be scaled in the ionic solution. In this way, we have been able to develop a satisfactory non-polarizable force field for NaCl(aq). We evaluate a number of thermodynamic properties of the solution (equation of state, maximum in density, enthalpies of solution, activity coefficients, radial distribution functions, solubility, surface tension, diffusion coefficients, and viscosity). Overall the results for the solution are very good. An important achievement of our model is that it also accounts for the dynamical properties of the solution, a test for which the force fields so far proposed failed. The same is true for the solubility and for the maximum in density where the model describes the experimental results almost quantitatively. The price to pay is that the model is not so good at describing NaCl in the solid phase, although the results for several properties (density and melting temperature) are still acceptable. We conclude that the scaling of the charges improves the overall description of NaCl aqueous solutions when the polarization is not included.

Stationary spiral flow in polytropic stellar models

PubMed Central

Pekeris, C. L.

1980-01-01

It is shown that, in addition to the static Emden solution, a self-gravitating polytropic gas has a dynamic option in which there is stationary flow along spiral trajectories wound around the surfaces of concentric tori. The motion is obtained as a solution of a partial differential equation which is satisfied by the meridional stream function, coupled with Poisson's equation and a Bernoulli-type equation for the pressure (density). The pressure is affected by the whole of the Bernoulli term rather than by the centrifugal part only, which acts for a rotating model, and it may be reduced down to zero at the center. The spiral type of flow is illustrated for an incompressible fluid (n = 0), for which an exact solution is obtained. The features of the dynamic constant-density model are discussed as a basis for future comparison with the solution for compressible models. PMID:16592825

Lattice model for water-solute mixtures.

PubMed

Furlan, A P; Almarza, N G; Barbosa, M C

2016-10-14

A lattice model for the study of mixtures of associating liquids is proposed. Solvent and solute are modeled by adapting the associating lattice gas (ALG) model. The nature of interaction of solute/solvent is controlled by tuning the energy interactions between the patches of ALG model. We have studied three set of parameters, resulting in, hydrophilic, inert, and hydrophobic interactions. Extensive Monte Carlo simulations were carried out, and the behavior of pure components and the excess properties of the mixtures have been studied. The pure components, water (solvent) and solute, have quite similar phase diagrams, presenting gas, low density liquid, and high density liquid phases. In the case of solute, the regions of coexistence are substantially reduced when compared with both the water and the standard ALG models. A numerical procedure has been developed in order to attain series of results at constant pressure from simulations of the lattice gas model in the grand canonical ensemble. The excess properties of the mixtures, volume and enthalpy as the function of the solute fraction, have been studied for different interaction parameters of the model. Our model is able to reproduce qualitatively well the excess volume and enthalpy for different aqueous solutions. For the hydrophilic case, we show that the model is able to reproduce the excess volume and enthalpy of mixtures of small alcohols and amines. The inert case reproduces the behavior of large alcohols such as propanol, butanol, and pentanol. For the last case (hydrophobic), the excess properties reproduce the behavior of ionic liquids in aqueous solution.

A correction for Dupuit-Forchheimer interface flow models of seawater intrusion in unconfined coastal aquifers

NASA Astrophysics Data System (ADS)

Koussis, Antonis D.; Mazi, Katerina; Riou, Fabien; Destouni, Georgia

2015-06-01

Interface flow models that use the Dupuit-Forchheimer (DF) approximation for assessing the freshwater lens and the seawater intrusion in coastal aquifers lack representation of the gap through which fresh groundwater discharges to the sea. In these models, the interface outcrops unrealistically at the same point as the free surface, is too shallow and intersects the aquifer base too far inland, thus overestimating an intruding seawater front. To correct this shortcoming of DF-type interface solutions for unconfined aquifers, we here adapt the outflow gap estimate of an analytical 2-D interface solution for infinitely thick aquifers to fit the 50%-salinity contour of variable-density solutions for finite-depth aquifers. We further improve the accuracy of the interface toe location predicted with depth-integrated DF interface solutions by ∼20% (relative to the 50%-salinity contour of variable-density solutions) by combining the outflow-gap adjusted aquifer depth at the sea with a transverse-dispersion adjusted density ratio (Pool and Carrera, 2011), appropriately modified for unconfined flow. The effectiveness of the combined correction is exemplified for two regional Mediterranean aquifers, the Israel Coastal and Nile Delta aquifers.

Strong solutions for an incompressible Navier-Stokes/Allen-Cahn system with different densities

NASA Astrophysics Data System (ADS)

Li, Yinghua; Huang, Mingxia

2018-06-01

In this paper, we investigate a coupled Navier-Stokes/Allen-Cahn system describing a diffuse interface model for two-phase flow of viscous incompressible fluids with different densities in a bounded domain Ω \\subset R^N(N=2,3). We prove the existence and uniqueness of local strong solutions to the initial boundary value problem when the initial density function ρ _0 has a positive lower bound.

Higher dimensional strange quark matter solutions in self creation cosmology

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

Şen, R., E-mail: ramazansen-1991@hotmail.com; Aygün, S., E-mail: saygun@comu.edu.tr

In this study, we have generalized the higher dimensional flat Friedmann-Robertson-Walker (FRW) universe solutions for a cloud of string with perfect fluid attached strange quark matter (SQM) in Self Creation Cosmology (SCC). We have obtained that the cloud of string with perfect fluid does not survive and the string tension density vanishes for this model. However, we get dark energy model for strange quark matter with positive density and negative pressure in self creation cosmology.

Well-behaved relativistic charged super-dense star models

NASA Astrophysics Data System (ADS)

Faruqi, Shahab; Pant, Neeraj

2012-10-01

A new class of charged super-dense star models is obtained by using an electric intensity, which involves a parameter, K. The metric describing the model shares its metric potential g 44 with that of Durgapal's fourth solution (J. Phys. A, Math. Gen. 15:2637, 1982). The pressure-free surface is kept at the density ρ b =2×1014 g/cm3 and joins smoothly with the Reissner-Nordstrom solution. The charge analogues are well-behaved for a wide range, 0≤ K≤59, with the optimum value of X=0.264 i.e. the pressure, density, pressure-density ratio and velocity of sound are monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and the corresponding radius occupied by the neutral solution are 4.22 M Θ and 20 km, respectively for X=0.264. For the charged solution, the maximum mass and radius are defined by the expressions M≈(0.0059 K+4.22) M Θ and r b ≈-0.021464 K+20 km respectively.

Generalization of the binary structural phase field crystal model

NASA Astrophysics Data System (ADS)

Smith, Nathan; Provatas, Nikolas

2017-10-01

Two improvements to the binary structural phase field crystal (XPFC) theory are presented. The first is an improvement to the phenomenology for modelling density-density correlation functions and the second extends the free energy of the mixing term in the binary XPFC model beyond ideal mixing to a regular solution model. These improvements are applied to study kinetics of precipitation from solution. We observe a two-step nucleation pathway similar to recent experimental work [N. D. Loh, S. Sen, M. Bosman, S. F. Tan, J. Zhong, C. A. Nijhuis, P. Král, P. Matsudaira, and U. Mirsaidov, Nat. Chem. 9, 77 (2017), 10.1038/nchem.2618; A. F. Wallace, L. O. Hedges, A. Fernandez-Martinez, P. Raiteri, J. D. Gale, G. A. Waychunas, S. Whitelam, J. F. Banfield, and J. J. De Yoreo, Science 341, 885 (2013), 10.1126/science.1230915] in which the liquid solution first decomposes into solute-poor and solute-rich regions, followed by precipitate nucleation of the solute-rich regions. Additionally, we find a phenomenon not previously described in the literature in which the growth of precipitates is accelerated in the presence of uncrystallized solute-rich liquid regions.

Electrolyte solutions at curved electrodes. II. Microscopic approach

NASA Astrophysics Data System (ADS)

Reindl, Andreas; Bier, Markus; Dietrich, S.

2017-04-01

Density functional theory is used to describe electrolyte solutions in contact with electrodes of planar or spherical shape. For the electrolyte solutions, we consider the so-called civilized model, in which all species present are treated on equal footing. This allows us to discuss the features of the electric double layer in terms of the differential capacitance. The model provides insight into the microscopic structure of the electric double layer, which goes beyond the mesoscopic approach studied in Paper I. This enables us to judge the relevance of microscopic details, such as the radii of the particles forming the electrolyte solutions or the dipolar character of the solvent particles, and to compare the predictions of various models. Similar to Paper I, a general behavior is observed for small radii of the electrode in that in this limit the results become independent of the surface charge density and of the particle radii. However, for large electrode radii, non-trivial behaviors are observed. Especially the particle radii and the surface charge density strongly influence the capacitance. From the comparison with the Poisson-Boltzmann approach, it becomes apparent that the shape of the electrode determines whether the microscopic details of the full civilized model have to be taken into account or whether already simpler models yield acceptable predictions.

Electrolyte solutions at curved electrodes. II. Microscopic approach.

PubMed

Reindl, Andreas; Bier, Markus; Dietrich, S

2017-04-21

Density functional theory is used to describe electrolyte solutions in contact with electrodes of planar or spherical shape. For the electrolyte solutions, we consider the so-called civilized model, in which all species present are treated on equal footing. This allows us to discuss the features of the electric double layer in terms of the differential capacitance. The model provides insight into the microscopic structure of the electric double layer, which goes beyond the mesoscopic approach studied in Paper I. This enables us to judge the relevance of microscopic details, such as the radii of the particles forming the electrolyte solutions or the dipolar character of the solvent particles, and to compare the predictions of various models. Similar to Paper I, a general behavior is observed for small radii of the electrode in that in this limit the results become independent of the surface charge density and of the particle radii. However, for large electrode radii, non-trivial behaviors are observed. Especially the particle radii and the surface charge density strongly influence the capacitance. From the comparison with the Poisson-Boltzmann approach, it becomes apparent that the shape of the electrode determines whether the microscopic details of the full civilized model have to be taken into account or whether already simpler models yield acceptable predictions.

Forward modeling of gravity data using geostatistically generated subsurface density variations

USGS Publications Warehouse

Phelps, Geoffrey

2016-01-01

Using geostatistical models of density variations in the subsurface, constrained by geologic data, forward models of gravity anomalies can be generated by discretizing the subsurface and calculating the cumulative effect of each cell (pixel). The results of such stochastically generated forward gravity anomalies can be compared with the observed gravity anomalies to find density models that match the observed data. These models have an advantage over forward gravity anomalies generated using polygonal bodies of homogeneous density because generating numerous realizations explores a larger region of the solution space. The stochastic modeling can be thought of as dividing the forward model into two components: that due to the shape of each geologic unit and that due to the heterogeneous distribution of density within each geologic unit. The modeling demonstrates that the internally heterogeneous distribution of density within each geologic unit can contribute significantly to the resulting calculated forward gravity anomaly. Furthermore, the stochastic models match observed statistical properties of geologic units, the solution space is more broadly explored by producing a suite of successful models, and the likelihood of a particular conceptual geologic model can be compared. The Vaca Fault near Travis Air Force Base, California, can be successfully modeled as a normal or strike-slip fault, with the normal fault model being slightly more probable. It can also be modeled as a reverse fault, although this structural geologic configuration is highly unlikely given the realizations we explored.

Modeling the chemical kinetics of atmospheric plasma for cell treatment in a liquid solution

NASA Astrophysics Data System (ADS)

Kim, H. Y.; Lee, H. W.; Kang, S. K.; Wk. Lee, H.; Kim, G. C.; Lee, J. K.

2012-07-01

Low temperature atmospheric pressure plasmas have been known to be effective for living cell inactivation in a liquid solution but it is not clear yet which species are key factors for the cell treatment. Using a global model, we elucidate the processes through which pH level in the solution is changed from neutral to acidic after plasma exposure and key components with pH and air variation. First, pH level in a liquid solution is changed by He+ and He(21S) radicals. Second, O3 density decreases as pH level in the solution decreases and air concentration decreases. It can be a method of removing O3 that causes chest pain and damages lung tissue when the density is very high. H2O2, HO2, and NO radicals are found to be key factors for cell inactivation in the solution with pH and air variation.

Density-functional theory of spherical electric double layers and zeta potentials of colloidal particles in restricted-primitive-model electrolyte solutions.

PubMed

Yu, Yang-Xin; Wu, Jianzhong; Gao, Guang-Hua

2004-04-15

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The theoretical predictions are in good agreement with the results from Monte Carlo simulations and from previous investigations using integral-equation theory for the ionic density profiles and the zeta potentials of spherical particles at a variety of solution conditions. Like the integral-equation approaches, the density-functional theory is able to capture the oscillatory density profiles of small ions and the charge inversion (overcharging) phenomena for particles with elevated charge density. In particular, our density-functional theory predicts the formation of a second counterion layer near the surface of highly charged spherical particle. Conversely, the nonlinear Poisson-Boltzmann theory and its variations are unable to represent the oscillatory behavior of small ion distributions and charge inversion. Finally, our density-functional theory predicts charge inversion even in a 1:1 electrolyte solution as long as the salt concentration is sufficiently high. (c) 2004 American Institute of Physics.

On the Geometrical Optics Approach in the Theory of Freely-Localized Microwave Gas Breakdown

NASA Astrophysics Data System (ADS)

Shapiro, Michael; Schaub, Samuel; Hummelt, Jason; Temkin, Richard; Semenov, Vladimir

2015-11-01

Large filamentary arrays of high pressure gas microwave breakdown have been experimentally studied at MIT using a 110 GHz, 1.5 MW pulsed gyrotron. The experiments have been modeled by other groups using numerical codes. The plasma density distribution in the filaments can be as well analytically calculated using the geometrical optics approach neglecting plasma diffusion. The field outside the filament is a solution of an inverse electromagnetic problem. The solutions are found for the cylindrical and spherical filaments and for the multi-layered planar filaments with a finite plasma density at the boundaries. We present new results of this theory showing a variety of filaments with complex shapes. The solutions for plasma density distribution are found with a zero plasma density at the boundary of the filament. Therefore, to solve the inverse problem within the geometrical optics approximation, it can be assumed that there is no reflection from the filament. The results of this research are useful for modeling future MIT experiments.

A scaled-ionic-charge simulation model that reproduces enhanced and suppressed water diffusion in aqueous salt solutions.

PubMed

Kann, Z R; Skinner, J L

2014-09-14

Non-polarizable models for ions and water quantitatively and qualitatively misrepresent the salt concentration dependence of water diffusion in electrolyte solutions. In particular, experiment shows that the water diffusion coefficient increases in the presence of salts of low charge density (e.g., CsI), whereas the results of simulations with non-polarizable models show a decrease of the water diffusion coefficient in all alkali halide solutions. We present a simple charge-scaling method based on the ratio of the solvent dielectric constants from simulation and experiment. Using an ion model that was developed independently of a solvent, i.e., in the crystalline solid, this method improves the water diffusion trends across a range of water models. When used with a good-quality water model, e.g., TIP4P/2005 or E3B, this method recovers the qualitative behaviour of the water diffusion trends. The model and method used were also shown to give good results for other structural and dynamic properties including solution density, radial distribution functions, and ion diffusion coefficients.

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

PubMed

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Exact Solutions for Wind-Driven Coastal Upwelling and Downwelling over Sloping Topography

NASA Astrophysics Data System (ADS)

Choboter, P.; Duke, D.; Horton, J.; Sinz, P.

2009-12-01

The dynamics of wind-driven coastal upwelling and downwelling are studied using a simplified dynamical model. Exact solutions are examined as a function of time and over a family of sloping topographies. Assumptions in the two-dimensional model include a frictionless ocean interior below the surface Ekman layer, and no alongshore dependence of the variables; however, dependence in the cross-shore and vertical directions is retained. Additionally, density and alongshore momentum are advected by the cross-shore velocity in order to maintain thermal wind. The time-dependent initial-value problem is solved with constant initial stratification and no initial alongshore flow. An alongshore pressure gradient is added to allow the cross-shore flow to be geostrophically balanced far from shore. Previously, this model has been used to study upwelling over flat-bottom and sloping topographies, but the novel feature in this work is the discovery of exact solutions for downwelling. These exact solutions are compared to numerical solutions from a primitive-equation ocean model, based on the Princeton Ocean Model, configured in a similar two-dimensional geometry. Many typical features of the evolution of density and velocity during downwelling are displayed by the analytical model.

Vibrational Power Flow Analysis of Rods and Beams

NASA Technical Reports Server (NTRS)

Wohlever, James Christopher; Bernhard, R. J.

1988-01-01

A new method to model vibrational power flow and predict the resulting energy density levels in uniform rods and beams is investigated. This method models the flow of vibrational power in a manner analogous to the flow of thermal power in a heat conduction problem. The classical displacement solutions for harmonically excited, hysteretically damped rods and beams are used to derive expressions for the vibrational power flow and energy density in the rod and beam. Under certain conditions, the power flow in these two structural elements will be shown to be proportional to the energy density gradient. Using the relationship between power flow and energy density, an energy balance on differential control volumes in the rod and beam leads to a Poisson's equation which models the energy density distribution in the rod and beam. Coupling the energy density and power flow solutions for rods and beams is also discussed. It is shown that the resonant behavior of finite structures complicates the coupling of solutions, especially when the excitations are single frequency inputs. Two coupling formulations are discussed, the first based on the receptance method, and the second on the travelling wave approach used in Statistical Energy Analysis. The receptance method is the more computationally intensive but is capable of analyzing single frequency excitation cases. The traveling wave approach gives a good approximation of the frequency average of energy density and power flow in coupled systems, and thus, is an efficient technique for use with broadband frequency excitation.

PDF approach for compressible turbulent reacting flows

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Tsai, Y.-L. P.; Raju, M. S.

1993-01-01

The objective of the present work is to develop a probability density function (pdf) turbulence model for compressible reacting flows for use with a CFD flow solver. The probability density function of the species mass fraction and enthalpy are obtained by solving a pdf evolution equation using a Monte Carlo scheme. The pdf solution procedure is coupled with a compressible CFD flow solver which provides the velocity and pressure fields. A modeled pdf equation for compressible flows, capable of capturing shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed, and an averaging procedure is developed to provide smooth Monte-Carlo solutions to ensure convergence. Two supersonic diffusion flames are studied using the proposed pdf model and the results are compared with experimental data; marked improvements over CFD solutions without pdf are observed. Preliminary applications of pdf to 3D flows are also reported.

Modeling ultrafast solvated electronic dynamics using time-dependent density functional theory and polarizable continuum model.

PubMed

Liang, Wenkel; Chapman, Craig T; Ding, Feizhi; Li, Xiaosong

2012-03-01

A first-principles solvated electronic dynamics method is introduced. Solvent electronic degrees of freedom are coupled to the time-dependent electronic density of a solute molecule by means of the implicit reaction field method, and the entire electronic system is propagated in time. This real-time time-dependent approach, incorporating the polarizable continuum solvation model, is shown to be very effective in describing the dynamical solvation effect in the charge transfer process and yields a consistent absorption spectrum in comparison to the conventional linear response results in solution. © 2012 American Chemical Society

Documentation of the seawater intrusion (SWI2) package for MODFLOW

USGS Publications Warehouse

Bakker, Mark; Schaars, Frans; Hughes, Joseph D.; Langevin, Christian D.; Dausman, Alyssa M.

2013-01-01

The SWI2 Package is the latest release of the Seawater Intrusion (SWI) Package for MODFLOW. The SWI2 Package allows three-dimensional vertically integrated variable-density groundwater flow and seawater intrusion in coastal multiaquifer systems to be simulated using MODFLOW-2005. Vertically integrated variable-density groundwater flow is based on the Dupuit approximation in which an aquifer is vertically discretized into zones of differing densities, separated from each other by defined surfaces representing interfaces or density isosurfaces. The numerical approach used in the SWI2 Package does not account for diffusion and dispersion and should not be used where these processes are important. The resulting differential equations are equivalent in form to the groundwater flow equation for uniform-density flow. The approach implemented in the SWI2 Package allows density effects to be incorporated into MODFLOW-2005 through the addition of pseudo-source terms to the groundwater flow equation without the need to solve a separate advective-dispersive transport equation. Vertical and horizontal movement of defined density surfaces is calculated separately using a combination of fluxes calculated through solution of the groundwater flow equation and a simple tip and toe tracking algorithm. Use of the SWI2 Package in MODFLOW-2005 only requires the addition of a single additional input file and modification of boundary heads to freshwater heads referenced to the top of the aquifer. Fluid density within model layers can be represented using zones of constant density (stratified flow) or continuously varying density (piecewise linear in the vertical direction) in the SWI2 Package. The main advantage of using the SWI2 Package instead of variable-density groundwater flow and dispersive solute transport codes, such as SEAWAT and SUTRA, is that fewer model cells are required for simulations using the SWI2 Package because every aquifer can be represented by a single layer of cells. This reduction in number of required model cells and the elimination of the need to solve the advective-dispersive transport equation results in substantial model run-time savings, which can be large for regional aquifers. The accuracy and use of the SWI2 Package is demonstrated through comparison with existing exact solutions and numerical solutions with SEAWAT. Results for an unconfined aquifer are also presented to demonstrate application of the SWI2 Package to a large-scale regional problem.

How ions affect the structure of water.

PubMed

Hribar, Barbara; Southall, Noel T; Vlachy, Vojko; Dill, Ken A

2002-10-16

We model ion solvation in water. We use the MB model of water, a simple two-dimensional statistical mechanical model in which waters are represented as Lennard-Jones disks having Gaussian hydrogen-bonding arms. We introduce a charge dipole into MB waters. We perform (NPT) Monte Carlo simulations to explore how water molecules are organized around ions and around nonpolar solutes in salt solutions. The model gives good qualitative agreement with experiments, including Jones-Dole viscosity B coefficients, Samoilov and Hirata ion hydration activation energies, ion solvation thermodynamics, and Setschenow coefficients for Hofmeister series ions, which describe the salt concentration dependence of the solubilities of hydrophobic solutes. The two main ideas captured here are (1) that charge densities govern the interactions of ions with water, and (2) that a balance of forces determines water structure: electrostatics (water's dipole interacting with ions) and hydrogen bonding (water interacting with neighboring waters). Small ions (kosmotropes) have high charge densities so they cause strong electrostatic ordering of nearby waters, breaking hydrogen bonds. In contrast, large ions (chaotropes) have low charge densities, and surrounding water molecules are largely hydrogen bonded.

Densities and apparent molar volumes of atmospherically important electrolyte solutions. 1. The solutes H2SO4, HNO3, HCl, Na2SO4, NaNO3, NaCl, (NH4)2SO4, NH4NO3, and NH4Cl from 0 to 50 °C, including extrapolations to very low temperature and to the pure liquid state, and NaHSO4, NaOH, and NH3 at 25 °C.

PubMed

Clegg, S L; Wexler, A S

2011-04-21

Calculations of the size and density of atmospheric aerosols are complicated by the fact that they can exist at concentrations highly supersaturated with respect to dissolved salts and supercooled with respect to ice. Densities and apparent molar volumes of solutes in aqueous solutions containing the solutes H(2)SO(4), HNO(3), HCl, Na(2)SO(4), NaNO(3), NaCl, (NH(4))(2)SO(4), NH(4)NO(3), and NH(4)Cl have been critically evaluated and represented using fitted equations from 0 to 50 °C or greater and from infinite dilution to concentrations saturated or supersaturated with respect to the dissolved salts. Using extrapolated densities of high-temperature solutions and melts, the relationship between density and concentration is extended to the hypothetical pure liquid solutes. Above a given reference concentration of a few mol kg(-1), it is observed that density increases almost linearly with decreasing temperature, and comparisons with available data below 0 °C suggest that the fitted equations for density can be extrapolated to very low temperatures. As concentration is decreased below the reference concentration, the variation of density with temperature tends to that of water (which decreases as temperature is reduced below 3.98 °C). In this region below the reference concentration, and below 0 °C, densities are calculated using extrapolated apparent molar volumes which are constrained to agree at the reference concentrations with an equation for the directly fitted density. Calculated volume properties agree well with available data at low temperatures, for both concentrated and dilute solutions. Comparisons are made with literature data for temperatures of maximum density. Apparent molar volumes at infinite dilution are consistent, on a single ion basis, to better than ±0.1 cm(3) mol(-1) from 0 to 50 °C. Volume properties of aqueous NaHSO(4), NaOH, and NH(3) have also been evaluated, at 25 °C only. In part 2 of this work (ref 1 ) an ion interaction (Pitzer) model has been used to calculate apparent molar volumes of H(2)SO(4) in 0-3 mol kg(-1) aqueous solutions of the pure acid and to represent directly the effect of the HSO(4)(-) ↔ H(+) + SO(4)(2-) reaction. The results are incorporated into the treatment of aqueous H(2)SO(4) density described here. Densities and apparent molar volumes from -20 to 50 °C, and from 0 to 100 wt % of solute, are tabulated for the electrolytes listed in the title and have also been incorporated into the extended aerosol inorganics model (E-AIM, http://www.aim.env.uea.ac.uk/aim/aim.php) together with densities of the solid salts and hydrates.

New analytical technique for carbon dioxide absorption solvents

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

Pouryousefi, F.; Idem, R.O.

2008-02-15

The densities and refractive indices of two binary systems (water + MEA and water + MDEA) and three ternary systems (water + MEA + CO{sub 2}, water + MDEA + CO{sub 2}, and water + MEA + MDEA) used for carbon dioxide (CO{sub 2}) capture were measured over the range of compositions of the aqueous alkanolamine(s) used for CO{sub 2} absorption at temperatures from 295 to 338 K. Experimental densities were modeled empirically, while the experimental refractive indices were modeled using well-established models from the known values of their pure-component densities and refractive indices. The density and Gladstone-Dale refractive indexmore » models were then used to obtain the compositions of unknown samples of the binary and ternary systems by simultaneous solution of the density and refractive index equations. The results from this technique have been compared with HPLC (high-performance liquid chromatography) results, while a third independent technique (acid-base titration) was used to verify the results. The results show that the systems' compositions obtained from the simple and easy-to-use refractive index/density technique were very comparable to the expensive and laborious HPLC/titration techniques, suggesting that the refractive index/density technique can be used to replace existing methods for analysis of fresh or nondegraded, CO{sub 2}-loaded, single and mixed alkanolamine solutions.« less

A two-dimensional MHD global coronal model - Steady-state streamers

NASA Technical Reports Server (NTRS)

Wang, A.-H.; Wu, S. T.; Suess, S. T.; Poletto, G.

1992-01-01

A 2D, time-dependent, numerical, MHD model for the simulation of coronal streamers from the solar surface to 15 solar is presented. Three examples are given; for dipole, quadrupole and hexapole (Legendre polynomials P1, P2, and P3) initial field topologies. The computed properties are density, temperature, velocity, and magnetic field. The calculation is set up as an initial-boundary value problem wherein a relaxation in time produces the steady state solution. In addition to the properties of the solutions, their accuracy is discussed. Besides solutions for dipole, quadrupole, and hexapole geometries, the model use of realistic values for the density and Alfven speed while still meeting the requirement that the flow speed be super-Alfvenic at the outer boundary by extending the outer boundary to 15 solar radii.

Exact results of 1D traffic cellular automata: The low-density behavior of the Fukui-Ishibashi model

NASA Astrophysics Data System (ADS)

Salcido, Alejandro; Hernández-Zapata, Ernesto; Carreón-Sierra, Susana

2018-03-01

The maximum entropy states of the cellular automata models for traffic flow in a single-lane with no anticipation are presented and discussed. The exact analytical solutions for the low-density behavior of the stochastic Fukui-Ishibashi traffic model were obtained and compared with computer simulations of the model. An excellent agreement was found.

Modeling and simulation of deformation of hydrogels responding to electric stimulus.

PubMed

Li, Hua; Luo, Rongmo; Lam, K Y

2007-01-01

A model for simulation of pH-sensitive hydrogels is refined in this paper to extend its application to electric-sensitive hydrogels, termed the refined multi-effect-coupling electric-stimulus (rMECe) model. By reformulation of the fixed-charge density and consideration of finite deformation, the rMECe model is able to predict the responsive deformations of the hydrogels when they are immersed in a bath solution subject to externally applied electric field. The rMECe model consists of nonlinear partial differential governing equations with chemo-electro-mechanical coupling effects and the fixed-charge density with electric-field effect. By comparison between simulation and experiment extracted from literature, the model is verified to be accurate and stable. The rMECe model performs quantitatively for deformation analysis of the electric-sensitive hydrogels. The influences of several physical parameters, including the externally applied electric voltage, initial fixed-charge density, hydrogel strip thickness, ionic strength and valence of surrounding solution, are discussed in detail on the displacement and average curvature of the hydrogels.

ZrB 2-HfB 2 solid solutions as electrode materials for hydrogen reaction in acidic and basic solutions

DOE PAGES

Sitler, Steven J.; Raja, Krishnan S.; Charit, Indrajit

2016-11-09

Spark plasma sintered transition metal diborides such as HfB 2, ZrB 2 and their solid solutions were investigated as electrode materials for electrochemical hydrogen evolutions reactions (HER) in 1 M H 2SO 4 and 1 M NaOH electrolytes. HfB 2 and ZrB 2 formed complete solid solutions when mixed in 1:1, 1:4, and 4:1 ratios and they were stable in both electrolytes. The HER kinetics of the diborides were slower in the basic solution than in the acidic solutions. The Tafel slopes in 1 M H 2SO 4 were in the range of 0.15 - 0.18 V/decade except for puremore » HfB 2 which showed a Tafel slope of 0.38 V/decade. In 1 M NaOH the Tafel slopes were in the range of 0.12 - 0.27 V/decade. The composition of Hf xZr 1-xB 2 solid solutions with x = 0.2 - 0.8, influenced the exchange current densities, overpotentials and Tafel slopes of the HER. As a result, the EIS data were fitted with a porous film equivalent circuit model in order to better understand the HER behavior. In addition, modeling calculations, using density functional theory approach, were carried out to estimate the density of states and band structure of the boride solid solutions.« less

Bouncing cosmological solutions from f(R,T) gravity

NASA Astrophysics Data System (ADS)

Shabani, Hamid; Ziaie, Amir Hadi

2018-05-01

In this work we study classical bouncing solutions in the context of f(R,T)=R+h(T) gravity in a flat FLRW background using a perfect fluid as the only matter content. Our investigation is based on introducing an effective fluid through defining effective energy density and pressure; we call this reformulation as the " effective picture". These definitions have been already introduced to study the energy conditions in f(R,T) gravity. We examine various models to which different effective equations of state, corresponding to different h(T) functions, can be attributed. It is also discussed that one can link between an assumed f(R,T) model in the effective picture and the theories with generalized equation of state ( EoS). We obtain cosmological scenarios exhibiting a nonsingular bounce before and after which the Universe lives within a de-Sitter phase. We then proceed to find general solutions for matter bounce and investigate their properties. We show that the properties of bouncing solution in the effective picture of f(R,T) gravity are as follows: for a specific form of the f(R,T) function, these solutions are without any future singularities. Moreover, stability analysis of the nonsingular solutions through matter density perturbations revealed that except two of the models, the parameters of scalar-type perturbations for the other ones have a slight transient fluctuation around the bounce point and damp to zero or a finite value at late times. Hence these bouncing solutions are stable against scalar-type perturbations. It is possible that all energy conditions be respected by the real perfect fluid, however, the null and the strong energy conditions can be violated by the effective fluid near the bounce event. These solutions always correspond to a maximum in the real matter energy density and a vanishing minimum in the effective density. The effective pressure varies between negative values and may show either a minimum or a maximum.

Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions

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

Marenich, Aleksandr; Cramer, Christopher J; Truhlar, Donald G

2009-04-30

We present a new continuum solvation model based on the quantum mechanical charge density of a solute molecule interacting with a continuum description of the solvent. The model is called SMD, where the “D” stands for “density” to denote that the full solute electron density is used without defining partial atomic charges. “Continuum” denotes that the solvent is not represented explicitly but rather as a dielectric medium with surface tension at the solute-solvent boundary. SMD is a universal solvation model, where “universal” denotes its applicability to any charged or uncharged solute in any solvent or liquid medium for which amore » few key descriptors are known (in particular, dielectric constant, refractive index, bulk surface tension, and acidity and basicity parameters). The model separates the observable solvation free energy into two main components. The first component is the bulk electrostatic contribution arising from a self-consistent reaction field treatment that involves the solution of the nonhomogeneous Poisson equation for electrostatics in terms of the integral-equation-formalism polarizable continuum model (IEF-PCM). The cavities for the bulk electrostatic calculation are defined by superpositions of nuclear-centered spheres. The second component is called the cavity-dispersion-solvent-structure term and is the contribution arising from short-range interactions between the solute and solvent molecules in the first solvation shell. This contribution is a sum of terms that are proportional (with geometry-dependent proportionality constants called atomic surface tensions) to the solvent-accessible surface areas of the individual atoms of the solute. The SMD model has been parametrized with a training set of 2821 solvation data including 112 aqueous ionic solvation free energies, 220 solvation free energies for 166 ions in acetonitrile, methanol, and dimethyl sulfoxide, 2346 solvation free energies for 318 neutral solutes in 91 solvents (90 nonaqueous organic solvents and water), and 143 transfer free energies for 93 neutral solutes between water and 15 organic solvents. The elements present in the solutes are H, C, N, O, F, Si, P, S, Cl, and Br. The SMD model employs a single set of parameters (intrinsic atomic Coulomb radii and atomic surface tension coefficients) optimized over six electronic structure methods: M05-2X/MIDI!6D, M05-2X/6-31G*, M05-2X/6-31+G**, M05-2X/cc-pVTZ, B3LYP/6-31G*, and HF/6-31G*. Although the SMD model has been parametrized using the IEF-PCM protocol for bulk electrostatics, it may also be employed with other algorithms for solving the nonhomogeneous Poisson equation for continuum solvation calculations in which the solute is represented by its electron density in real space. This includes, for example, the conductor-like screening algorithm. With the 6-31G* basis set, the SMD model achieves mean unsigned errors of 0.6-1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on average for ions with either Gaussian03 or GAMESS.« less

EFFECTIVE POROSITY IMPLIES EFFECTIVE BULK DENSITY IN SORBING SOLUTE TRANSPORT

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

Flach, G.

2012-02-27

The concept of an effective porosity is widely used in solute transport modeling to account for the presence of a fraction of the medium that effectively does not influence solute migration, apart from taking up space. This non-participating volume or ineffective porosity plays the same role as the gas phase in single-phase liquid unsaturated transport: it increases pore velocity, which is useful towards reproducing observed solute travel times. The prevalent use of the effective porosity concept is reflected by its prominent inclusion in popular texts, e.g., de Marsily (1986), Fetter (1988, 1993) and Zheng and Bennett (2002). The purpose ofmore » this commentary is to point out that proper application of the concept for sorbing solutes requires more than simply reducing porosity while leaving other material properties unchanged. More specifically, effective porosity implies the corresponding need for an effective bulk density in a conventional single-porosity model. The reason is that the designated non-participating volume is composed of both solid and fluid phases, both of which must be neglected for consistency. Said another way, if solute does not enter the ineffective porosity then it also cannot contact the adjoining solid. Conceptually neglecting the fluid portion of the non-participating volume leads to a lower (effective) porosity. Likewise, discarding the solid portion of the non-participating volume inherently leads to a lower or effective bulk density. In the author's experience, practitioners virtually never adjust bulk density when adopting the effective porosity approach.« less

MODFLOW/MT3DMS-based simulation of variable-density ground water flow and transport

USGS Publications Warehouse

Langevin, C.D.; Guo, W.

2006-01-01

This paper presents an approach for coupling MODFLOW and MT3DMS for the simulation of variable-density ground water flow. MODFLOW routines were modified to solve a variable-density form of the ground water flow equation in which the density terms are calculated using an equation of state and the simulated MT3DMS solute concentrations. Changes to the MODFLOW and MT3DMS input files were kept to a minimum, and thus existing data files and data files created with most pre- and postprocessors can be used directly with the SEAWAT code. The approach was tested by simulating the Henry problem and two of the saltpool laboratory experiments (low- and high-density cases). For the Henry problem, the simulated results compared well with the steady-state semianalytic solution and also the transient isochlor movement as simulated by a finite-element model. For the saltpool problem, the simulated breakthrough curves compared better with the laboratory measurements for the low-density case than for the high-density case but showed good agreement with the measured salinity isosurfaces for both cases. Results from the test cases presented here indicate that the MODFLOW/MT3DMS approach provides accurate solutions for problems involving variable-density ground water flow and solute transport. ?? 2006 National Ground Water Association.

Simulating Osmotic Equilibria: A New Tool for Calculating Activity Coefficients in Concentrated Aqueous Salt Solutions.

PubMed

Bley, Michael; Duvail, Magali; Guilbaud, Philippe; Dufrêche, Jean-François

2017-10-19

Herein, a new theoretical method is presented for predicting osmotic equilibria and activities, where a bulk liquid and its corresponding vapor phase are simulated by means of molecular dynamics using explicit polarization. Calculated time-averaged number density profiles provide the amount of evaporated molecules present in the vapor phase and consequently the vapor-phase density. The activity of the solvent and the corresponding osmotic coefficient are determined by the vapor density at different solute concentrations with respect to the reference vapor density of the pure solvent. With the extended Debye-Hückel equation for the activity coefficient along with the corresponding Gibbs-Duhem relation, the activity coefficients of the solutes are calculated by fitting the osmotic coefficients. A simple model based on the combination of Poisson processes and Maxwell-Boltzmann velocity distributions is introduced to interpret statistical phenomena observed during the simulations, which are related to evaporation and recondensation. This method is applied to aqueous dysprosium nitrate [Dy(NO 3 ) 3 ] solutions at different concentrations. The obtained densities of the liquid bulk and the osmotic and activity coefficients are in good agreement with the experimental results for concentrated and saturated solutions. Density profiles of the liquid-vapor interface at different concentrations provide detailed insight into the spatial distributions of all compounds.

Mantle viscosity structure constrained by joint inversions of seismic velocities and density

NASA Astrophysics Data System (ADS)

Rudolph, M. L.; Moulik, P.; Lekic, V.

2017-12-01

The viscosity structure of Earth's deep mantle affects the thermal evolution of Earth, the ascent of mantle upwellings, sinking of subducted oceanic lithosphere, and the mixing of compositional heterogeneities in the mantle. Modeling the long-wavelength dynamic geoid allows us to constrain the radial viscosity profile of the mantle. Typically, in inversions for the mantle viscosity structure, wavespeed variations are mapped into density variations using a constant- or depth-dependent scaling factor. Here, we use a newly developed joint model of anisotropic Vs, Vp, density and transition zone topographies to generate a suite of solutions for the mantle viscosity structure directly from the seismologically constrained density structure. The density structure used to drive our forward models includes contributions from both thermal and compositional variations, including important contributions from compositionally dense material in the Large Low Velocity Provinces at the base of the mantle. These compositional variations have been neglected in the forward models used in most previous inversions and have the potential to significantly affect large-scale flow and thus the inferred viscosity structure. We use a transdimensional, hierarchical, Bayesian approach to solve the inverse problem, and our solutions for viscosity structure include an increase in viscosity below the base of the transition zone, in the shallow lower mantle. Using geoid dynamic response functions and an analysis of the correlation between the observed geoid and mantle structure, we demonstrate the underlying reason for this inference. Finally, we present a new family of solutions in which the data uncertainty is accounted for using covariance matrices associated with the mantle structure models.

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

Sitler, Steven J.; Raja, Krishnan S.; Charit, Indrajit

Spark plasma sintered transition metal diborides such as HfB 2, ZrB 2 and their solid solutions were investigated as electrode materials for electrochemical hydrogen evolutions reactions (HER) in 1 M H 2SO 4 and 1 M NaOH electrolytes. HfB 2 and ZrB 2 formed complete solid solutions when mixed in 1:1, 1:4, and 4:1 ratios and they were stable in both electrolytes. The HER kinetics of the diborides were slower in the basic solution than in the acidic solutions. The Tafel slopes in 1 M H 2SO 4 were in the range of 0.15 - 0.18 V/decade except for puremore » HfB 2 which showed a Tafel slope of 0.38 V/decade. In 1 M NaOH the Tafel slopes were in the range of 0.12 - 0.27 V/decade. The composition of Hf xZr 1-xB 2 solid solutions with x = 0.2 - 0.8, influenced the exchange current densities, overpotentials and Tafel slopes of the HER. As a result, the EIS data were fitted with a porous film equivalent circuit model in order to better understand the HER behavior. In addition, modeling calculations, using density functional theory approach, were carried out to estimate the density of states and band structure of the boride solid solutions.« less

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

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

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

2014-05-15

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

Raising the Bar: Increased Hydraulic Pressure Allows Unprecedented High Power Densities in Pressure-Retarded Osmosis

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

Straub, AP; Yip, NY; Elimelech, M

2014-01-01

Pressure-retarded osmosis (PRO) has the potential to generate sustainable energy from salinity gradients. PRO is typically considered for operation with river water and seawater, but a far greater energy of mixing can be harnessed from hypersaline solutions. This study investigates the power density that can be obtained in PRO from such concentrated solutions. Thin-film composite membranes with an embedded woven mesh were supported by tricot fabric feed spacers in a specially designed crossflow cell to maximize the operating pressure of the system, reaching a stable applied hydraulic pressure of 48 bar (700 psi) for more than 10 h. Operation atmore » this increased hydraulic pressure allowed unprecedented power densities, up to 60 W/m(2) with a 3 M (180 g/L) NaCl draw solution. Experimental power densities demonstrate reasonable agreement with power densities modeled using measured membrane properties, indicating high-pressure operation does not drastically alter membrane performance. Our findings exhibit the promise of the generation of power from high-pressure PRO with concentrated solutions.« less

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

NASA Astrophysics Data System (ADS)

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

2002-02-01

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

Size-dependent error of the density functional theory ionization potential in vacuum and solution

DOE PAGES

Sosa Vazquez, Xochitl A.; Isborn, Christine M.

2015-12-22

Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potentialmore » for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. As a result, in vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.« less

Size-dependent error of the density functional theory ionization potential in vacuum and solution

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

Sosa Vazquez, Xochitl A.; Isborn, Christine M., E-mail: cisborn@ucmerced.edu

2015-12-28

Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potentialmore » for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. In vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.« less

Surface tension and density of Si-Ge melts

NASA Astrophysics Data System (ADS)

Ricci, Enrica; Amore, Stefano; Giuranno, Donatella; Novakovic, Rada; Tuissi, Ausonio; Sobczak, Natalia; Nowak, Rafal; Korpala, Bartłomiej; Bruzda, Grzegorz

2014-06-01

In this work, the surface tension and density of Si-Ge liquid alloys were determined by the pendant drop method. Over the range of measurements, both properties show a linear temperature dependence and a nonlinear concentration dependence. Indeed, the density decreases with increasing silicon content exhibiting positive deviation from ideality, while the surface tension increases and deviates negatively with respect to the ideal solution model. Taking into account the Si-Ge phase diagram, a simple lens type, the surface tension behavior of the Si-Ge liquid alloys was analyzed in the framework of the Quasi-Chemical Approximation for the Regular Solutions model. The new experimental results were compared with a few data available in the literature, obtained by the containerless method.

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

NASA Astrophysics Data System (ADS)

Vedernikov, A.; Balapanov, D.

2016-11-01

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

Analytic model to estimate thermonuclear neutron yield in z-pinches using the magnetic Noh problem

NASA Astrophysics Data System (ADS)

Allen, Robert C.

The objective was to build a model which could be used to estimate neutron yield in pulsed z-pinch experiments, benchmark future z-pinch simulation tools and to assist scaling for breakeven systems. To accomplish this, a recent solution to the magnetic Noh problem was utilized which incorporates a self-similar solution with cylindrical symmetry and azimuthal magnetic field (Velikovich, 2012). The self-similar solution provides the conditions needed to calculate the time dependent implosion dynamics from which batch burn is assumed and used to calculate neutron yield. The solution to the model is presented. The ion densities and time scales fix the initial mass and implosion velocity, providing estimates of the experimental results given specific initial conditions. Agreement is shown with experimental data (Coverdale, 2007). A parameter sweep was done to find the neutron yield, implosion velocity and gain for a range of densities and time scales for DD reactions and a curve fit was done to predict the scaling as a function of preshock conditions.

Models for Experimental High Density Housing

NASA Astrophysics Data System (ADS)

Bradecki, Tomasz; Swoboda, Julia; Nowak, Katarzyna; Dziechciarz, Klaudia

2017-10-01

The article presents the effects of research on models of high density housing. The authors present urban projects for experimental high density housing estates. The design was based on research performed on 38 examples of similar housing in Poland that have been built after 2003. Some of the case studies show extreme density and that inspired the researchers to test individual virtual solutions that would answer the question: How far can we push the limits? The experimental housing projects show strengths and weaknesses of design driven only by such indexes as FAR (floor attenuation ratio - housing density) and DPH (dwellings per hectare). Although such projects are implemented, the authors believe that there are reasons for limits since high index values may be in contradiction to the optimum character of housing environment. Virtual models on virtual plots presented by the authors were oriented toward maximising the DPH index and DAI (dwellings area index) which is very often the main driver for developers. The authors also raise the question of sustainability of such solutions. The research was carried out in the URBAN model research group (Gliwice, Poland) that consists of academic researchers and architecture students. The models reflect architectural and urban regulations that are valid in Poland. Conclusions might be helpful for urban planners, urban designers, developers, architects and architecture students.

Congested Aggregation via Newtonian Interaction

NASA Astrophysics Data System (ADS)

Craig, Katy; Kim, Inwon; Yao, Yao

2018-01-01

We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on repulsive-attractive nonlocal interaction models, where the repulsive effects instead arise from an interaction kernel or the addition of diffusion. We formulate our model as the Wasserstein gradient flow of an interaction energy, with a penalization to enforce the constraint on the height of the density. From this perspective, the problem can be seen as a singular limit of the Keller-Segel equation with degenerate diffusion. Two key properties distinguish our problem from previous work on height constrained equations: nonconvexity of the interaction kernel (which places the model outside the scope of classical gradient flow theory) and nonlocal dependence of the velocity field on the density (which causes the problem to lack a comparison principle). To overcome these obstacles, we combine recent results on gradient flows of nonconvex energies with viscosity solution theory. We characterize the dynamics of patch solutions in terms of a Hele-Shaw type free boundary problem and, using this characterization, show that in two dimensions patch solutions converge to a characteristic function of a disk in the long-time limit, with an explicit rate on the decay of the energy. We believe that a key contribution of the present work is our blended approach, combining energy methods with viscosity solution theory.

C-field cosmological models: revisited

NASA Astrophysics Data System (ADS)

Yadav, Anil Kumar; Tawfiq Ali, Ahmad; Ray, Saibal; Rahaman, Farook; Hossain Sardar, Iftikar

2016-12-01

We investigate plane symmetric spacetime filled with perfect fluid in the C-field cosmology of Hoyle and Narlikar. A new class of exact solutions has been obtained by considering the creation field C as a function of time only. To get the deterministic solution, it has been assumed that the rate of creation of matter-energy density is proportional to the strength of the existing C-field energy density. Several physical aspects and geometrical properties of the models are discussed in detail, especially showing that some of our solutions of C-field cosmology are free from singularity in contrast to the Big Bang cosmology. A comparative study has been carried out between two models, one singular and the other nonsingular, by contrasting the behaviour of the physical parameters. We note that the model in a unique way represents both the features of the accelerating as well as decelerating universe depending on the parameters and thus seems to provide glimpses of the oscillating or cyclic model of the universe without invoking any other agent or theory in allowing cyclicity.

Probability density function of non-reactive solute concentration in heterogeneous porous formations

Treesearch

Alberto Bellin; Daniele Tonina

2007-01-01

Available models of solute transport in heterogeneous formations lack in providing complete characterization of the predicted concentration. This is a serious drawback especially in risk analysis where confidence intervals and probability of exceeding threshold values are required. Our contribution to fill this gap of knowledge is a probability distribution model for...

A numerical model for density-and-viscosity-dependent flows in two-dimensional variably saturated porous media

NASA Astrophysics Data System (ADS)

Boufadel, Michel C.; Suidan, Makram T.; Venosa, Albert D.

1999-04-01

We present a formulation for water flow and solute transport in two-dimensional variably saturated media that accounts for the effects of the solute on water density and viscosity. The governing equations are cast in a dimensionless form that depends on six dimensionless groups of parameters. These equations are discretized in space using the Galerkin finite element formulation and integrated in time using the backward Euler scheme with mass lumping. The modified Picard method is used to linearize the water flow equation. The resulting numerical model, the MARUN model, is verified by comparison to published numerical results. It is then used to investigate beach hydraulics at seawater concentration (about 30 g l -1) in the context of nutrients delivery for bioremediation of oil spills on beaches. Numerical simulations that we conducted in a rectangular section of a hypothetical beach revealed that buoyancy in the unsaturated zone is significant in soils that are fine textured, with low anisotropy ratio, and/or exhibiting low physical dispersion. In such situations, application of dissolved nutrients to a contaminated beach in a freshwater solution is superior to their application in a seawater solution. Concentration-engendered viscosity effects were negligible with respect to concentration-engendered density effects for the cases that we considered.

Effects of ethanol addition on micellar solubilization and plume migration during surfactant enhanced recovery of tetrachloroethene.

PubMed

Taylor, Tammy P; Rathfelder, Klaus M; Pennell, Kurt D; Abriola, Linda M

2004-03-01

Alcohol addition has been suggested for use in combination with surfactant flushing to enhance solubilization kinetics and permit density control of dense non-aqueous phase liquid (DNAPL)-laden surfactant plumes. This study examined the effects of adding ethanol (EtOH) to a 4% Tween 80 (polyoxyethylene (20) sorbitan monooleate) solution used to flush tetrachloroethene (PCE)-contaminated porous media. The influence of EtOH concentration, subsurface layering and scale on flushing solution delivery and PCE recovery was investigated through a combination of experimental and mathematical modeling studies. Results of batch experiments demonstrated that the addition of 2.5%, 5% and 10% (wt.) EtOH incrementally increased the PCE solubilization capacity and viscosity of the surfactant solution, while reducing solution density from 1.002 to 0.986 g/cm3. Effluent concentration data obtained from one-dimensional (1-D) column experiments were used to characterize rate-limited micellar solubilization of residual PCE, which was strongly dependent upon flow velocity and weakly dependent upon EtOH concentration. Two-dimensional (2-D) box studies illustrated that minor differences (0.008 g/cm3) between flushing and resident solution density can strongly influence surfactant front propagation. A two-dimensional multiphase simulator, MISER, was used to model the influence of EtOH composition on the aqueous flow field and PCE mass recovery. The ability of the numerical simulator to predict effluent concentrations and front propagation was demonstrated for both 1-D columns and 2-D boxes flushed with EtOH-amended Tween 80 solutions. Results of this study quantify the potential influence of alcohol addition on surfactant solution properties and solubilization capacity, and demonstrate the importance of considering small density variations in remedial design.

Second harmonic generation study of malachite green adsorption at the interface between air and an electrolyte solution: observing the effect of excess electrical charge density at the interface.

PubMed

Song, Jinsuk; Kim, Mahn Won

2010-03-11

Understanding the differential adsorption of ions at the interface of an electrolyte solution is very important because it is closely related, not only to the fundamental aspects of biological systems, but also to many industrial applications. We have measured the excess interfacial negative charge density at air-electrolyte solution interfaces by using resonant second harmonic generation of oppositely charged probe molecules. The excess charge density increased with the square root of the bulk electrolyte concentration. A new adsorption model that includes the electrostatic interaction between adsorbed molecules is proposed to explain the measured adsorption isotherm, and it is in good agreement with the experimental results.

Fragmentation of protostars dust shells at the Hayashi stage

NASA Astrophysics Data System (ADS)

Abdulmyanov, T. R.

2017-09-01

The aim of this study is to determine the density variations of a protostars dust shells at the Hayashi stage. The simplified model of the density wave perturbations are obtained on the base hydrodynamic equations. According to this model, the fragmentation of dust shells may occur at the stage of slow compression of protostar. Using the solution of the wave equation, the 3-D profiles of the density of the dust shell are defined.

Documentation and verification of VST2D; a model for simulating transient, Variably Saturated, coupled water-heat-solute Transport in heterogeneous, anisotropic 2-Dimensional, ground-water systems with variable fluid density

USGS Publications Warehouse

Friedel, Michael J.

2001-01-01

This report describes a model for simulating transient, Variably Saturated, coupled water-heatsolute Transport in heterogeneous, anisotropic, 2-Dimensional, ground-water systems with variable fluid density (VST2D). VST2D was developed to help understand the effects of natural and anthropogenic factors on quantity and quality of variably saturated ground-water systems. The model solves simultaneously for one or more dependent variables (pressure, temperature, and concentration) at nodes in a horizontal or vertical mesh using a quasi-linearized general minimum residual method. This approach enhances computational speed beyond the speed of a sequential approach. Heterogeneous and anisotropic conditions are implemented locally using individual element property descriptions. This implementation allows local principal directions to differ among elements and from the global solution domain coordinates. Boundary conditions can include time-varying pressure head (or moisture content), heat, and/or concentration; fluxes distributed along domain boundaries and/or at internal node points; and/or convective moisture, heat, and solute fluxes along the domain boundaries; and/or unit hydraulic gradient along domain boundaries. Other model features include temperature and concentration dependent density (liquid and vapor) and viscosity, sorption and/or decay of a solute, and capability to determine moisture content beyond residual to zero. These features are described in the documentation together with development of the governing equations, application of the finite-element formulation (using the Galerkin approach), solution procedure, mass and energy balance considerations, input requirements, and output options. The VST2D model was verified, and results included solutions for problems of water transport under isohaline and isothermal conditions, heat transport under isobaric and isohaline conditions, solute transport under isobaric and isothermal conditions, and coupled water-heat-solute transport. The first three problems considered in model verification were compared to either analytical or numerical solutions, whereas the coupled problem was compared to measured laboratory results for which no known analytic solutions or numerical models are available. The test results indicate the model is accurate and applicable for a wide range of conditions, including when water (liquid and vapor), heat (sensible and latent), and solute are coupled in ground-water systems. The cumulative residual errors for the coupled problem tested was less than 10-8 cubic centimeter per cubic centimeter, 10-5 moles per kilogram, and 102 calories per cubic meter for liquid water content, solute concentration and heat content, respectively. This model should be useful to hydrologists, engineers, and researchers interested in studying coupled processes associated with variably saturated transport in ground-water systems.

Densities and apparent molar volumes of atmospherically important electrolyte solutions. 2. The systems H(+)-HSO4(-)-SO4(2-)-H2O from 0 to 3 mol kg(-1) as a function of temperature and H(+)-NH4(+)-HSO4(-)-SO4)2-)-H2O from 0 to 6 mol kg(-1) at 25 °C using a Pitzer ion interaction model, and NH4HSO4-H2O and (NH4)3H(SO4)2-H2O over the entire concentration range.

PubMed

Clegg, S L; Wexler, A S

2011-04-21

A Pitzer ion interaction model has been applied to the systems H(2)SO(4)-H(2)O (0-3 mol kg(-1), 0-55 °C) and H(2)SO(4)-(NH(4))(2)SO(4)-H(2)O (0-6 mol kg(-1), 25 °C) for the calculation of apparent molar volume and density. The dissociation reaction HSO(4)(-)((aq)) ↔ H(+)((aq)) + SO(4)(2-)((aq)) is treated explicitly. Apparent molar volumes of the SO(4)(2-) ion at infinite dilution were obtained from part 1 of this work, (1) and the value for the bisulfate ion was determined in this study from 0 to 55 °C. In dilute solutions of both systems, the change in the degree of dissociation of the HSO(4)(-) ion with concentration results in much larger variations of the apparent molar volumes of the solutes than for conventional strong (fully dissociated) electrolytes. Densities and apparent molar volumes are tabulated. Apparent molar volumes calculated using the model are combined with other data for the solutes NH(4)HSO(4) and (NH(4))(3)H(SO(4))(2) at 25 °C to obtain apparent molar volumes and densities over the entire concentration range (including solutions supersaturated with respect to the salts).

Electron Density and Two-Channel Neutron Emission Measurements in Steady-State Spherical Inertial-Electrostatically Confined Plasmas, with Review of the 1-D Kinetic Model

NASA Technical Reports Server (NTRS)

Dobson, Chris C.; Hrbud, Ivana

2004-01-01

Electron density measurements have been made in steady-state plasmas in a spherical inertial electrostatic confinement (IEC) discharge using microwave interferometry. Plasma cores interior to two cathodes, having diameters of 15 and 23 cm, respectively, were probed over a transverse range of 10 cm with a spatial resolution of about 1.4 cm for buffer gas pressures from 0.2 to 6 Pa in argon and deuterium. The transverse profiles are generally flat, in some cases with eccentric symmetric minima, and give mean densities of from approx. = 0.4 to 7x 10(exp 10)/cu cm, the density generally increasing with the neutral gas pressure. Numerical solutions of the 1-D Poisson equation for EC plasmas are reviewed and energy distribution functions are identified which give flat transverse profiles. These functions are used with the plasma approximation to obtain solutions which also give densities consistent with the measurements, and a double potential well solution is obtained which has minima qualitatively similar to those observed. Explicit consideration is given to the compatibility of the solutions interior and exterior to the cathode, and to grid transparency. Deuterium fusion neutron emission rates were also measured and found to be isotropic, to within the measurement error, over two simultaneous directions. Anisotropy was observed in residual emissions during operation with non-fusing hydrogen-1. The deuterium rates are consistent with predictions from the model.

The Hubbard Dimer: A Complete DFT Solution to a Many-Body Problem

NASA Astrophysics Data System (ADS)

Smith, Justin; Carrascal, Diego; Ferrer, Jaime; Burke, Kieron

2015-03-01

In this work we explain the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site asymmetric Hubbard model. We discuss the connection between the lattice and real-space and how this is a simple model for stretched H2. We can solve this elementary example analytically, and with that we can illuminate the underlying logic and aims of DFT. While the many-body solution is analytic, the density functional is given only implicitly. We overcome this difficulty by creating a highly accurate parameterization of the exact function. We use this parameterization to perform benchmark calculations of correlation kinetic energy, the adiabatic connection, etc. We also test Hartree-Fock and the Bethe Ansatz Local Density Approximation. We also discuss and illustrate the derivative discontinuity in the exchange-correlation energy and the infamous gap problem in DFT. DGE-1321846, DE-FG02-08ER46496.

Riemannian geometry of thermodynamics and systems with repulsive power-law interactions.

PubMed

Ruppeiner, George

2005-07-01

A Riemannian geometric theory of thermodynamics based on the postulate that the curvature scalar R is proportional to the inverse free energy density is used to investigate three-dimensional fluid systems of identical classical point particles interacting with each other via a power-law potential energy gamma r(-alpha) . Such systems are useful in modeling melting transitions. The limit alpha-->infinity corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (alpha>3) and repulsive (gamma>0) interactions. The geometric theory solutions for given alpha>3 , gamma>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b (rho T(-3/alpha) ) , where rho is the density; (2) all solutions are equivalent up to a single scaling constant for rho T(-3/alpha) , related to gamma via the virial theorem; (3) at low density, solutions correspond to the ideal gas; (4) at high density there are solutions with pressure and energy depending on density as expected from solid state physics, though not with a Dulong-Petit heat capacity limit; (5) for 33.7913 a phase transition is required to go between these regimes; (7) for any alpha>3 we may include a first-order phase transition, which is expected from computer simulations; and (8) if alpha-->infinity, the density approaches a finite value as the pressure increases to infinity, with the pressure diverging logarithmically in the density difference.

Benchmarking variable-density flow in saturated and unsaturated porous media

NASA Astrophysics Data System (ADS)

Guevara Morel, Carlos Roberto; Cremer, Clemens; Graf, Thomas

2015-04-01

In natural environments, fluid density and viscosity can be affected by spatial and temporal variations of solute concentration and/or temperature. These variations can occur, for example, due to salt water intrusion in coastal aquifers, leachate infiltration from waste disposal sites and upconing of saline water from deep aquifers. As a consequence, potentially unstable situations may exist in which a dense fluid overlies a less dense fluid. This situation can produce instabilities that manifest as dense plume fingers that move vertically downwards counterbalanced by vertical upwards flow of the less dense fluid. Resulting free convection increases solute transport rates over large distances and times relative to constant-density flow. Therefore, the understanding of free convection is relevant for the protection of freshwater aquifer systems. The results from a laboratory experiment of saturated and unsaturated variable-density flow and solute transport (Simmons et al., Transp. Porous Medium, 2002) are used as the physical basis to define a mathematical benchmark. The HydroGeoSphere code coupled with PEST are used to estimate the optimal parameter set capable of reproducing the physical model. A grid convergency analysis (in space and time) is also undertaken in order to obtain the adequate spatial and temporal discretizations. The new mathematical benchmark is useful for model comparison and testing of variable-density variably saturated flow in porous media.

Extended analytical solutions for effective elastic moduli of cracked porous media

NASA Astrophysics Data System (ADS)

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

2017-05-01

Extended solutions are derived, on the basis of the micromechanical methods, for the effective elastic moduli of porous media containing stiff pores and both open and closed cracks. Analytical formulas of the overall bulk and shear moduli are obtained as functions of the elastic moduli of the solid skeleton, porosity and the densities of open and closed cracks families. We show that the obtained results are extensions of the classical widely used Walsh's (JGR, 1965) and Budiansky-O‧Connell's (JGR, 1974) solutions. Parametric sensitivity analysis clarifies the impact of the model parameters on the effective elastic properties. An inverse analysis, using sonic and density data, is considered to quantify the density of both open and closed cracks. It is observed that the density of closed cracks depends strongly on stress condition while the dependence of open cracks on the confining stress is negligible.

Kinetic Theory and Fast Wind Observations of the Electron Strahl

NASA Astrophysics Data System (ADS)

Horaites, Konstantinos; Boldyrev, Stanislav; Wilson, Lynn B., III; Viñas, Adolfo F.; Merka, Jan

2018-02-01

We develop a model for the strahl population in the solar wind - a narrow, low-density and high-energy electron beam centred on the magnetic field direction. Our model is based on the solution of the electron drift-kinetic equation at heliospheric distances where the plasma density, temperature and the magnetic field strength decline as power laws of the distance along a magnetic flux tube. Our solution for the strahl depends on a number of parameters that, in the absence of the analytic solution for the full electron velocity distribution function (eVDF), cannot be derived from the theory. We however demonstrate that these parameters can be efficiently found from matching our solution with observations of the eVDF made by the Wind satellite's SWE strahl detector. The model is successful at predicting the angular width (FWHM) of the strahl for the Wind data at 1 au, in particular by predicting how this width scales with particle energy and background density. We find that the strahl distribution is largely determined by the local temperature Knudsen number γ ∼ |T dT/dx|/n, which parametrizes solar wind collisionality. We compute averaged strahl distributions for typical Knudsen numbers observed in the solar wind, and fit our model to these data. The model can be matched quite closely to the eVDFs at 1 au; however, it then overestimates the strahl amplitude at larger heliocentric distances. This indicates that our model may be improved through the inclusion of additional physics, possibly through the introduction of 'anomalous diffusion' of the strahl electrons.

An empirical model to estimate density of sodium hydroxide solution: An activator of geopolymer concretes

NASA Astrophysics Data System (ADS)

Rajamane, N. P.; Nataraja, M. C.; Jeyalakshmi, R.; Nithiyanantham, S.

2016-02-01

Geopolymer concrete is zero-Portland cement concrete containing alumino-silicate based inorganic polymer as binder. The polymer is obtained by chemical activation of alumina and silica bearing materials, blast furnace slag by highly alkaline solutions such as hydroxide and silicates of alkali metals. Sodium hydroxide solutions of different concentrations are commonly used in making GPC mixes. Often, it is seen that sodium hydroxide solution of very high concentration is diluted with water to obtain SHS of desired concentration. While doing so it was observed that the solute particles of NaOH in SHS tend to occupy lower volumes as the degree of dilution increases. This aspect is discussed in this paper. The observed phenomenon needs to be understood while formulating the GPC mixes since this influences considerably the relationship between concentration and density of SHS. This paper suggests an empirical formula to relate density of SHS directly to concentration expressed by w/w.

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

A structured population model with diffusion in structure space.

PubMed

Pugliese, Andrea; Milner, Fabio

2018-05-09

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

The Surface Density Distribution in the Solar Nebula

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

2004-01-01

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

Modeling Solar Zenith Angle Effects on the Polar Wind

NASA Technical Reports Server (NTRS)

Glocer, A; Kitamura, N.; Toth, G; Gombosi, T.

2012-01-01

We use the Polar Wind Outflow Model (PWOM) to study the geomagnetically quiet conditions in the polar cap during solar maximum. The PWOM solves the gyrotropic transport equations for O+, H+, and He+ along several magnetic field lines in the polar region in order to reconstruct the full 3D solution. We directly compare our simulation results to the data based empirical model of Kitamura et al. (2011) of electron density which is based on 63 months of Akebono satellite observations. The modeled ion and electron temperatures are also compared with a statistical compilation of quiet time data obtained by the EISCAT Svalbard Radar (ESR) and Intercosmos Satellites. The data and model agree reasonably well, albeit with some differences. This study shows that photoelectrons play an important role in explaining the differences between sunlit and dark results of electron density, ion composition, as well as ion and electron temperatures of the quiet time polar wind solution. Moreover, these results provide an initial validation of the PWOM s ability to model the quiet time "background" solution.

Comparison of Methods for Predicting the Compositional Dependence of the Density and Refractive Index of Organic-Aqueous Aerosols.

PubMed

Cai, Chen; Miles, Rachael E H; Cotterell, Michael I; Marsh, Aleksandra; Rovelli, Grazia; Rickards, Andrew M J; Zhang, Yun-Hong; Reid, Jonathan P

2016-08-25

Representing the physicochemical properties of aerosol particles of complex composition is of crucial importance for understanding and predicting aerosol thermodynamic, kinetic, and optical properties and processes and for interpreting and comparing analysis methods. Here, we consider the representations of the density and refractive index of aqueous-organic aerosol with a particular focus on the dependence of these properties on relative humidity and water content, including an examination of the properties of solution aerosol droplets existing at supersaturated solute concentrations. Using bulk phase measurements of density and refractive index for typical organic aerosol components, we provide robust approaches for the estimation of these properties for aerosol at any intermediate composition between pure water and pure solute. Approximately 70 compounds are considered, including mono-, di- and tricarboxylic acids, alcohols, diols, nitriles, sulfoxides, amides, ethers, sugars, amino acids, aminium sulfates, and polyols. We conclude that the molar refraction mixing rule should be used to predict the refractive index of the solution using a density treatment that assumes ideal mixing or, preferably, a polynomial dependence on the square root of the mass fraction of solute, depending on the solubility limit of the organic component. Although the uncertainties in the density and refractive index predictions depend on the range of subsaturated compositional data available for each compound, typical errors for estimating the solution density and refractive index are less than ±0.1% and ±0.05%, respectively. Owing to the direct connection between molar refraction and the molecular polarizability, along with the availability of group contribution models for predicting molecular polarizability for organic species, our rigorous testing of the molar refraction mixing rule provides a route to predicting refractive indices for aqueous solutions containing organic molecules of arbitrary structure.

Effect of solute elements in Ni alloys on blistering under He + and D + ion irradiation

NASA Astrophysics Data System (ADS)

Wakai, E.; Ezawa, T.; Takenaka, T.; Imamura, J.; Tanabe, T.; Oshima, R.

2007-08-01

Effects of solute atoms on microstructural evolution and blister formation have been investigated using Ni alloys under 25 keV He + and 20 keV D + irradiation at 500 °C to a dose of about 4 × 10 21 ions/m 2. The specimens used were pure Ni, Ni-Si, Ni-Co, Ni-Cu, Ni-Mn and Ni-Pd alloys. The volume size factors of solute elements for the Ni alloys range from -5.8% to +63.6%. The formations of blisters were observed in the helium-irradiated specimens, but not in the deuteron-irradiated specimens. The areal number densities of blisters increased with volume size difference of solute atoms. The dependence of volume size on the areal number densities of blisters was very similar to that of the number densities of bubbles on solute atoms. The size of the blisters inversely decreased with increasing size of solute atoms. The formation of blisters was intimately related to the bubble growth, and the gas pressure model for the formation of blisters was supported by this study.

Incorporation of Hydrogen Bond Angle Dependency into the Generalized Solvation Free Energy Density Model.

PubMed

Ma, Songling; Hwang, Sungbo; Lee, Sehan; Acree, William E; No, Kyoung Tai

2018-04-23

To describe the physically realistic solvation free energy surface of a molecule in a solvent, a generalized version of the solvation free energy density (G-SFED) calculation method has been developed. In the G-SFED model, the contribution from the hydrogen bond (HB) between a solute and a solvent to the solvation free energy was calculated as the product of the acidity of the donor and the basicity of the acceptor of an HB pair. The acidity and basicity parameters of a solute were derived using the summation of acidities and basicities of the respective acidic and basic functional groups of the solute, and that of the solvent was experimentally determined. Although the contribution of HBs to the solvation free energy could be evenly distributed to grid points on the surface of a molecule, the G-SFED model was still inadequate to describe the angle dependency of the HB of a solute with a polarizable continuum solvent. To overcome this shortcoming of the G-SFED model, the contribution of HBs was formulated using the geometric parameters of the grid points described in the HB coordinate system of the solute. We propose an HB angle dependency incorporated into the G-SFED model, i.e., the G-SFED-HB model, where the angular-dependent acidity and basicity densities are defined and parametrized with experimental data. The G-SFED-HB model was then applied to calculate the solvation free energies of organic molecules in water, various alcohols and ethers, and the log P values of diverse organic molecules, including peptides and a protein. Both the G-SFED model and the G-SFED-HB model reproduced the experimental solvation free energies with similar accuracy, whereas the distributions of the SFED on the molecular surface calculated by the G-SFED and G-SFED-HB models were quite different, especially for molecules having HB donors or acceptors. Since the angle dependency of HBs was included in the G-SFED-HB model, the SFED distribution of the G-SFED-HB model is well described as compared to that of the G-SFED model.

Kinetic Theory and Fast Wind Observations of the Electron Strahl

NASA Astrophysics Data System (ADS)

Horaites, K.; Boldyrev, S.; Wilson, L. B., III; Figueroa-Vinas, A.; Merka, J.

2017-12-01

We develop a model for the strahl population in the solar wind - a narrow, low-density and high-energy electron beam centered on the magnetic field direction. Our model is based on the solution of the electron drift-kinetic equation at heliospheric distances where the plasma density, temperature, and the strength of the magnetic field decline as power-laws of the distance along a magnetic flux tube. Our solution for the strahl depends on a number of parameters that, in the absence of the analytic solution for the full electron velocity distribution function (eVDF), cannot be derived from the theory. We however demonstrate that these parameters can be efficiently found from matching our solution with the observations. To this end, we compare our model with the eVDF measured by the Wind satellite's SWE strahl detector. The model is successful at predicting the angular width (FWHM) of the strahl for the Wind data at 1 AU, in particular by predicting how this width scales with particle energy and background density. We find the shape of the strahl distribution is largely determined by the local temperature Knudsen number γ |T dT/dx|/n, which parametrizes solar wind collisionality. We compute averaged strahl distributions for typical Knudsen numbers observed in the solar wind, and fit our model to these data. The model can be matched quite closely to the eVDFs at 1 AU; however, it then overestimates the strahl amplitude compared to the amplitude of the electron core at larger heliocentric distances. This indicates that our model may need to be improved through the inclusion of additional physics, possibly through the introduction of "anomalous diffusion" of the strahl electrons.

Thermospheric density variations: Observability using precision satellite orbits and effects on orbit propagation

NASA Astrophysics Data System (ADS)

Lechtenberg, Travis; McLaughlin, Craig A.; Locke, Travis; Krishna, Dhaval Mysore

2013-01-01

paper examines atmospheric density estimated using precision orbit ephemerides (POE) from the CHAMP and GRACE satellites during short periods of greater atmospheric density variability. The results of the calibration of CHAMP densities derived using POEs with those derived using accelerometers are examined for three different types of density perturbations, [traveling atmospheric disturbances (TADs), geomagnetic cusp phenomena, and midnight density maxima] in order to determine the temporal resolution of POE solutions. In addition, the densities are compared to High-Accuracy Satellite Drag Model (HASDM) densities to compare temporal resolution for both types of corrections. The resolution for these models of thermospheric density was found to be inadequate to sufficiently characterize the short-term density variations examined here. Also examined in this paper is the effect of differing density estimation schemes by propagating an initial orbit state forward in time and examining induced errors. The propagated POE-derived densities incurred errors of a smaller magnitude than the empirical models and errors on the same scale or better than those incurred using the HASDM model.

Flattened halos in a nontopological soliton model of dark matter

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

Mielke, Eckehard W.; Peralta, Humberto H.

2004-12-15

Soliton type solutions of a scalar model with a {phi}{sup 6} self-interaction are analyzed for their density profiles as toy model of dark matter halos. We construct exact solutions with nontrivial ellipticity due to angular momentum and propose a 'nonlinear superposition' of round and flattened halos in order to improve the scaling relations and the correspondence of the predicted rotation curves to the empirical Burkert fit.

Penetrable square-well fluids: exact results in one dimension.

PubMed

Santos, Andrés; Fantoni, Riccardo; Giacometti, Achille

2008-05-01

We introduce a model of attractive penetrable spheres by adding a short-range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact impenetrable counterpart as a starting point. The model is expected to describe star polymers in regimes of good and moderate solvent under dilute conditions. We derive the exact coefficients of a low-density expansion up to second order for the radial distribution function and up to fourth order in the virial expansion. These exact results are used as a benchmark to test the reliability of approximate theories (Percus-Yevick and hypernetted chain). Notwithstanding the lack of an exact solution for arbitrary densities, our results are expected to be rather precise within a wide range of temperatures and densities. A detailed analysis of some limiting cases is carried out. In particular, we provide a complete solution of the sticky penetrable-sphere model in one dimension up to the same order in density. The issue of Ruelle's thermodynamics stability is analyzed and the region of a well-defined thermodynamic limit is identified.

Attacking a Dense Problem: A Learner-Centered Approach to Teaching Density

ERIC Educational Resources Information Center

Hitt, Austin M.

2005-01-01

Density is a difficult concept for students to learn because it is abstract and because it is derived from the concepts of mass and volume. The solution is to address density at each of the three levels of scientific understanding: macroscopic, particle/modeling, and symbolic. This article demonstrates how to help students gain a conceptual…

Numerical modeling of the elution peak profiles of retained solutes in supercritical fluid chromatography

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

Kaczmarski, Krzysztof; Guiochon, Georges A

2011-01-01

In supercritical fluid chromatography (SFC), the significant expansion of the mobile phase along the column causes the formation of axial and radial gradients of temperature. Due to these gradients, the mobile phase density, its viscosity, its velocity, its diffusion coefficients, etc. are not constant throughout the column. This results in a nonuniform flow velocity distribution, itself causing a loss of column efficiency in certain cases, even at low flow rates, as they do in HPLC. At high flow rates, an important deformation of the elution profiles of the sample components may occur. The model previously used to account satisfactorily formore » the retention of an unsorbed solute in SFC is applied to the modeling of the elution peak profiles of retained compounds. The numerical solution of the combined heat and mass balance equations provides the temperature and the pressure profiles inside the column and values of the retention time and the band profiles of retained compounds that are in excellent agreement with independent experimental data for large value of mobile phase reduced density. At low reduced densities, the band profiles can strongly depend on the column axial distribution of porosity.« less

Collisionless Electrostatic Shock Modeling and Simulation

DTIC Science & Technology

2016-10-21

unlimited. PA#16490 Dissipation Controls Wave Train Under- and Over-damped Shocks – Under-damped: • Dissipation is weak, ripples persist. • High...Density Position – Over-damped: ● Strong dissipation damps ripples . ● Low Density Position 12 Position Distribution A. Approved for public release...distribution unlimited. PA#16490 Model Verification Comparison with Linearized Solution – Evolution of the First Ripple Wavelength: • Simulated

Methods for Combination of GRACE Gravimetry and ICESat Altimetry over Antarctica on Monthly Timescales

NASA Astrophysics Data System (ADS)

Hardy, R. A.; Nerem, R. S.; Wiese, D. N.

2017-12-01

Gravity and surface elevation change data altimetry provide different perspectives on mass variability in Antarctica. In anticipation of the concurrent operation of the successors of GRACE and ICESat, GRACE Follow-On and ICESat-2, we approach the problem of combining these data for enhanced spatial resolution and disaggregation of Antarctica's major mass transport processes. Using elevation changes gathered from over 500 million overlapping ICESat laser shot pairs between 2003 and 2009, we construct gridded models of Antarctic elevation change for each ICESat operational period. Comparing these elevation grids with temporally registered JPL RL05M mascon solutions, we exploit the relationship between surface mass flux and elevation change to inform estimates of effective surface density. These density estimates enable solutions for glacial isostatic adjustment and monthly estimates of surface mass change. These are used alongside spatial statistics from both the data and models of surface mass balance to produce enhanced estimates of Antarctic mass balance. We validate our solutions by modeling the effects of elastic loading and GIA from these solutions on the vertical motion of Antarctica's GNSS sites.

Nonrelativistic grey S n -transport radiative-shock solutions

DOE PAGES

Ferguson, J. M.; Morel, J. E.; Lowrie, R. B.

2017-06-01

We present semi-analytic radiative-shock solutions in which grey Sn-transport is used to model the radiation, and we include both constant cross sections and cross sections that depend on temperature and density. These new solutions solve for a variable Eddington factor (VEF) across the shock domain, which allows for interesting physics not seen before in radiative-shock solutions. Comparisons are made with the grey nonequilibrium-diffusion radiative-shock solutions of Lowrie and Edwards [1], which assumed that the Eddington factor is constant across the shock domain. It is our experience that the local Mach number is monotonic when producing nonequilibrium-diffusion solutions, but that thismore » monotonicity may disappear while integrating the precursor region to produce Sn-transport solutions. For temperature- and density-dependent cross sections we show evidence of a spike in the VEF in the far upstream portion of the radiative-shock precursor. We show evidence of an adaptation zone in the precursor region, adjacent to the embedded hydrodynamic shock, as conjectured by Drake [2, 3], and also confirm his expectation that the precursor temperatures adjacent to the Zel’dovich spike take values that are greater than the downstream post-shock equilibrium temperature. We also show evidence that the radiation energy density can be nonmonotonic under the Zel’dovich spike, which is indicative of anti-diffusive radiation flow as predicted by McClarren and Drake [4]. We compare the angle dependence of the radiation flow for the Sn-transport and nonequilibriumdiffusion radiation solutions, and show that there are considerable differences in the radiation flow between these models across the shock structure. Lastly, we analyze the radiation flow to understand the cause of the adaptation zone, as well as the structure of the Sn-transport radiation-intensity solutions across the shock structure.« less

Nonrelativistic grey S n -transport radiative-shock solutions

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

Ferguson, J. M.; Morel, J. E.; Lowrie, R. B.

We present semi-analytic radiative-shock solutions in which grey Sn-transport is used to model the radiation, and we include both constant cross sections and cross sections that depend on temperature and density. These new solutions solve for a variable Eddington factor (VEF) across the shock domain, which allows for interesting physics not seen before in radiative-shock solutions. Comparisons are made with the grey nonequilibrium-diffusion radiative-shock solutions of Lowrie and Edwards [1], which assumed that the Eddington factor is constant across the shock domain. It is our experience that the local Mach number is monotonic when producing nonequilibrium-diffusion solutions, but that thismore » monotonicity may disappear while integrating the precursor region to produce Sn-transport solutions. For temperature- and density-dependent cross sections we show evidence of a spike in the VEF in the far upstream portion of the radiative-shock precursor. We show evidence of an adaptation zone in the precursor region, adjacent to the embedded hydrodynamic shock, as conjectured by Drake [2, 3], and also confirm his expectation that the precursor temperatures adjacent to the Zel’dovich spike take values that are greater than the downstream post-shock equilibrium temperature. We also show evidence that the radiation energy density can be nonmonotonic under the Zel’dovich spike, which is indicative of anti-diffusive radiation flow as predicted by McClarren and Drake [4]. We compare the angle dependence of the radiation flow for the Sn-transport and nonequilibriumdiffusion radiation solutions, and show that there are considerable differences in the radiation flow between these models across the shock structure. Lastly, we analyze the radiation flow to understand the cause of the adaptation zone, as well as the structure of the Sn-transport radiation-intensity solutions across the shock structure.« less

On N. Park's Analytical solution for steady state density- and mixing regime—dependent solute transport in a vertical soil column

NASA Astrophysics Data System (ADS)

Thiele, Michael

1998-04-01

Recently, Park [1996] presented an analytical solution for stationary one-dimensional solute transport in a variable-density fluid flow through a vertical soil column. He used the widespread Bear-Scheidegger dispersion model describing solute mixing as a sum of molecular diffusion and velocity-proportional mechanical dispersion effects. His closed-form implicit concentration and pressure distributions thus allow for a discussion of the combined impact of molecular diffusion and mechanical dispersion in a variable-density environment. Whereas Park only considered the example of vanishing molecular diffusion in detail, both phenomena are taken into account simultaneously in the present study in order to elucidate their different influences on concentration distribution characteristics. The boundary value problem dealt with herein is based on an upward inflow of high-density fluid of constant solute concentration and corresponding outflow of a lower constant concentration fluid at the upper end of the column when dispersivity does not change along the flow path. The thickness of the transition zone between the two fluids appeared to strongly depend on the prevailing share of the molecular diffusion and mechanical dispersion mechanisms. The latter can be characterized by a molecular Peclet number Pe, which here is defined as the ratio of the column outflow velocity multiplied by a characteristic pore size and the molecular diffusion coefficient. For very small values of Pe, when molecular diffusion represents the exclusive mixing process, density differences have no impact on transition zone thicknesses. A relative density-;dependent thickness increases with flow velocities (increasing Pe values) very rapidly compared to the density-independent case, and after having passed a maximum decreases asymptotically to a constant value for the large Peclet number limit when mechanical dispersion is the only mixing mechanism. Hence the special transport problem analyzed gives further evidence for the importance of simultaneously considering molecular diffusion and mechanical dispersion in gravity-affected solute transport in porous media.

Systematic investigation of non-Boussinesq effects in variable-density groundwater flow simulations.

PubMed

Guevara Morel, Carlos R; van Reeuwijk, Maarten; Graf, Thomas

2015-12-01

The validity of three mathematical models describing variable-density groundwater flow is systematically evaluated: (i) a model which invokes the Oberbeck-Boussinesq approximation (OB approximation), (ii) a model of intermediate complexity (NOB1) and (iii) a model which solves the full set of equations (NOB2). The NOB1 and NOB2 descriptions have been added to the HydroGeoSphere (HGS) model, which originally contained an implementation of the OB description. We define the Boussinesq parameter ερ=βω Δω where βω is the solutal expansivity and Δω is the characteristic difference in solute mass fraction. The Boussinesq parameter ερ is used to systematically investigate three flow scenarios covering a range of free and mixed convection problems: 1) the low Rayleigh number Elder problem (Van Reeuwijk et al., 2009), 2) a convective fingering problem (Xie et al., 2011) and 3) a mixed convective problem (Schincariol et al., 1994). Results indicate that small density differences (ερ≤ 0.05) produce no apparent changes in the total solute mass in the system, plume penetration depth, center of mass and mass flux independent of the mathematical model used. Deviations between OB, NOB1 and NOB2 occur for large density differences (ερ>0.12), where lower description levels will underestimate the vertical plume position and overestimate mass flux. Based on the cases considered here, we suggest the following guidelines for saline convection: the OB approximation is valid for cases with ερ<0.05, and the full NOB set of equations needs to be used for cases with ερ>0.10. Whether NOB effects are important in the intermediate region differ from case to case. Copyright © 2015 Elsevier B.V. All rights reserved.

Uniqueness of a solution of a steady state photochemical problem: Applications to Mars

NASA Technical Reports Server (NTRS)

Krasnopolsky, V. A.

1994-01-01

Based on the conservation of chemical elements in chemical reactions, a rule is proved that the number of boundary conditions given by densities and/or non-zero velocities should not be less than the number of chemical elements in the system, and the components given by densities and velocities should include all elements in the system. Applications of this rule to Mars are considered. It is proved that a problem of CO2-H2O chemistry in the lower and middle atmosphere of Mars, say, in the range of 0-80 km does not have an unique solution, if only CO2 and H2O densities are given at the lower boundary, while all other boundary conditions are fluxes. Two models of this type are discussed. These models fit the same boundary conditions, are balanced with a relative uncertainty of 10(exp -4) for H2, and predict the O2, CO, and H2 mixing ratios which differ by order of magnitude. One more species density, e.g. that of O2, should be specified at the boundary to obtain the unique solution. The situation is better if the upper boundary is extended to the exobase where thermal escape velocities of H and H2 can be specified. However, in this case, either oxygen nonthermal escape rate or the O2 density at the surface should be given as the boundary condition. Two models of Mars' photochemistry, with and without nitrogen chemistry, are considered. The oxygen nonthermal escape rate of 1.2 x 10(exp 8) cm(exp -2) s(exp -1) is given at 240 km and is balanced with the total hydrogen escape rate within uncertainty of 1 percent for both models. Both models fit the measured O2 and CO mixing ratios, the O3 line absorption at 9.6 microns, and the O2 1.27 microns dayglow within the uncertainties of the measured values; although, the model without nitrogen chemistry fits better.

Fracture analysis of a transversely isotropic high temperature superconductor strip based on real fundamental solutions

NASA Astrophysics Data System (ADS)

Gao, Zhiwen; Zhou, Youhe

2015-04-01

Real fundamental solution for fracture problem of transversely isotropic high temperature superconductor (HTS) strip is obtained. The superconductor E-J constitutive law is characterized by the Bean model where the critical current density is independent of the flux density. Fracture analysis is performed by the methods of singular integral equations which are solved numerically by Gauss-Lobatto-Chybeshev (GSL) collocation method. To guarantee a satisfactory accuracy, the convergence behavior of the kernel function is investigated. Numerical results of fracture parameters are obtained and the effects of the geometric characteristics, applied magnetic field and critical current density on the stress intensity factors (SIF) are discussed.

A family of well behaved charge analogues of Durgapal's perfect fluid exact solution in general relativity

NASA Astrophysics Data System (ADS)

Murad, Mohammad Hassan; Fatema, Saba

2013-02-01

This paper presents a new family of interior solutions of Einstein-Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of charge distribution. This solution gives us wide range of parameter, K, for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a star is maximized with all degree of suitability by assuming the surface density equal to normal nuclear density, ρ nm=2.5×1017 kg m-3. By this model we obtain the mass of the Crab pulsar, M Crab, 1.36 M ⊙ and radius 13.21 km, constraining the moment of inertia > 1.61×1038 kg m2 for the conservative estimate of Crab nebula mass 2 M ⊙. And M Crab=1.96 M ⊙ with radius R Crab=14.38 km constraining the moment of inertia > 3.04×1038 kg m2 for the newest estimate of Crab nebula mass, 4.6 M ⊙. These results are quite well in agreement with the possible values of mass and radius of Crab pulsar. Besides this, our model yields moments of inertia for PSR J0737-3039A and PSR J0737-3039B, I A =1.4285×1038 kg m2 and I B =1.3647×1038 kg m2 respectively. It has been observed that under well behaved conditions this class of solutions gives us the overall maximum gravitational mass of super dense object, M G(max)=4.7487 M ⊙ with radius R_{M_{max}}=15.24 km, surface redshift 0.9878, charge 7.47×1020 C, and central density 4.31 ρ nm.

Effect of Environmental Density and Buoyancy on Growth and Gravitropic Response in Maize Roots

NASA Astrophysics Data System (ADS)

Robbins, J. L.; Mulkey, T. J.

2008-06-01

The mechanism by which plants sense gravity is not fully understood. The hydrostatic model was proposed as an alternative to the statolith model. These experiments are designed to provide further understanding about the underlying mechanism of the gravitropic sensing. Primary roots of maize with a length of about 1 cm were used. The roots were placed in environments of various density and buoyancy using air, water, sucrose, sucrose/polyethylene glycol 4000 (PEG), PEG 8000, and Ficoll PM 400. The rates of growth and gravitropic curvature were monitored using time-lapse video and digital recordings. Comparison of roots in air to roots in oxygenated water indicate that there is no significant difference in growth rates but the higher density of water and the other test solutions significantly slows the gravitropic response. Altering the environmental density and buoyancy of the solution surrounding the root does not appear to alter sedimentation of statoliths within the root tip.

Gravitational Collapse of Spherical Interstellar Clouds

NASA Astrophysics Data System (ADS)

Ogino, Shinya; Tomisaka, Kohji; Nakamura, Fumitaka

1999-10-01

In this paper, the gravitational collapse of spherical interstellar clouds is discussed based on hydro\\-dynamical simulations. The evolution is divided into two phases: former runaway collapse phase, in which the central density increases greatly on a finite time scale, and later contraction, associated with accretion onto a newborn star. The initial density distribution is expressed using a ratio of the gravitational force to the pressure force alpha . The equation of state for a polytropic gas is used. The central, high-density part of the solution converges on a self-similar solution, which was first derived for the runaway collapse by Larson and Penston (LP). In the later accretion phase, gas behaves like a particle, and the infall speed is accelerated by the gravity of the central object. The solution at this stage is qualitatively similar to the inside-out similarity solutions first found by Shu. However, it is shown that the gas-inflow (accretion) rate is time-dependent, in contrast to the constant rate of the inside-out similarity solutions. For isothermal models in which the pressure is important, 1 <~ alpha <~ 3.35, the accretion rate reaches its maximum when the central part, which obeys the LP solution, contracts and accretes. On the other hand, in isothermal models in which gravity is dominant, alpha >~ 3.35, the accretion becomes most active at the epoch when the outer part of the cloud falls onto the center. The effect of the non-isothermal equation of state is discussed.

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

Cao, Siqin; Department of Chemistry, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon; Sheong, Fu Kit

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

Atmospheric density models comparison and impact on orbit solutions of GRACE-1, Sentinel-1A, TerraSAR-X

NASA Astrophysics Data System (ADS)

Colace, Marco; Hackel, Stefan; Kirschner, Michael; Kahle, Ralph; Circi, Christian

2017-04-01

Satellites in Low Earth Orbit (LEO) are notably affected by the presence of the atmosphere, a predominant source of perturbations of the Keplerian motion at the altitudes of interest. For spacecraft of this class the main source of error in propagated trajectories is due to the mismodeling of the neutral density in the thermosphere and the associated drag force, which steadily decelerates orbital motion with both secular and periodic effects. Thermospheric density varies significantly with space and time because of complex interactions between solar activity and the Earth's atmosphere and magnetic field. Properly reproducing this variability by means of empirical dynamic models has always represented a difficult task but is of vital importance for orbit determination and propagation. The present study shows the influence of different atmospheric density models, predicted space weather proxies, and their related uncertainties on the orbit solutions of representative satellite missions. The study has been carried out by using a routine-like orbit propagation scenario applied to GRACE-1, Sentinel-1A, and TerraSAR-X, three LEO orbiting spacecraft with operational altitudes well spaced within the 400-700 km range. Archived space weather data predictions and some of the most recent and promising empirical atmospheric models (Naval Research Laboratory's NRLMSISE-00 and Jacchia-Bowman 2008) were used side-by-side with the well-known Jacchia 1971 model in order to assess potential gains in prediction accuracy. To evaluate the influence of solar variability on the atmospheric density models and associated orbit quality, two 2-month test time frames, in high and low solar activity periods, have been selected. The scope of the presentation is a detailed comparison of atmospheric density models and their influence on the estimated orbits of GRACE-1, Sentinel-1A and TerraSAR-X.

Global low-energy weak solution and large-time behavior for the compressible flow of liquid crystals

NASA Astrophysics Data System (ADS)

Wu, Guochun; Tan, Zhong

2018-06-01

In this paper, we consider the weak solution of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in R3. When the initial data are of small energy and initial density is positive and essentially bounded, we prove the existence of a global weak solution in R3. The large-time behavior of a global weak solution is also established.

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.

Ionization of Interstellar Hydrogen

NASA Astrophysics Data System (ADS)

Whang, Y. C.

1996-09-01

Interstellar hydrogen can penetrate through the heliopause, enter the heliosphere, and may become ionized by photoionization and by charge exchange with solar wind protons. A fluid model is introduced to study the flow of interstellar hydrogen in the heliosphere. The flow is governed by moment equations obtained from integration of the Boltzmann equation over the velocity space. Under the assumption that the flow is steady axisymmetric and the pressure is isotropic, we develop a method of solution for this fluid model. This model and the method of solution can be used to study the flow of neutral hydrogen with various forms of ionization rate β and boundary conditions for the flow on the upwind side. We study the solution of a special case in which the ionization rate β is inversely proportional to R2 and the interstellar hydrogen flow is uniform at infinity on the upwind side. We solve the moment equations directly for the normalized density NH/NN∞, bulk velocity VH/VN∞, and temperature TH/TN∞ of interstellar hydrogen as functions of r/λ and z/λ, where λ is the ionization scale length. The solution is compared with the kinetic theory solution of Lallement et al. The fluid solution is much less time-consuming than the kinetic theory solutions. Since the ionization rate for production of pickup protons is directly proportional to the local density of neutral hydrogen, the high-resolution solution of interstellar neutral hydrogen obtained here will be used to study the global distribution of pickup protons.

Electronic Excitations in Solution: The Interplay between State Specific Approaches and a Time-Dependent Density Functional Theory Description.

PubMed

Guido, Ciro A; Jacquemin, Denis; Adamo, Carlo; Mennucci, Benedetta

2015-12-08

We critically analyze the performances of continuum solvation models when coupled to time-dependent density functional theory (TD-DFT) to predict solvent effects on both absorption and emission energies of chromophores in solution. Different polarization schemes of the polarizable continuum model (PCM), such as linear response (LR) and three different state specific (SS) approaches, are considered and compared. We show the necessity of introducing a SS model in cases where large electron density rearrangements are involved in the excitations, such as charge-transfer transitions in both twisted and quadrupolar compounds, and underline the very delicate interplay between the selected polarization method and the chosen exchange-correlation functional. This interplay originates in the different descriptions of the transition and ground/excited state multipolar moments by the different functionals. As a result, the choice of both the DFT functional and the solvent polarization scheme has to be consistent with the nature of the studied electronic excitation.

Addition of simultaneous heat and solute transport and variable fluid viscosity to SEAWAT

USGS Publications Warehouse

Thorne, D.; Langevin, C.D.; Sukop, M.C.

2006-01-01

SEAWAT is a finite-difference computer code designed to simulate coupled variable-density ground water flow and solute transport. This paper describes a new version of SEAWAT that adds the ability to simultaneously model energy and solute transport. This is necessary for simulating the transport of heat and salinity in coastal aquifers for example. This work extends the equation of state for fluid density to vary as a function of temperature and/or solute concentration. The program has also been modified to represent the effects of variable fluid viscosity as a function of temperature and/or concentration. The viscosity mechanism is verified against an analytical solution, and a test of temperature-dependent viscosity is provided. Finally, the classic Henry-Hilleke problem is solved with the new code. ?? 2006 Elsevier Ltd. All rights reserved.

Rapid temporal evolution of radiation from non-thermal electrons in solar flares

NASA Technical Reports Server (NTRS)

Lu, Edward T.; Petrosian, Vahe

1987-01-01

Solutions of the time dependent Fokker-Planck equation was found for accelerated electrons undergoing Coulomb collisions in a magnetized, fully ionized plasma. An exact solution was found for arbitrary pitch angle and energy distribution in a uniform background plasma. Then, for an inhomogeneous plasma, a solution was found for particles with small pitch angles. These solutions were used to calculate the temporal evolution of bremsstrahlung x-rays from short bursts of nonthermal electron beams, and these spectra were compared with observed high time resolution spectra of short timescale solar hard x-ray bursts. It is shown that the observed softening in time of the spectra rules out a homogeneous background and therefore the possibility of electrons being confined to the corona either because of converging magnetic field or high densities. The inhomogeneous solution was also applied to a model with constant coronal density and exponentially rising chromospheric density. The spectra are shown to be consistent with that produced by a collimated beam of electrons accelerated in the corona with certain given conditions. These conditions could be violated if large pitch angle electrons are present.

3-D linear inversion of gravity data: method and application to Basse-Terre volcanic island, Guadeloupe, Lesser Antilles

NASA Astrophysics Data System (ADS)

Barnoud, Anne; Coutant, Olivier; Bouligand, Claire; Gunawan, Hendra; Deroussi, Sébastien

2016-04-01

We use a Bayesian formalism combined with a grid node discretization for the linear inversion of gravimetric data in terms of 3-D density distribution. The forward modelling and the inversion method are derived from seismological inversion techniques in order to facilitate joint inversion or interpretation of density and seismic velocity models. The Bayesian formulation introduces covariance matrices on model parameters to regularize the ill-posed problem and reduce the non-uniqueness of the solution. This formalism favours smooth solutions and allows us to specify a spatial correlation length and to perform inversions at multiple scales. We also extract resolution parameters from the resolution matrix to discuss how well our density models are resolved. This method is applied to the inversion of data from the volcanic island of Basse-Terre in Guadeloupe, Lesser Antilles. A series of synthetic tests are performed to investigate advantages and limitations of the methodology in this context. This study results in the first 3-D density models of the island of Basse-Terre for which we identify: (i) a southward decrease of densities parallel to the migration of volcanic activity within the island, (ii) three dense anomalies beneath Petite Plaine Valley, Beaugendre Valley and the Grande-Découverte-Carmichaël-Soufrière Complex that may reflect the trace of former major volcanic feeding systems, (iii) shallow low-density anomalies in the southern part of Basse-Terre, especially around La Soufrière active volcano, Piton de Bouillante edifice and along the western coast, reflecting the presence of hydrothermal systems and fractured and altered rocks.

Hydrostatic factors affect the gravity responses of algae and roots

NASA Technical Reports Server (NTRS)

Staves, Mark P.; Wayne, Randy; Leopold, A. C.

1991-01-01

The hypothesis of Wayne et al. (1990) that plant cells perceive gravity by sensing a pressure differential between the top and the bottom of the cell was tested by subjecting rice roots and cells of Caracean algae to external solutions of various densities. It was found that increasing the density of the external medium had a profound effect on the polar ratio (PR, the ratio between velocities of the downwardly and upwardly streaming cytoplasm) of the Caracean algae cells. When these cells were placed in solutions of denser compound, the PR decreased to less than 1, as the density of the external medium became higher than that of the cell; thus, the normal gravity-induced polarity was reversed, indicating that the osmotic pressure of the medium affects the cell's ability to respond to gravity. In rice roots, an increase of the density of the solution inhibited the rate of gravitropism. These results agree with predictions of a hydrostatic model for graviperception.

Using Micromechanical Resonators to Measure Rheological Properties and Alcohol Content of Model Solutions and Commercial Beverages

PubMed Central

Paxman, Rosemary; Stinson, Jake; Dejardin, Anna; McKendry, Rachel A.; Hoogenboom, Bart W.

2012-01-01

Micromechanic resonators provide a small-volume and potentially high-throughput method to determine rheological properties of fluids. Here we explore the accuracy in measuring mass density and viscosity of ethanol-water and glycerol-water model solutions, using a simple and easily implemented model to deduce the hydrodynamic effects on resonating cantilevers of various length-to-width aspect ratios. We next show that these measurements can be extended to determine the alcohol percentage of both model solutions and commercial beverages such as beer, wine and liquor. This demonstrates how micromechanical resonators can be used for quality control of every-day drinks. PMID:22778654

Density of ocular components of the bovine eye.

PubMed

Su, Xiao; Vesco, Christina; Fleming, Jacquelyn; Choh, Vivian

2009-10-01

Density is essential for acoustic characterization of tissues and provides a basic input for ultrasound backscatter and absorption models. Despite the existence of extensive compilations of acoustic properties, neither unified data on ocular density nor comparisons of the densities between all ocular components can be found. This study was undertaken to determine the mass density of all the ocular components of the bovine eye. Liquid components were measured through mass/volume ratio, whereas solid tissues were measured with two different densitometry techniques based on Archimedes Principle. The first method determines the density by measuring dry and wet weight of the tissues. The second method consists of immersing the tissues in sucrose solutions of varying densities and observing their buoyancy. Although the mean densities for all tissues were found to be within 0.02 g/cm by both methods, only the sucrose solution method offered a consistent relative order for all measured ocular components, as well as a considerably smaller standard deviation (a maximum standard deviation of 0.004 g/cm for cornea). The lens was found to be the densest component, followed by the sclera, cornea, choroid, retina, aqueous, and vitreous humors. The consistent results of the sucrose solution tests suggest that the ocular mass density is a physical property that is more dependent on the compositional and structural characteristics of the tissue and than on population variability.

Fundamental incorporation of the density change during melting of a confined phase change material

NASA Astrophysics Data System (ADS)

Hernández, Ernesto M.; Otero, José A.

2018-02-01

The modeling of thermal diffusion processes taking place in a phase change material presents a challenge when the dynamics of the phase transition is coupled to the mechanical properties of the container. Thermo-mechanical models have been developed by several authors, however, it will be shown that these models only explain the phase transition dynamics at low pressures when the density of each phase experiences negligible changes. In our proposal, a new energy-mass balance equation at the interface is derived and found to be a consequence of mass conservation. The density change experienced in each phase is predicted by the proposed formulation of the problem. Numerical and semi-analytical solutions to the proposed model are presented for an example on a high temperature phase change material. The solutions to the models presented by other authors are observed to be well-behaved close to the isobaric limit. However, compared to the results obtained from our model, the change in the fusion temperature, latent heat, and absolute pressure is found to be greatly overestimated by other proposals when the phase transition is studied close to the isochoric regime.

Equations for O2 and CO2 solubilities in saline and plasma: combining temperature and density dependences.

PubMed

Christmas, Kevin M; Bassingthwaighte, James B

2017-05-01

Solubilities of respiratory gasses in water, saline, and plasma decrease with rising temperatures and solute concentrations. Henry's Law, C = α·P, states that the equilibrium concentration of a dissolved gas is solubility times partial pressure. Solubilities in the water of a solution depend on temperature and the content of other solutes. Blood temperatures may differ more than 20°C between skin and heart, and an erythrocyte will undergo that range as blood circulates. The concentrations of O 2 and CO 2 are the driving forces for diffusion, exchanges, and for reactions. We provide an equation for O 2 and CO 2 solubilities, α, that allows for continuous changes in temperature, T, and solution density, ρ, in dynamically changing states:[Formula: see text]This two-exponential expression with a density scalar γ, and a density exponent β, accounts for solubility changes due to density changes of an aqueous solution. It fits experimental data on solubilities in water, saline, and plasma over temperatures from 20 to 40°C, and for plasma densities, ρ sol up to 1.020 g/ml with ~0.3% error. The amounts of additional bound O 2 (to Hb) and CO 2 (bicarbonate and carbamino) depend on the concentrations in the local water space and the reaction parameters. During exercise, solubility changes are large; both ρ sol and T change rapidly with spatial position and with time. In exercise hemoconcentration plasma, ρ sol exceeds 1.02, whereas T may range over 20°C. The six parameters for O 2 and the six for CO 2 are constants, so solubilities are calculable continuously as T and ρ sol change. NEW & NOTEWORTHY Solubilities for oxygen and carbon dioxide are dependent on the density of the solution, on temperature, and on the partial pressure. We provide a brief equation suitable for hand calculators or mathematical modeling, accounting for these factors over a wide range of temperatures and solution densities for use in rapidly changing conditions, such as extreme exercise or osmotic transients, with better than 0.5% accuracy. Copyright © 2017 the American Physiological Society.

Driven neutron star collapse: Type I critical phenomena and the initial black hole mass distribution

NASA Astrophysics Data System (ADS)

Noble, Scott C.; Choptuik, Matthew W.

2016-01-01

We study the general relativistic collapse of neutron star (NS) models in spherical symmetry. Our initially stable models are driven to collapse by the addition of one of two things: an initially ingoing velocity profile, or a shell of minimally coupled, massless scalar field that falls onto the star. Tolman-Oppenheimer-Volkoff (TOV) solutions with an initially isentropic, gamma-law equation of state serve as our NS models. The initial values of the velocity profile's amplitude and the star's central density span a parameter space which we have surveyed extensively and which we find provides a rich picture of the possible end states of NS collapse. This parameter space survey elucidates the boundary between Type I and Type II critical behavior in perfect fluids which coincides, on the subcritical side, with the boundary between dispersed and bound end states. For our particular model, initial velocity amplitudes greater than 0.3 c are needed to probe the regime where arbitrarily small black holes can form. In addition, we investigate Type I behavior in our system by varying the initial amplitude of the initially imploding scalar field. In this case we find that the Type I critical solutions resemble TOV solutions on the 1-mode unstable branch of equilibrium solutions, and that the critical solutions' frequencies agree well with the fundamental mode frequencies of the unstable equilibria. Additionally, the critical solution's scaling exponent is shown to be well approximated by a linear function of the initial star's central density.

A mean-density model of ionic surfactants for the dispersion of carbon nanotubes in aqueous solutions

NASA Astrophysics Data System (ADS)

Joung, Young Soo

2018-05-01

We propose a new analytical model of ionic surfactants used for the dispersion of carbon nanotubes (CNTs) in aqueous solutions. Although ionic surfactants are commonly used to facilitate the dispersion of CNTs in aqueous solutions, understanding the dispersion process is challenging and time-consuming owing to its complexity and nonlinearity. In this work, we develop a mean-density model of ionic surfactants to simplify the calculation of interaction forces between CNTs stabilized by ionic surfactants. Using this model, we can evaluate various interaction forces between the CNTs and ionic surfactants under different conditions. The dispersion mechanism is investigated by estimating the potential of mean force (PMF) as a function of van der Waals forces, electrostatic forces, interfacial tension, and osmotic pressure. To verify the proposed model, we compare the PMFs derived using our method with those derived from molecular dynamics simulations using comparable CNTs and ionic surfactants. Notably, for stable dispersions, the osmotic pressure and interfacial energy are important for long-range and short-range interactions, respectively, in comparison with the effect of electrostatic forces. Our model effectively prescribes specific surfactants and their concentrations to achieve stable aqueous suspensions of CNTs.

Super H-mode: theoretical prediction and initial observations of a new high performance regime for tokamak operation

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

Snyder, Philip B.; Solomon, Wayne M.; Burrell, Keith H.

2015-07-21

A new “Super H-mode” regime is predicted, which enables pedestal height and predicted fusion performance substantially higher than for H-mode operation. This new regime is predicted to exist by the EPED pedestal model, which calculates criticality constraints for peeling-ballooning and kinetic ballooning modes, and combines them to predict the pedestal height and width. EPED usually predicts a single (“H-mode”) pedestal solution for each set of input parameters, however, in strongly shaped plasmas above a critical density, multiple pedestal solutions are found, including the standard “Hmode” solution, and a “Super H-Mode” solution at substantially larger pedestal height and width. The Supermore » H-mode regime is predicted to be accessible by controlling the trajectory of the density, and to increase fusion performance for ITER, as well as for DEMO designs with strong shaping. A set of experiments on DIII-D has identified the predicted Super H-mode regime, and finds pedestal height and width, and their variation with density, in good agreement with theoretical predictions from the EPED model. Finally, the very high pedestal enables operation at high global beta and high confinement, including the highest normalized beta achieved on DIII-D with a quiescent edge.« less

Recent advances in PDF modeling of turbulent reacting flows

NASA Technical Reports Server (NTRS)

Leonard, Andrew D.; Dai, F.

1995-01-01

This viewgraph presentation concludes that a Monte Carlo probability density function (PDF) solution successfully couples with an existing finite volume code; PDF solution method applied to turbulent reacting flows shows good agreement with data; and PDF methods must be run on parallel machines for practical use.

Satellite orbit computation methods

NASA Technical Reports Server (NTRS)

1977-01-01

Mathematical and algorithmical techniques for solution of problems in satellite dynamics were developed, along with solutions to satellite orbit motion. Dynamical analysis of shuttle on-orbit operations were conducted. Computer software routines for use in shuttle mission planning were developed and analyzed, while mathematical models of atmospheric density were formulated.

Influence of distributed delays on the dynamics of a generalized immune system cancerous cells interactions model

NASA Astrophysics Data System (ADS)

Piotrowska, M. J.; Bodnar, M.

2018-01-01

We present a generalisation of the mathematical models describing the interactions between the immune system and tumour cells which takes into account distributed time delays. For the analytical study we do not assume any particular form of the stimulus function describing the immune system reaction to presence of tumour cells but we only postulate its general properties. We analyse basic mathematical properties of the considered model such as existence and uniqueness of the solutions. Next, we discuss the existence of the stationary solutions and analytically investigate their stability depending on the forms of considered probability densities that is: Erlang, triangular and uniform probability densities separated or not from zero. Particular instability results are obtained for a general type of probability densities. Our results are compared with those for the model with discrete delays know from the literature. In addition, for each considered type of probability density, the model is fitted to the experimental data for the mice B-cell lymphoma showing mean square errors at the same comparable level. For estimated sets of parameters we discuss possibility of stabilisation of the tumour dormant steady state. Instability of this steady state results in uncontrolled tumour growth. In order to perform numerical simulation, following the idea of linear chain trick, we derive numerical procedures that allow us to solve systems with considered probability densities using standard algorithm for ordinary differential equations or differential equations with discrete delays.

LIMEPY: Lowered Isothermal Model Explorer in PYthon

NASA Astrophysics Data System (ADS)

Gieles, Mark; Zocchi, Alice

2017-10-01

LIMEPY solves distribution function (DF) based lowered isothermal models. It solves Poisson's equation used on input parameters and offers fast solutions for isotropic/anisotropic, single/multi-mass models, normalized DF values, density and velocity moments, projected properties, and generates discrete samples.

Sample Results From Tank 48H Samples HTF-48-14-158, -159, -169, and -170

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

Peters, T.; Hang, T.

2015-04-28

Savannah River National Laboratory (SRNL) analyzed samples from Tank 48H in support of determining the cause for the unusually high dose rates at the sampling points for this tank. A set of two samples was taken from the quiescent tank, and two additional samples were taken after the contents of the tank were mixed. The results of the analyses of all the samples show that the contents of the tank have changed very little since the analysis of the previous sample in 2012. The solids are almost exclusively composed of tetraphenylborate (TPB) salts, and there is no indication of accelerationmore » in the TPB decomposition. The filtrate composition shows a moderate increase in salt concentration and density, which is attributable to the addition of NaOH for the purposes of corrosion control. An older modeling simulation of the TPB degradation was updated, and the supernate results from a 2012 sample were run in the model. This result was compared to the results from the 2014 recent sample results reported in this document. The model indicates there is no change in the TPB degradation from 2012 to 2014. SRNL measured the buoyancy of the TPB solids in Tank 48H simulant solutions. It was determined that a solution of density 1.279 g/mL (~6.5M sodium) was capable of indefinitely suspending the TPB solids evenly throughout the solution. A solution of density 1.296 g/mL (~7M sodium) caused a significant fraction of the solids to float on the solution surface. As the experiments could not include the effect of additional buoyancy elements such as benzene or hydrogen generation, the buoyancy measurements provide an upper bound estimate of the density in Tank 48H required to float the solids.« less

Electroepitaxy of multicomponent systems - Ternary and quarternary compounds

NASA Technical Reports Server (NTRS)

Bryskiewicz, T.; Lagowski, J.; Gatos, H. C.

1980-01-01

A theoretical model is presented which accounts for the electroepitaxial growth kinetics and composition of multicomponent compounds in terms of mass transport in the liquid and phase diagram relationships. The mass transport in the interface is dominated by electromigration in the absence of convection and by diffusion in the presence of convection. The composition of the solid is controlled by the Peltier effect at the growth interface and by the diffusion and mobility constants of the solute components and the growth velocity (current density). Thus, for a given solution composition, the composition of the solid can be varied by varying the current density. For a given current density the composition remains constant even in the case of relatively thick epitaxial layers. All aspects of the model were found to be in good agreement with the growth and composition characteristics of Ga/x-1/Al/x/As layers.

Identification of the population density of a species model with nonlocal diffusion and nonlinear reaction

NASA Astrophysics Data System (ADS)

Tuan, Nguyen Huy; Van Au, Vo; Khoa, Vo Anh; Lesnic, Daniel

2017-05-01

The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L 2-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.

Charge exchange in solar wind-cometary interactions

NASA Technical Reports Server (NTRS)

Gombosi, T. I.; Horanyi, M.; Kecskemety, K.; Cravens, T. E.; Nagy, A. F.

1983-01-01

A simple model of a cometary spherically symmetrical atmosphere and ionosphere is considered. An analytic solution of the governing equations describing the radial distribution of the neutral and ion densities is found. The new solution is compared to the well-known solution of the equations containing only ionization terms. Neglecting recombination causes a significant overestimate of the ion density in the vicinity of the comet. An axisymmetric model of the solar wind-cometary interaction is considered, taking into account the loss of solar wind ions due to charge exchange. The calculations predict that for active comets, solar wind absorption due to charge exchange becomes important at a few thousand kilometers from the nucleus, and a surface separating the shocked solar wind from the cometary ionosphere develops in this region. These calculations are in reasonable agreement with the few observations available for the ionopause location at comets.

On Comparing Precision Orbit Solutions of Geodetic Satellites Given Several Atmospheric Density Models

DTIC Science & Technology

2014-08-01

Astrodynamics, drag, atmospheric density, geodesy 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER OF PAGES 12 19a...Translation of ’Le satellite de geodesie ’Starlette’,’ Groupe de Recherches de Geodesie Spatiale, Centre National d’Etudes Spatiales, Bretigny-sur-Orge

Complete analytical solution of electromagnetic field problem of high-speed spinning ball

NASA Astrophysics Data System (ADS)

Reichert, T.; Nussbaumer, T.; Kolar, J. W.

2012-11-01

In this article, a small sphere spinning in a rotating magnetic field is analyzed in terms of the resulting magnetic flux density distribution and the current density distribution inside the ball. From these densities, the motor torque and the eddy current losses can be calculated. An analytical model is derived, and its results are compared to a 3D finite element analysis. The model gives insight into the torque and loss characteristics of a solid rotor induction machine setup, which aims at rotating the sphere beyond 25 Mrpm.

A minimal model for the structural energetics of VO2

NASA Astrophysics Data System (ADS)

Kim, Chanul; Marianetti, Chris; The Marianetti Group Team

Resolving the structural, magnetic, and electronic structure of VO2 from the first-principles of quantum mechanics is still a forefront problem despite decades of attention. Hybrid functionals have been shown to qualitatively ruin the structural energetics. While density functional theory (DFT) combined with cluster extensions of dynamical mean-field theory (DMFT) have demonstrated promising results in terms of the electronic properties, structural phase stability has not yet been addressed. In order to capture the basic physics of the structural transition, we propose a minimal model of VO2 based on the one dimensional Peierls-Hubbard model and parameterize this based on DFT calculations of VO2. The total energy versus dimerization in the minimal mode is then solved numerically exactly using density matrix renormalization group (DMRG) and compared to the Hartree-Fock solution. We demonstrate that the Hartree-Fock solution exhibits the same pathologies as DFT+U, and spin density functional theory for that matter, while the DMRG solution is consistent with experimental observation. Our results demonstrate the critical role of non-locality in the total energy, and this will need to be accounted for to obtain a complete description of VO2 from first-principles. The authors acknowledge support from FAME, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.

Lane-Emden equation with inertial force and general polytropic dynamic model for molecular cloud cores

NASA Astrophysics Data System (ADS)

Li, DaLei; Lou, Yu-Qing; Esimbek, Jarken

2018-01-01

We study self-similar hydrodynamics of spherical symmetry using a general polytropic (GP) equation of state and derive the GP dynamic Lane-Emden equation (LEE) with a radial inertial force. In reference to Lou & Cao, we solve the GP dynamic LEE for both polytropic index γ = 1 + 1/n and the isothermal case n → +∞; our formalism is more general than the conventional polytropic model with n = 3 or γ = 4/3 of Goldreich & Weber. For proper boundary conditions, we obtain an exact constant solution for arbitrary n and analytic variable solutions for n = 0 and n = 1, respectively. Series expansion solutions are derived near the origin with the explicit recursion formulae for the series coefficients for both the GP and isothermal cases. By extensive numerical explorations, we find that there is no zero density at a finite radius for n ≥ 5. For 0 ≤ n < 5, we adjust the inertial force parameter c and find the range of c > 0 for monotonically decreasing density from the origin and vanishing at a finite radius for c being less than a critical value Ccr. As astrophysical applications, we invoke our solutions of the GP dynamic LEE with central finite boundary conditions to fit the molecular cloud core Barnard 68 in contrast to the static isothermal Bonnor-Ebert sphere by Alves et al. Our GP dynamic model fits appear to be sensibly consistent with several more observations and diagnostics for density, temperature and gas pressure profiles.

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

PubMed Central

Lu, Benzhuo; Zhou, Y.C.

2011-01-01

The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

Performance evaluation of Maxwell and Cercignani-Lampis gas-wall interaction models in the modeling of thermally driven rarefied gas transport.

PubMed

Liang, Tengfei; Li, Qi; Ye, Wenjing

2013-07-01

A systematic study on the performance of two empirical gas-wall interaction models, the Maxwell model and the Cercignani-Lampis (CL) model, in the entire Knudsen range is conducted. The models are evaluated by examining the accuracy of key macroscopic quantities such as temperature, density, and pressure, in three benchmark thermal problems, namely the Fourier thermal problem, the Knudsen force problem, and the thermal transpiration problem. The reference solutions are obtained from a validated hybrid DSMC-MD algorithm developed in-house. It has been found that while both models predict temperature and density reasonably well in the Fourier thermal problem, the pressure profile obtained from Maxwell model exhibits a trend that opposes that from the reference solution. As a consequence, the Maxwell model is unable to predict the orientation change of the Knudsen force acting on a cold cylinder embedded in a hot cylindrical enclosure at a certain Knudsen number. In the simulation of the thermal transpiration coefficient, although all three models overestimate the coefficient, the coefficient obtained from CL model is the closest to the reference solution. The Maxwell model performs the worst. The cause of the overestimated coefficient is investigated and its link to the overly constrained correlation between the tangential momentum accommodation coefficient and the tangential energy accommodation coefficient inherent in the models is pointed out. Directions for further improvement of models are suggested.

Precision Orbit Derived Atmospheric Density: Development and Performance

NASA Astrophysics Data System (ADS)

McLaughlin, C.; Hiatt, A.; Lechtenberg, T.; Fattig, E.; Mehta, P.

2012-09-01

Precision orbit ephemerides (POE) are used to estimate atmospheric density along the orbits of CHAMP (Challenging Minisatellite Payload) and GRACE (Gravity Recovery and Climate Experiment). The densities are calibrated against accelerometer derived densities and considering ballistic coefficient estimation results. The 14-hour density solutions are stitched together using a linear weighted blending technique to obtain continuous solutions over the entire mission life of CHAMP and through 2011 for GRACE. POE derived densities outperform the High Accuracy Satellite Drag Model (HASDM), Jacchia 71 model, and NRLMSISE-2000 model densities when comparing cross correlation and RMS with accelerometer derived densities. Drag is the largest error source for estimating and predicting orbits for low Earth orbit satellites. This is one of the major areas that should be addressed to improve overall space surveillance capabilities; in particular, catalog maintenance. Generally, density is the largest error source in satellite drag calculations and current empirical density models such as Jacchia 71 and NRLMSISE-2000 have significant errors. Dynamic calibration of the atmosphere (DCA) has provided measurable improvements to the empirical density models and accelerometer derived densities of extremely high precision are available for a few satellites. However, DCA generally relies on observations of limited accuracy and accelerometer derived densities are extremely limited in terms of measurement coverage at any given time. The goal of this research is to provide an additional data source using satellites that have precision orbits available using Global Positioning System measurements and/or satellite laser ranging. These measurements strike a balance between the global coverage provided by DCA and the precise measurements of accelerometers. The temporal resolution of the POE derived density estimates is around 20-30 minutes, which is significantly worse than that of accelerometer derived density estimates. However, major variations in density are observed in the POE derived densities. These POE derived densities in combination with other data sources can be assimilated into physics based general circulation models of the thermosphere and ionosphere with the possibility of providing improved density forecasts for satellite drag analysis. POE derived density estimates were initially developed using CHAMP and GRACE data so comparisons could be made with accelerometer derived density estimates. This paper presents the results of the most extensive calibration of POE derived densities compared to accelerometer derived densities and provides the reasoning for selecting certain parameters in the estimation process. The factors taken into account for these selections are the cross correlation and RMS performance compared to the accelerometer derived densities and the output of the ballistic coefficient estimation that occurs simultaneously with the density estimation. This paper also presents the complete data set of CHAMP and GRACE results and shows that the POE derived densities match the accelerometer densities better than empirical models or DCA. This paves the way to expand the POE derived densities to include other satellites with quality GPS and/or satellite laser ranging observations.

Analysis of silicon stress/strain relationships

NASA Technical Reports Server (NTRS)

Dillon, O.

1985-01-01

In the study of stress-strain relationships in silicon ribbon, numerous solutions were calculated for stresses, strain rates, and dislocation densities through the use of the Sumino model. It was concluded that many cases of failure of computer solutions to converge are analytical manifestations of shear bands (Luder's band) observed in experiments.

Low-density lipoprotein transport through an arterial wall under hyperthermia and hypertension conditions--An analytical solution.

PubMed

Iasiello, Marcello; Vafai, Kambiz; Andreozzi, Assunta; Bianco, Nicola

2016-01-25

An analytical solution for Low-Density Lipoprotein transport through an arterial wall under hyperthermia conditions is established in this work. A four-layer model is used to characterize the arterial wall. Transport governing equations are obtained as a combination between Staverman-Kedem-Katchalsky membrane equations and volume-averaged porous media equations. Temperature and solute transport fields are coupled by means of Ludwig-Soret effect. Results are in excellent agreement with numerical and analytical literature data under isothermal conditions, and with numerical literature data for the hyperthermia case. Effects of hypertension combined with hyperthermia, are also analyzed in this work. Copyright © 2015 Elsevier Ltd. All rights reserved.

Vibrational spectra of water solutions of azoles from QM/MM calculations: effects of solvation.

PubMed

Tanzi, Luana; Ramondo, Fabio; Guidoni, Leonardo

2012-10-18

Using microsolvation models and mixed quantum/classical ab initio molecular dynamics simulations, we investigate the vibrational properties of two azoles in water solution: pyrazole and oxazole. The effects of the water-azole hydrogen bonding are rationalized by an extensive comparison between structural parameters and harmonic frequencies obtained by microsolvation models. Following the effective normal-mode analysis introduced by Martinez et al. [Martinez et al., J. Chem. Phys. 2006, 125, 144106], we identify the vibrational frequencies of the solutes using the decomposition of the vibrational density of states of the gas phase and solution dynamics. The calculated shifts from gas phase to solution are fairly in agreement with the available experimental data.

Analytical solution to the fractional polytropic gas spheres

NASA Astrophysics Data System (ADS)

Nouh, Mohamed I.; Abdel-Salam, Emad A.-B.

2018-04-01

The Lane-Emden equation can be used to model stellar interiors, star clusters and many configurations in astrophysics. Unfortunately, there is an exact solution only for the polytropic indices n = 0, 1 and 5. In the present paper, a series solution for the fractional Lane-Emden equation is presented. The solution is performed in the frame of modified Rienmann Liouville derivatives. The obtained results recover the well-known series solutions when α =1. The fractional model of n = 3 is calculated and the mass-radius relation, density ratio, pressure ratio and temperature ratio are investigated. The fractional star appears much different than the integer star, as it is denser, more stressed and hotter than the integer star.

A two-dimensional cascade solution using minimized surface singularity density distributions - with application to film cooled turbine blades

NASA Technical Reports Server (NTRS)

Mcfarland, E.; Tabakoff, W.; Hamed, A.

1977-01-01

An investigation of the effects of coolant injection on the aerodynamic performance of cooled turbine blades is presented. The coolant injection is modeled in the inviscid irrotational adiabatic flow analysis through the cascade using the distributed singularities approach. The resulting integral equations are solved using a minimized surface singularity density criteria. The aerodynamic performance was evaluated using this solution in conjunction with an existing mixing theory analysis. The results of the present analysis are compared with experimental measurements in cold flow tests.

Sn ion energy distributions of ns- and ps-laser produced plasmas

NASA Astrophysics Data System (ADS)

Bayerle, A.; Deuzeman, M. J.; van der Heijden, S.; Kurilovich, D.; de Faria Pinto, T.; Stodolna, A.; Witte, S.; Eikema, K. S. E.; Ubachs, W.; Hoekstra, R.; Versolato, O. O.

2018-04-01

Ion energy distributions arising from laser-produced plasmas of Sn are measured over a wide laser parameter space. Planar-solid and liquid-droplet targets are exposed to infrared laser pulses with energy densities between 1 J cm‑2 and 4 kJ cm‑2 and durations spanning 0.5 ps to 6 ns. The measured ion energy distributions are compared to two self-similar solutions of a hydrodynamic approach assuming isothermal expansion of the plasma plume into vacuum. For planar and droplet targets exposed to ps-long pulses, we find good agreement between the experimental results and the self-similar solution of a semi-infinite simple planar plasma configuration with an exponential density profile. The ion energy distributions resulting from solid Sn exposed to ns-pulses agrees with solutions of a limited-mass model that assumes a Gaussian-shaped initial density profile.

3DRISM-HI-D2MSA: an improved analytic theory to compute solvent structure around hydrophobic solutes with proper treatment of solute–solvent electrostatic interactions

NASA Astrophysics Data System (ADS)

Cao, Siqin; Zhu, Lizhe; Huang, Xuhui

2018-04-01

The 3D reference interaction site model (3DRISM) is a powerful tool to study the thermodynamic and structural properties of liquids. However, for hydrophobic solutes, the inhomogeneity of the solvent density around them poses a great challenge to the 3DRISM theory. To address this issue, we have previously introduced the hydrophobic-induced density inhomogeneity theory (HI) for purely hydrophobic solutes. To further consider the complex hydrophobic solutes containing partial charges, here we propose the D2MSA closure to incorporate the short-range and long-range interactions with the D2 closure and the mean spherical approximation, respectively. We demonstrate that our new theory can compute the solvent distributions around real hydrophobic solutes in water and complex organic solvents that agree well with the explicit solvent molecular dynamics simulations.

Two-lane traffic-flow model with an exact steady-state solution.

PubMed

Kanai, Masahiro

2010-12-01

We propose a stochastic cellular-automaton model for two-lane traffic flow based on the misanthrope process in one dimension. The misanthrope process is a stochastic process allowing for an exact steady-state solution; hence, we have an exact flow-density diagram for two-lane traffic. In addition, we introduce two parameters that indicate, respectively, driver's driving-lane preference and passing-lane priority. Due to the additional parameters, the model shows a deviation of the density ratio for driving-lane use and a biased lane efficiency in flow. Then, a mean-field approach explicitly describes the asymmetric flow by the hop rates, the driving-lane preference, and the passing-lane priority. Meanwhile, the simulation results are in good agreement with an observational data, and we thus estimate these parameters. We conclude that the proposed model successfully produces two-lane traffic flow particularly with the driving-lane preference and the passing-lane priority.

Active Plasma Resonance Spectroscopy: Evaluation of a fluiddynamic-model of the planar multipole resonance probe using functional analytic methods

NASA Astrophysics Data System (ADS)

Friedrichs, Michael; Brinkmann, Ralf Peter; Oberrath, Jens

2016-09-01

Measuring plasma parameters, e.g. electron density and electron temperature, is an important procedure to verify the stability and behavior of a plasma process. For this purpose the multipole resonance probe (MRP) represents a satisfying solution to measure the electron density. However the influence of the probe on the plasma through its physical presence makes it unattractive for some processes in industrial application. A solution to combine the benefits of the spherical MRP with the ability to integrate the probe into the plasma reactor is introduced by the planar model of the MRP. By coupling the model of the cold plasma with the maxwell equations for electrostatics an analytical model for the admittance of the plasma is derivated, adjusted to cylindrical geometry and solved analytically for the planar MRP using functional analytic methods.

A straightforward method for measuring the range of apparent density of microplastics.

PubMed

Li, Lingyun; Li, Mengmeng; Deng, Hua; Cai, Li; Cai, Huiwen; Yan, Beizhan; Hu, Jun; Shi, Huahong

2018-10-15

Density of microplastics has been regarded as the primary property that affect the distribution and bioavailability of microplastics in the water column. For measuring the density of microplastis, we developed a simple and rapid method based on density gradient solutions. In this study, we tested four solvents to make the density gradient solutions, i.e., ethanol (0.8 g/cm 3 ), ultrapure water (1.0 g/cm 3 ), saturated NaI (1.8 g/cm 3 ) and ZnCl 2 (1.8 g/cm 3 ). Density of microplastics was measured via observing the float or sink status in the density gradient solutions. We found that density gradient solutions made from ZnCl 2 had a larger uncertainty in measuring density than that from NaI, most likely due to a higher surface tension of ZnCl 2 solution. Solutions made from ethanol, ultrapure water, and NaI showed consistent density results with listed densities of commercial products, indicating that these density gradient solutions were suitable for measuring microplastics with a density range of 0.8-1.8 g/cm 3 . Copyright © 2018 Elsevier B.V. All rights reserved.

Stability of the Einstein static universe in Einstein-Cartan theory

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

Atazadeh, K., E-mail: atazadeh@azaruniv.ac.ir

The existence and stability of the Einstein static solution have been built in the Einstein-Cartan gravity. We show that this solution in the presence of perfect fluid with spin density satisfying the Weyssenhoff restriction is cyclically stable around a center equilibrium point. Thus, study of this solution is interesting because it supports non-singular emergent cosmological models in which the early universe oscillates indeterminately about an initial Einstein static solution and is thus past eternal.

Plane Symmetric Solutions in f(G) Gravity

NASA Astrophysics Data System (ADS)

Shamir, M. Farasat; Saeed, Atrooba

2017-12-01

The purpose of this document is to investigate the universe in f(G) gravity. A wgeneral static plane symmetric space-time is chosen and exact solutions are explored using a viable f(G) gravity model. In particular, power and exponential law solutions are discussed. In addition, the physical relevance of the solutions with Taub's metric and anti-deSitter space-time is shown. Graphical analysis of energy density and pressure of the universe is done to substantiate the study.

Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts

NASA Astrophysics Data System (ADS)

Ren, Zhengyong; Zhong, Yiyuan; Chen, Chaojian; Tang, Jingtian; Kalscheuer, Thomas; Maurer, Hansruedi; Li, Yang

2018-03-01

During the last 20 years, geophysicists have developed great interest in using gravity gradient tensor signals to study bodies of anomalous density in the Earth. Deriving exact solutions of the gravity gradient tensor signals has become a dominating task in exploration geophysics or geodetic fields. In this study, we developed a compact and simple framework to derive exact solutions of gravity gradient tensor measurements for polyhedral bodies, in which the density contrast is represented by a general polynomial function. The polynomial mass contrast can continuously vary in both horizontal and vertical directions. In our framework, the original three-dimensional volume integral of gravity gradient tensor signals is transformed into a set of one-dimensional line integrals along edges of the polyhedral body by sequentially invoking the volume and surface gradient (divergence) theorems. In terms of an orthogonal local coordinate system defined on these edges, exact solutions are derived for these line integrals. We successfully derived a set of unified exact solutions of gravity gradient tensors for constant, linear, quadratic and cubic polynomial orders. The exact solutions for constant and linear cases cover all previously published vertex-type exact solutions of the gravity gradient tensor for a polygonal body, though the associated algorithms may differ in numerical stability. In addition, to our best knowledge, it is the first time that exact solutions of gravity gradient tensor signals are derived for a polyhedral body with a polynomial mass contrast of order higher than one (that is quadratic and cubic orders). Three synthetic models (a prismatic body with depth-dependent density contrasts, an irregular polyhedron with linear density contrast and a tetrahedral body with horizontally and vertically varying density contrasts) are used to verify the correctness and the efficiency of our newly developed closed-form solutions. Excellent agreements are obtained between our solutions and other published exact solutions. In addition, stability tests are performed to demonstrate that our exact solutions can safely be used to detect shallow subsurface targets.

Application of Self-Similarity Constrained Reynolds-Averaged Turbulence Models to Rayleigh-Taylor and Richtmyer-Meshkov Unstable Turbulent Mixing

NASA Astrophysics Data System (ADS)

Hartland, Tucker A.; Schilling, Oleg

2016-11-01

Analytical self-similar solutions corresponding to Rayleigh-Taylor, Richtmyer-Meshkov and Kelvin-Helmholtz instability are combined with observed values of the growth parameters in these instabilities to derive coefficient sets for K- ɛ and K- L- a Reynolds-averaged turbulence models. It is shown that full numerical solutions of the model equations give mixing layer widths, fields, and budgets in good agreement with the corresponding self-similar quantities for small Atwood number. Both models are then applied to Rayleigh-Taylor instability with increasing density contrasts to estimate the Atwood number above which the self-similar solutions become invalid. The models are also applied to a reshocked Richtmyer-Meshkov instability, and the predictions are compared with data. The expressions for the growth parameters obtained from the similarity analysis are used to develop estimates for the sensitivity of their values to changes in important model coefficients. Numerical simulations using these modified coefficient values are then performed to provide bounds on the model predictions associated with uncertainties in these coefficient values. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. This work was supported by the 2016 LLNL High-Energy-Density Physics Summer Student Program.

Electrochemistry at a Metal Nanoparticle on a Tunneling Film: A Steady-State Model of Current Densities at a Tunneling Ultramicroelectrode.

PubMed

Hill, Caleb M; Kim, Jiyeon; Bard, Allen J

2015-09-09

Here, a new methodology is proposed for treating electrochemical current densities in metal-insulator-metal nanoparticle (M-I-MNP) systems. The described model provides broad, practical insights about MNP-mediated electron transfer to redox species in solution, where electron transfer from the underlying electrode to a MNP via tunneling and heterogeneous electron transfer from the MNP to redox species in solution are treated as sequential steps. Tunneling is treated through an adaptation of the Simmons model of tunneling in metal-insulator-metal structures, and explicit equations are provided for tunneling currents, which demonstrate the effect of various experimental parameters, such as insulator thickness and MNP size. Overall, a general approach is demonstrated for determining experimental conditions where tunneling will have a measurable impact on the electrochemistry of M-I-MNP systems.

Planar Multipol-Resonance-Probe: A Spectral Kinetic Approach

NASA Astrophysics Data System (ADS)

Friedrichs, Michael; Gong, Junbo; Brinkmann, Ralf Peter; Oberrath, Jens; Wilczek, Sebastian

2016-09-01

Measuring plasma parameters, e.g. electron density and electron temperature, is an important procedure to verify the stability and behavior of a plasma process. For this purpose the multipole resonance probe (MRP) represents a satisfying solution to measure the electron density. However the influence of the probe on the plasma through its physical presence makes it unattractive for some processes in industrial application. A solution to combine the benefits of the spherical MRP with the ability to integrate the probe into the plasma reactor is introduced by the planar model of the MRP (pMRP). Introducing the spectral kinetic formalism leads to a reduced simulation-circle compared to particle-in-cell simulations. The model of the pMRP is implemented and first simulation results are presented.

Analytical potential-density pairs for bars

NASA Astrophysics Data System (ADS)

Vogt, D.; Letelier, P. S.

2010-11-01

An identity that relates multipolar solutions of the Einstein equations to Newtonian potentials of bars with linear densities proportional to Legendre polynomials is used to construct analytical potential-density pairs of infinitesimally thin bars with a given linear density profile. By means of a suitable transformation, softened bars that are free of singularities are also obtained. As an application we study the equilibrium points and stability for the motion of test particles in the gravitational field for three models of rotating bars.

Theory and analysis of statistical discriminant techniques as applied to remote sensing data

NASA Technical Reports Server (NTRS)

Odell, P. L.

1973-01-01

Classification of remote earth resources sensing data according to normed exponential density statistics is reported. The use of density models appropriate for several physical situations provides an exact solution for the probabilities of classifications associated with the Bayes discriminant procedure even when the covariance matrices are unequal.

Impact of kinetic mass transfer on free convection in a porous medium

NASA Astrophysics Data System (ADS)

Lu, Chunhui; Shi, Liangsheng; Chen, Yiming; Xie, Yueqing; Simmons, Craig T.

2016-05-01

We investigate kinetic mass transfer effects on unstable density-driven flow and transport processes by numerical simulations of a modified Elder problem. The first-order dual-domain mass transfer model coupled with a variable-density-flow model is employed to describe transport behavior in porous media. Results show that in comparison to the no-mass-transfer case, a higher degree of instability and more unstable system is developed in the mass transfer case due to the reduced effective porosity and correspondingly a larger Rayleigh number (assuming permeability is independent on the mobile porosity). Given a constant total porosity, the magnitude of capacity ratio (i.e., immobile porosity/mobile porosity) controls the macroscopic plume profile in the mobile domain, while the magnitude of mass transfer timescale (i.e., the reciprocal of the mass transfer rate coefficient) dominates its evolution rate. The magnitude of capacity ratio plays an important role on the mechanism driving the mass flux into the aquifer system. Specifically, for a small capacity ratio, solute loading is dominated by the density-driven transport, while with increasing capacity ratio local mass transfer dominated solute loading may occur at later times. At significantly large times, however, both mechanisms contribute comparably to solute loading. Sherwood Number could be a nonmonotonic function of mass transfer timescale due to complicated interactions of solute between source zone, mobile zone and immobile zone in the top boundary layer, resulting in accordingly a similar behavior of the total mass. The initial assessment provides important insights into unstable density-driven flow and transport in the presence of kinetic mass transfer.

High density liquid structure enhancement in glass forming aqueous solution of LiCl.

PubMed

Camisasca, G; De Marzio, M; Rovere, M; Gallo, P

2018-06-14

We investigate using molecular dynamics simulations the dynamical and structural properties of LiCl:6H 2 O aqueous solution upon supercooling. This ionic solution is a glass forming liquid of relevant interest in connection with the study of the anomalies of supercooled water. The LiCl:6H 2 O solution is easily supercooled and the liquid state can be maintained over a large decreasing temperature range. We performed simulations from ambient to 200 K in order to investigate how the presence of the salt modifies the behavior of supercooled water. The study of the relaxation time of the self-density correlation function shows that the system follows the prediction of the mode coupling theory and behaves like a fragile liquid in all the range explored. The analysis of the changes in the water structure induced by the salt shows that while the salt preserves the water hydrogen bonds in the system, it strongly affects the tetrahedral hydrogen bond network. Following the interpretation of the anomalies of water in terms of a two-state model, the modifications of the oxygen radial distribution function and the angular distribution function of the hydrogen bonds in water indicate that LiCl has the role of enhancing the high density liquid component of water with respect to the low density component. This is in agreement with recent experiments on aqueous ionic solutions.

High density liquid structure enhancement in glass forming aqueous solution of LiCl

NASA Astrophysics Data System (ADS)

Camisasca, G.; De Marzio, M.; Rovere, M.; Gallo, P.

2018-06-01

We investigate using molecular dynamics simulations the dynamical and structural properties of LiCl:6H2O aqueous solution upon supercooling. This ionic solution is a glass forming liquid of relevant interest in connection with the study of the anomalies of supercooled water. The LiCl:6H2O solution is easily supercooled and the liquid state can be maintained over a large decreasing temperature range. We performed simulations from ambient to 200 K in order to investigate how the presence of the salt modifies the behavior of supercooled water. The study of the relaxation time of the self-density correlation function shows that the system follows the prediction of the mode coupling theory and behaves like a fragile liquid in all the range explored. The analysis of the changes in the water structure induced by the salt shows that while the salt preserves the water hydrogen bonds in the system, it strongly affects the tetrahedral hydrogen bond network. Following the interpretation of the anomalies of water in terms of a two-state model, the modifications of the oxygen radial distribution function and the angular distribution function of the hydrogen bonds in water indicate that LiCl has the role of enhancing the high density liquid component of water with respect to the low density component. This is in agreement with recent experiments on aqueous ionic solutions.

Mean, covariance, and effective dimension of stochastic distributed delay dynamics

NASA Astrophysics Data System (ADS)

René, Alexandre; Longtin, André

2017-11-01

Dynamical models are often required to incorporate both delays and noise. However, the inherently infinite-dimensional nature of delay equations makes formal solutions to stochastic delay differential equations (SDDEs) challenging. Here, we present an approach, similar in spirit to the analysis of functional differential equations, but based on finite-dimensional matrix operators. This results in a method for obtaining both transient and stationary solutions that is directly amenable to computation, and applicable to first order differential systems with either discrete or distributed delays. With fewer assumptions on the system's parameters than other current solution methods and no need to be near a bifurcation, we decompose the solution to a linear SDDE with arbitrary distributed delays into natural modes, in effect the eigenfunctions of the differential operator, and show that relatively few modes can suffice to approximate the probability density of solutions. Thus, we are led to conclude that noise makes these SDDEs effectively low dimensional, which opens the possibility of practical definitions of probability densities over their solution space.

Time Dependent Solution for the He I Line Ratio Electron Temperature and Density Diagnostic in TEXTOR and DIII-D

NASA Astrophysics Data System (ADS)

Munoz Burgos, J. M.; Schmitz, O.; Unterberg, E. A.; Loch, S. D.; Balance, C. P.

2010-11-01

We developed a time dependent solution for the He I line ratio diagnostic. Stationary solution is applied for L-mode at TEXTOR. The radial range is typically limited to a region near the separatrix due to metastable effects, and the atomic data used. We overcome this problem by applying a time dependent solution and thus avoid unphysical results. We use a new R-Matrix with Pseudostates and Convergence Cross-Coupling electron impact excitation and ionization atomic data set into the Collisional Radiative Model (CRM). We include contributions from higher Rydberg states into the CRM by means of the projection matrix. By applying this solution (to the region near the wall) and the stationary solution (near the separatrix), we triple the radial range of the current diagnostic. We explore the possibility of extending this approach to H-mode plasmas in DIII-D by estimating line emission profiles from electron temperature and density Thomson scattering data.

n-dimensional isotropic Finch-Skea stars

NASA Astrophysics Data System (ADS)

Chilambwe, Brian; Hansraj, Sudan

2015-02-01

We study the impact of dimension on the physical properties of the Finch-Skea astrophysical model. It is shown that a positive definite, monotonically decreasing pressure and density are evident. A decrease in stellar radius emerges as the order of the dimension increases. This is accompanied by a corresponding increase in energy density. The model continues to display the necessary qualitative features inherent in the 4-dimensional Finch-Skea star and the conformity to the Walecka theory is preserved under dimensional increase. The causality condition is always satisfied for all dimensions considered resulting in the proposed models demonstrating a subluminal sound speed throughout the interior of the distribution. Moreover, the pressure and density decrease monotonically outwards from the centre and a pressure-free hypersurface exists demarcating the boundary of the perfect-fluid sphere. Since the study of the physical conditions is performed graphically, it is necessary to specify certain constants in the model. Reasonable values for such constants are arrived at on examining the behaviour of the model at the centre and demanding the satisfaction of all elementary conditions for physical plausibility. Finally two constants of integration are settled on matching of our solutions with the appropriate Schwarzschild-Tangherlini exterior metrics. Furthermore, the solution admits a barotropic equation of state despite the higher dimension. The compactification parameter as well as the density variation parameter are also computed. The models satisfy the weak, strong and dominant energy conditions in the interior of the stellar configuration.

Densities of L-Glutamic Acid HCl Drug in Aqueous NaCl and KCl Solutions at Different Temperatures

NASA Astrophysics Data System (ADS)

Ryshetti, Suresh; Raghuram, Noothi; Rani, Emmadi Jayanthi; Tangeda, Savitha Jyostna

2016-04-01

Densities (ρ ) of (0.01 to 0.07) {mol}{\\cdot } {kg}^{-1} L-Glutamic acid HCl (L-HCl) drug in water, and in aqueous NaCl and KCl (0.5 and 1.0) {mol}{\\cdot } {kg}^{-1} solutions have been reported as a function of temperature at T = (298.15, 303.15, 308.15, and 313.15) K and atmospheric pressure. The accurate density (ρ ) values are used to estimate the various parameters such as the apparent molar volume (V_{2,{\\upphi }}), the partial molar volume (V2^{∞}), the isobaric thermal expansion coefficient (α 2), the partial molar expansion (E2^{∞}), and Hepler's constant (partial 2V2^{∞}/partial T2)P. The Cosphere overlap model is used to understand the solute-solvent interactions in a ternary mixture (L-HCl drug + NaCl or KCl + water). Hepler's constant (partial 2V2^{∞}/partial T2)_P is utilized to interpret the structure-making or -breaking ability of L-HCl drug in aqueous NaCl and KCl solutions, and the results are inferred that L-HCl drug acts as a structure maker, i.e., kosmotrope in aqueous NaCl solutions and performs as a structure breaker, i.e., chaotrope in aqueous KCl solutions.

Weighted-density functionals for cavity formation and dispersion energies in continuum solvation models

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

Sundararaman, Ravishankar; Gunceler, Deniz; Arias, T. A.

2014-10-07

Continuum solvation models enable efficient first principles calculations of chemical reactions in solution, but require extensive parametrization and fitting for each solvent and class of solute systems. Here, we examine the assumptions of continuum solvation models in detail and replace empirical terms with physical models in order to construct a minimally-empirical solvation model. Specifically, we derive solvent radii from the nonlocal dielectric response of the solvent from ab initio calculations, construct a closed-form and parameter-free weighted-density approximation for the free energy of the cavity formation, and employ a pair-potential approximation for the dispersion energy. We show that the resulting modelmore » with a single solvent-independent parameter: the electron density threshold (n c), and a single solvent-dependent parameter: the dispersion scale factor (s 6), reproduces solvation energies of organic molecules in water, chloroform, and carbon tetrachloride with RMS errors of 1.1, 0.6 and 0.5 kcal/mol, respectively. We additionally show that fitting the solvent-dependent s 6 parameter to the solvation energy of a single non-polar molecule does not substantially increase these errors. Parametrization of this model for other solvents, therefore, requires minimal effort and is possible without extensive databases of experimental solvation free energies.« less

Weighted-density functionals for cavity formation and dispersion energies in continuum solvation models

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

Sundararaman, Ravishankar; Gunceler, Deniz; Arias, T. A.

2014-10-07

Continuum solvation models enable efficient first principles calculations of chemical reactions in solution, but require extensive parametrization and fitting for each solvent and class of solute systems. Here, we examine the assumptions of continuum solvation models in detail and replace empirical terms with physical models in order to construct a minimally-empirical solvation model. Specifically, we derive solvent radii from the nonlocal dielectric response of the solvent from ab initio calculations, construct a closed-form and parameter-free weighted-density approximation for the free energy of the cavity formation, and employ a pair-potential approximation for the dispersion energy. We show that the resulting modelmore » with a single solvent-independent parameter: the electron density threshold (n{sub c}), and a single solvent-dependent parameter: the dispersion scale factor (s{sub 6}), reproduces solvation energies of organic molecules in water, chloroform, and carbon tetrachloride with RMS errors of 1.1, 0.6 and 0.5 kcal/mol, respectively. We additionally show that fitting the solvent-dependent s{sub 6} parameter to the solvation energy of a single non-polar molecule does not substantially increase these errors. Parametrization of this model for other solvents, therefore, requires minimal effort and is possible without extensive databases of experimental solvation free energies.« less

3-D direct current resistivity anisotropic modelling by goal-oriented adaptive finite element methods

NASA Astrophysics Data System (ADS)

Ren, Zhengyong; Qiu, Lewen; Tang, Jingtian; Wu, Xiaoping; Xiao, Xiao; Zhou, Zilong

2018-01-01

Although accurate numerical solvers for 3-D direct current (DC) isotropic resistivity models are current available even for complicated models with topography, reliable numerical solvers for the anisotropic case are still an open question. This study aims to develop a novel and optimal numerical solver for accurately calculating the DC potentials for complicated models with arbitrary anisotropic conductivity structures in the Earth. First, a secondary potential boundary value problem is derived by considering the topography and the anisotropic conductivity. Then, two a posteriori error estimators with one using the gradient-recovery technique and one measuring the discontinuity of the normal component of current density are developed for the anisotropic cases. Combing the goal-oriented and non-goal-oriented mesh refinements and these two error estimators, four different solving strategies are developed for complicated DC anisotropic forward modelling problems. A synthetic anisotropic two-layer model with analytic solutions verified the accuracy of our algorithms. A half-space model with a buried anisotropic cube and a mountain-valley model are adopted to test the convergence rates of these four solving strategies. We found that the error estimator based on the discontinuity of current density shows better performance than the gradient-recovery based a posteriori error estimator for anisotropic models with conductivity contrasts. Both error estimators working together with goal-oriented concepts can offer optimal mesh density distributions and highly accurate solutions.

Semi-analytical modelling of positive corona discharge in air

NASA Astrophysics Data System (ADS)

Pontiga, Francisco; Yanallah, Khelifa; Chen, Junhong

2013-09-01

Semianalytical approximate solutions of the spatial distribution of electric field and electron and ion densities have been obtained by solving Poisson's equations and the continuity equations for the charged species along the Laplacian field lines. The need to iterate for the correct value of space charge on the corona electrode has been eliminated by using the corona current distribution over the grounded plane derived by Deutsch, which predicts a cos m θ law similar to Warburg's law. Based on the results of the approximated model, a parametric study of the influence of gas pressure, the corona wire radius, and the inter-electrode wire-plate separation has been carried out. Also, the approximate solutions of the electron number density has been combined with a simplified plasma chemistry model in order to compute the ozone density generated by the corona discharge in the presence of a gas flow. This work was supported by the Consejeria de Innovacion, Ciencia y Empresa (Junta de Andalucia) and by the Ministerio de Ciencia e Innovacion, Spain, within the European Regional Development Fund contracts FQM-4983 and FIS2011-25161.

On a nonlinear model for tumour growth with drug application

NASA Astrophysics Data System (ADS)

Donatelli, Donatella; Trivisa, Konstantina

2015-05-01

We investigate the dynamics of a nonlinear system modelling tumour growth with drug application. The tumour is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The system is given by a multi-phase flow model: the densities of the different cells are governed by a set of transport equations, the density of the nutrient and the density of the drug are governed by rather general diffusion equations, while the velocity of the tumour is given by Brinkman's equation. The domain occupied by the tumour in this setting is a growing continuum Ω with boundary ∂Ω both of which evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behaviour, diffusion and viscosity in the weak formulation. Both the solutions and the domain are rather general, no symmetry assumption is required and the result holds for large initial data. This article is part of a research programme whose aim is the investigation of the effect of drug application in tumour growth.

Kinetic Monte Carlo simulations of nucleation and growth in electrodeposition.

PubMed

Guo, Lian; Radisic, Aleksandar; Searson, Peter C

2005-12-22

Nucleation and growth during bulk electrodeposition is studied using kinetic Monte Carlo (KMC) simulations. Ion transport in solution is modeled using Brownian dynamics, and the kinetics of nucleation and growth are dependent on the probabilities of metal-on-substrate and metal-on-metal deposition. Using this approach, we make no assumptions about the nucleation rate, island density, or island distribution. The influence of the attachment probabilities and concentration on the time-dependent island density and current transients is reported. Various models have been assessed by recovering the nucleation rate and island density from the current-time transients.

An information theory approach to the density of the earth

NASA Technical Reports Server (NTRS)

Graber, M. A.

1977-01-01

Information theory can develop a technique which takes experimentally determined numbers and produces a uniquely specified best density model satisfying those numbers. A model was generated using five numerical parameters: the mass of the earth, its moment of inertia, three zero-node torsional normal modes (L = 2, 8, 26). In order to determine the stability of the solution, six additional densities were generated, in each of which the period of one of the three normal modes was increased or decreased by one standard deviation. The superposition of the seven models is shown. It indicates that current knowledge of the torsional modes is sufficient to specify the density in the upper mantle but that the lower mantle and core will require smaller standard deviations before they can be accurately specified.

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.

Rumor diffusion model with spatio-temporal diffusion and uncertainty of behavior decision in complex social networks

NASA Astrophysics Data System (ADS)

Zhu, Liang; Wang, Youguo

2018-07-01

In this paper, a rumor diffusion model with uncertainty of human behavior under spatio-temporal diffusion framework is established. Take physical significance of spatial diffusion into account, a diffusion threshold is set under which the rumor is not a trend topic and only spreads along determined physical connections. Heterogeneity of degree distribution and distance distribution has also been considered in theoretical model at the same time. The global existence and uniqueness of classical solution are proved with a Lyapunov function and an approximate classical solution in form of infinite series is constructed with a system of eigenfunction. Simulations and numerical solutions both on Watts-Strogatz (WS) network and Barabási-Albert (BA) network display the variation of density of infected connections from spatial and temporal dimensions. Relevant results show that the density of infected connections is dominated by network topology and uncertainty of human behavior at threshold time. With increase of social capability, rumor diffuses to the steady state in a higher speed. And the variation trends of diffusion size with uncertainty are diverse on different artificial networks.

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.

Numerical modeling of solute transport in a sand tank physical model under varying hydraulic gradient and hydrological stresses

NASA Astrophysics Data System (ADS)

Atlabachew, Abunu; Shu, Longcang; Wu, Peipeng; Zhang, Yongjie; Xu, Yang

2018-03-01

This laboratory study improves the understanding of the impacts of horizontal hydraulic gradient, artificial recharge, and groundwater pumping on solute transport through aquifers. Nine experiments and numerical simulations were carried out using a sand tank. The variable-density groundwater flow and sodium chloride transport were simulated using the three-dimensional numerical model SEAWAT. Numerical modelling results successfully reproduced heads and concentrations observed in the sand tank. A higher horizontal hydraulic gradient enhanced the migration of sodium chloride, particularly in the groundwater flow direction. The application of constant artificial recharge increased the spread of the sodium chloride plume in both the longitudinal and lateral directions. In addition, groundwater pumping accelerated spreading of the sodium chloride plume towards the pumping well. Both higher hydraulic gradient and pumping rate generated oval-shaped plumes in the horizontal plane. However, the artificial recharge process produced stretched plumes. These effects of artificial recharge and groundwater pumping were greater under higher hydraulic gradient. The concentration breakthrough curves indicated that emerging solutions never attained the concentration of the originally injected solution. This is probably because of sorption of sodium chloride onto the silica sand and/or the exchange of sodium chloride between the mobile and immobile liquid domains. The fingering and protruding plume shapes in the numerical models constitute instability zones produced by buoyancy-driven flow. Overall, the results have substantiated the influences of hydraulic gradient, boundary condition, artificial recharge, pumping rate and density differences on solute transport through a homogeneous unconfined aquifer. The implications of these findings are important for managing liquid wastes.

A local leaky-box model for the local stellar surface density-gas surface density-gas phase metallicity relation

NASA Astrophysics Data System (ADS)

Zhu, Guangtun Ben; Barrera-Ballesteros, Jorge K.; Heckman, Timothy M.; Zakamska, Nadia L.; Sánchez, Sebastian F.; Yan, Renbin; Brinkmann, Jonathan

2017-07-01

We revisit the relation between the stellar surface density, the gas surface density and the gas-phase metallicity of typical disc galaxies in the local Universe with the SDSS-IV/MaNGA survey, using the star formation rate surface density as an indicator for the gas surface density. We show that these three local parameters form a tight relationship, confirming previous works (e.g. by the PINGS and CALIFA surveys), but with a larger sample. We present a new local leaky-box model, assuming star-formation history and chemical evolution is localized except for outflowing materials. We derive closed-form solutions for the evolution of stellar surface density, gas surface density and gas-phase metallicity, and show that these parameters form a tight relation independent of initial gas density and time. We show that, with canonical values of model parameters, this predicted relation match the observed one well. In addition, we briefly describe a pathway to improving the current semi-analytic models of galaxy formation by incorporating the local leaky-box model in the cosmological context, which can potentially explain simultaneously multiple properties of Milky Way-type disc galaxies, such as the size growth and the global stellar mass-gas metallicity relation.

A low-dimensional analogue of holographic baryons

NASA Astrophysics Data System (ADS)

Bolognesi, Stefano; Sutcliffe, Paul

2014-04-01

Baryons in holographic QCD correspond to topological solitons in the bulk. The most prominent example is the Sakai-Sugimoto model, where the bulk soliton in the five-dimensional spacetime of AdS-type can be approximated by the flat space self-dual Yang-Mills instanton with a small size. Recently, the validity of this approximation has been verified by comparison with the numerical field theory solution. However, multi-solitons and solitons with finite density are currently beyond numerical field theory computations. Various approximations have been applied to investigate these important issues and have led to proposals for finite density configurations that include dyonic salt and baryonic popcorn. Here we introduce and investigate a low-dimensional analogue of the Sakai-Sugimoto model, in which the bulk soliton can be approximated by a flat space sigma model instanton. The bulk theory is a baby Skyrme model in a three-dimensional spacetime with negative curvature. The advantage of the lower-dimensional theory is that numerical simulations of multi-solitons and finite density solutions can be performed and compared with flat space instanton approximations. In particular, analogues of dyonic salt and baryonic popcorn configurations are found and analysed.

Uncertainty propagation by using spectral methods: A practical application to a two-dimensional turbulence fluid model

NASA Astrophysics Data System (ADS)

Riva, Fabio; Milanese, Lucio; Ricci, Paolo

2017-10-01

To reduce the computational cost of the uncertainty propagation analysis, which is used to study the impact of input parameter variations on the results of a simulation, a general and simple to apply methodology based on decomposing the solution to the model equations in terms of Chebyshev polynomials is discussed. This methodology, based on the work by Scheffel [Am. J. Comput. Math. 2, 173-193 (2012)], approximates the model equation solution with a semi-analytic expression that depends explicitly on time, spatial coordinates, and input parameters. By employing a weighted residual method, a set of nonlinear algebraic equations for the coefficients appearing in the Chebyshev decomposition is then obtained. The methodology is applied to a two-dimensional Braginskii model used to simulate plasma turbulence in basic plasma physics experiments and in the scrape-off layer of tokamaks, in order to study the impact on the simulation results of the input parameter that describes the parallel losses. The uncertainty that characterizes the time-averaged density gradient lengths, time-averaged densities, and fluctuation density level are evaluated. A reasonable estimate of the uncertainty of these distributions can be obtained with a single reduced-cost simulation.

Free-energy-based lattice Boltzmann model for the simulation of multiphase flows with density contrast.

PubMed

Shao, J Y; Shu, C; Huang, H B; Chew, Y T

2014-03-01

A free-energy-based phase-field lattice Boltzmann method is proposed in this work to simulate multiphase flows with density contrast. The present method is to improve the Zheng-Shu-Chew (ZSC) model [Zheng, Shu, and Chew, J. Comput. Phys. 218, 353 (2006)] for correct consideration of density contrast in the momentum equation. The original ZSC model uses the particle distribution function in the lattice Boltzmann equation (LBE) for the mean density and momentum, which cannot properly consider the effect of local density variation in the momentum equation. To correctly consider it, the particle distribution function in the LBE must be for the local density and momentum. However, when the LBE of such distribution function is solved, it will encounter a severe numerical instability. To overcome this difficulty, a transformation, which is similar to the one used in the Lee-Lin (LL) model [Lee and Lin, J. Comput. Phys. 206, 16 (2005)] is introduced in this work to change the particle distribution function for the local density and momentum into that for the mean density and momentum. As a result, the present model still uses the particle distribution function for the mean density and momentum, and in the meantime, considers the effect of local density variation in the LBE as a forcing term. Numerical examples demonstrate that both the present model and the LL model can correctly simulate multiphase flows with density contrast, and the present model has an obvious improvement over the ZSC model in terms of solution accuracy. In terms of computational time, the present model is less efficient than the ZSC model, but is much more efficient than the LL model.

Study of the effect of electron irradiation on the density of the activated sludge in aqueous solution

NASA Astrophysics Data System (ADS)

Kupchishin, A. I.; Niyazov, M. N.; Taipova, B. G.; Voronova, N. A.; Khodarina, N. N.

2018-01-01

Complex experimental studies on the effect of electron irradiation on the deposition rate of active sludge in aqueous systems by the optical method have been carried out. The obtained dependences of density (ρ) on time (t) are of the same nature for different radiation sources. The experimental curves of the dependence of the active sludge density on time are satisfactorily described by an exponential model.

Binding selectivity of dibenzo-18-crown-6 for alkali metal cations in aqueous solution: A density functional theory study using a continuum solvation model.

PubMed

Choi, Chang Min; Heo, Jiyoung; Kim, Nam Joon

2012-08-08

Dibenzo-18-crown-6 (DB18C6) exhibits the binding selectivity for alkali metal cations in solution phase. In this study, we investigate the main forces that determine the binding selectivity of DB18C6 for the metal cations in aqueous solution using the density functional theory (DFT) and the conductor-like polarizable continuum model (CPCM). The bond dissociation free energies (BDFE) of DB18C6 complexes with alkali metal cations (M+-DB18C6, M = Li, Na, K, Rb, and Cs) in aqueous solution are calculated at the B3LYP/6-311++G(d,p)//B3LYP/6-31 + G(d) level using the CPCM. It is found that the theoretical BDFE is the largest for K+-DB18C6 and decreases as the size of the metal cation gets larger or smaller than that of K+, which agrees well with previous experimental results. The solvation energy of M+-DB18C6 in aqueous solution plays a key role in determining the binding selectivity of DB18C6. In particular, the non-electrostatic dispersion interaction between the solute and solvent, which depends strongly on the complex structure, is largely responsible for the different solvation energies of M+-DB18C6. This study shows that the implicit solvation model like the CPCM works reasonably well in predicting the binding selectivity of DB18C6 in aqueous solution.

Reconstruction of cosmological matter perturbations in modified gravity

NASA Astrophysics Data System (ADS)

Gonzalez, J. E.

2017-12-01

The analysis of perturbative quantities is a powerful tool to distinguish between different dark energy models and gravity theories degenerated at the background level. In this work, we generalize the integral solution of the matter density contrast for general relativity gravity [V. Sahni and A. Starobinsky, Int. J. Mod. Phys. D 15, 2105 (2006)., 10.1142/S0218271806009704, U. Alam, V. Sahni, and A. A. Starobinsky, Astrophys. J. 704, 1086 (2009)., 10.1088/0004-637X/704/2/1086] to a wide class of modified gravity (MG) theories. To calculate this solution, it is necessary to have prior knowledge of the Hubble rate, the density parameter at the present epoch (Ωm 0), and the functional form of the effective Newton's constant that characterizes the gravity theory. We estimate in a model-independent way the Hubble expansion rate by applying a nonparametric reconstruction method to model-independent cosmic chronometer data and high-z quasar data. In order to compare our generalized solution of the matter density contrast, using the nonparametric reconstruction of H (z ) from observational data, with a purely theoretical one, we choose a parametrization of the screened modified gravity and the Ωm 0 from WMAP-9 Collaborations. Finally, we calculate the growth index for the analyzed cases, finding very good agreement between theoretical values and the obtained ones using the approach presented in this work.

Bright, dark, and mixed vector soliton solutions of the general coupled nonlinear Schrödinger equations.

PubMed

Agalarov, Agalar; Zhulego, Vladimir; Gadzhimuradov, Telman

2015-04-01

The reduction procedure for the general coupled nonlinear Schrödinger (GCNLS) equations with four-wave mixing terms is proposed. It is shown that the GCNLS system is equivalent to the well known integrable families of the Manakov and Makhankov U(n,m)-vector models. This equivalence allows us to construct bright-bright and dark-dark solitons and a quasibreather-dark solution with unconventional dynamics: the density of the first component oscillates in space and time, whereas the density of the second component does not. The collision properties of solitons are also studied.

Conformational statistics of stiff macromolecules as solutions to partial differential equations on the rotation and motion groups

PubMed

Chirikjian; Wang

2000-07-01

Partial differential equations (PDE's) for the probability density function (PDF) of the position and orientation of the distal end of a stiff macromolecule relative to its proximal end are derived and solved. The Kratky-Porod wormlike chain, the Yamakawa helical wormlike chain, and the original and revised Marko-Siggia models are examples of stiffness models to which the present formulation is applied. The solution technique uses harmonic analysis on the rotation and motion groups to convert PDE's governing the PDF's of interest into linear algebraic equations which have mathematically elegant solutions.

Polder maps: Improving OMIT maps by excluding bulk solvent

DOE PAGES

Liebschner, Dorothee; Afonine, Pavel V.; Moriarty, Nigel W.; ...

2017-02-01

The crystallographic maps that are routinely used during the structure-solution workflow are almost always model-biased because model information is used for their calculation. As these maps are also used to validate the atomic models that result from model building and refinement, this constitutes an immediate problem: anything added to the model will manifest itself in the map and thus hinder the validation. OMIT maps are a common tool to verify the presence of atoms in the model. The simplest way to compute an OMIT map is to exclude the atoms in question from the structure, update the corresponding structure factorsmore » and compute a residual map. It is then expected that if these atoms are present in the crystal structure, the electron density for the omitted atoms will be seen as positive features in this map. This, however, is complicated by the flat bulk-solvent model which is almost universally used in modern crystallographic refinement programs. This model postulates constant electron density at any voxel of the unit-cell volume that is not occupied by the atomic model. Consequently, if the density arising from the omitted atoms is weak then the bulk-solvent model may obscure it further. A possible solution to this problem is to prevent bulk solvent from entering the selected OMIT regions, which may improve the interpretative power of residual maps. This approach is called a polder (OMIT) map. Polder OMIT maps can be particularly useful for displaying weak densities of ligands, solvent molecules, side chains, alternative conformations and residues both in terminal regions and in loops. As a result, the tools described in this manuscript have been implemented and are available in PHENIX.« less

The influence of surface roughness and solution concentration on pool boiling process in Diethanolamine aqueous solution

NASA Astrophysics Data System (ADS)

Khoshechin, Mohsen; Salimi, Farhad; Jahangiri, Alireza

2018-04-01

In this research, the effect of surface roughness and concentration of solution on bubble departing frequency and nucleation site density for pool boiling of water/diethanolamine (DEA) binary solution were investigated experimentally. In this investigation, boiling heat transfer coefficient, bubble departing frequency and nucleation site density have been experimentally investigated in various concentrations and heat fluxes. Microstructured surfaces with a wide range of well-defined surface roughness were fabricated, and a heat flux between 1.5-86 kW/m2 was achieved under atmospheric conditions. The Results indicated that surface roughness and concentration of solution increase the bubble departing frequency and nucleation site density with increasing heat flux. The boiling heat transfer coefficient in mixtures of water/DEA increases with increasing concentration of DEA in water. The experimental results were compared with predictions of several used correlations in the literatures. Results showed that the boiling heat transfer coefficients of this case study are much higher than the predicted values by major existing correlations and models. The excellent agreement for bubble departing frequency found between the models of Jackob and Fritz (1966) and experimental data and also the nucleation site density were in close agreement with the model of Paul (1983) data. f bubble departure frequency, 1/s or Hz N Number of nucleation sites per area per time R c Minimum cavity size, m D c critical diameter, m g gravitational acceleration, m/s2 ρ density, kg/m3 T temperature, °c ΔT temperature difference, °c d d vapor bubble diameter, m h fg enthalpy of vaporization, J/kg R Roughness, μm Ja Jakob number cp specific heat, J/kg °c Pr Prandtl number Ar Archimedes number h Heat transfer coefficient, J/(m2 °c) tg time it takes to grow a bubble, s q/A heat flux (kW/m2) tw time required to heat the layer, s gc Correction coefficient of incompatible units R a Surface roughness A heated surface area d departure ONB onset of nucleate boiling w surface wall s saturation v vapor l liquid θ groove angle (o) γ influence parameter of heating surface material σ surface tension, N/m.

A Hierarchy of Models for Two-Phase Flows

NASA Astrophysics Data System (ADS)

Bouchut, F.; Brenier, Y.; Cortes, J.; Ripoll, J.-F.

2000-12-01

We derive a hierarchy of models for gas-liquid two-phase flows in the limit of infinite density ratio, when the liquid is assumed to be incompressible. The starting model is a system of nonconservative conservation laws with relaxation. At first order in the density ratio, we get a simplified system with viscosity, while at the limit we obtain a system of two conservation laws, the system of pressureless gases with constraint and undetermined pressure. Formal properties of this constraint model are provided, and sticky blocks solutions are introduced. We propose numerical methods for this last model, and the results are compared with the two previous models.

Measurements of thermodynamic and optical properties of selected aqueous organic and organic-inorganic mixtures of atmospheric relevance.

PubMed

Lienhard, Daniel M; Bones, David L; Zuend, Andreas; Krieger, Ulrich K; Reid, Jonathan P; Peter, Thomas

2012-10-11

Atmospheric aerosol particles can exhibit liquid solution concentrations supersaturated with respect to the dissolved organic and inorganic species and supercooled with respect to ice. In this study, thermodynamic and optical properties of sub- and supersaturated aqueous solutions of atmospheric interest are presented. The density, refractive index, water activity, ice melting temperatures, and homogeneous ice freezing temperatures of binary aqueous solutions containing L(+)-tartaric acid, tannic acid, and levoglucosan and ternary aqueous solutions containing levoglucosan and one of the salts NH(4)HSO(4), (NH(4))(2)SO(4), and NH(4)NO(3) have been measured in the supersaturated concentration range for the first time. In addition, the density and refractive index of binary aqueous citric acid and raffinose solutions and the glass transition temperatures of binary aqueous L(+)-tartaric acid and levoglucosan solutions have been measured. The data presented here are derived from experiments on single levitated microdroplets and bulk solutions and should find application in thermodynamic and atmospheric aerosol models as well as in food science applications.

Models for the dynamics of dust-like matter in the self-gravity field: The method of hydrodynamic substitutions

NASA Astrophysics Data System (ADS)

Zhuravlev, V. M.

2017-09-01

Models for the dynamics of a dust-like medium in the self-gravity field are investigated. Solutions of the corresponding problems are constructed by the method of hydrodynamic substitutions generalizing the Cole-Hopf substitutions. The method is extended to multidimensional ideal and viscous fluid flows with cylindrical and spherical symmetries for which exact solutions are constructed. Solutions for the dynamics of self-gravitating dust with arbitrary initial distributions of both fluid density and velocity are constructed using special coordinate transformations. In particular, the problem of cosmological expansion is considered in terms of Newton's gravity theory. Models of a one-dimensional viscous dust fluid flow and some problems of gas hydrodynamics are considered. Examples of exact solutions and their brief analysis are provided.

Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations

NASA Astrophysics Data System (ADS)

He, Wei

2015-02-01

The Gauge/Bethe correspondence relates Omega-deformed N = 2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory with an adjoint matter, or with 4 fundamental matters, the potential of corresponding quantum model is the elliptic function. If the mass of matter takes special value then the potential is an elliptic solution of KdV hierarchy. We show that the deformed prepotential of gauge theory can be obtained from the average densities of conserved charges of the classical KdV solution, the UV gauge coupling dependence is assembled into the Eisenstein series. The gauge theory with adjoint mass is taken as the example.

Modeling the controllable pH-responsive swelling and pore size of networked alginate based biomaterials.

PubMed

Chan, Ariel W; Neufeld, Ronald J

2009-10-01

Semisynthetic network alginate polymer (SNAP), synthesized by acetalization of linear alginate with di-aldehyde, is a pH-responsive tetrafunctionally linked 3D gel network, and has potential application in oral delivery of protein therapeutics and active biologicals, and as tissue bioscaffold for regenerative medicine. A constitutive polyelectrolyte gel model based on non-Gaussian polymer elasticity, Flory-Huggins liquid lattice theory, and non-ideal Donnan membrane equilibria was derived, to describe SNAP gel swelling in dilute and ionic solutions containing uni-univalent, uni-bivalent, bi-univalent or bi-bi-valent electrolyte solutions. Flory-Huggins interaction parameters as a function of ionic strength and characteristic ratio of alginates of various molecular weights were determined experimentally to numerically predict SNAP hydrogel swelling. SNAP hydrogel swells pronouncedly to 1000 times in dilute solution, compared to its compact polymer volume, while behaving as a neutral polymer with limited swelling in high ionic strength or low pH solutions. The derived model accurately describes the pH-responsive swelling of SNAP hydrogel in acid and alkaline solutions of wide range of ionic strength. The pore sizes of the synthesized SNAP hydrogels of various crosslink densities were estimated from the derived model to be in the range of 30-450 nm which were comparable to that measured by thermoporometry, and diffusion of bovine serum albumin. The derived equilibrium swelling model can characterize hydrogel structure such as molecular weight between crosslinks and crosslinking density, or can be used as predictive model for swelling, pore size and mechanical properties if gel structural information is known, and can potentially be applied to other point-link network polyelectrolytes such as hyaluronic acid gel.

Property Changes in Aqueous Solutions due to Surfactant Treatment of PCE: Implications to Geophysical Measurements

NASA Astrophysics Data System (ADS)

Werkema, D. D.

2007-12-01

Select physicochemical properties of aqueous solutions composed of surfactants, dye, and perchloroethylene (PCE) were evaluated through a response surface quadratic design model of experiment. Nine surfactants, which are conventionally used in the remediation of PCE, were evaluated with varying concentrations of PCE and indicator dyes in aqueous solutions. Two hundred forty experiments were performed using PCE as a numerical factor (coded A) from 0 to 200 parts per million (ppm), dye type (coded B) as a 3-level categorical factor, and surfactant type (coded C) as a 10-level categorical factor. Five responses were measured: temperature (°C), pH, conductivity (μS/cm), dissolved oxygen (DO, mg/L), and density (g/mL). Diagnostics proved a normally distributed predictable response for all measured responses except pH. The Box-Cox plot for transforms recommended a power transform for the conductivity response with lambda (λ) = 0.50, and for the DO response, λ =2.2. The overall mean of the temperature response proved to be a better predictor than the linear model. The conductivity response is best fitted with a linear model using significant coded terms B and C. Both DO and density also showed a linear model with coded terms A, B, and C for DO; and terms A and C for density. Some of the surfactant treatments of PCE significantly alter the conductivity, DO, and density of the aqueous solution. However, the magnitude of the density response is so small that it does not exceed the instrument tolerance. Results for the conductivity and DO responses provide predictive models for the surfactant treatment of PCE and may be useful in determining the potential for geophysically monitoring surfactant enhanced aquifer remediation (SEAR) of PCE. As the aqueous physicochemical properties change due to surfactant remediation efforts, so will the properties of the subsurface pore water which are influential factors in geophysical measurements. Geoelectrical methods are potentially the best suited to measure SEAR alterations in the subsurface because the conductivity of the pore fluid has the largest relative change. This research has provided predictive models for alterations in the physicochemical properties of the pore fluid to SEAR of PCE. Future investigations should address the contribution of the solid matrix in the subsurface and the solid-fluid interaction during SEAR of PCE contamination. Notice: Although this work was reviewed by EPA and approved for publication, it may not necessarily reflect official Agency policy. Mention of trade names or commercial products does not constitute endorsement or recommendation by EPA for use.

Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay.

PubMed

Akimenko, Vitalii; Anguelov, Roumen

2017-12-01

In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtained system is studied both theoretically and numerically. Three different regimes of population dynamics for asymptotically stable states of autonomous systems are obtained in numerical experiments for the different initial values of population density. The quasi-periodical travelling wave solutions are studied numerically for the autonomous system with the different values of time delays and for the system with oscillating death rate and birth modulus. In both cases it is observed three types of travelling wave solutions: harmonic oscillations, pulse sequence and single pulse.

Improving Fermi Orbit Determination and Prediction in an Uncertain Atmospheric Drag Environment

NASA Technical Reports Server (NTRS)

Vavrina, Matthew A.; Newman, Clark P.; Slojkowski, Steven E.; Carpenter, J. Russell

2014-01-01

Orbit determination and prediction of the Fermi Gamma-ray Space Telescope trajectory is strongly impacted by the unpredictability and variability of atmospheric density and the spacecraft's ballistic coefficient. Operationally, Global Positioning System point solutions are processed with an extended Kalman filter for orbit determination, and predictions are generated for conjunction assessment with secondary objects. When these predictions are compared to Joint Space Operations Center radar-based solutions, the close approach distance between the two predictions can greatly differ ahead of the conjunction. This work explores strategies for improving prediction accuracy and helps to explain the prediction disparities. Namely, a tuning analysis is performed to determine atmospheric drag modeling and filter parameters that can improve orbit determination as well as prediction accuracy. A 45% improvement in three-day prediction accuracy is realized by tuning the ballistic coefficient and atmospheric density stochastic models, measurement frequency, and other modeling and filter parameters.

SoftWAXS: a computational tool for modeling wide-angle X-ray solution scattering from biomolecules.

PubMed

Bardhan, Jaydeep; Park, Sanghyun; Makowski, Lee

2009-10-01

This paper describes a computational approach to estimating wide-angle X-ray solution scattering (WAXS) from proteins, which has been implemented in a computer program called SoftWAXS. The accuracy and efficiency of SoftWAXS are analyzed for analytically solvable model problems as well as for proteins. Key features of the approach include a numerical procedure for performing the required spherical averaging and explicit representation of the solute-solvent boundary and the surface of the hydration layer. These features allow the Fourier transform of the excluded volume and hydration layer to be computed directly and with high accuracy. This approach will allow future investigation of different treatments of the electron density in the hydration shell. Numerical results illustrate the differences between this approach to modeling the excluded volume and a widely used model that treats the excluded-volume function as a sum of Gaussians representing the individual atomic excluded volumes. Comparison of the results obtained here with those from explicit-solvent molecular dynamics clarifies shortcomings inherent to the representation of solvent as a time-averaged electron-density profile. In addition, an assessment is made of how the calculated scattering patterns depend on input parameters such as the solute-atom radii, the width of the hydration shell and the hydration-layer contrast. These results suggest that obtaining predictive calculations of high-resolution WAXS patterns may require sophisticated treatments of solvent.

Non-uniform Continuum Model for Solvated Species Based on Frozen-Density Embedding Theory: The Study Case of Solvatochromism of Coumarin 153.

PubMed

Shedge, Sapana V; Zhou, Xiuwen; Wesolowski, Tomasz A

2014-09-01

Recent application of the Frozen-Density Embedding Theory based continuum model of the solvent, which is used for calculating solvatochromic shifts in the UV/Vis range, are reviewed. In this model, the solvent is represented as a non-uniform continuum taking into account both the statistical nature of the solvent and specific solute-solvent interactions. It offers, therefore, a computationally attractive alternative to methods in which the solvent is described at atomistic level. The evaluation of the solvatochromic shift involves only two calculations of excitation energy instead of at least hundreds needed to account for inhomogeneous broadening. The present review provides a detailed graphical analysis of the key quantities of this model: the average charge density of the solvent (<ρB>) and the corresponding Frozen-Density Embedding Theory derived embedding potential for coumarin 153.

How can we model selectively neutral density dependence in evolutionary games.

PubMed

Argasinski, Krzysztof; Kozłowski, Jan

2008-03-01

The problem of density dependence appears in all approaches to the modelling of population dynamics. It is pertinent to classic models (i.e., Lotka-Volterra's), and also population genetics and game theoretical models related to the replicator dynamics. There is no density dependence in the classic formulation of replicator dynamics, which means that population size may grow to infinity. Therefore the question arises: How is unlimited population growth suppressed in frequency-dependent models? Two categories of solutions can be found in the literature. In the first, replicator dynamics is independent of background fitness. In the second type of solution, a multiplicative suppression coefficient is used, as in a logistic equation. Both approaches have disadvantages. The first one is incompatible with the methods of life history theory and basic probabilistic intuitions. The logistic type of suppression of per capita growth rate stops trajectories of selection when population size reaches the maximal value (carrying capacity); hence this method does not satisfy selective neutrality. To overcome these difficulties, we must explicitly consider turn-over of individuals dependent on mortality rate. This new approach leads to two interesting predictions. First, the equilibrium value of population size is lower than carrying capacity and depends on the mortality rate. Second, although the phase portrait of selection trajectories is the same as in density-independent replicator dynamics, pace of selection slows down when population size approaches equilibrium, and then remains constant and dependent on the rate of turn-over of individuals.

Electrolyte effects in a model of proton discharge on charged electrodes

NASA Astrophysics Data System (ADS)

Wiebe, Johannes; Kravchenko, Kateryna; Spohr, Eckhard

2015-01-01

We report results on the influence of NaCl electrolyte dissolved in water on proton discharge reactions from aqueous solution to charged platinum electrodes. We have extended a recently developed combined proton transfer/proton discharge model on the basis of empirical valence bond theory to include NaCl solutions with several different concentrations of cations and anions, both stoichiometric (1:1) compositions and non-stoichiometric ones with an excess of cations. The latter solutions partially screen the electrostatic potential from the surface charge of the negatively charged electrode. 500-1000 trajectories of a discharging proton were integrated by molecular dynamics simulations until discharge occurred, or for at most 1.5 ns. The results show a strong dependence on ionic strength, but only a weak dependence on the screening behavior, when comparing stoichiometric and non-stoichiometric solutions. Overall, the Na+ cations exert a more dominant effect on the discharge reaction, which we argue is likely due to the very rigid arrangements of the cations on the negatively polarized electrode surface. Thus, our model predicts, for the given and very high negative surface charge densities, the fastest discharge reaction for pure water, but obviously cannot take into account the fact that such high charge densities are even more out of reach experimentally than for higher electrolyte concentrations.

Percolation and epidemics in a two-dimensional small world

NASA Astrophysics Data System (ADS)

Newman, M. E.; Jensen, I.; Ziff, R. M.

2002-02-01

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of ``shortcuts'' in the small-world network. Our results agree with scaling hypotheses and numerical simulations for the same model.

Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations.

PubMed

Nick, H M; Paluszny, A; Blunt, M J; Matthai, S K

2011-11-01

A second order in space accurate implicit scheme for time-dependent advection-dispersion equations and a discrete fracture propagation model are employed to model solute transport in porous media. We study the impact of the fractures on mass transport and dispersion. To model flow and transport, pressure and transport equations are integrated using a finite-element, node-centered finite-volume approach. Fracture geometries are incrementally developed from a random distributions of material flaws using an adoptive geomechanical finite-element model that also produces fracture aperture distributions. This quasistatic propagation assumes a linear elastic rock matrix, and crack propagation is governed by a subcritical crack growth failure criterion. Fracture propagation, intersection, and closure are handled geometrically. The flow and transport simulations are separately conducted for a range of fracture densities that are generated by the geomechanical finite-element model. These computations show that the most influential parameters for solute transport in fractured porous media are as follows: fracture density and fracture-matrix flux ratio that is influenced by matrix permeability. Using an equivalent fracture aperture size, computed on the basis of equivalent permeability of the system, we also obtain an acceptable prediction of the macrodispersion of poorly interconnected fracture networks. The results hold for fractures at relatively low density.

On the magnetic circular dichroism of benzene. A density-functional study

NASA Astrophysics Data System (ADS)

Kaminský, Jakub; Kříž, Jan; Bouř, Petr

2017-04-01

Spectroscopy of magnetic circular dichroism (MCD) provides enhanced information on molecular structure and a more reliable assignment of spectral bands than absorption alone. Theoretical modeling can significantly enhance the information obtained from experimental spectra. In the present study, the time dependent density functional theory is employed to model the lowest-energy benzene transitions, in particular to investigate the role of the Rydberg states and vibrational interference in spectral intensities. The effect of solvent is explored on model benzene-methane clusters. For the lowest-energy excitation, the vibrational sub-structure of absorption and MCD spectra is modeled within the harmonic approximation, providing a very good agreement with the experiment. The simulations demonstrate that the Rydberg states have a much stronger effect on the MCD intensities than on the absorption, and a very diffuse basis set must be used to obtain reliable results. The modeling also indicates that the Rydberg-like states and associated transitions may persist in solutions. Continuum-like solvent models are thus not suitable for their modeling; solvent-solute clusters appear to be more appropriate, providing they are large enough.

Zinc electrodeposition from flowing alkaline zincate solutions: Role of hydrogen evolution reaction

NASA Astrophysics Data System (ADS)

Dundálek, Jan; Šnajdr, Ivo; Libánský, Ondřej; Vrána, Jiří; Pocedič, Jaromír; Mazúr, Petr; Kosek, Juraj

2017-12-01

The hydrogen evolution reaction is known as a parasitic reaction during the zinc electrodeposition from alkaline zincate solutions and is thus responsible for current efficiency losses during the electrolysis. Besides that, the rising hydrogen bubbles may cause an extra convection within a diffusion layer, which leads to an enhanced mass transport of zincate ions to an electrode surface. In this work, the mentioned phenomena were studied experimentally in a flow through electrolyzer and the obtained data were subsequently evaluated by mathematical models. The results prove the indisputable influence of the rising hydrogen bubbles on the additional mixing of the diffusion layer, which partially compensates the drop of the current efficiency of the zinc deposition at higher current flows. Moreover, the results show that the current density ratio (i.e., the ratio of an overall current density to a zinc limiting current density) is not suitable for the description of the zinc deposition, because the hydrogen evolution current density is always involved in the overall current density.

Integrable model for density-modulated quantum condensates: Solitons passing through a soliton lattice.

PubMed

Takahashi, Daisuke A

2016-06-01

An integrable model possessing inhomogeneous ground states is proposed as an effective model of nonuniform quantum condensates such as supersolids and Fulde-Ferrell-Larkin-Ovchinnikov superfluids. The model is a higher-order analog of the nonlinear Schrödinger equation. We derive an n-soliton solution via the inverse scattering theory with elliptic-functional background and reveal various kinds of soliton dynamics such as dark soliton billiards, dislocations, gray solitons, and envelope solitons. We also provide the exact bosonic and fermionic quasiparticle eigenstates and show their tunneling phenomena. The solutions are expressed by a determinant of theta functions.

Size effects of pore density and solute size on water osmosis through nanoporous membrane.

PubMed

Zhao, Kuiwen; Wu, Huiying

2012-11-15

Understanding the behavior of osmotic transport across nanoporous membranes at molecular level is critical to their design and applications, and it is also beneficial to the comprehension of the mechanism of biological transmembrane transport processes. Pore density is an important parameter for nanoporous membranes. To better understand the influence of pore density on osmotic transport, we have performed systematic molecular dynamics simulations on water osmosis across nanoporous membranes with different pore densities (i.e., number of pores per unit area of membrane). The simulation results reveal that significant size effects occur when the pore density is so high that the center-to-center distance between neighboring nanopores is comparable to the solute size. The size effects are independent of the pore diameter and solute concentration. A simple quantitative correlation between pore density, solute size, and osmotic flux has been established. The results are excellently consistent with the theoretical predictions. It is also shown that solute hydration plays an important role in real osmotic processes. Solute hydration strengthens the size effects of pore density on osmotic processes due to the enlarged effective solute size induced by hydration. The influence of pore density, solute size, and solute hydration on water osmosis through nanoporous membranes can be introduced to eliminate the deviations of real osmotic processes from ideal behavior.

Water Density in the Electric Double Layer at the Insulator/Electrolyte Solution Interface

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

Tikhonov,A.

I studied the spatial structure of the thick transition region between n-hexane and a colloidal solution of 7-nm silica particles by X-ray reflectivity and grazing incidence small-angle scattering. The interfacial structure is discussed in terms of a semiquantitative interface model wherein the potential gradient at the n-hexane/sol interface reflects the difference in the potentials of 'image forces' between the cationic Na{sup +} and anions (nanoparticles) and the specific adsorption of surface charge at the interface between the adsorbed layer and the solution, as well as at the interface between the adsorbed layer and n-hexane. The X-ray scattering data revealed thatmore » the average density of water in the field {approx}10{sup 9}-10{sup 10} V/m of the electrical double layer at the hexane/silica sol interface is the same as, or only few percent higher (1-7%) than, its density under normal conditions.« less

Theoretical study of the influence of chemical reactions and physical parameters on the convective dissolution of CO2 in aqueous solutions

NASA Astrophysics Data System (ADS)

Loodts, Vanessa; Rongy, Laurence; De Wit, Anne

2014-05-01

Subsurface carbon sequestration has emerged as a promising solution to the problem of increasing atmospheric carbon dioxide (CO2) levels. How does the efficiency of such a sequestration process depend on the physical and chemical characteristics of the storage site? This question is emblematic of the need to better understand the dynamics of CO2 in subsurface formations, and in particular, the properties of the convective dissolution of CO2 in the salt water of aquifers. This dissolution is known to improve the safety of the sequestration by reducing the risks of leaks of CO2 to the atmosphere. Buoyancy-driven convection makes this dissolution faster by transporting dissolved CO2 further away from the interface. Indeed, upon injection, the less dense CO2 phase rises above the aqueous layer where it starts to dissolve. The dissolved CO2 increases the density of the aqueous solution, thereby creating a layer of denser CO2-rich solution above less dense solution. This unstable density gradient in the gravity field is at the origin of convection. In this framework, we theoretically investigate the effect of CO2 pressure, salt concentration, temperature, and chemical reactions on the dissolution-driven convection of CO2 in aqueous solutions. On the basis of a linear stability analysis, we assess the stability of the time-dependent density profiles developing when CO2 dissolves in an aqueous layer below it. We predict that increasing CO2 pressure destabilizes the system with regard to buoyancy-driven convection, because it increases the density gradient at the origin of the instability. By contrast, increasing salt concentration or temperature stabilizes the system via effects on CO2 solubility, solutal expansion coefficient, diffusion coefficient and on the viscosity and density of the solution. We also show that a reaction of CO2 with chemical species dissolved in the aqueous solution can either enhance or decrease the amplitude of the convective dissolution compared to the non reactive one. On the basis of a reaction-diffusion-convection model, we classify the various possible cases and show that the difference between the solutal expansion coefficients of the reactant and of the product governs the type of density profile building up in the aqueous solution and thus the stability of the system. By contrast to non reactive density profiles, reactive density profiles can feature a minimum that induces a delay of the buoyancy-driven convection. This work identifies the parameters that could influence the dissolution-driven convection in the aquifers, and thus impact the safety of the sequestration. In other words, this theoretical study shows that it is crucial to analyse the composition and reactivity of potential storage sites to choose those that will be most efficient for long-term CO2 sequestration.

Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices

NASA Astrophysics Data System (ADS)

Huang, Feimin; Li, Tianhong; Yu, Huimin; Yuan, Difan

2018-06-01

We are concerned with the global existence and large time behavior of entropy solutions to the one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations in a bounded interval. In this paper, we first prove the global existence of entropy solution by vanishing viscosity and compensated compactness framework. In particular, the solutions are uniformly bounded with respect to space and time variables by introducing modified Riemann invariants and the theory of invariant region. Based on the uniform estimates of density, we further show that the entropy solution converges to the corresponding unique stationary solution exponentially in time. No any smallness condition is assumed on the initial data and doping profile. Moreover, the novelty in this paper is about the unform bound with respect to time for the weak solutions of the isentropic Euler-Poisson system.

Measurement and modeling of diameter distributions of particulate matter in terrestrial solutions

NASA Astrophysics Data System (ADS)

Levia, Delphis F.; Michalzik, Beate; Bischoff, Sebastian; NäThe, Kerstin; Legates, David R.; Gruselle, Marie-Cecile; Richter, Susanne

2013-04-01

Particulate matter (PM) plays an important role in biogeosciences, affecting biosphere-atmosphere interactions and ecosystem health. This is the first known study to quantify and model PM diameter distributions of bulk precipitation, throughfall, stemflow, and organic layer (Oa) solution. Solutions were collected from a European beech (Fagus sylvatica L.) forest during leafed and leafless periods. Following scanning electron microscopy and image analysis, PM distributions were quantified and then modeled with the Box-Cox transformation. Based on an analysis of 43,278 individual particulates, median PM diameter of all solutions was around 3.0 µm. All PM diameter frequency distributions were skewed significantly to the right. Optimal power transformations of PM diameter distributions were between -1.00 and -1.56. The utility of this model reconstruction would be that large samples having a similar probability density function can be developed for similar forests. Further work on the shape and chemical composition of particulates is warranted.

Quantification of surface charge density and its effect on boundary slip.

PubMed

Jing, Dalei; Bhushan, Bharat

2013-06-11

Reduction of fluid drag is important in the micro-/nanofluidic systems. Surface charge and boundary slip can affect the fluid drag, and surface charge is also believed to affect boundary slip. The quantification of surface charge and boundary slip at a solid-liquid interface has been widely studied, but there is a lack of understanding of the effect of surface charge on boundary slip. In this paper, the surface charge density of borosilicate glass and octadecyltrichlorosilane (OTS) surfaces immersed in saline solutions with two ionic concentrations and deionized (DI) water with different pH values and electric field values is quantified by fitting experimental atomic force microscopy (AFM) electrostatic force data using a theoretical model relating the surface charge density and electrostatic force. Results show that pH and electric field can affect the surface charge density of glass and OTS surfaces immersed in saline solutions and DI water. The mechanisms of the effect of pH and electric field on the surface charge density are discussed. The slip length of the OTS surface immersed in saline solutions with two ionic concentrations and DI water with different pH values and electric field values is measured, and their effects on the slip length are analyzed from the point of surface charge. Results show that a larger absolute value of surface charge density leads to a smaller slip length for the OTS surface.

Development and Validation of the Whole Atmosphere Community Climate Model With Thermosphere and Ionosphere Extension (WACCM-X 2.0)

NASA Astrophysics Data System (ADS)

Liu, Han-Li; Bardeen, Charles G.; Foster, Benjamin T.; Lauritzen, Peter; Liu, Jing; Lu, Gang; Marsh, Daniel R.; Maute, Astrid; McInerney, Joseph M.; Pedatella, Nicholas M.; Qian, Liying; Richmond, Arthur D.; Roble, Raymond G.; Solomon, Stanley C.; Vitt, Francis M.; Wang, Wenbin

2018-02-01

Key developments have been made to the NCAR Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension (WACCM-X). Among them, the most important are the self-consistent solution of global electrodynamics, and transport of O+ in the F-region. Other ionosphere developments include time-dependent solution of electron/ion temperatures, metastable O+ chemistry, and high-cadence solar EUV capability. Additional developments of the thermospheric components are improvements to the momentum and energy equation solvers to account for variable mean molecular mass and specific heat, a new divergence damping scheme, and cooling by O(3P) fine structure. Simulations using this new version of WACCM-X (2.0) have been carried out for solar maximum and minimum conditions. Thermospheric composition, density, and temperatures are in general agreement with measurements and empirical models, including the equatorial mass density anomaly and the midnight density maximum. The amplitudes and seasonal variations of atmospheric tides in the mesosphere and lower thermosphere are in good agreement with observations. Although global mean thermospheric densities are comparable with observations of the annual variation, they lack a clear semiannual variation. In the ionosphere, the low-latitude E × B drifts agree well with observations in their magnitudes, local time dependence, seasonal, and solar activity variations. The prereversal enhancement in the equatorial region, which is associated with ionospheric irregularities, displays patterns of longitudinal and seasonal variation that are similar to observations. Ionospheric density from the model simulations reproduces the equatorial ionosphere anomaly structures and is in general agreement with observations. The model simulations also capture important ionospheric features during storms.

Atmospheric constituent density profiles from full disk solar occultation experiments

NASA Technical Reports Server (NTRS)

Lumpe, J. D.; Chang, C. S.; Strickland, D. J.

1991-01-01

Mathematical methods are described which permit the derivation of the number of density profiles of atmospheric constituents from solar occultation measurements. The algorithm is first applied to measurements corresponding to an arbitrary solar-intensity distribution to calculate the normalized absorption profile. The application of Fourier transform to the integral equation yields a precise expression for the corresponding number density, and the solution is employed with the data given in the form of Laguerre polynomials. The algorithm is employed to calculate the results for the case of uniform distribution of solar intensity, and the results demonstrate the convergence properties of the method. The algorithm can be used to effectively model representative model-density profiles with constant and altitude-dependent scale heights.

Time-dependent density functional theory (TD-DFT) coupled with reference interaction site model self-consistent field explicitly including spatial electron density distribution (RISM-SCF-SEDD)

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

Yokogawa, D., E-mail: d.yokogawa@chem.nagoya-u.ac.jp; Institute of Transformative Bio-Molecules

2016-09-07

Theoretical approach to design bright bio-imaging molecules is one of the most progressing ones. However, because of the system size and computational accuracy, the number of theoretical studies is limited to our knowledge. To overcome the difficulties, we developed a new method based on reference interaction site model self-consistent field explicitly including spatial electron density distribution and time-dependent density functional theory. We applied it to the calculation of indole and 5-cyanoindole at ground and excited states in gas and solution phases. The changes in the optimized geometries were clearly explained with resonance structures and the Stokes shift was correctly reproduced.

Accurate coarse-grained models for mixtures of colloids and linear polymers under good-solvent conditions

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

D’Adamo, Giuseppe, E-mail: giuseppe.dadamo@sissa.it; Pelissetto, Andrea, E-mail: andrea.pelissetto@roma1.infn.it; Pierleoni, Carlo, E-mail: carlo.pierleoni@aquila.infn.it

2014-12-28

A coarse-graining strategy, previously developed for polymer solutions, is extended here to mixtures of linear polymers and hard-sphere colloids. In this approach, groups of monomers are mapped onto a single pseudoatom (a blob) and the effective blob-blob interactions are obtained by requiring the model to reproduce some large-scale structural properties in the zero-density limit. We show that an accurate parametrization of the polymer-colloid interactions is obtained by simply introducing pair potentials between blobs and colloids. For the coarse-grained (CG) model in which polymers are modelled as four-blob chains (tetramers), the pair potentials are determined by means of the iterative Boltzmannmore » inversion scheme, taking full-monomer (FM) pair correlation functions at zero-density as targets. For a larger number n of blobs, pair potentials are determined by using a simple transferability assumption based on the polymer self-similarity. We validate the model by comparing its predictions with full-monomer results for the interfacial properties of polymer solutions in the presence of a single colloid and for thermodynamic and structural properties in the homogeneous phase at finite polymer and colloid density. The tetramer model is quite accurate for q ≲ 1 (q=R{sup ^}{sub g}/R{sub c}, where R{sup ^}{sub g} is the zero-density polymer radius of gyration and R{sub c} is the colloid radius) and reasonably good also for q = 2. For q = 2, an accurate coarse-grained description is obtained by using the n = 10 blob model. We also compare our results with those obtained by using single-blob models with state-dependent potentials.« less

Modeling the Quiet Time Outflow Solution in the Polar Cap

NASA Technical Reports Server (NTRS)

Glocer, Alex

2011-01-01

We use the Polar Wind Outflow Model (PWOM) to study the geomagnetically quiet conditions in the polar cap during solar maximum, The PWOM solves the gyrotropic transport equations for O(+), H(+), and He(+) along several magnetic field lines in the polar region in order to reconstruct the full 3D solution. We directly compare our simulation results to the data based empirical model of Kitamura et al. [2011] of electron density, which is based on 63 months of Akebono satellite observations. The modeled ion and electron temperatures are also compared with a statistical compilation of quiet time data obtained by the EISCAT Svalbard Radar (ESR) and Intercosmos Satellites (Kitamura et al. [2011]). The data and model agree reasonably well. This study shows that photoelectrons play an important role in explaining the differences between sunlit and dark results, ion composition, as well as ion and electron temperatures of the quiet time polar wind solution. Moreover, these results provide validation of the PWOM's ability to model the quiet time ((background" solution.

Electronic and elastic mode locking in charge density wave conductors

NASA Astrophysics Data System (ADS)

Zettl, A.

1986-12-01

Mode locking phenomena are investigated in the charge density wave (CDW) materials NbSe 3 and TaS 3. The joint application of ac and dc electric fields results in free running and mode locked solutions for the CDW drift velocity, with associated ac-induced dynamic coherence lengths ξ D(ac) on the order of several hundred microns. The electronic response couples directly to the elastic properties of the crystal, with corresponding free running and mode locked solutions for the velocity of sound. Phase slip center-induced discontinuities in the CDW phase velocity lead to mode locked solutions with period doubling routes to chaos, and noisy precursor effects at bifurcation points. These results are discussed in terms of simple models of CDW domain synchronization, and internal CDW dynamics.

Phase-plane analysis of the totally asymmetric simple exclusion process with binding kinetics and switching between antiparallel lanes

PubMed Central

Kuan, Hui-Shun; Betterton, Meredith D.

2016-01-01

Motor protein motion on biopolymers can be described by models related to the totally asymmetric simple exclusion process (TASEP). Inspired by experiments on the motion of kinesin-4 motors on antiparallel microtubule overlaps, we analyze a model incorporating the TASEP on two antiparallel lanes with binding kinetics and lane switching. We determine the steady-state motor density profiles using phase-plane analysis of the steady-state mean field equations and kinetic Monte Carlo simulations. We focus on the density-density phase plane, where we find an analytic solution to the mean field model. By studying the phase-space flows, we determine the model’s fixed points and their changes with parameters. Phases previously identified for the single-lane model occur for low switching rate between lanes. We predict a multiple coexistence phase due to additional fixed points that appear as the switching rate increases: switching moves motors from the higher-density to the lower-density lane, causing local jamming and creating multiple domain walls. We determine the phase diagram of the model for both symmetric and general boundary conditions. PMID:27627345

The rotating movement of three immiscible fluids - A benchmark problem

USGS Publications Warehouse

Bakker, M.; Oude, Essink G.H.P.; Langevin, C.D.

2004-01-01

A benchmark problem involving the rotating movement of three immiscible fluids is proposed for verifying the density-dependent flow component of groundwater flow codes. The problem consists of a two-dimensional strip in the vertical plane filled with three fluids of different densities separated by interfaces. Initially, the interfaces between the fluids make a 45??angle with the horizontal. Over time, the fluids rotate to the stable position whereby the interfaces are horizontal; all flow is caused by density differences. Two cases of the problem are presented, one resulting in a symmetric flow field and one resulting in an asymmetric flow field. An exact analytical solution for the initial flow field is presented by application of the vortex theory and complex variables. Numerical results are obtained using three variable-density groundwater flow codes (SWI, MOCDENS3D, and SEAWAT). Initial horizontal velocities of the interfaces, as simulated by the three codes, compare well with the exact solution. The three codes are used to simulate the positions of the interfaces at two times; the three codes produce nearly identical results. The agreement between the results is evidence that the specific rotational behavior predicted by the models is correct. It also shows that the proposed problem may be used to benchmark variable-density codes. It is concluded that the three models can be used to model accurately the movement of interfaces between immiscible fluids, and have little or no numerical dispersion. ?? 2003 Elsevier B.V. All rights reserved.

High-throughput ab-initio dilute solute diffusion database.

PubMed

Wu, Henry; Mayeshiba, Tam; Morgan, Dane

2016-07-19

We demonstrate automated generation of diffusion databases from high-throughput density functional theory (DFT) calculations. A total of more than 230 dilute solute diffusion systems in Mg, Al, Cu, Ni, Pd, and Pt host lattices have been determined using multi-frequency diffusion models. We apply a correction method for solute diffusion in alloys using experimental and simulated values of host self-diffusivity. We find good agreement with experimental solute diffusion data, obtaining a weighted activation barrier RMS error of 0.176 eV when excluding magnetic solutes in non-magnetic alloys. The compiled database is the largest collection of consistently calculated ab-initio solute diffusion data in the world.

Approximate solution for the electronic density profile at the surface of jellium

NASA Astrophysics Data System (ADS)

Schmickler, Wolfgang; Henderson, Douglas

1984-09-01

A simple family of trial functions for the electronic density at the surface of jellium, which accounts for Friedel oscillations and incorporates the Budd-Vannimenus theorem, is proposed. The free parameters are determined by energy minimization. Model calculations give good results for the work function and for the induced surface charge in the presence of an external field.

On the Solution of the Continuity Equation for Precipitating Electrons in Solar Flares

NASA Technical Reports Server (NTRS)

Emslie, A. Gordon; Holman, Gordon D.; Litvinenko, Yuri E.

2014-01-01

Electrons accelerated in solar flares are injected into the surrounding plasma, where they are subjected to the influence of collisional (Coulomb) energy losses. Their evolution is modeled by a partial differential equation describing continuity of electron number. In a recent paper, Dobranskis & Zharkova claim to have found an "updated exact analytical solution" to this continuity equation. Their solution contains an additional term that drives an exponential decrease in electron density with depth, leading them to assert that the well-known solution derived by Brown, Syrovatskii & Shmeleva, and many others is invalid. We show that the solution of Dobranskis & Zharkova results from a fundamental error in the application of the method of characteristics and is hence incorrect. Further, their comparison of the "new" analytical solution with numerical solutions of the Fokker-Planck equation fails to lend support to their result.We conclude that Dobranskis & Zharkova's solution of the universally accepted and well-established continuity equation is incorrect, and that their criticism of the correct solution is unfounded. We also demonstrate the formal equivalence of the approaches of Syrovatskii & Shmeleva and Brown, with particular reference to the evolution of the electron flux and number density (both differential in energy) in a collisional thick target. We strongly urge use of these long-established, correct solutions in future works.

Influence of thermal effects on buoyancy-driven convection around autocatalytic chemical fronts propagating horizontally.

PubMed

Rongy, L; Schuszter, G; Sinkó, Z; Tóth, T; Horváth, D; Tóth, A; De Wit, A

2009-06-01

The spatiotemporal dynamics of vertical autocatalytic fronts traveling horizontally in thin solution layers closed to the air can be influenced by buoyancy-driven convection induced by density gradients across the front. We perform here a combined experimental and theoretical study of the competition between solutal and thermal effects on such convection. Experimentally, we focus on the antagonistic chlorite-tetrathionate reaction for which solutal and thermal contributions to the density jump across the front have opposite signs. We show that in isothermal conditions the heavier products sink below the lighter reactants, providing an asymptotic constant finger shape deformation of the front by convection. When thermal effects are present, the hotter products, on the contrary, climb above the reactants for strongly exothermic conditions. These various observations as well as the influence of the relative weight of the solutal and thermal effects and of the thickness of the solution layer on the dynamics are discussed in terms of a two-dimensional reaction-diffusion-convection model parametrized by a solutal R(C) and a thermal R(T) Rayleigh number.

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

Coughlin, Eric R., E-mail: eric_coughlin@berkeley.edu

We present the exact solutions for the collapse of a spherically symmetric cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston’s solution of pressureless self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly short, implying that much of the collapse proceedsmore » non-self-similarly. We show that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities—potentially generated by such turbulence—as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their dynamical influence is small, and we recover exact solutions for these quantities. Our results may provide important constraints on numerical models that attempt to elucidate the details of protostellar collapse when the initial conditions are far less idealized.« less

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

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

PubMed

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

2014-06-01

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

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.

Model improvements and validation of TerraSAR-X precise orbit determination

NASA Astrophysics Data System (ADS)

Hackel, S.; Montenbruck, O.; Steigenberger, P.; Balss, U.; Gisinger, C.; Eineder, M.

2017-05-01

The radar imaging satellite mission TerraSAR-X requires precisely determined satellite orbits for validating geodetic remote sensing techniques. Since the achieved quality of the operationally derived, reduced-dynamic (RD) orbit solutions limits the capabilities of the synthetic aperture radar (SAR) validation, an effort is made to improve the estimated orbit solutions. This paper discusses the benefits of refined dynamical models on orbit accuracy as well as estimated empirical accelerations and compares different dynamic models in a RD orbit determination. Modeling aspects discussed in the paper include the use of a macro-model for drag and radiation pressure computation, the use of high-quality atmospheric density and wind models as well as the benefit of high-fidelity gravity and ocean tide models. The Sun-synchronous dusk-dawn orbit geometry of TerraSAR-X results in a particular high correlation of solar radiation pressure modeling and estimated normal-direction positions. Furthermore, this mission offers a unique suite of independent sensors for orbit validation. Several parameters serve as quality indicators for the estimated satellite orbit solutions. These include the magnitude of the estimated empirical accelerations, satellite laser ranging (SLR) residuals, and SLR-based orbit corrections. Moreover, the radargrammetric distance measurements of the SAR instrument are selected for assessing the quality of the orbit solutions and compared to the SLR analysis. The use of high-fidelity satellite dynamics models in the RD approach is shown to clearly improve the orbit quality compared to simplified models and loosely constrained empirical accelerations. The estimated empirical accelerations are substantially reduced by 30% in tangential direction when working with the refined dynamical models. Likewise the SLR residuals are reduced from -3 ± 17 to 2 ± 13 mm, and the SLR-derived normal-direction position corrections are reduced from 15 to 6 mm, obtained from the 2012-2014 period. The radar range bias is reduced from -10.3 to -6.1 mm with the updated orbit solutions, which coincides with the reduced standard deviation of the SLR residuals. The improvements are mainly driven by the satellite macro-model for the purpose of solar radiation pressure modeling, improved atmospheric density models, and the use of state-of-the-art gravity field models.

SOLPS modeling of the effect on plasma detachment of closing the lower divertor in DIII-D

DOE PAGES

Sang, C. F.; Stangeby, P. C.; Guo, H. Y.; ...

2016-12-15

SOLPS modeling has been carried out to assess the effect of tightly closing the lower divertor in DIII-D, which at present is almost fully open, on the achievement of cold dissipative/detached divertor conditions. To isolate the impact of other factors on the divertor plasma solution and to make direct comparisons, most of the parameters including the meshes were kept as similar as possible. Only the neutral baffling was modified to compare a fully open divertor with a tightly closed one. The modeling shows that the tightly closed divertor greatly improves trapping of recycling neutrals, thereby increasing radiative and charge exchangemore » losses in the divertor and reducing the electron temperature T et and deposited power density q dep at the target plate. Furthermore, the closed structure enables the divertor plasma to enter into highly dissipative and detached divertor conditions at a significantly lower upstream density. The effects of divertor closure on the neutral density and pressure, and their correlation with the divertor plasma conditions are also demonstrated. The effect of molecular D 2- ion D + elastic collisions and neutral-neutral collisions on the divertor plasma solution are assessed.« less

Horizontal pre-asymptotic solute transport in a plane fracture with significant density contrasts.

PubMed

Bouquain, J; Meheust, Y; Davy, P

2011-03-01

We investigate the dispersion of a finite amount of solute after it has been injected into the laminar flow occurring in a horizontal smooth fracture of constant aperture. When solute buoyancy is negligible, the dispersion process eventually leads to the well-known asymptotic Taylor-Aris dispersion regime, in which the solute progresses along the fracture at the average fluid velocity, according to a one-dimensional longitudinal advection-dispersion process. This paper addresses more realistic configurations for which the solute-induced density contrasts within the fluid play an important role on solute transport, in particular at small and moderate times. Flow and transport are coupled, since the solute distribution impacts the variations in time of the advecting velocity field. Transport is simulated using (i) a mathematical description based on the Boussinesq approximation and (ii) a numerical scheme based on a finite element analysis. This enables complete characterization of the process, in particular at moderate times for which existing analytical models are not valid. At very short times as well as very long times, the overall downward advective solute mass flow is observed to scale as the square of the injected concentration. The asymptotic Taylor-Aris effective dispersion coefficient is reached eventually, but vertical density currents, which are significant at short and moderate times, are responsible for a systematic retardation of the asymptotic mean solute position with respect to the frame moving at the mean fluid velocity, as well as for a time shift in the establishment of the asymptotic dispersion regime. These delays are characterized as functions of the Péclet number and another non-dimensional number which we call advective Archimedes number, and which quantifies the ratio of buoyancy to viscous forces. Depending on the Péclet number, the asymptotic dispersion is measured to be either larger or smaller than what it would be in the absence of buoyancy effects. Breakthrough curves measured at distances larger than the typical distance needed to reach the asymptotic dispersion regime are impacted accordingly. These findings suggest that, under certain conditions, density/buoyancy effects may have to be taken into consideration when interpreting field measurement of solute transport in fractured media. They also allow an estimate of the conditions under which density effects related to fracture wall roughness are likely to be significant. Copyright © 2010 Elsevier B.V. All rights reserved.

A quadrature based method of moments for nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin L.; Vedula, Prakash

2011-09-01

Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.

Particle flows to shape and voltage surface discontinuities in the electron sheath surrounding a high voltage solar array in LEO

NASA Technical Reports Server (NTRS)

Metz, Roger N.

1991-01-01

This paper discusses the numerical modeling of electron flows from the sheath surrounding high positively biased objects in LEO (Low Earth Orbit) to regions of voltage or shape discontinuity on the biased surfaces. The sheath equations are derived from the Two-fluid, Warm Plasma Model. An equipotential corner and a plane containing strips of alternating voltage bias are treated in two dimensions. A self-consistent field solution of the sheath equations is outlined and is pursued through one cycle. The electron density field is determined by numerical solution of Poisson's equation for the electrostatic potential in the sheath using the NASCAP-LEO relation between electrostatic potential and charge density. Electron flows are calculated numerically from the electron continuity equation. Magnetic field effects are not treated.

Electronic Structure and Properties of Deformed Carbon Nanotubes

NASA Technical Reports Server (NTRS)

Yang, Liu; Arnold, Jim (Technical Monitor)

2001-01-01

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

Method for solvent extraction with near-equal density solutions

DOEpatents

Birdwell, Joseph F.; Randolph, John D.; Singh, S. Paul

2001-01-01

Disclosed is a modified centrifugal contactor for separating solutions of near equal density. The modified contactor has a pressure differential establishing means that allows the application of a pressure differential across fluid in the rotor of the contactor. The pressure differential is such that it causes the boundary between solutions of near-equal density to shift, thereby facilitating separation of the phases. Also disclosed is a method of separating solutions of near-equal density.

On the possible use of radio occultation middle latitude electron density profiles to retrieve thermospheric parameters

NASA Astrophysics Data System (ADS)

Mikhailov, Andrei V.; Belehaki, Anna; Perrone, Loredanna; Zolesi, Bruno; Tsagouri, Ioanna

2014-04-01

This paper investigates possible use of middle latitude daytime COSMIC and CHAMP ionospheric radio occultation (IRO) electron density profiles (EDPs) to retrieve thermospheric parameters, based on the Mikhailov et al. (2012) method. The aim of this investigation is to assess the applicability of this type of observations for the routine implementation of the method. According to the results extracted from the analysis presented here, about half of COSMIC IRO EDP observed under solar minimum (2007-2008) conditions gave neutral gas density with an inaccuracy close to the declared absolute inaccuracy ±(10-15)% of CHAMP observations, with the results being better than the empirical models JB-2008 and MSISE-00 provide. For the other half of IRO EDP, either the solution provided by the method had to be rejected due to insufficient accuracy or no solution could be obtained. For these cases, the parameters foF2 and hmF2 extracted from the corresponding IRO profiles have been found to be inconsistent with the classic mid-latitude daytime F2-layer formalism that the method relies on, and they are incompatible with the general trend provided by the IRI model. For solar maximum conditions (2002) the method was tested with IRO EDP from CHAMP and it is indicated that its performance is quite stable in the sense that a solution could be obtained for all the cases analyzed here. However available CHAMP EDP are confined by ~ 400 km in altitude and this might be the reason for the 20% bias of the retrieved densities toward larger values in respect to the observed densities. IRO observations up to 600 km under solar maximum are required to confirm the exact performance of the method.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Fractional Gaussian model in global optimization

NASA Astrophysics Data System (ADS)

Dimri, V. P.; Srivastava, R. P.

2009-12-01

Earth system is inherently non-linear and it can be characterized well if we incorporate no-linearity in the formulation and solution of the problem. General tool often used for characterization of the earth system is inversion. Traditionally inverse problems are solved using least-square based inversion by linearizing the formulation. The initial model in such inversion schemes is often assumed to follow posterior Gaussian probability distribution. It is now well established that most of the physical properties of the earth follow power law (fractal distribution). Thus, the selection of initial model based on power law probability distribution will provide more realistic solution. We present a new method which can draw samples of posterior probability density function very efficiently using fractal based statistics. The application of the method has been demonstrated to invert band limited seismic data with well control. We used fractal based probability density function which uses mean, variance and Hurst coefficient of the model space to draw initial model. Further this initial model is used in global optimization inversion scheme. Inversion results using initial models generated by our method gives high resolution estimates of the model parameters than the hitherto used gradient based liner inversion method.

Molecular dynamics simulation of solute diffusion in Lennard-Jones fluids

NASA Astrophysics Data System (ADS)

Yamaguchi, T.; Kimura, Y.; Hirota, N.

We performed a molecular dynamics (MD) simulation for a system of 5 solute molecules in 495 solvent molecules interacting through the Lennard-Jones (LJ) 12-6 potential, in order to study solvent density effects on the diffusion coefficients in supercritical fluids. The effects of the size of the solute and the strength of the solute-solvent attractive interaction on the diffusion coefficient of the solute were examined. The diffusion coefficients of the solute molecules were calculated at T = 1.5 (in the LJ reduced unit), slightly above the critical temperature, from rho = 0.1 to rho = 0.95, where rho is the number density in the LJ reduced unit. The memory function in the generalized Langevin equation was calculated, in order to know the molecular origin of the friction on a solute. The memory function is separated into fast and slow components. The former arises from the solute-solvent repulsive interaction, and is interpreted as collisional Enskog-like friction. The interaction strength dependence of the collisional friction is larger in the low- and medium-density regions, which is consistent with the 'clustering' picture, i.e., the local density enhancement due to the solute-solvent attractive interaction. However, the slow component of the memory function suppresses the effect of the local density on the diffusion coefficients, and as a result the effect of the attractive interaction is smaller on the diffusion coefficients than on the local density. Nonetheless, the solvent density dependence of the effect of the attraction on the diffusion coefficient varies with the local density, and it is concluded that the local density is the principal factor that determines the interaction strength dependence of the diffusion coefficient in the low- and medium-density regions (p < 0.6).

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-07-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in a closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2017a) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2018b) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Modeling wormholes in f (R ,T ) gravity

NASA Astrophysics Data System (ADS)

Moraes, P. H. R. S.; Sahoo, P. K.

2017-08-01

In this work, we propose the modeling of static wormholes within the f (R ,T ) extended theory of gravity perspective. We present some models of wormholes, which are constructed from different hypotheses for their matter content, i.e., different relations for their pressure components (radial and lateral) and different equations of state. The solutions obtained for the shape function of the wormholes obey the necessary metric conditions. They show a behavior similar to those found in previous references about wormholes, which also happens to our solutions for the energy density of such objects. We also apply the energy conditions for the wormholes' physical content.

Washout and non-washout solutions of a system describing microbial fermentation process under the influence of growth inhibitions and maximal concentration of yeast cells.

PubMed

Kasbawati; Gunawan, Agus Yodi; Sidarto, Kuntjoro Adjie

2017-07-01

An unstructured model for the growth of yeast cell on glucose due to growth inhibitions by substrate, products, and cell density is discussed. The proposed model describes the dynamical behavior of fermentation system that shows multiple steady states for a certain regime of operating parameters such as inlet glucose and dilution rate. Two types of steady state solutions are found, namely washout and non-washout solutions. Furthermore, different numerical impositions to the two parameters put in evidence three results regarding non-washout solution: a unique locally stable non-washout solution, a unique locally stable non-washout solution towards which other nearby solutions exhibit damped oscillations, and multiple non-washout solutions where one is locally stable while the other is unstable. It is also found an optimal inlet glucose which produces the highest cell and ethanol concentration. Copyright © 2017 Elsevier Inc. All rights reserved.

Joint density-functional theory and its application to systems in solution

NASA Astrophysics Data System (ADS)

Petrosyan, Sahak A.

The physics of solvation, the interaction of water with solutes, plays a central role in chemistry and biochemistry, and it is essential for the very existence of life. Despite the central importance of water and the advent of the quantum theory early in the twentieth century, the link between the fundamental laws of physics and the observable properties of water remain poorly understood to this day. The central goal of this thesis is to develop a new formalism and framework to make the study of systems (solutes or surfaces) in contact with liquid water as practical and accurate as standard electronic structure calculations without the need for explicit averaging over large ensembles of configurations of water molecules. The thesis introduces a new form of density functional theory for the ab initio description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of a solute with a classical density-functional theory for the liquid into a single variational principle for the free energy of the combined system. Using the new form of density-functional theory for the ab initio description of electronic systems in contact with a molecular liquid environment, the thesis then presents the first detailed study of the impact of a solvent on the surface chemistry of Cr2O3, the passivating layer of stainless steel alloys. In comparison to a vacuum, we predict that the presence of water has little impact on the adsorption of chloride ions to the oxygen-terminated surface but has a dramatic effect on the binding of hydrogen to that surface. A key ingredient of a successful joint density functional theory is a good approximate functional for describing the solvent. We explore how the simplest examples of the best known class of approximate forms for the classical density functional fail when applied directly to water. The thesis then presents a computationally efficient density-functional theory for water which overcomes this difficulty and gives reasonable agreement with molecular dynamics simulation data for the solvation of hard spheres in water and sufficient agreement with experimental data for hydration of inert gas atoms to justify its use in a joint theory with standard approximate density functionals used in electronic structure calculations. The last study in the thesis combines the previous ideas and presenting an approximate model density functional which includes a description of cavitation effects through a classical density-functional theory; a description of dielectric effects through a non-local polarizability, and a description of the coupling of the solvent to the electrons of the solute through a pseudopotential. Without any empirical fitting of parameters to solvation data, this theory predicts solvation energies at least as well as state-of-the-art quantum-chemical cavity approaches, which do employ such fitting. Although this agreement without adjustable parameters is very encouraging and shows the promise of the joint density-functional approach, the functionals which we develop here are models and do not yet include all of the microscopic physics. The thesis concludes with a description of the directions future work should take to address this weakness.

Water based on a molecular model behaves like a hard-sphere solvent for a nonpolar solute when the reference interaction site model and related theories are employed

NASA Astrophysics Data System (ADS)

Hayashi, Tomohiko; Oshima, Hiraku; Harano, Yuichi; Kinoshita, Masahiro

2016-09-01

For neutral hard-sphere solutes, we compare the reduced density profile of water around a solute g(r), solvation free energy μ, energy U, and entropy S under the isochoric condition predicted by the two theories: dielectrically consistent reference interaction site model (DRISM) and angle-dependent integral equation (ADIE) theories. A molecular model for water pertinent to each theory is adopted. The hypernetted-chain (HNC) closure is employed in the ADIE theory, and the HNC and Kovalenko-Hirata (K-H) closures are tested in the DRISM theory. We also calculate g(r), U, S, and μ of the same solute in a hard-sphere solvent whose molecular diameter and number density are set at those of water, in which case the radial-symmetric integral equation (RSIE) theory is employed. The dependences of μ, U, and S on the excluded volume and solvent-accessible surface area are analyzed using the morphometric approach (MA). The results from the ADIE theory are in by far better agreement with those from computer simulations available for g(r), U, and μ. For the DRISM theory, g(r) in the vicinity of the solute is quite high and becomes progressively higher as the solute diameter d U increases. By contrast, for the ADIE theory, it is much lower and becomes further lower as d U increases. Due to unphysically positive U and significantly larger |S|, μ from the DRISM theory becomes too high. It is interesting that μ, U, and S from the K-H closure are worse than those from the HNC closure. Overall, the results from the DRISM theory with a molecular model for water are quite similar to those from the RSIE theory with the hard-sphere solvent. Based on the results of the MA analysis, we comparatively discuss the different theoretical methods for cases where they are applied to studies on the solvation of a protein.

Experimental Phasing: Substructure Solution and Density Modification as Implemented in SHELX.

PubMed

Thorn, Andrea

2017-01-01

This chapter describes experimental phasing methods as implemented in SHELX. After introducing fundamental concepts underlying all experimental phasing approaches, the methods used by SHELXC/D/E are described in greater detail, such as dual-space direct methods, Patterson seeding and density modification with the sphere of influence algorithm. Intensity differences from data for experimental phasing can also be used for the generation and usage of difference maps with ANODE for validation and phasing purposes. A short section describes how molecular replacement can be combined with experimental phasing methods. The second half covers practical challenges, such as prerequisites for successful experimental phasing, evaluation of potential solutions, and what to do if substructure search or density modification fails. It is also shown how auto-tracing in SHELXE can improve automation and how it ties in with automatic model building after phasing.

An LES-PBE-PDF approach for modeling particle formation in turbulent reacting flows

NASA Astrophysics Data System (ADS)

Sewerin, Fabian; Rigopoulos, Stelios

2017-10-01

Many chemical and environmental processes involve the formation of a polydispersed particulate phase in a turbulent carrier flow. Frequently, the immersed particles are characterized by an intrinsic property such as the particle size, and the distribution of this property across a sample population is taken as an indicator for the quality of the particulate product or its environmental impact. In the present article, we propose a comprehensive model and an efficient numerical solution scheme for predicting the evolution of the property distribution associated with a polydispersed particulate phase forming in a turbulent reacting flow. Here, the particulate phase is described in terms of the particle number density whose evolution in both physical and particle property space is governed by the population balance equation (PBE). Based on the concept of large eddy simulation (LES), we augment the existing LES-transported probability density function (PDF) approach for fluid phase scalars by the particle number density and obtain a modeled evolution equation for the filtered PDF associated with the instantaneous fluid composition and particle property distribution. This LES-PBE-PDF approach allows us to predict the LES-filtered fluid composition and particle property distribution at each spatial location and point in time without any restriction on the chemical or particle formation kinetics. In view of a numerical solution, we apply the method of Eulerian stochastic fields, invoking an explicit adaptive grid technique in order to discretize the stochastic field equation for the number density in particle property space. In this way, sharp moving features of the particle property distribution can be accurately resolved at a significantly reduced computational cost. As a test case, we consider the condensation of an aerosol in a developed turbulent mixing layer. Our investigation not only demonstrates the predictive capabilities of the LES-PBE-PDF model but also indicates the computational efficiency of the numerical solution scheme.

Relativistic Outflows from Advection-dominated Accretion Disks around Black Holes

NASA Astrophysics Data System (ADS)

Becker, Peter A.; Subramanian, Prasad; Kazanas, Demosthenes

2001-05-01

Advection-dominated accretion flows (ADAFs) have a positive Bernoulli parameter and are therefore gravitationally unbound. The Newtonian ADAF model has been generalized recently to obtain the ADIOS model that includes outflows of energy and angular momentum, thereby allowing accretion to proceed self-consistently. However, the utilization of a Newtonian gravitational potential limits the ability of this model to describe the inner region of the disk, where any relativistic outflows are likely to originate. In this paper we modify the ADIOS scenario to incorporate a pseudo-Newtonian potential, which approximates the effects of general relativity. The analysis yields a unique, self-similar solution for the structure of the coupled disk/wind system. Interesting features of the new solution include the relativistic character of the outflow in the vicinity of the radius of marginal stability, which represents the inner edge of the quasi-Keplerian disk in our model. Hence, our self-similar solution may help to explain the origin of relativistic jets in active galaxies. At large distances the radial dependence of the accretion rate approaches the unique form M~r1/2, with an associated density variation given by ρ~r-1. This density variation agrees with that implied by the dependence of the hard X-ray time lags on the Fourier frequency for a number of accreting galactic black hole candidates. While intriguing, the predictions made using our self-similar solution need to be confirmed in the future using a detailed model that includes a physical description of the energization mechanism that drives the outflow, which is likely to be powered by the shear of the underlying accretion disk.

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

Jiménez, Jose Beltrán; Heisenberg, Lavinia; Olmo, Gonzalo J., E-mail: jose.beltran@uclouvain.be, E-mail: Lavinia.Heisenberg@unige.ch, E-mail: gonzalo.olmo@csic.es

We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a minimal version of the theory, for which we study solutions in the presence of a perfect fluid with special attention to the cosmological evolution. Inmore » vacuum we recover Ricci-flat solutions, but also an additional physical solution corresponding to an Einstein space. The existence of two physical branches remains for non-vacuum solutions and, in addition, the branch that connects to the Einstein space in vacuum is not very sensitive to the specific value of the energy density. For the branch that connects to the General Relativity limit we generically find three behaviours for the Hubble function depending on the equation of state of the fluid, namely: either there is a maximum value for the energy density that connects continuously with vacuum, or the energy density can be arbitrarily large but the Hubble function saturates and remains constant at high energy densities, or the energy density is unbounded and the Hubble function grows faster than in General Relativity. The second case is particularly interesting because it could offer an interesting inflationary epoch even in the presence of a dust component. Finally, we discuss the possibility of avoiding certain types of singularities within the minimal model.« less

Site-occupation embedding theory using Bethe ansatz local density approximations

NASA Astrophysics Data System (ADS)

Senjean, Bruno; Nakatani, Naoki; Tsuchiizu, Masahisa; Fromager, Emmanuel

2018-06-01

Site-occupation embedding theory (SOET) is an alternative formulation of density functional theory (DFT) for model Hamiltonians where the fully interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a noninteracting) one. It provides a rigorous framework for combining wave-function (or Green function)-based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key density functional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single-impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wave function has been performed with the density-matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials.

Theoretical study on the sound absorption of electrolytic solutions. I. Theoretical formulation.

PubMed

Yamaguchi, T; Matsuoka, T; Koda, S

2007-04-14

A theory is formulated that describes the sound absorption of electrolytic solutions due to the relative motion of ions, including the formation of ion pairs. The theory is based on the Kubo-Green formula for the bulk viscosity. The time correlation function of the pressure is projected onto the bilinear product of the density modes of ions. The time development of the product of density modes is described by the diffusive limit of the generalized Langevin equation, and approximate expressions for the three- and four-body correlation functions required are given with the hypernetted-chain integral equation theory. Calculations on the aqueous solutions of model electrolytes are performed. It is demonstrated that the theory describes both the activated barrier crossing between contact and solvent-separated ion pairs and the Coulombic correlation between ions.

Theoretical study on the sound absorption of electrolytic solutions. I. Theoretical formulation

NASA Astrophysics Data System (ADS)

Yamaguchi, T.; Matsuoka, T.; Koda, S.

2007-04-01

A theory is formulated that describes the sound absorption of electrolytic solutions due to the relative motion of ions, including the formation of ion pairs. The theory is based on the Kubo-Green formula for the bulk viscosity. The time correlation function of the pressure is projected onto the bilinear product of the density modes of ions. The time development of the product of density modes is described by the diffusive limit of the generalized Langevin equation, and approximate expressions for the three- and four-body correlation functions required are given with the hypernetted-chain integral equation theory. Calculations on the aqueous solutions of model electrolytes are performed. It is demonstrated that the theory describes both the activated barrier crossing between contact and solvent-separated ion pairs and the Coulombic correlation between ions.

New solutions with accelerated expansion in string theory

DOE PAGES

Dodelson, Matthew; Dong, Xi; Silverstein, Eva; ...

2014-12-05

We present concrete solutions with accelerated expansion in string theory, requiring a small, tractable list of stress energy sources. We explain how this construction (and others in progress) evades previous no go theorems for simple accelerating solutions. Our solutions respect an approximate scaling symmetry and realize discrete sequences of values for the equation of state, including one with an accumulation point at w = –1 and another accumulating near w = –1/3 from below. In another class of models, a density of defects generates scaling solutions with accelerated expansion. Here, we briefly discuss potential applications to dark energy phenomenology, andmore » to holography for cosmology.« less

Ionosphere Profile Estimation Using Ionosonde & GPS Data in an Inverse Refraction Calculation

NASA Astrophysics Data System (ADS)

Psiaki, M. L.

2014-12-01

A method has been developed to assimilate ionosonde virtual heights and GPS slant TEC data to estimate the parameters of a local ionosphere model, including estimates of the topside and of latitude and longitude variations. This effort seeks to better assimilate a variety of remote sensing data in order to characterize local (and eventually regional and global) ionosphere electron density profiles. The core calculations involve a forward refractive ray-tracing solution and a nonlinear optimal estimation algorithm that inverts the forward model. The ray-tracing calculations solve a nonlinear two-point boundary value problem for the curved ionosonde or GPS ray path through a parameterized electron density profile. It implements a full 3D solution that can handle the case of a tilted ionosphere. These calculations use Hamiltonian equivalents of the Appleton-Hartree magneto-plasma refraction index model. The current ionosphere parameterization is a modified Booker profile. It has been augmented to include latitude and longitude dependencies. The forward ray-tracing solution yields a given signal's group delay and beat carrier phase observables. An auxiliary set of boundary value problem solutions determine the sensitivities of the ray paths and observables with respect to the parameters of the augmented Booker profile. The nonlinear estimation algorithm compares the measured ionosonde virtual-altitude observables and GPS slant-TEC observables to the corresponding values from the forward refraction model. It uses the parameter sensitivities of the model to iteratively improve its parameter estimates in a way the reduces the residual errors between the measurements and their modeled values. This method has been applied to data from HAARP in Gakona, AK and has produced good TEC and virtual height fits. It has been extended to characterize electron density perturbations caused by HAARP heating experiments through the use of GPS slant TEC data for an LOS through the heated zone. The next planned extension of the method is to estimate the parameters of a regional ionosphere profile. The input observables will be slant TEC from an array of GPS receivers and group delay and carrier phase observables from an array of high-frequency beacons. The beacon array will function as a sort of multi-static ionosonde.

The effect of the electric wind on the spatial distribution of chemical species in the positive corona discharge

NASA Astrophysics Data System (ADS)

Yanallah, K.; Pontiga, F.; Bouazza, M. R.; Chen, J. H.

2017-08-01

The electrohydrodynamic air flow generated by a positive corona discharge, and its effect on the spatial distribution of chemical species within a wire-plate corona reactor, have been numerically simulated. The computational model is based on the solutions of the Navier-Stokes equation and the continuity equation of each chemical species generated by the electrical discharge. A simplified analytical expression of the electric force density, which only requires the current density as the input parameter, has been used in the Navier-Stokes equation to obtain the velocity field. For the solution of the continuity equations, a plasma chemistry model that includes the most important reactions between electrons, atoms and molecules in air has been used. Similar to the electric force, the electron density distribution has been approximated by using a semi-analytical expression appropriate for the electrode geometry. The results of the study show that the spatial distribution of chemical species can be very different, and depends on the interplay between the electrohydrodynamic flow, the chemical kinetics of the species and its characteristic lifetime.

High-throughput ab-initio dilute solute diffusion database

PubMed Central

Wu, Henry; Mayeshiba, Tam; Morgan, Dane

2016-01-01

We demonstrate automated generation of diffusion databases from high-throughput density functional theory (DFT) calculations. A total of more than 230 dilute solute diffusion systems in Mg, Al, Cu, Ni, Pd, and Pt host lattices have been determined using multi-frequency diffusion models. We apply a correction method for solute diffusion in alloys using experimental and simulated values of host self-diffusivity. We find good agreement with experimental solute diffusion data, obtaining a weighted activation barrier RMS error of 0.176 eV when excluding magnetic solutes in non-magnetic alloys. The compiled database is the largest collection of consistently calculated ab-initio solute diffusion data in the world. PMID:27434308

Evolution of the single-mode Rayleigh-Taylor instability under the influence of time-dependent accelerations

NASA Astrophysics Data System (ADS)

Ramaprabhu, P.; Karkhanis, V.; Banerjee, R.; Varshochi, H.; Khan, M.; Lawrie, A. G. W.

2016-01-01

From nonlinear models and direct numerical simulations we report on several findings of relevance to the single-mode Rayleigh-Taylor (RT) instability driven by time-varying acceleration histories. The incompressible, direct numerical simulations (DNSs) were performed in two (2D) and three dimensions (3D), and at a range of density ratios of the fluid combinations (characterized by the Atwood number). We investigated several acceleration histories, including acceleration profiles of the general form g (t ) ˜tn , with n ≥0 and acceleration histories reminiscent of the linear electric motor experiments. For the 2D flow, results from numerical simulations compare well with a 2D potential flow model and solutions to a drag-buoyancy model reported as part of this work. When the simulations are extended to three dimensions, bubble and spike growth rates are in agreement with the so-called level 2 and level 3 models of Mikaelian [K. O. Mikaelian, Phys. Rev. E 79, 065303(R) (2009), 10.1103/PhysRevE.79.065303], and with corresponding 3D drag-buoyancy model solutions derived in this article. Our generalization of the RT problem to study variable g (t ) affords us the opportunity to investigate the appropriate scaling for bubble and spike amplitudes under these conditions. We consider two candidates, the displacement Z and width s2, but find the appropriate scaling is dependent on the density ratios between the fluids—at low density ratios, bubble and spike amplitudes are explained by both s2 and Z , while at large density differences the displacement collapses the spike data. Finally, for all the acceleration profiles studied here, spikes enter a free-fall regime at lower Atwood numbers than predicted by all the models.

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

Marra, Valerio; Kolb, Edward W.; Matarrese, Sabino

We analyze a toy Swiss-cheese cosmological model to study the averaging problem. In our Swiss-cheese model, the cheese is a spatially flat, matter only, Friedmann-Robertson-Walker solution (i.e., the Einstein-de Sitter model), and the holes are constructed from a Lemaitre-Tolman-Bondi solution of Einstein's equations. We study the propagation of photons in the Swiss-cheese model, and find a phenomenological homogeneous model to describe observables. Following a fitting procedure based on light-cone averages, we find that the expansion scalar is unaffected by the inhomogeneities (i.e., the phenomenological homogeneous model is the cheese model). This is because of the spherical symmetry of the model;more » it is unclear whether the expansion scalar will be affected by nonspherical voids. However, the light-cone average of the density as a function of redshift is affected by inhomogeneities. The effect arises because, as the universe evolves, a photon spends more and more time in the (large) voids than in the (thin) high-density structures. The phenomenological homogeneous model describing the light-cone average of the density is similar to the {lambda}CDM concordance model. It is interesting that, although the sole source in the Swiss-cheese model is matter, the phenomenological homogeneous model behaves as if it has a dark-energy component. Finally, we study how the equation of state of the phenomenological homogeneous model depends on the size of the inhomogeneities, and find that the equation-of-state parameters w{sub 0} and w{sub a} follow a power-law dependence with a scaling exponent equal to unity. That is, the equation of state depends linearly on the distance the photon travels through voids. We conclude that, within our toy model, the holes must have a present size of about 250 Mpc to be able to mimic the concordance model.« less

Density functional theory study on carbon dioxide absorption into aqueous solutions of 2-amino-2-methyl-1-propanol using a continuum solvation model.

PubMed

Yamada, Hidetaka; Matsuzaki, Yoichi; Higashii, Takayuki; Kazama, Shingo

2011-04-14

We used density functional theory (DFT) calculations with the latest continuum solvation model (SMD/IEF-PCM) to determine the mechanism of CO(2) absorption into aqueous solutions of 2-amino-2-methyl-1-propanol (AMP). Possible absorption process reactions were investigated by transition-state optimization and intrinsic reaction coordinate (IRC) calculations in the aqueous solution at the SMD/IEF-PCM/B3LYP/6-31G(d) and SMD/IEF-PCM/B3LYP/6-311++G(d,p) levels of theory to determine the absorption pathways. We show that the carbamate anion forms by a two-step reaction via a zwitterion intermediate, and this occurs faster than the formation of the bicarbonate anion. However, we also predict that the carbamate readily decomposes by a reverse reaction rather than by hydrolysis. As a result, the final product is dominated by the thermodynamically stable bicarbonate anion that forms from AMP, H(2)O, and CO(2) in a single-step termolecular reaction.

Techniques of orbital decay and long-term ephemeris prediction for satellites in earth orbit

NASA Technical Reports Server (NTRS)

Barry, B. F.; Pimm, R. S.; Rowe, C. K.

1971-01-01

In the special perturbation method, Cowell and variation-of-parameters formulations of the motion equations are implemented and numerically integrated. Variations in the orbital elements due to drag are computed using the 1970 Jacchia atmospheric density model, which includes the effects of semiannual variations, diurnal bulge, solar activity, and geomagnetic activity. In the general perturbation method, two-variable asymptotic series and automated manipulation capabilities are used to obtain analytical solutions to the variation-of-parameters equations. Solutions are obtained considering the effect of oblateness only and the combined effects of oblateness and drag. These solutions are then numerically evaluated by means of a FORTRAN program in which an updating scheme is used to maintain accurate epoch values of the elements. The atmospheric density function is approximated by a Fourier series in true anomaly, and the 1970 Jacchia model is used to periodically update the Fourier coefficients. The accuracy of both methods is demonstrated by comparing computed orbital elements to actual elements over time spans of up to 8 days for the special perturbation method and up to 356 days for the general perturbation method.

A selfsimilar behavior of the urban structure in the spatially inhomogeneous model

NASA Astrophysics Data System (ADS)

Echkina, E. Y.; Inovenkov, O. I.; Kostomarov, D. P.

2006-03-01

At present there is a strong tendency to use new methods for the description of the regional and spatial economy. In increasing frequency we consider that any economic activity is spatially dependent. The problem of the evolution of internal urban formation can be described with the exact supposition. So that is why we use partial derivative equations set with the appropriate boundary and initial conditions for the solving the problem of the urban evolution. Here we describe the model of urban population's density modification taking into account a modification of the housing quality. A program has been created which realizes difference method of mixed problem solution for population's density. For the wide class of coefficients it has been shown that the problem's solution “quickly forgets” the parts of the initial conditions and comes out to the intermediate asymptotic form, which nature depends only on the problem's operator. Actually it means that the urban structure does not depend on external circumstances and is formed by the internal structure of the model.

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.

Underscreening in ionic liquids: a first principles analysis.

PubMed

Rotenberg, Benjamin; Bernard, Olivier; Hansen, Jean-Pierre

2018-02-07

An attempt is made to understand the underscreening effect, observed in concentrated electrolyte solutions or melts, on the basis of simple, admittedly crude models involving charged (for the ions) and neutral (for the solvent molecules) hard spheres. The thermodynamic and structural properties of these 'primitive' and 'semi-primitive' models are calculated within mean spherical approximation, which provides the basic input required to determine the partial density response functions. The screening length [Formula: see text], which is unambiguously defined in terms of the wave-number-dependent response functions, exhibits a cross-over from a low density, Debye-like regime, to a regime where [Formula: see text] increases with density beyond a critical density at which the Debye length [Formula: see text] becomes comparable to the ion diameter. In this high density regime the ratio [Formula: see text] increases according to a power law, in qualitative agreement with experimental measurements, albeit at a much slower rate.

Underscreening in ionic liquids: a first principles analysis

NASA Astrophysics Data System (ADS)

Rotenberg, Benjamin; Bernard, Olivier; Hansen, Jean-Pierre

2018-02-01

An attempt is made to understand the underscreening effect, observed in concentrated electrolyte solutions or melts, on the basis of simple, admittedly crude models involving charged (for the ions) and neutral (for the solvent molecules) hard spheres. The thermodynamic and structural properties of these ‘primitive’ and ‘semi-primitive’ models are calculated within mean spherical approximation, which provides the basic input required to determine the partial density response functions. The screening length λS , which is unambiguously defined in terms of the wave-number-dependent response functions, exhibits a cross-over from a low density, Debye-like regime, to a regime where λS increases with density beyond a critical density at which the Debye length λD becomes comparable to the ion diameter. In this high density regime the ratio λ_S/λD increases according to a power law, in qualitative agreement with experimental measurements, albeit at a much slower rate.

Synthesis and characterization of ion containing polymers

NASA Astrophysics Data System (ADS)

Dou, Shichen

Two types of ion-containing polymers are included in this dissertation. The first was focused on the rheology, solvation, and correlation length of polyelectrolyte solutions in terms of charge density, solvent dielectric constant, and solvent quality. The second was focused on the PEO-based polyester ionomers as single ion conductors. A series of polyelectrolytes with varied charge density (0.03 < alpha < 0.6) and counterions (Cl- and I-) were investigated in good solvent (EG, NMF, and GC) and poor solvent (DW and F). The concentration dependence of the specific viscosity and relaxation time of polyelectrolytes in solution agrees with Dobrynin's theoretical predictions at c < c**. Effective charge density greatly impacts the viscosity of polyelectrolyte semidilute solutions, while residual salt significantly reduces the viscosity of polyelectrolyte solutions at concentrations c < 2cs/f. For polyelectrolyte solutions with less condensed counterions, the correlation length obtained from SAXS and rheology perfectly matches and agrees with de Gennes prediction. Dobrynin scaling model successfully predicts the rheology of polyelectrolyte solutions in all cases: without salt, with low residual salt, and with high residual salt concentration. PEO-based polyester ionomers were synthesized by melt polycondensation. Mn was determined using the 1H NMR of ionomers. No ion-cluster was observed from the DSC, SAXS, and rheology measurements. Ionic conductivity greatly depends on the Tg, T-T g and ion content of the ionomers. PEG600-PTMO650 (z)-Li copolyester ionomers show microphase separation and much lower ionic conductivity, compared to that of PE600-Li. PTMO650-Li shows nonconductor behavior.

Nonlinear structure formation in flat cosmological models

NASA Technical Reports Server (NTRS)

Martel, Hugo

1995-01-01

This paper describes the formation of nonlinear structure in flat (zero curvature) Friedmann cosmological models. We consider models with two components: the usual nonrelativistic component that evolves under gravity and eventually forms the large-scale structure of the universe, and a uniform dark matter component that does not clump under gravity, and whose energy density varies with the scale factor a(t) like a(t)(sup -n), where n is a free parameter. Each model is characterized by two parameters: the exponent n and the present density parameter Omega(sub 0) of the nonrelativistic component. The linear perturbation equations are derived and solved for these models, for the three different cases n = 3, n is greater than 3, and n is less than 3. The case n = 3 is relevant to model with massive neutrinos. The presence of the uniform component strongly reduces the growth of the perturbation compared with the Einstein-de Sitter model. We show that the Meszaros effect (suppression of growth at high redshift) holds not only for n = 4, radiation-dominated models, but for all models with n is greater than 3. This essentially rules out any such model. For the case n is less than 3, we numerically integrate the perturbation equations from the big bang to the present, for 620 different models with various values of Omega(sub 0) and n. Using these solutions, we show that the function f(Omega(sub 0), n) = (a/delta(sub +))d(delta)(sub +)/da, which enters in the relationship between the present density contrast delta(sub 0) and peculiar velocity field u(sub 0) is essentially independent of n. We derive approximate solutions for the second-order perturbation equations. These second-order solutions are tested against the exact solutions and the Zel'dovich approximation for spherically symmetric perturbations in the marginally nonlinear regime (the absolute value of delta is less than or approximately 1). The second-order and Zel'dovich solutions have comparable accuracy, significantly higher than the accuracy of the linear solutions. We then investigate the dependence of the delta(sub 0) - u(sub 0) relationship upon the value of n in the nonlinear regime using the second-order solutions for marginally nonlinear, general perturbations, and the exact solutions for strongly nonlinear, spherically symmetric perturbations. In both cases, we find that the delta(sub 0) - u(sub 0) relationship remains independent of n. We speculate that this result extends to strongly nonlinear, general perturbations as well. This eliminates any hope to determine the presence of the uniform component or the value of n using dynamical methods. Finally, we compute the nonlinear evolution of the skewness of the distribution of values of delta, assuming Gaussian initial conditions. We find that the skewness is not only independent of n, but also of Omega(sub 0). Thus the skewness cannot be used to discriminate among various models with Gaussian initial conditions. However, it can be used for testing the Gaussianity of the initial conditions themselves. We conclude that the uniform component leaves no observable signature in the present large-scale structure of the universe. To determine its presence and nature, we must investigate the relationship between the past and present universe, using redshift-dependent tests.

Solubility of small-chain carboxylic acids in supercritical carbon dioxide

DOE PAGES

Sparks, Darrell L.; Estevez, L. Antonio; Hernandez, Rafael; ...

2010-07-08

The solubility of heptanoic acid and octanoic acid in supercritical carbon dioxide has been determined at temperatures of (313.15, 323.15, and 333.15) K over a pressure range of (8.5 to 30.0) MPa, depending upon the solute. The solubility of heptanoic acid ranged from a solute concentration of (0.08 ± 0.03) kg • m -3 (T = 323.15 K, p = 8.5 MPa) to (147 ± 0.2) kg • m -3 (T = 323.15 K, p = 20.0 MPa). The lowest octanoic acid solubility obtained was a solute concentration of (0.40 ± 0.1) kg • m -3 (T = 333.15 K,more » p = 10.0 MPa), while the highest solute concentration was (151 ± 2) kg • m -3 (T = 333.15 K, p = 26.7 MPa). In addition, solubility experiments were performed for nonanoic acid in supercritical carbon dioxide at 323.15 K and pressures of (10.0 to 30.0) MPa to add to the solubility data previously published by the authors. In general, carboxylic acid solubility increased with increasing solvent density. The results also showed that the solubility of the solutes decreased with increasing molar mass at constant supercritical-fluid density. Additionally, the efficacy of Chrastil's equation and other density-based models was evaluated for each fatty acid.« less

Self-similar solutions to isothermal shock problems

NASA Astrophysics Data System (ADS)

Deschner, Stephan C.; Illenseer, Tobias F.; Duschl, Wolfgang J.

We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary differential equations. We test the numerical solutions against the analytical expressions to verify the correctness of all numerical algorithms. We use similarity methods to derive a system of ordinary differential equations (ODE) yielding exact solutions for power law density distributions as initial conditions. Further, the system of ODEs accounts for implosion problems (IP) as well as explosion problems (EP) by changing the initial or boundary conditions, respectively. Taking genuinely isothermal approximations into account leads to additional insights of EPs in contrast to earlier models. We neglect a constant initial energy contribution but introduce a parameter to adjust the initial mass distribution of the system. Moreover, we show that due to this parameter a constant initial density is not allowed for isothermal EPs. Reasonable restrictions for this parameter are given. Both, the (genuinely) isothermal implosion as well as the explosion problem are solved for the first time.

Inverse gravity modeling for depth varying density structures through genetic algorithm, triangulated facet representation, and switching routines

NASA Astrophysics Data System (ADS)

King, Thomas Steven

A hybrid gravity modeling method is developed to investigate the structure of sedimentary mass bodies. The method incorporates as constraints surficial basement/sediment contacts and topography of a mass target with a quadratically varying density distribution. The inverse modeling utilizes a genetic algorithm (GA) to scan a wide range of the solution space to determine initial models and the Marquardt-Levenberg (ML) nonlinear inversion to determine final models that meet pre-assigned misfit criteria, thus providing an estimate of model variability and uncertainty. The surface modeling technique modifies Delaunay triangulation by allowing individual facets to be manually constructed and non-convex boundaries to be incorporated into the triangulation scheme. The sedimentary body is represented by a set of uneven prisms and edge elements, comprised of tetrahedrons, capped by polyhedrons. Each underlying prism and edge element's top surface is located by determining its point of tangency with the overlying terrain. The remaining overlying mass is gravitationally evaluated and subtracted from the observation points. Inversion then proceeds in the usual sense, but on an irregular tiered surface with each element's density defined relative to their top surface. Efficiency is particularly important due to the large number of facets evaluated for surface representations and the many repeated element evaluations of the stochastic GA. The gravitation of prisms, triangular faceted polygons, and tetrahedrons can be formulated in different ways, either mathematically or by physical approximations, each having distinct characteristics, such as evaluation time, accuracy over various spatial ranges, and computational singularities. A decision tree or switching routine is constructed for each element by combining these characteristics into a single cohesive package that optimizes the computation for accuracy and speed while avoiding singularities. The GA incorporates a subspace technique and parameter dependency to maintain model smoothness during development, thus minimizing creating nonphysical models. The stochastic GA explores the solution space, producing a broad range of unbiased initial models, while the ML inversion is deterministic and thus quickly converges to the final model. The combination allows many solution models to be determined from the same observed data.

Dark energy fingerprints in the nonminimal Wu-Yang wormhole structure

NASA Astrophysics Data System (ADS)

Balakin, Alexander B.; Zayats, Alexei E.

2014-08-01

We discuss new exact solutions to nonminimally extended Einstein-Yang-Mills equations describing spherically symmetric static wormholes supported by the gauge field of the Wu-Yang type in a dark energy environment. We focus on the analysis of three types of exact solutions to the gravitational field equations. Solutions of the first type relate to the model, in which the dark energy is anisotropic; i.e., the radial and tangential pressures do not coincide. Solutions of the second type correspond to the isotropic pressure tensor; in particular, we discuss the exact solution, for which the dark energy is characterized by the equation of state for a string gas. Solutions of the third type describe the dark energy model with constant pressure and energy density. For the solutions of the third type, we consider in detail the problem of horizons and find constraints for the parameters of nonminimal coupling and for the constitutive parameters of the dark energy equation of state, which guarantee that the nonminimal wormholes are traversable.

On the solution of the continuity equation for precipitating electrons in solar flares

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

Emslie, A. Gordon; Holman, Gordon D.; Litvinenko, Yuri E., E-mail: emslieg@wku.edu, E-mail: gordon.d.holman@nasa.gov

2014-09-01

Electrons accelerated in solar flares are injected into the surrounding plasma, where they are subjected to the influence of collisional (Coulomb) energy losses. Their evolution is modeled by a partial differential equation describing continuity of electron number. In a recent paper, Dobranskis and Zharkova claim to have found an 'updated exact analytical solution' to this continuity equation. Their solution contains an additional term that drives an exponential decrease in electron density with depth, leading them to assert that the well-known solution derived by Brown, Syrovatskii and Shmeleva, and many others is invalid. We show that the solution of Dobranskis andmore » Zharkova results from a fundamental error in the application of the method of characteristics and is hence incorrect. Further, their comparison of the 'new' analytical solution with numerical solutions of the Fokker-Planck equation fails to lend support to their result. We conclude that Dobranskis and Zharkova's solution of the universally accepted and well-established continuity equation is incorrect, and that their criticism of the correct solution is unfounded. We also demonstrate the formal equivalence of the approaches of Syrovatskii and Shmeleva and Brown, with particular reference to the evolution of the electron flux and number density (both differential in energy) in a collisional thick target. We strongly urge use of these long-established, correct solutions in future works.« less

Effect of surface charge of immortalized mouse cerebral endothelial cell monolayer on transport of charged solutes.

PubMed

Yuan, Wei; Li, Guanglei; Gil, Eun Seok; Lowe, Tao Lu; Fu, Bingmei M

2010-04-01

Charge carried by the surface glycocalyx layer (SGL) of the cerebral endothelium has been shown to significantly modulate the permeability of the blood-brain barrier (BBB) to charged solutes in vivo. The cultured monolayer of bEnd3, an immortalized mouse cerebral endothelial cell line, is becoming a popular in vitro BBB model due to its easy growth and maintenance of many BBB characteristics over repeated passages. To test whether the SGL of bEnd3 monolayer carries similar charge as that in the intact BBB and quantify this charge, which can be characterized by the SGL thickness (L(f)) and charge density (C(mf)), we measured the solute permeability of bEnd3 monolayer to neutral solutes and to solutes with similar size but opposite charges: negatively charged alpha-lactalbumin (-11) and positively charged ribonuclease (+3). Combining the measured permeability data with a transport model across the cell monolayer, we predicted the L(f) and the C(mf) of bEnd3 monolayer, which is approximately 160 nm and approximately 25 mEq/L, respectively. We also investigated whether orosomucoid, a plasma glycoprotein modulating the charge of the intact BBB, alters the charge of bEnd3 monolayer. We found that 1 mg/mL orosomucoid would increase SGL charge density of bEnd3 monolayer to approximately 2-fold of its control value.

A high-order 3-D spectral-element method for the forward modelling and inversion of gravimetric data—Application to the western Pyrenees

NASA Astrophysics Data System (ADS)

Martin, Roland; Chevrot, Sébastien; Komatitsch, Dimitri; Seoane, Lucia; Spangenberg, Hannah; Wang, Yi; Dufréchou, Grégory; Bonvalot, Sylvain; Bruinsma, Sean

2017-04-01

We image the internal density structure of the Pyrenees by inverting gravity data using an a priori density model derived by scaling a Vp model obtained by full waveform inversion of teleseismic P-waves. Gravity anomalies are computed via a 3-D high-order finite-element integration in the same high-order spectral-element grid as the one used to solve the wave equation and thus to obtain the velocity model. The curvature of the Earth and surface topography are taken into account in order to obtain a density model as accurate as possible. The method is validated through comparisons with exact semi-analytical solutions. We show that the spectral-element method drastically accelerates the computations when compared to other more classical methods. Different scaling relations between compressional velocity and density are tested, and the Nafe-Drake relation is the one that leads to the best agreement between computed and observed gravity anomalies. Gravity data inversion is then performed and the results allow us to put more constraints on the density structure of the shallow crust and on the deep architecture of the mountain range.

Study of helium emissions from active solar regions

NASA Technical Reports Server (NTRS)

Kulander, J. L.

1973-01-01

A theoretical study is made of the visible and UV line radiation of He I atoms and He II ions from a plane-parallel model flare layer. Codes were developed for the solution of the statistically steady state equation for a 30 level He I - II - III model, and the line and continuum transport equations. These codes are described and documented in the report along with sample solutions. Optical depths and some line intensities are presented for a 1000 km thick layer. Solutions of the steady state equations are presented for electron temperatures 10,000 to 50,000 K and electron densities 10 to the 10th power to 10 to the 14th power/cu cm.

The construction of a two-dimensional reproducing kernel function and its application in a biomedical model.

PubMed

Guo, Qi; Shen, Shu-Ting

2016-04-29

There are two major classes of cardiac tissue models: the ionic model and the FitzHugh-Nagumo model. During computer simulation, each model entails solving a system of complex ordinary differential equations and a partial differential equation with non-flux boundary conditions. The reproducing kernel method possesses significant applications in solving partial differential equations. The derivative of the reproducing kernel function is a wavelet function, which has local properties and sensitivities to singularity. Therefore, study on the application of reproducing kernel would be advantageous. Applying new mathematical theory to the numerical solution of the ventricular muscle model so as to improve its precision in comparison with other methods at present. A two-dimensional reproducing kernel function inspace is constructed and applied in computing the solution of two-dimensional cardiac tissue model by means of the difference method through time and the reproducing kernel method through space. Compared with other methods, this method holds several advantages such as high accuracy in computing solutions, insensitivity to different time steps and a slow propagation speed of error. It is suitable for disorderly scattered node systems without meshing, and can arbitrarily change the location and density of the solution on different time layers. The reproducing kernel method has higher solution accuracy and stability in the solutions of the two-dimensional cardiac tissue model.

Exact models for isotropic matter

NASA Astrophysics Data System (ADS)

Thirukkanesh, S.; Maharaj, S. D.

2006-04-01

We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.

An ion interaction model for the volumetric properties of natural waters: Density of the solution and partial molal volumes of electrolytes to high concentrations at 25°C

NASA Astrophysics Data System (ADS)

Monnin, Christophe

1989-06-01

Literature density data for binary and common ion ternary solutions in the Na-K-Ca-Mg-Cl-SO 4-HCO 3-CO3-H 2O system at 25°C have been analysed with Pitzer's ion interaction model, which provides an adequate representation of the experimental data for binary and common ion ternary solutions up to high concentration. This analysis yields Pitzer's interaction parameters for the apparent and partial molal volumes, which are the first derivatives with respect to pressure of the interaction parameters for the free energy. From this information, densities of natural waters as well as partial molal volumes of their solutes can be predicted with good accuracy, as shown by several comparisons of calculated and measured values. It is shown that V¯MX - V¯0mx, the excess partial molal volume of the salt MX, depends more on the type of salt than on the electrolyte itself and that it increases with the charges of the salt components. The influence of concentration and composition on the variation of activity coefficients with pressure and on the partial molal volumes of the salts is discussed, using as an example the partial molal volume of CaSO 4(aq) in solutions of various compositions. The increase of V¯CaSO 4, with ionic strength is very large but is not very different for a NaCl-dominated natural water like the Red Sea lower brine than for a simple NaCl solution. Although the variation of activity coefficients with pressure is usually ignored for moderate pressures, like those found in hydrothermal environments, the present example shows that it can be as large as 30% for a 2-2 salt for a pressure increase from 1 to 500 bars at high ionic strength.

Interfacial Ordering and Accompanying Divergent Capacitance at Ionic Liquid-Metal Interfaces.

PubMed

Limmer, David T

2015-12-18

A theory is constructed for dense ionic solutions near charged planar walls that is valid for strong interionic correlations. This theory predicts a fluctuation-induced, first-order transition and spontaneous charge density ordering at the interface, in the presence of an otherwise disordered bulk solution. The surface ordering is driven by applied voltage and results in an anomalous differential capacitance, in agreement with recent simulation results and consistent with experimental observations of a wide array of systems. Explicit forms for the charge density profile and capacitance are given. The theory is compared with numerical results for the charge frustrated Ising model, which is also found to exhibit a voltage driven first-order transition.

Interfacial Ordering and Accompanying Divergent Capacitance at Ionic Liquid-Metal Interfaces

NASA Astrophysics Data System (ADS)

Limmer, David T.

2015-12-01

A theory is constructed for dense ionic solutions near charged planar walls that is valid for strong interionic correlations. This theory predicts a fluctuation-induced, first-order transition and spontaneous charge density ordering at the interface, in the presence of an otherwise disordered bulk solution. The surface ordering is driven by applied voltage and results in an anomalous differential capacitance, in agreement with recent simulation results and consistent with experimental observations of a wide array of systems. Explicit forms for the charge density profile and capacitance are given. The theory is compared with numerical results for the charge frustrated Ising model, which is also found to exhibit a voltage driven first-order transition.

Numerical method and FORTRAN program for the solution of an axisymmetric electrostatic collector design problem

NASA Technical Reports Server (NTRS)

Reese, O. W.

1972-01-01

The numerical calculation is described of the steady-state flow of electrons in an axisymmetric, spherical, electrostatic collector for a range of boundary conditions. The trajectory equations of motion are solved alternately with Poisson's equation for the potential field until convergence is achieved. A direct (noniterative) numerical technique is used to obtain the solution to Poisson's equation. Space charge effects are included for initial current densities as large as 100 A/sq cm. Ways of dealing successfully with the difficulties associated with these high densities are discussed. A description of the mathematical model, a discussion of numerical techniques, results from two typical runs, and the FORTRAN computer program are included.

Kinklike structures in models of the Dirac-Born-Infeld type

NASA Astrophysics Data System (ADS)

Bazeia, D.; Lima, Elisama E. M.; Losano, L.

2018-01-01

The present work investigates several models of a single real scalar field, engendering kinetic term of the Dirac-Born- Infeld type. Such theories introduce nonlinearities to the kinetic part of the Lagrangian, which presents a square root restricting the field evolution and including additional powers in derivatives of the scalar field, controlled by a real parameter. In order to obtain topological solutions analytically, we propose a first-order framework that simplifies the equation of motion ensuring solutions that are linearly stable. This is implemented using the deformation method, and we introduce examples presenting two categories of potentials, one having polynomial interactions and the other with nonpolynomial interactions. We also explore how the Dirac-Born-Infeld kinetic term affects the properties of the solutions. In particular, we note that the kinklike solutions are similar to the ones obtained through models with standard kinetic term and canonical potential, but their energy densities and stability potentials vary according to the parameter introduced to control the new models.

Development of indirect EFBEM for radiating noise analysis including underwater problems

NASA Astrophysics Data System (ADS)

Kwon, Hyun-Wung; Hong, Suk-Yoon; Song, Jee-Hun

2013-09-01

For the analysis of radiating noise problems in medium-to-high frequency ranges, the Energy Flow Boundary Element Method (EFBEM) was developed. EFBEM is the analysis technique that applies the Boundary Element Method (BEM) to Energy Flow Analysis (EFA). The fundamental solutions representing spherical wave property for radiating noise problems in open field and considering the free surface effect in underwater are developed. Also the directivity factor is developed to express wave's directivity patterns in medium-to-high frequency ranges. Indirect EFBEM by using fundamental solutions and fictitious source was applied to open field and underwater noise problems successfully. Through numerical applications, the acoustic energy density distributions due to vibration of a simple plate model and a sphere model were compared with those of commercial code, and the comparison showed good agreement in the level and pattern of the energy density distributions.

Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups

NASA Astrophysics Data System (ADS)

Topaz, Chad

2004-03-01

We construct a continuum model for the motion of biological organisms experiencing social interactions and study its pattern-forming behavior. The model takes the form of a conservation law in two spatial dimensions. Social interactions are modeled in the velocity term, which is nonlocal in the population density. The dynamics of the model may be uniquely decomposed into incompressible motion and potential motion. For the purely incompressible case, the model resembles that for fluid dynamical vortex patches. There exist solutions that have constant population density and compact support for all time. Numerical simulations produce rotating structures with circular cores and spiral arms, reminiscent of naturally observed swarms such as ant mills. For the purely potential case, the model resembles a nonlocal (forwards or backwards) porous media equation, describing aggregation or dispersion of the population. For the aggregative case, the population clumps into regions of high and low density with a predictable characteristic length scale that is confirmed by numerical simulations.

Toroidal halos in a nontopological soliton model of dark matter

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

Mielke, Eckehard W.; Perez, Jose A. Velez

2007-02-15

Soliton type solutions of an axionlike scalar model with self-interaction are analyzed further as a toy model of dark matter halos. For a 'nonlinear superposition' of round and flattened configurations we found ringlike substructures in the density profile similarly as has been inferred for our Galaxy from the observed excess of the diffuse component of cosmic gamma rays.

Co-existence and switching between fast and Ω-slow wind solutions in rapidly rotating massive stars

NASA Astrophysics Data System (ADS)

Araya, I.; Curé, M.; ud-Doula, A.; Santillán, A.; Cidale, L.

2018-06-01

Most radiation-driven winds of massive stars can be modelled with m-CAK theory, resulting in the so-called fast solution. However, the most rapidly rotating stars among them, especially when the rotational speed is higher than {˜ } 75 per cent of the critical rotational speed, can adopt a different solution, the so-called Ω-slow solution, characterized by a dense and slow wind. Here, we study the transition region of the solutions where the fast solution changes to the Ω-slow solution. Using both time-steady and time-dependent numerical codes, we study this transition region for various equatorial models of B-type stars. In all cases, in a certain range of rotational speeds we find a region where the fast and the Ω-slow solution can co-exist. We find that the type of solution obtained in this co-existence region depends stongly on the initial conditions of our models. We also test the stability of the solutions within the co-existence region by performing base-density perturbations in the wind. We find that under certain conditions, the fast solution can switch to the Ω-slow solution, or vice versa. Such solution-switching may be a possible contributor of material injected into the circumstellar environment of Be stars, without requiring rotational speeds near critical values.

Kinetics, isothermal and thermodynamics studies of electrocoagulation removal of basic dye rhodamine B from aqueous solution using steel electrodes

NASA Astrophysics Data System (ADS)

Adeogun, Abideen Idowu; Balakrishnan, Ramesh Babu

2017-07-01

Electrocoagulation was used for the removal of basic dye rhodamine B from aqueous solution, and the process was carried out in a batch electrochemical cell with steel electrodes in monopolar connection. The effects of some important parameters such as current density, pH, temperature and initial dye concentration, on the process, were investigated. Equilibrium was attained after 10 min at 30 °C. Pseudo-first-order, pseudo-second-order, Elovich and Avrami kinetic models were used to test the experimental data in order to elucidate the kinetic adsorption process; pseudo-first-order and Avrami models best fitted the data. Experimental data were analysed using six model equations: Langmuir, Freudlinch, Redlich-Peterson, Temkin, Dubinin-Radushkevich and Sips isotherms and it was found that the data fitted well with Sips isotherm model. The study showed that the process depends on current density, temperature, pH and initial dye concentration. The calculated thermodynamics parameters (Δ G°, Δ H° and Δ S°) indicated that the process is spontaneous and endothermic in nature.

Non-Fickian dispersion of groundwater age

PubMed Central

Engdahl, Nicholas B.; Ginn, Timothy R.; Fogg, Graham E.

2014-01-01

We expand the governing equation of groundwater age to account for non-Fickian dispersive fluxes using continuous random walks. Groundwater age is included as an additional (fifth) dimension on which the volumetric mass density of water is distributed and we follow the classical random walk derivation now in five dimensions. The general solution of the random walk recovers the previous conventional model of age when the low order moments of the transition density functions remain finite at their limits and describes non-Fickian age distributions when the transition densities diverge. Previously published transition densities are then used to show how the added dimension in age affects the governing differential equations. Depending on which transition densities diverge, the resulting models may be nonlocal in time, space, or age and can describe asymptotic or pre-asymptotic dispersion. A joint distribution function of time and age transitions is developed as a conditional probability and a natural result of this is that time and age must always have identical transition rate functions. This implies that a transition density defined for age can substitute for a density in time and this has implications for transport model parameter estimation. We present examples of simulated age distributions from a geologically based, heterogeneous domain that exhibit non-Fickian behavior and show that the non-Fickian model provides better descriptions of the distributions than the Fickian model. PMID:24976651

Prediction of heat release effects on a mixing layer

NASA Technical Reports Server (NTRS)

Farshchi, M.

1986-01-01

A fully second-order closure model for turbulent reacting flows is suggested based on Favre statistics. For diffusion flames the local thermodynamic state is related to single conserved scalar. The properties of pressure fluctuations are analyzed for turbulent flows with fluctuating density. Closure models for pressure correlations are discussed and modeled transport equations for Reynolds stresses, turbulent kinetic energy dissipation, density-velocity correlations, scalar moments and dissipation are presented and solved, together with the mean equations for momentum and mixture fraction. Solutions of these equations are compared with the experimental data for high heat release free mixing layers of fluorine and hydrogen in a nitrogen diluent.

Limit Theorems and Their Relation to Solute Transport in Simulated Fractured Media

NASA Astrophysics Data System (ADS)

Reeves, D. M.; Benson, D. A.; Meerschaert, M. M.

2003-12-01

Solute particles that travel through fracture networks are subject to wide velocity variations along a restricted set of directions. This may result in super-Fickian dispersion along a few primary scaling directions. The fractional advection-dispersion equation (FADE), a modification of the original advection-dispersion equation in which a fractional derivative replaces the integer-order dispersion term, has the ability to model rapid, non-Gaussian solute transport. The FADE assumes that solute particle motions converge to either α -stable or operator stable densities, which are modeled by spatial fractional derivatives. In multiple dimensions, the multi-fractional dispersion derivative dictates the order and weight of differentiation in all directions, which correspond to the statistics of large particle motions in all directions. This study numerically investigates the presence of super- Fickian solute transport through simulated two-dimensional fracture networks. An ensemble of networks is gen

Exact general relativistic disks with magnetic fields

NASA Astrophysics Data System (ADS)

Letelier, Patricio S.

1999-11-01

The well-known ``displace, cut, and reflect'' method used to generate cold disks from given solutions of Einstein equations is extended to solutions of Einstein-Maxwell equations. Four exact solutions of the these last equations are used to construct models of hot disks with surface density, azimuthal pressure, and azimuthal current. The solutions are closely related to Kerr, Taub-NUT, Lynden-Bell-Pinault, and to a one-soliton solution. We find that the presence of the magnetic field can change in a nontrivial way the different properties of the disks. In particular, the pure general relativistic instability studied by Bic̆ák, Lynden-Bell, and Katz [Phys. Rev. D 47, 4334 (1993)] can be enhanced or cured by different distributions of currents inside the disk. These currents, outside the disk, generate a variety of axial symmetric magnetic fields. As far as we know these are the first models of hot disks studied in the context of general relativity.

Role of bond adaptability in the passivation of colloidal quantum dot solids.

PubMed

Thon, Susanna M; Ip, Alexander H; Voznyy, Oleksandr; Levina, Larissa; Kemp, Kyle W; Carey, Graham H; Masala, Silvia; Sargent, Edward H

2013-09-24

Colloidal quantum dot (CQD) solids are attractive materials for photovoltaic devices due to their low-cost solution-phase processing, high absorption cross sections, and their band gap tunability via the quantum size effect. Recent advances in CQD solar cell performance have relied on new surface passivation strategies. Specifically, cadmium cation passivation of surface chalcogen sites in PbS CQDs has been shown to contribute to lowered trap state densities and improved photovoltaic performance. Here we deploy a generalized solution-phase passivation strategy as a means to improving CQD surface management. We connect the effects of the choice of metal cation on solution-phase surface passivation, film-phase trap density of states, minority carrier mobility, and photovoltaic power conversion efficiency. We show that trap passivation and midgap density of states determine photovoltaic device performance and are strongly influenced by the choice of metal cation. Supported by density functional theory simulations, we propose a model for the role of cations, a picture wherein metals offering the shallowest electron affinities and the greatest adaptability in surface bonding configurations eliminate both deep and shallow traps effectively even in submonolayer amounts. This work illustrates the importance of materials choice in designing a flexible passivation strategy for optimum CQD device performance.

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

PubMed

Demidenko, Eugene

2017-09-01

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

Refractive index and solubility control of para-cymene solutions for index-matched fluid-structure interaction studies

NASA Astrophysics Data System (ADS)

Fort, Charles; Fu, Christopher D.; Weichselbaum, Noah A.; Bardet, Philippe M.

2015-12-01

To deploy optical diagnostics such as particle image velocimetry or planar laser-induced fluorescence (PLIF) in complex geometries, it is beneficial to use index-matched facilities. A binary mixture of para-cymene and cinnamaldehyde provides a viable option for matching the refractive index of acrylic, a common material for scaled models and test sections. This fluid is particularly appropriate for large-scale facilities and when a low-density and low-viscosity fluid is sought, such as in fluid-structure interaction studies. This binary solution has relatively low kinematic viscosity and density; its use enables the experimentalist to select operating temperature and to increase fluorescence signal in PLIF experiments. Measurements of spectral and temperature dependence of refractive index, density, and kinematic viscosity are reported. The effect of the binary mixture on solubility control of Rhodamine 6G is also characterized.

GeV-scale hot sterile neutrino oscillations: a numerical solution

NASA Astrophysics Data System (ADS)

Ghiglieri, J.; Laine, M.

2018-02-01

The scenario of baryogenesis through GeV-scale sterile neutrino oscillations is governed by non-linear differential equations for the time evolution of a sterile neutrino density matrix and Standard Model lepton and baryon asymmetries. By employing up-to-date rate coefficients and a non-perturbatively estimated Chern-Simons diffusion rate, we present a numerical solution of this system, incorporating the full momentum and helicity dependences of the density matrix. The density matrix deviates significantly from kinetic equilibrium, with the IR modes equilibrating much faster than the UV modes. For equivalent input parameters, our final results differ moderately (˜50%) from recent benchmarks in the literature. The possibility of producing an observable baryon asymmetry is nevertheless confirmed. We illustrate the dependence of the baryon asymmetry on the sterile neutrino mass splitting and on the CP-violating phase measurable in active neutrino oscillation experiments.

Potassium bromide, KBr/ ε: New Force Field

NASA Astrophysics Data System (ADS)

Fuentes-Azcatl, Raúl; Barbosa, Marcia C.

2018-02-01

We propose a new force field for the Potassium Bromide, the KBr/ ε. The crystal density and structure, as well as, the density, the viscosity and the dielectric constant of the solution in water were computed and compared with the experiments and other atomistic models. Next, the transferability of the KBr/ ε and of the NaCl/ ε models is verified by creating the KCl/ ε and the NaBr/ ε models. The strategy was to employ the same parameters obtained for the NaCl/ ε and for the KBr/ ε force fields for the building up of the KCl/ ε and the NaBr/ ε models . The thermodynamic and dynamic properties of these two new models were compared with the experimental

Anti-anthropic solutions to the cosmic coincidence problem

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

Fedrow, Joseph M.; Griest, Kim, E-mail: j.m.fedrow@gmail.com, E-mail: kgriest@ucsd.edu

2014-01-01

A cosmological constant fits all current dark energy data, but requires two extreme fine tunings, both of which are currently explained by anthropic arguments. Here we discuss anti-anthropic solutions to one of these problems: the cosmic coincidence problem- that today the dark energy density is nearly equal to the matter density. We replace the ensemble of Universes used in the anthropic solution with an ensemble of tracking scalar fields that do not require fine-tuning. This not only does away with the coincidence problem, but also allows for a Universe that has a very different future than the one currently predictedmore » by a cosmological constant. These models also allow for transient periods of significant scalar field energy (SSFE) over the history of the Universe that can give very different observational signatures as compared with a cosmological constant, and so can be confirmed or disproved in current and upcoming experiments.« less

Solution of the Fokker-Planck equation in a wind turbine array boundary layer

NASA Astrophysics Data System (ADS)

Melius, Matthew S.; Tutkun, Murat; Cal, Raúl Bayoán

2014-07-01

Hot-wire velocity signals from a model wind turbine array boundary layer flow wind tunnel experiment are analyzed. In confirming Markovian properties, a description of the evolution of the probability density function of velocity increments via the Fokker-Planck equation is attained. Solution of the Fokker-Planck equation is possible due to the direct computation of the drift and diffusion coefficients from the experimental measurement data which were acquired within the turbine canopy. A good agreement is observed in the probability density functions between the experimental data and numerical solutions resulting from the Fokker-Planck equation, especially in the far-wake region. The results serve as a tool for improved estimation of wind velocity within the array and provide evidence that the evolution of such a complex and turbulent flow is also governed by a Fokker-Planck equation at certain scales.

Isotope effect on the circular dichroism spectrum of methyl α-D-glucopyranoside in aqueous solution

PubMed Central

Kanematsu, Yusuke; Kamiya, Yukiko; Matsuo, Koichi; Gekko, Kunihiko; Kato, Koichi; Tachikawa, Masanori

2015-01-01

H/D isotope effect on the circular dichroism spectrum of methyl α-D-glucopyranoside in aqueous solution has been analyzed by multicomponent density functional theory calculations using the polarizable continuum model. By comparing the computational spectra with the corresponding experimental spectrum obtained with a vacuum-ultraviolet circular dichroism spectrophotometer, it was demonstrated that the isotope effect provides insights not only into the isotopic difference of the intramolecular interactions of the solutes, but also into that of the solute–solvent intermolecular interaction. PMID:26658851

Balancing anisotropic curvature with gauge fields in a class of shear-free cosmological models

NASA Astrophysics Data System (ADS)

Thorsrud, Mikjel

2018-05-01

We present a complete list of general relativistic shear-free solutions in a class of anisotropic, spatially homogeneous and orthogonal cosmological models containing a collection of n independent p-form gauge fields, where p\\in\\{0, 1, 2, 3\\} , in addition to standard ΛCDM matter fields modelled as perfect fluids. Here a (collection of) gauge field(s) balances anisotropic spatial curvature on the right-hand side of the shear propagation equation. The result is a class of solutions dynamically equivalent to standard FLRW cosmologies, with an effective curvature constant Keff that depends both on spatial curvature and the energy density of the gauge field(s). In the case of a single gauge field (n  =  1) we show that the only spacetimes that admit such solutions are the LRS Bianchi type III, Bianchi type VI0 and Kantowski–Sachs metric, which are dynamically equivalent to open (Keff<0 ), flat (Keff=0 ) and closed (Keff>0 ) FLRW models, respectively. With a collection of gauge fields (n  >  1) also Bianchi type II admits a shear-free solution (Keff>0 ). We identify the LRS Bianchi type III solution to be the unique shear-free solution with a gauge field Hamiltonian bounded from below in the entire class of models.

Model Order Reduction for the fast solution of 3D Stokes problems and its application in geophysical inversion

NASA Astrophysics Data System (ADS)

Ortega Gelabert, Olga; Zlotnik, Sergio; Afonso, Juan Carlos; Díez, Pedro

2017-04-01

The determination of the present-day physical state of the thermal and compositional structure of the Earth's lithosphere and sub-lithospheric mantle is one of the main goals in modern lithospheric research. All this data is essential to build Earth's evolution models and to reproduce many geophysical observables (e.g. elevation, gravity anomalies, travel time data, heat flow, etc) together with understanding the relationship between them. Determining the lithospheric state involves the solution of high-resolution inverse problems and, consequently, the solution of many direct models is required. The main objective of this work is to contribute to the existing inversion techniques in terms of improving the estimation of the elevation (topography) by including a dynamic component arising from sub-lithospheric mantle flow. In order to do so, we implement an efficient Reduced Order Method (ROM) built upon classic Finite Elements. ROM allows to reduce significantly the computational cost of solving a family of problems, for example all the direct models that are required in the solution of the inverse problem. The strategy of the method consists in creating a (reduced) basis of solutions, so that when a new problem has to be solved, its solution is sought within the basis instead of attempting to solve the problem itself. In order to check the Reduced Basis approach, we implemented the method in a 3D domain reproducing a portion of Earth that covers up to 400 km depth. Within the domain the Stokes equation is solved with realistic viscosities and densities. The different realizations (the family of problems) is created by varying viscosities and densities in a similar way as it would happen in an inversion problem. The Reduced Basis method is shown to be an extremely efficiently solver for the Stokes equation in this context.

Description and Verification of a Novel Flow and Transport Model for Silicate-Gel Emplacement

NASA Astrophysics Data System (ADS)

Walther, M.; Solpuker, U.; Böttcher, N.; Kolditz, O.; Liedl, R.; Schwartz, F. W.

2013-12-01

Remediation of contamination is one of the basic tasks associated with groundwater management. While many different methods exist to reduce contaminant mass in situ, there is still a need for research on new approaches to significantly speed-up decontamination and to lower costs. Solpuker et al. (2012) describe flow-tank experiments that utilize dense, viscous silicate solutions to aid in the remediation process. The unique silicate solutions exhibit density-dependent flow and rapid gelation after some time that can be altered by adjusting the solute's composition. Based on the experiments, a novel approach was developed to simulate the behaviour of the rapidly gelating solute. The approach was implenented in the open-source software package OpenGeoSys (Kolditz et al. 2012). Specifically, the method involves simulating two mass transport processes: one is related to the density-dependent flow, while the other does not alter the fluid density but is designed to provide a first order decay process. While both concentrations are subject to standard mass transport processes (i.e. advection, dispersion, diffusion), the difference in the two concentrations yields information on the residence time of the injected solute. This information can be used to calculate the fluid viscosity and the appropriate change in fluid properties when gelation takes place. As with all models that involve the implementation of ';new' physics, it is crucial to verify the ability of the code to rigorously reproduce the vital processes that describe the movement of fluids and solutes. This step is particularly important here because such a density-dependent, viscosity-changing flow and transport process poses unique requirements in terms of stability for the numerical code. Therefore, our theoretical approach was verified successfully against the experimental data for three different gelation behaviors. Comparison of both, laboratory and numerical results, show that the key processes can be reproduced correctly, including e.g. persistence of solute in regions of gelation due to high viscosity, or concentration-dependent gelation. Further research is needed to relate the empirical parameters describing the viscosity-change function to measurable laboratory data, or to study field-scale implementations. Literature SOLPUKER, U., HAWKINS, J., SCHINCARIOL, R., IBARAKI, M., & SCHWARTZ, F. W. (2012). HARNESSING THE COMPLEX BEHAVIOR OF ULTRA-DENSE AND VISCOUS TREATMENT FLUIDS AS A STRATEGY FOR AQUIFER REMEDIATION. MODELS - REPOSITORIES OF KNOWLEDGE. MODELCARE2011, LEIPZIG, GERMANY. KOLDITZ, O., BAUER, S., BILKE, L., BÖTTCHER, N., DELFS, J. O., FISCHER, T., GÖRKE, U. J., ET AL. (2012). OPENGEOSYS: AN OPEN-SOURCE INITIATIVE FOR NUMERICAL SIMULATION OF THERMO-HYDRO-MECHANICAL/CHEMICAL (THM/C) PROCESSES IN POROUS MEDIA. ENVIRONMENTAL EARTH SCIENCES, 67(2), 589-599. DOI:10.1007/S12665-012-1546-X

Surrogate Immiscible Liquid Solution Pairs with Refractive Indexes Matchable Over a Wide Range of Density and Viscosity Ratios

NASA Astrophysics Data System (ADS)

Saksena, Rajat; Christensen, Kenneth T.; Pearlstein, Arne J.

2014-11-01

Use of laser diagnostics in liquid-liquid flows is limited by refractive index mismatch. This can be avoided using a surrogate pair of immiscible index-matched liquids, with density and viscosity ratios matching those of the original liquid pair. We demonstrate that a wide range of density and viscosity ratios is accessible using aqueous solutions of 1,2-propanediol and CsBr (for which index, density, and viscosity are available), and solutions of light and heavy silicone oils and 1-bromooctane (for which we measured the same properties at 119 compositions). For each liquid phase, polynomials in the composition variables were fitted to index and density and to the logarithm of kinematic viscosity, and the fits were used to determine accessible density and viscosity ratios for each matchable index. Index-matched solution pairs can be prepared with density and viscosity ratios equal to those for water-liquid CO2 at 0oC over a range of pressure, and for water-crude oil and water-trichloroethylene, each over a range of temperature. For representative index-matched solutions, equilibration changes index, density, and viscosity only slightly, and chemical analysis show that no component of either solution has significant interphase solubility. Partially supported by Intl. Inst. for Carbon-Neutral Energy Research.

A Hele-Shaw-Cahn-Hilliard Model for Incompressible Two-Phase Flows with Different Densities

NASA Astrophysics Data System (ADS)

Dedè, Luca; Garcke, Harald; Lam, Kei Fong

2017-07-01

Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a Cahn-Hilliard-Navier-Stokes model introduced by Abels et al. (Math Models Methods Appl Sci 22(3):1150013, 2012), which uses a volume-averaged velocity, we derive a diffuse interface model in a Hele-Shaw geometry, which in the case of non-matched densities, simplifies an earlier model of Lee et al. (Phys Fluids 14(2):514-545, 2002). We recover the classical Hele-Shaw model as a sharp interface limit of the diffuse interface model. Furthermore, we show the existence of weak solutions and present several numerical computations including situations with rising bubbles and fingering instabilities.

Three-dimensional model for multi-component reactive transport with variable density groundwater flow

USGS Publications Warehouse

Mao, X.; Prommer, H.; Barry, D.A.; Langevin, C.D.; Panteleit, B.; Li, L.

2006-01-01

PHWAT is a new model that couples a geochemical reaction model (PHREEQC-2) with a density-dependent groundwater flow and solute transport model (SEAWAT) using the split-operator approach. PHWAT was developed to simulate multi-component reactive transport in variable density groundwater flow. Fluid density in PHWAT depends not on only the concentration of a single species as in SEAWAT, but also the concentrations of other dissolved chemicals that can be subject to reactive processes. Simulation results of PHWAT and PHREEQC-2 were compared in their predictions of effluent concentration from a column experiment. Both models produced identical results, showing that PHWAT has correctly coupled the sub-packages. PHWAT was then applied to the simulation of a tank experiment in which seawater intrusion was accompanied by cation exchange. The density dependence of the intrusion and the snow-plough effect in the breakthrough curves were reflected in the model simulations, which were in good agreement with the measured breakthrough data. Comparison simulations that, in turn, excluded density effects and reactions allowed us to quantify the marked effect of ignoring these processes. Next, we explored numerical issues involved in the practical application of PHWAT using the example of a dense plume flowing into a tank containing fresh water. It was shown that PHWAT could model physically unstable flow and that numerical instabilities were suppressed. Physical instability developed in the model in accordance with the increase of the modified Rayleigh number for density-dependent flow, in agreement with previous research. ?? 2004 Elsevier Ltd. All rights reserved.

Submarine groundwater discharge and solute transport under a transgressive barrier island

NASA Astrophysics Data System (ADS)

Evans, Tyler B.; Wilson, Alicia M.

2017-04-01

Many recent investigations of groundwater dynamics in beaches employed groundwater models that assumed isotropic, numerically-convenient hydrogeological conditions. Real beaches exhibit local variability with respect to stratigraphy, sediment grain size and associated topographic profile, so that groundwater flow may diverge significantly from idealized models. We used a combination of hydrogeologic field methods and a variable-density, saturated-unsaturated, transient groundwater flow model to investigate SGD and solute transport under Cabretta Beach, a small transgressive barrier island seaward of Sapelo Island, Georgia. We found that the inclusion of real beach heterogeneity drove important deviations from predictions based on theoretical beaches. Cabretta Beach sustained a stronger upper saline plume than predicted due to the presence of a buried silty mud layer beneath the surface. Infiltration of seawater was greater for neap tides than for spring tides due to variations in beach slope. The strength of the upper saline plume was greatest during spring tides, contrary to recent model predictions. The position and width of the upper saline plume was highly dynamic through the lunar cycle. Our results suggest that field measurements of salinity gradients may be useful for estimating rates of tidally and density driven recirculation through the beach. Finally, our results indicate that several important biogeochemical cycles recently studied at Cabretta Beach were heavily influenced by groundwater flow and associated solute transport.

Soliton matter in the two-dimensional linear sigma model

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

Dodd, L.R.; Lohe, M.A.; Rossi, M.

1987-10-01

We consider a one-dimensional model of nuclear matter where the quark clusters are described by solutions of the sigma model on a linear lattice in the self-consistent mean field approximation. Exact expressions are given for the baglike solutions confined to a finite interval, corresponding in the infinite interval limit to the free solitons previously found by Campbell and Liao. Periodic, self-consistent solutions which satisfy Bloch's theorem are constructed. Their energies and associated quark sigma field distributions are calculated numerically as functions of the baryon spacing, and compared with those of the uniform quark plasma. The predicted configuration of the groundmore » state depends critically on the assumed manner of filling the lowest band of quark single-particle levels, and on the density. In the absence of additional repulsive forces in the model, we find that the high density massless quark plasma is energetically favored and that there is a smooth transition from the baglike state to a uniform plasma with nonvanishing sigma field at comparatively large lattice constants 2dapprox. =10m/sub q//sup -1/ (m/sub q/ is the quark mass). If dilute filling of the entire band is employed, the clustered state is stable and a first order phase transition can occur for a range of much smaller lattice spacings 2dapprox. =4m/sub q//sup -1/. .AE« less

Use of a spread sheet to calculate the current-density distribution produced in human and rat models by low-frequency electric fields.

PubMed

Hart, F X

1990-01-01

The current-density distribution produced inside irregularly shaped, homogeneous human and rat models by low-frequency electric fields is obtained by a two-stage finite-difference procedure. In the first stage the model is assumed to be equipotential. Laplace's equation is solved by iteration in the external region to obtain the capacitive-current densities at the model's surface elements. These values then provide the boundary conditions for the second-stage relaxation solution, which yields the internal current-density distribution. Calculations were performed with the Excel spread-sheet program on a Macintosh-II microcomputer. A spread sheet is a two-dimensional array of cells. Each cell of the sheet can represent a square element of space. Equations relating the values of the cells can represent the relationships between the potentials in the corresponding spatial elements. Extension to three dimensions is readily made. Good agreement was obtained with current densities measured on human models with both, one, or no legs grounded and on rat models in four different grounding configurations. The results also compared well with predictions of more sophisticated numerical analyses. Spread sheets can provide an inexpensive and relatively simple means to perform good, approximate dosimetric calculations on irregularly shaped objects.

Spinning solutions in general relativity with infinite central density

NASA Astrophysics Data System (ADS)

Flammer, P. D.

2018-05-01

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

Multibunch solutions of the differential-difference equation for traffic flow

PubMed

Nakanishi

2000-09-01

The Newell-Whitham type of car-following model, with a hyperbolic tangent as the optimal velocity function, has a finite number of exact steady traveling wave solutions that can be expressed in terms of elliptic theta functions. Each such solution describes a density wave with a definite number of car bunches on a circuit. In our numerical simulations, we observe a transition process from uniform flow to congested flow described by a one-bunch analytic solution, which appears to be an attractor of the system. In this process, the system exhibits a series of transitions through which it comes to assume configurations closely approximating multibunch solutions with successively fewer bunches.

Infrared lessons for ultraviolet gravity: the case of massive gravity and Born-Infeld

NASA Astrophysics Data System (ADS)

Beltrán Jiménez, Jose; Heisenberg, Lavinia; Olmo, Gonzalo J.

2014-11-01

We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a minimal version of the theory, for which we study solutions in the presence of a perfect fluid with special attention to the cosmological evolution. In vacuum we recover Ricci-flat solutions, but also an additional physical solution corresponding to an Einstein space. The existence of two physical branches remains for non-vacuum solutions and, in addition, the branch that connects to the Einstein space in vacuum is not very sensitive to the specific value of the energy density. For the branch that connects to the General Relativity limit we generically find three behaviours for the Hubble function depending on the equation of state of the fluid, namely: either there is a maximum value for the energy density that connects continuously with vacuum, or the energy density can be arbitrarily large but the Hubble function saturates and remains constant at high energy densities, or the energy density is unbounded and the Hubble function grows faster than in General Relativity. The second case is particularly interesting because it could offer an interesting inflationary epoch even in the presence of a dust component. Finally, we discuss the possibility of avoiding certain types of singularities within the minimal model.

Modeling the heliolatitudinal gradient of the solar wind parameters with exact MHD solutions

NASA Technical Reports Server (NTRS)

Lima, J. J. G.; Tsinganos, K.

1995-01-01

The heliolatitudinal dependence of observations of the solar wind macroscopic quantities such as the averaged proton speed, density and the mass and momentum flux are modeled. The published observations covering the last two and a half solar cycles, are obtained either via the technique of interplanetary scintillations for the last 2 solar cycles (1970-1990), or, from the plasma experiment aboard the ULYSSES spacecraft for the recent period 1990-1994. Exact, two dimensional solutions of the full set of the steady MHD equations are used which are obtained through a nonlinear separation of the variables in the MHD equations. The three parameters emerging from the solutions are fixed from these observations, as well as from observations of the solar rotation. It is found that near solar maximum the solar wind speed is uniformly low, around the 400 km/s over a wide range of latitudes. On the other hand, during solar minimum and the declining phase of the solar activity cycle, there is a strong heliolatitudinal gradient in proton speed between 400-800 from equator to pole. This modeling also agrees with previous findings that the gradient in wind speed with the latitude is offset by a gradient in density such that the mass and momentum flux vary relatively little.

On the Theory of Solitons of Fluid Pressure and Solute Density in Geologic Porous Media, with Applications to Shale, Clay and Sandstone

NASA Astrophysics Data System (ADS)

Caserta, A.; Kanivetsky, R.; Salusti, E.

2017-11-01

We here analyze a new model of transients of pore pressure p and solute density ρ in geologic porous media. This model is rooted in the nonlinear wave theory, its focus is on advection and effect of large pressure jumps on strain. It takes into account nonlinear and also time-dependent versions of the Hooke law about stress, rate and strain. The model solutions strictly relate p and ρ evolving under the effect of a strong external stress. As a result, the presence of quick and sharp transients in low permeability rocks is unveiled, i.e., the nonlinear "Burgers solitons". We, therefore, show that the actual transport process in porous rocks for large signals is not only the linear diffusion, but also a solitons presence could control the process. A test of a presence of solitons is applied to Pierre shale, Bearpaw shale, Boom clay and Oznam-Mugu silt and clay. An application about the presence of solitons for nuclear waste disposal and salt water intrusions is also discussed. Finally, in a kind of "theoretical experiment" we show that solitons could also be present in higher permeability rocks (Jordan and St. Peter sandstones), thus supporting the idea of a possible occurrence of osmosis also in sandstones.

Analytical model for the density distribution in the Io plasma torus

NASA Technical Reports Server (NTRS)

Mei, YI; Thorne, Richard M.; Bagenal, Fran

1995-01-01

An analytical model is developed for the diffusive equilibrium plasma density distribution in the Io plasma torus. The model has been employed successfully to follow the ray path of plasma waves in the multi-ion Jovian magnetosphere; it would also be valuable for other studies of the Io torus that require a smooth and continuous description of the plasma density and its gradients. Validity of the analytical treatment requires that the temperature of thermal electrons be much lower than the ion temperature and that superthermal electrons be much less abundant than the thermal electrons; these two conditions are satisfied in the warm outer region of the Io torus from L = 6 to L = 10. The analytical solutions agree well with exact numerical calculations for the most dense portion of the Io torus within 30 deg of the equator.

Day and night models of the Venus thermosphere

NASA Technical Reports Server (NTRS)

Massie, S. T.; Hunten, D. M.; Sowell, D. R.

1983-01-01

A model atmosphere of Venus for altitudes between 100 and 178 km is presented for the dayside and nightside. Densities of CO2, CO, O, N2, He, and O2 on the dayside, for 0800 and 1600 hours local time, are obtained by simultaneous solution of continuity equations. These equations couple ionospheric and neutral chemistry and the transport processes of molecular and eddy diffusion. Photodissociation and photoionization J coefficients are presented to facilitate the incorporation of chemistry into circulation models of the Venus atmosphere. Midnight densities of CO2 CO, O, N2, He, and N are derived from integration of the continuity equations, subject to specified fluxes. The nightside densities and fluxes are consistent with the observed airglow of NO and O2(1 Delta). The homopause of Venus is located near 133 km on both the dayside and nightside.

Interaction of a sodium ion with the water liquid-vapor interface

NASA Technical Reports Server (NTRS)

Wilson, M. A.; Pohorille, A.; Pratt, L. R.; MacElroy, R. D. (Principal Investigator)

1989-01-01

Molecular dynamics results are presented for the density profile of a sodium ion near the water liquid-vapor interface at 320 K. These results are compared with the predictions of a simple dielectric model for the interaction of a monovalent ion with this interface. The interfacial region described by the model profile is too narrow and the profile decreases too abruptly near the solution interface. Thus, the simple model does not provide a satisfactory description of the molecular dynamics results for ion positions within two molecular diameters from the solution interface where appreciable ion concentrations are observed. These results suggest that surfaces associated with dielectric models of ionic processes at aqueous solution interfaces should be located at least two molecular diameters inside the liquid phase. A free energy expense of about 2 kcal/mol is required to move the ion within two molecular layers of the free water liquid-vapor interface.

A power-law coupled three-form dark energy model

NASA Astrophysics Data System (ADS)

Yao, Yan-Hong; Yan, Yang-Jie; Meng, Xin-He

2018-02-01

We consider a field theory model of coupled dark energy which treats dark energy as a three-form field and dark matter as a spinor field. By assuming the effective mass of dark matter as a power-law function of the three-form field and neglecting the potential term of dark energy, we obtain three solutions of the autonomous system of evolution equations, including a de Sitter attractor, a tracking solution and an approximate solution. To understand the strength of the coupling, we confront the model with the latest Type Ia Supernova, Baryon Acoustic Oscillations and Cosmic Microwave Background radiation observations, with the conclusion that the combination of these three databases marginalized over the present dark matter density parameter Ω _{m0} and the present three-form field κ X0 gives stringent constraints on the coupling constant, - 0.017< λ <0.047 (2σ confidence level), by which we present the model's applicable parameter range.

Kinetic modeling of electro-Fenton reaction in aqueous solution.

PubMed

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

2007-03-01

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

The Effect of the Density Ratio on the Nonlinear Dynamics of the Unstable Fluid Interface

NASA Technical Reports Server (NTRS)

Abarzhi, S. I.

2003-01-01

Here we report multiple harmonic theoretical solutions for a complete system of conservation laws, which describe the large-scale coherent dynamics in RTI and RMI for fluids with a finite density ratio in the general three-dimensional case. The analysis yields new properties of the bubble front dynamics. In either RTI or RMI, the obtained dependencies of the bubble velocity and curvature on the density ratio differ qualitatively and quantitatively from those suggested by the models of Sharp (1984), Oron et al. (2001), and Goncharov (2002). We show explicitly that these models violate the conservation laws. For the first time, our theory reveals an important qualitative distinction between the dynamics of the RT and RM bubbles.

Stochastic modeling of the migration of Cs-137 in the soil considering a power law tailing in space

NASA Astrophysics Data System (ADS)

Oka, Hiroki; Hatano, Yuko

2016-04-01

We develop a theoretical model to reproduce the measured data of Cs-137 in the soil due to the Fukushima Daiichi NPP accident. In our past study, we derived the analytic solution under the generalized Robin boundary condition (Oka-Yamamoto solution). This is a generalization of the He-Walling solution (1996). We compared our solution with the Fukushima soil data of for 3 years after the accident and found that the concentration of Cs-137 has a discrepancy from our solution, specifically in a deep part because the depth profiles have a power law tailing. Therefore, we improved our model in the following aspect. When Cs particle (or Cs solution) migrate in the soil, the diffusion coefficient should be the results of many processes in the soil. These processes include the effect of various materials which constitute the soil (clay, litter, sand), or the variations of pore size in the soil. Hence we regard the diffusion coefficient as the stochastic variable, we derive the model. Specifically, we consider the solution of ADE to be the conditional probability C(x,t|D) in terms of the diffusion coefficient D and calculate C(x,t)=∫_(0~∞) C(x,t|D)*f(D)*dD, where f(D) is the probability density function of D. This model has a power law tailing in space like the space-fractional ADE.

Validation of Mars-GRAM and Planned New Features

NASA Technical Reports Server (NTRS)

Justus, C. G.; Duvall, Aleta; Keller, Vernon W.

2004-01-01

For altitudes below 80 km, Mars Global Reference Atmospheric Model (Mars-GRAM 2001) is based on output climatology from NASA Ames Mars General Circulation Model (MGCM). At COSPAR 2002, results were presented of validation tests of Mars-GRAM versus data from Mars Global Surveyor Thermal Emission Spectrometer (TES) and Radio Science (RS) experiment. Further validation tests are presented comparing Mars- GRAM densities with those from the European Mars Climate Database (MCD), and comparing densities from both Mars-GRAM and MCD against TES observations. Throughout most of the height and latitude range of TES data (040 km and 70s to 70N), good agreement is found between atmospheric densities from Mars-GRAM and MCD. However, at the season and latitude zone for Mars Phoenix arrival and landing (Ls = 65 to 80 degrees and latitude 65 to 75N), Mars-GRAM densities are about 30 to 45 percent higher than MCD densities near 40 km altitude. Further evaluation is warranted concerning potential impact of these model differences on planning for Phoenix entry and descent. Three planned features for Mars-GRAM update are also discussed: (1) new MGCM and Thermospheric General Circulation Model data sets to be used as a revised basis for Mars-GRAM mean atmosphere, (2) a new feature to represent planetary-scale traveling waves for upper altitude density variations (such as found during Mars Odyssey aerobraking), and (3) a new model for effects of high resolution topographic slope on winds near the surface (0 to 4.5 km above MOLA topography level). Mars-GRAM slope winds will be computed from a diagnostic (algebraic) relationship based on Ye, Segal, and Pielke (1990). This approach differs from mesoscale models (such as MRAMS and Mars MM5), which use prognostic, full-physics solutions of the time- and space-dependent differential equations of motion. As such, slope winds in Mars-GRAM will be consistent with its "engineering-level" approach, and will be extremely fast and easy to evaluate, compared with mesoscale model solutions. Mars-GRAM slope winds are not being suggested as a replacement for sophisticated, full-physics Mars mesoscale models, but may have value, particularly for preliminary screening of large numbers of candidate landing sites for future Mars missions, such as Phoenix and Mars Science Laboratory. Test output is presented from Mars-GRAM slope winds in the area of Gusev Crater and Valles Marineris.

Elastic parabolic equation and normal mode solutions for seismo-acoustic propagation in underwater environments with ice covers.

PubMed

Collis, Jon M; Frank, Scott D; Metzler, Adam M; Preston, Kimberly S

2016-05-01

Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea.

The general form of the coupled Horndeski Lagrangian that allows cosmological scaling solutions

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

Gomes, Adalto R.; Amendola, Luca, E-mail: argomes.ufma@gmail.com, E-mail: l.amendola@thphys.uni-heidelberg.de

We consider the general scalar field Horndeski Lagrangian coupled to dark matter. Within this class of models, we present two results that are independent of the particular form of the model. First, we show that in a Friedmann-Robertson-Walker metric the Horndeski Lagrangian coincides with the pressure of the scalar field. Second, we employ the previous result to identify the most general form of the Lagrangian that allows for cosmological scaling solutions, i.e. solutions where the ratio of dark matter to field density and the equation of state remain constant. Scaling solutions of this kind may help solving the coincidence problemmore » since in this case the presently observed ratio of matter to dark energy does not depend on initial conditions, but rather on the theoretical parameters.« less

Coupled Boltzmann computation of mixed axion neutralino dark matter in the SUSY DFSZ axion model

NASA Astrophysics Data System (ADS)

Bae, Kyu Jung; Baer, Howard; Lessa, Andre; Serce, Hasan

2014-10-01

The supersymmetrized DFSZ axion model is highly motivated not only because it offers solutions to both the gauge hierarchy and strong CP problems, but also because it provides a solution to the SUSY μ-problem which naturally allows for a Little Hierarchy. We compute the expected mixed axion-neutralino dark matter abundance for the SUSY DFSZ axion model in two benchmark cases—a natural SUSY model with a standard neutralino underabundance (SUA) and an mSUGRA/CMSSM model with a standard overabundance (SOA). Our computation implements coupled Boltzmann equations which track the radiation density along with neutralino, axion, axion CO (produced via coherent oscillations), saxion, saxion CO, axino and gravitino densities. In the SUSY DFSZ model, axions, axinos and saxions go through the process of freeze-in—in contrast to freeze-out or out-of-equilibrium production as in the SUSY KSVZ model—resulting in thermal yields which are largely independent of the re-heat temperature. We find the SUA case with suppressed saxion-axion couplings (ξ=0) only admits solutions for PQ breaking scale falesssim 6× 1012 GeV where the bulk of parameter space tends to be axion-dominated. For SUA with allowed saxion-axion couplings (ξ =1), then fa values up to ~ 1014 GeV are allowed. For the SOA case, almost all of SUSY DFSZ parameter space is disallowed by a combination of overproduction of dark matter, overproduction of dark radiation or violation of BBN constraints. An exception occurs at very large fa~ 1015-1016 GeV where large entropy dilution from CO-produced saxions leads to allowed models.

Structural model of the 50S subunit of E.Coli ribosomes from solution scattering

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

Svergun, D.I.; Koch, M.H.J.; Pedersen, J.S.

1994-12-31

The application of new methods of small-angle scattering data interpretation to a contrast variation study of the 50S ribosomal subunit of Escherichia coli in solution is described. The X-ray data from contrast variation with sucrose are analyzed in terms of the basic scattering curves from the volume inaccessible to sucrose and from the regions inside this volume occupied mainly by RNA and by proteins. From these curves models of the shape of the 50S and its RNA-rich core are evaluated and positioned so that their difference produces a scattering curve which is in good agreement with the scattering from themore » protein moiety. Basing on this preliminary model, the X-ray and neutron contrast variation data of the 50S subunit in aqueous solutions are interpreted in the frame of the advanced two-phase model described by the shapes of the 50S subunit and its RNA-rich core taking into account density fluctuations inside the RNA and the protein moiety. The shape of the envelope of the 50S subunit and of the RNA-rich core are evaluated with a resolution of about 40A. The shape of the envelope is in good agreement with the models of the 50S subunit obtained from electron microscopy on isolated particles. The shape of the RNA-rich core correlates well with the model of the entire particle determined by the image reconstruction from ordered sheets indicating that the latter model which is based on the subjective contouring of density maps is heavily biased towards the RNA.« less

Porosity development in coastal carbonate aquifers

USGS Publications Warehouse

Sanford, W.E.; Konikow, Leonard F.

1989-01-01

Combines geochemical mixing theory with the hydrodynamics of fresh-water-salt-water mixing zones in a coupled reaction-transport model. Results from the reaction-path model PHREEQE are used with a variable-density groundwater flow and solute-transport model to simulate an idealized cross section of a coastal carbonate aquifer. The dissolution process is sensitive to fresh-water chemistry, groundwater velocities, and sea-level movement. -from Authors

Bivariate spline solution of time dependent nonlinear PDE for a population density over irregular domains.

PubMed

Gutierrez, Juan B; Lai, Ming-Jun; Slavov, George

2015-12-01

We study a time dependent partial differential equation (PDE) which arises from classic models in ecology involving logistic growth with Allee effect by introducing a discrete weak solution. Existence, uniqueness and stability of the discrete weak solutions are discussed. We use bivariate splines to approximate the discrete weak solution of the nonlinear PDE. A computational algorithm is designed to solve this PDE. A convergence analysis of the algorithm is presented. We present some simulations of population development over some irregular domains. Finally, we discuss applications in epidemiology and other ecological problems. Copyright © 2015 Elsevier Inc. All rights reserved.

Constant-concentration boundary condition: Lessons from the HYDROCOIN variable-density groundwater benchmark problem

USGS Publications Warehouse

Konikow, Leonard F.; Sanford, W.E.; Campbell, P.J.

1997-01-01

In a solute-transport model, if a constant-concentration boundary condition is applied at a node in an active flow field, a solute flux can occur by both advective and dispersive processes. The potential for advective release is demonstrated by reexamining the Hydrologic Code Intercomparison (HYDROCOIN) project case 5 problem, which represents a salt dome overlain by a shallow groundwater system. The resulting flow field includes significant salinity and fluid density variations. Several independent teams simulated this problem using finite difference or finite element numerical models. We applied a method-of-characteristics model (MOCDENSE). The previous numerical implementations by HYDROCOIN teams of a constant-concentration boundary to represent salt release by lateral dispersion only (as stipulated in the original problem definition) was flawed because this boundary condition allows the release of salt into the flow field by both dispersion and advection. When the constant-concentration boundary is modified to allow salt release by dispersion only, significantly less salt is released into the flow field. The calculated brine distribution for case 5 depends very little on which numerical model is used, as long as the selected model is solving the proper equations. Instead, the accuracy of the solution depends strongly on the proper conceptualization of the problem, including the detailed design of the constant-concentration boundary condition. The importance and sensitivity to the manner of specification of this boundary does not appear to have been recognized previously in the analysis of this problem.

A computational kinetic model of diffusion for molecular systems.

PubMed

Teo, Ivan; Schulten, Klaus

2013-09-28

Regulation of biomolecular transport in cells involves intra-protein steps like gating and passage through channels, but these steps are preceded by extra-protein steps, namely, diffusive approach and admittance of solutes. The extra-protein steps develop over a 10-100 nm length scale typically in a highly particular environment, characterized through the protein's geometry, surrounding electrostatic field, and location. In order to account for solute energetics and mobility of solutes in this environment at a relevant resolution, we propose a particle-based kinetic model of diffusion based on a Markov State Model framework. Prerequisite input data consist of diffusion coefficient and potential of mean force maps generated from extensive molecular dynamics simulations of proteins and their environment that sample multi-nanosecond durations. The suggested diffusion model can describe transport processes beyond microsecond duration, relevant for biological function and beyond the realm of molecular dynamics simulation. For this purpose the systems are represented by a discrete set of states specified by the positions, volumes, and surface elements of Voronoi grid cells distributed according to a density function resolving the often intricate relevant diffusion space. Validation tests carried out for generic diffusion spaces show that the model and the associated Brownian motion algorithm are viable over a large range of parameter values such as time step, diffusion coefficient, and grid density. A concrete application of the method is demonstrated for ion diffusion around and through the Eschericia coli mechanosensitive channel of small conductance ecMscS.

"Photographing money" task pricing

NASA Astrophysics Data System (ADS)

Jia, Zhongxiang

2018-05-01

"Photographing money" [1]is a self-service model under the mobile Internet. The task pricing is reasonable, related to the success of the commodity inspection. First of all, we analyzed the position of the mission and the membership, and introduced the factor of membership density, considering the influence of the number of members around the mission on the pricing. Multivariate regression of task location and membership density using MATLAB to establish the mathematical model of task pricing. At the same time, we can see from the life experience that membership reputation and the intensity of the task will also affect the pricing, and the data of the task success point is more reliable. Therefore, the successful point of the task is selected, and its reputation, task density, membership density and Multiple regression of task positions, according to which a nhew task pricing program. Finally, an objective evaluation is given of the advantages and disadvantages of the established model and solution method, and the improved method is pointed out.

A Solution to ``Too Big to Fail''

NASA Astrophysics Data System (ADS)

Kohler, Susanna

2016-10-01

Its a tricky business to reconcile simulations of our galaxys formation with our current observations of the Milky Way and its satellites. In a recent study, scientists have addressed one discrepancy between simulations and observations: the so-called to big to fail problem.From Missing Satellites to Too Big to FailThe favored model of the universe is the lambda-cold-dark-matter (CDM) cosmological model. This model does a great job of correctly predicting the large-scale structure of the universe, but there are still a few problems with it on smaller scales.Hubble image of UGC 5497, a dwarf galaxy associated with Messier 81. In the missing satellite problem, simulations of galaxy formation predict that there should be more such satellite galaxies than we observe. [ESA/NASA]The first is the missing satellites problem: CDM cosmology predicts that galaxies like the Milky Way should have significantly more satellite galaxies than we observe. A proposed solution to this problem is the argument that there may exist many more satellites than weve observed, but these dwarf galaxies have had their stars stripped from them during tidal interactions which prevents us from being able to see them.This solution creates a new problem, though: the too big to fail problem. This problem states that many of the satellites predicted by CDM cosmology are simply so massive that theres no way they couldnt have visible stars. Another way of looking at it: the observed satellites of the Milky Way are not massive enough to be consistent with predictions from CDM.Artists illustration of a supernova, a type of stellar feedback that can modify the dark-matter distribution of a satellite galaxy. [NASA/CXC/M. Weiss]Density Profiles and Tidal StirringLed by Mihai Tomozeiu (University of Zurich), a team of scientists has published a study in which they propose a solution to the too big to fail problem. By running detailed cosmological zoom simulations of our galaxys formation, Tomozeiu and collaborators modeled the dark matter and the stellar content of the galaxy, tracking the formation and evolution of dark-matter subhalos.Based on the results of their simulations, the team argues that the too big to fail problem can be resolved by combining two effects:Stellar feedback in a satellite galaxy can modify its dark-matter distribution, lowering the dark-matter density in the galaxys center and creating a shallower density profile. Satellites with such shallow density profiles evolve differently than those typically modeled, which have a high concentration of dark matter in their centers.After these satellites fall into the Milky Ways potential, tidal effects such as shocks and stripping modify the mass distribution of both the dark matter and the baryons even further.Each curve represents a simulated satellites circular velocity (which corresponds to its total mass) at z=0. Left: results using typical dark-matter density profiles. Right: results using the shallower profiles expected when stellar feedback is included. Results from the shallower profiles are consistent with observed Milky-Way satellites(black crosses). [Adapted from Tomozeiu et al. 2016]A Match to ObservationsTomozeiu and collaborators found that when they used traditional density profiles to model the satellites, the satellites at z=0 in the simulation were much larger than those we observe around the Milky Way consistent with the too big to fail problem.When the team used shallower density profiles and took into account tidal effects, however, the simulations produced a distribution of satellites at z=0 that is consistent with what we observe.This study provides a tidy potential solution to the too big to fail problem, further strengthening the support for CDM cosmology.CitationMihai Tomozeiu et al 2016 ApJ 827 L15. doi:10.3847/2041-8205/827/1/L15

Exploration of interactions between bioactive solutes and vitamin B9 in aqueous medium by physico-chemical contrivances

NASA Astrophysics Data System (ADS)

Roy, Mahendra Nath; Chakraborti, Palash; Ekka, Deepak

2014-09-01

Molecular interaction prevailing in α-amino acids (glycine, L-alanine, L-valine) and aqueous solution of folic acid (FA) has been reported by physico-chemical properties as density (ρ), viscosity (η), refractive index (nD) and ultrasonic speed (u) at 298.15 K. The extent of interaction (solute-solvent interaction) is expressed in terms of the limiting apparent molar volume (φ0V), viscosity B-coefficient, molar refraction (RM) and limiting apparent molar adiabatic compressibility (φ0K). The trends in transfer volumes, Δφ0V, have been interpreted in terms of solute-cosolute interactions on the basis of a co-sphere overlap model. The role of the cosolute (FA), and the contribution of solute-solute and solute-solvent interactions to the solution complexes, has also been analysed through the derived properties.

Benchmark Results Of Active Tracer Particles In The Open Souce Code ASPECT For Modelling Convection In The Earth's Mantle

NASA Astrophysics Data System (ADS)

Jiang, J.; Kaloti, A. P.; Levinson, H. R.; Nguyen, N.; Puckett, E. G.; Lokavarapu, H. V.

2016-12-01

We present the results of three standard benchmarks for the new active tracer particle algorithm in ASPECT. The three benchmarks are SolKz, SolCx, and SolVI (also known as the 'inclusion benchmark') first proposed by Duretz, May, Gerya, and Tackley (G Cubed, 2011) and in subsequent work by Theilman, May, and Kaus (Pure and Applied Geophysics, 2014). Each of the three benchmarks compares the accuracy of the numerical solution to a steady (time-independent) solution of the incompressible Stokes equations with a known exact solution. These benchmarks are specifically designed to test the accuracy and effectiveness of the numerical method when the viscosity varies up to six orders of magnitude. ASPECT has been shown to converge to the exact solution of each of these benchmarks at the correct design rate when all of the flow variables, including the density and viscosity, are discretized on the underlying finite element grid (Krobichler, Heister, and Bangerth, GJI, 2012). In our work we discretize the density and viscosity by initially placing the true values of the density and viscosity at the intial particle positions. At each time step, including the initialization step, the density and viscosity are interpolated from the particles onto the finite element grid. The resulting Stokes system is solved for the velocity and pressure, and the particle positions are advanced in time according to this new, numerical, velocity field. Note that this procedure effectively changes a steady solution of the Stokes equaton (i.e., one that is independent of time) to a solution of the Stokes equations that is time dependent. Furthermore, the accuracy of the active tracer particle algorithm now also depends on the accuracy of the interpolation algorithm and of the numerical method one uses to advance the particle positions in time. Finally, we will present new interpolation algorithms designed to increase the overall accuracy of the active tracer algorithms in ASPECT and interpolation algotithms designed to conserve properties, such as mass density, that are being carried by the particles.

A 3D, finite element model for baroclinic circulation on the Vancouver Island continental shelf

USGS Publications Warehouse

Walters, R.A.; Foreman, M.G.G.

1992-01-01

This paper describes the development and application of a 3-dimensional model of the barotropic and baroclinic circulation on the continental shelf west of Vancouver Island, Canada. A previous study with a 2D barotropic model and field data revealed that several tidal constituents have a significant baroclinic component (the K1 in particular). Thus we embarked on another study with a 3D model to study the baroclinic effects on the residual and several selected tidal constituents. The 3D model uses a harmonic expansion in time and a finite element discretization in space. All nonlinear terms are retained, including quadratic bottom stress, advection and wave transport (continuity nonlinearity). The equations are solved as a global and a local problem, where the global problem is the solution of the wave equation formulation of the shallow water equations, and the local problem is the solution of the momentum equation for the vertical velocity profile. These equations are coupled to the advection-diffusion equation for density so that density gradient forcing is included in the momentum equations. However, the study presented here describes diagnostic calculations for the baroclinic residual circulation only. The model is sufficiently efficient that it encourages sensitivity testing with a large number of model runs. In this sense, the model is akin to an extension of analytical solutions to the domain of irregular geometry and bottom topography where this parameter space can be explored in some detail. In particular, the consequences of the sigma coordinate system used by the model are explored. Test cases using an idealized representation of the continental shelf, shelf break and shelf slope, lead to an estimation of the velocity errors caused by interpolation errors inherent in the sigma coordinate system. On the basis of these estimates, the computational grid used in the 2D model is found to have inadequate resolution. Thus a new grid is generated with increased accuracy in the region of the shelf break. However, even with increased resolution, spurious baroclinic circulation seaward of the shelf break and in the vicinity of Juan de Fuca canyon remained a significant problem when the pressure gradient terms were evaluated using the ?? coordinate system and using a realistic density profile. With the new grid, diagnostic calculations of the barotropic and baroclinic residual circulation are performed using forcing from the observed ??t (density) field and from the gradient of this field. ?? 1992.

Osmotically-driven membrane processes for water reuse and energy recovery

NASA Astrophysics Data System (ADS)

Achilli, Andrea

Osmotically-driven membrane processes are an emerging class of membrane separation processes that utilize concentrated brines to separate liquid streams. Their versatility of application make them an attractive alternative for water reuse and energy production/recovery. This work focused on innovative applications of osmotically-driven membrane processes. The novel osmotic membrane bioreactor (OMBR) system for water reuse was presented. Experimental results demonstrated high sustainable flux and relatively low reverse diffusion of solutes from the draw solution into the mixed liquor. Membrane fouling was minimal and controlled with osmotic backwashing. The OMBR system was found to remove greater than 99% of organic carbon and ammonium-nitrogen. Forward osmosis (FO) can employ different draw solution in its process. More than 500 inorganic compounds were screened as draw solution candidates, the desktop screening process resulted in 14 draw solutions suitable for FO applications. The 14 draw solutions were then tested in the laboratory to evaluate water flux and reverse salt diffusion through the membrane. Results indicated a wide range of water flux and reverse salt diffusion depending on the draw solution utilized. Internal concentration polarization was found to lower both water flux and reverse salt diffusion by reducing the draw solution concentration at the interface between the support and dense layer of the membrane. A small group of draw solutions was found to be most suitable for FO processes with currently available FO membranes. Another application of osmotically-driven membrane processes is pressure retarded osmosis (PRO). PRO was investigated as a viable source of renewable energy. A PRO model was developed to predict water flux and power density under specific experimental conditions. The predictive model was tested using experimental results from a bench-scale PRO system. Previous investigations of PRO were unable to verify model predictions due to the lack of suitable membranes and membrane modules. In this investigation, for the first time, the use of a custom-made laboratory-scale membrane module enabled the collection of experimental PRO data. Results obtained with a flat-sheet cellulose triacetate FO membrane and NaCl feed and draw solutions closely matched model predictions. Power density was substantially reduced due to internal concentration polarization in the asymmetric membrane and, to a lesser degree, to salt passage. External concentration polarization was found to exhibit a relatively small effect on reducing the osmotic pressure driving force. Using the predictive PRO model, optimal membrane characteristics and module configuration can be determined in order to design a system specifically tailored for PRO processes.

Thermophoresis of dissolved molecules and polymers: Consideration of the temperature-induced macroscopic pressure gradient

NASA Astrophysics Data System (ADS)

Semenov, Semen; Schimpf, Martin

2004-01-01

The movement of molecules and homopolymer chains dissolved in a nonelectrolyte solvent in response to a temperature gradient is considered a consequence of temperature-induced pressure gradients in the solvent layer surrounding the solute molecules. Local pressure gradients are produced by nonuniform London van der Waals interactions, established by gradients in the concentration (density) of solvent molecules. The density gradient is produced by variations in solvent thermal expansion within the nonuniform temperature field. The resulting expression for the velocity of the solute contains the Hamaker constants for solute-solvent and solute-solute interactions, the radius of the solute molecule, and the viscosity and cubic coefficient of thermal expansion of the solvent. In this paper we consider an additional force that arises from directional asymmetry in the interaction between solvent molecules. In a closed cell, the resulting macroscopic pressure gradient gives rise to a volume force that affects the motion of dissolved solutes. An expression for this macroscopic pressure gradient is derived and the resulting force is incorporated into the expression for the solute velocity. The expression is used to calculate thermodiffusion coefficients for polystyrene in several organic solvents. When these values are compared to those measured in the laboratory, the consistency is better than that found in previous reports, which did not consider the macroscopic pressure gradient that arises in a closed thermodiffusion cell. The model also allows for the movement of solute in either direction, depending on the relative values of the solvent and solute Hamaker constants.

Isostatic GOCE Moho model for Iran

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi; Ebadi, Sahar; Tenzer, Robert

2017-05-01

One of the major issues associated with a regional Moho recovery from the gravity or gravity-gradient data is the optimal choice of the mean compensation depth (i.e., the mean Moho depth) for a certain area of study, typically for orogens characterised by large Moho depth variations. In case of selecting a small value of the mean compensation depth, the pattern of deep Moho structure might not be reproduced realistically. Moreover, the definition of the mean compensation depth in existing isostatic models affects only low-degrees of the Moho spectrum. To overcome this problem, in this study we reformulate the Sjöberg and Jeffrey's methods of solving the Vening-Meinesz isostatic problem so that the mean compensation depth contributes to the whole Moho spectrum. Both solutions are then defined for the vertical gravity gradient, allowing estimating the Moho depth from the GOCE satellite gravity-gradiometry data. Moreover, gravimetric solutions provide realistic results only when a priori information on the crust and upper mantle structure is known (usually from seismic surveys) with a relatively good accuracy. To investigate this aspect, we formulate our gravimetric solutions for a variable Moho density contrast to account for variable density of the uppermost mantle below the Moho interface, while taking into consideration also density variations within the sediments and consolidated crust down to the Moho interface. The developed theoretical models are applied to estimate the Moho depth from GOCE data at the regional study area of the Iranian tectonic block, including also parts of surrounding tectonic features. Our results indicate that the regional Moho depth differences between Sjöberg and Jeffrey's solutions, reaching up to about 3 km, are caused by a smoothing effect of Sjöberg's method. The validation of our results further shows a relatively good agreement with regional seismic studies over most of the continental crust, but large discrepancies are detected under the Oman Sea and the Makran subduction zone. We explain these discrepancies by a low quality of seismic data offshore.

Inorganic and Protein Crystal Assembly in Solutions

NASA Technical Reports Server (NTRS)

Chernov, A. A.

2005-01-01

The basic kinetic and thermodynamic concepts of crystal growth will be revisited in view of recent AFM and interferometric findings. These concepts are as follows: 1) The Kossel crystal model that allows only one kink type on the crystal surface. The modern theory is developed overwhelmingly for the Kessel model; 2) Presumption that intensive step fluctuations maintain kink density sufficiently high to allow applicability of Gibbs-Thomson law; 3) Common experience that unlimited step bunching (morphological instability) during layer growth from solutions and supercooled melts always takes place if the step flow direction coincides with that of the fluid.

Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization

NASA Astrophysics Data System (ADS)

Espejo, Elio; Winkler, Michael

2018-04-01

The interplay of chemotaxis, convection and reaction terms is studied in the particular framework of a refined model for coral broadcast spawning, consisting of three equations describing the population densities of unfertilized sperms and eggs and the concentration of a chemical released by the latter, coupled to the incompressible Navier-Stokes equations. Under mild assumptions on the initial data, global existence of classical solutions to an associated initial-boundary value problem in bounded planar domains is established. Moreover, all these solutions are shown to approach a spatially homogeneous equilibrium in the large time limit.

Monte Carlo PDF method for turbulent reacting flow in a jet-stirred reactor

NASA Astrophysics Data System (ADS)

Roekaerts, D.

1992-01-01

A stochastic algorithm for the solution of the modeled scalar probability density function (PDF) transport equation for single-phase turbulent reacting flow is described. Cylindrical symmetry is assumed. The PDF is represented by ensembles of N representative values of the thermochemical variables in each cell of a nonuniform finite-difference grid and operations on these elements representing convection, diffusion, mixing and reaction are derived. A simplified model and solution algorithm which neglects the influence of turbulent fluctuations on mean reaction rates is also described. Both algorithms are applied to a selectivity problem in a real reactor.

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

Gillioz, M.; von Manteuffel, A.; Schwaller, P.

We study skyrmions in the littlest Higgs model and discuss their possible role as dark matter candidates. Stable massive skyrmions can exist in the littlest Higgs model also in absence of an exact parity symmetry, since they carry a conserved topological charge due to the non-trivial third homotopy group of the SU(5)/SO(5) coset. We find a spherically symmetric skyrmion solution in this coset. The effects of gauge fields on the skyrmion solutions are analyzed and found to lead to an upper bound on the skyrmion mass. The relic abundance is in agreement with the observed dark matter density for reasonablemore » parameter choices.« less

A viable dark fluid model

NASA Astrophysics Data System (ADS)

Elkhateeb, Esraa

2018-01-01

We consider a cosmological model based on a generalization of the equation of state proposed by Nojiri and Odintsov (2004) and Štefančić (2005, 2006). We argue that this model works as a dark fluid model which can interpolate between dust equation of state and the dark energy equation of state. We show how the asymptotic behavior of the equation of state constrained the parameters of the model. The causality condition for the model is also studied to constrain the parameters and the fixed points are tested to determine different solution classes. Observations of Hubble diagram of SNe Ia supernovae are used to further constrain the model. We present an exact solution of the model and calculate the luminosity distance and the energy density evolution. We also calculate the deceleration parameter to test the state of the universe expansion.

Effect of solute nature on the polyamorphic transition in glassy polyol aqueous solutions.

PubMed

Suzuki, Yoshiharu

2017-08-14

I examined the polyamorphic behavior of glassy dilute aqueous solutions of polyols (ethylene glycol, glycerol, meso-erythritol, xylitol, and D-sorbitol) under pressure at low temperatures. Although the volume change of the glassy aqueous solution varied continuously against pressure, the rate of the volume change appeared to vary discontinuously at the onset pressure of the gradual polyamorphic transition. It is thought that low-density liquid-like solvent water and high-density liquid-like solvent water coexist during the transition. Moreover, the existence of a solute induces the shift of polyamorphic transition to the lower-pressure side. The effect of a solute on the polyamorphic transition becomes larger in the order ethylene glycol, glycerol, meso-erythritol, xylitol, and D-sorbitol. Therefore, the solute can become a variable controlling the polyamorphic state of liquid water. This experimental result suggests that the metastable-equilibrium phase boundary between the low-density and the high-density amorphs for pure water is likely to be located at 0.22-0.23 GPa at about 150 K, which is slightly larger than the previously estimated pressure. Moreover, the solute-nature dependence on the polyamorphic transition seems to connect to that on the homogeneous nucleation temperature of polyol aqueous solution at ambient pressure. The region in which a low-density liquid appears coincides with the region in which the nucleus of ice Ih appears, suggesting that the formation of a low-density liquid is a precursory phenomenon of the nucleation of ice Ih.

Effect of solute nature on the polyamorphic transition in glassy polyol aqueous solutions

NASA Astrophysics Data System (ADS)

Suzuki, Yoshiharu

2017-08-01

I examined the polyamorphic behavior of glassy dilute aqueous solutions of polyols (ethylene glycol, glycerol, meso-erythritol, xylitol, and D-sorbitol) under pressure at low temperatures. Although the volume change of the glassy aqueous solution varied continuously against pressure, the rate of the volume change appeared to vary discontinuously at the onset pressure of the gradual polyamorphic transition. It is thought that low-density liquid-like solvent water and high-density liquid-like solvent water coexist during the transition. Moreover, the existence of a solute induces the shift of polyamorphic transition to the lower-pressure side. The effect of a solute on the polyamorphic transition becomes larger in the order ethylene glycol, glycerol, meso-erythritol, xylitol, and D-sorbitol. Therefore, the solute can become a variable controlling the polyamorphic state of liquid water. This experimental result suggests that the metastable-equilibrium phase boundary between the low-density and the high-density amorphs for pure water is likely to be located at 0.22-0.23 GPa at about 150 K, which is slightly larger than the previously estimated pressure. Moreover, the solute-nature dependence on the polyamorphic transition seems to connect to that on the homogeneous nucleation temperature of polyol aqueous solution at ambient pressure. The region in which a low-density liquid appears coincides with the region in which the nucleus of ice Ih appears, suggesting that the formation of a low-density liquid is a precursory phenomenon of the nucleation of ice Ih.

A study of the formation and dynamics of galaxies

NASA Astrophysics Data System (ADS)

Fillmore, J. A.

The first half of this thesis is a study on the growth of perturbations in the early universe which might lead to galaxies, clusters of galaxies, or regions void of galaxies. The growth of self-similar perturbations in an Einstein-deSitter universe with cold, collisionless particles is investigated. Three classes of solutions are obtained; one each with planar, cylindrical, and spherical symmetry. The solutions follow the development of structure in both the linear and nonlinear regimes. Self-similar spherical voids which develop from initially underdense regions are also investigated. The character of each solution depends upon the initial density deficit. The second half of this thesis details solutions of steady-state axisymmetric models of elliptical and disk galaxies, and considers which observable properties can be used as diagnostics of the kinematic configuration of the spheroidal component of these systems. Two component mass models are fitted to surface brightness measurements and used to fit kinematic models to the velocity data.

The Dynamics of a Viscous Gas Ring around a Kerr Black Hole

NASA Astrophysics Data System (ADS)

Riffert, H.

2000-01-01

The dynamics of a rotationally symmetric viscous gas ring around a Kerr black hole is calculated in the thin-disk approximation. An evolution equation for the surface density Σ(t,r) is derived, which is the relativistic extension of a classical equation obtained by R. Lüst. A singular point appears at the radius of the last stable circular orbit r=rc. The nature of this point is investigated, and it turns out that the solution is always bounded at rc, and no boundary condition can be obtained at this radius. A unique solution of an initial value problem requires a matching condition at rc which follows from the flow structure between rc and the horizon. In the model presented here, the density in this domain is zero, and the resulting boundary condition leads to a vanishing shear stress at r=rc, which is the condition used in the standard stationary thin-disk model of Novikov & Thorne. Numerical solutions of the evolution equation are presented for two different angular momenta of the black hole. The time evolution of the resulting accretion rate depends strongly on this angular momentum.

Self-assembly of Spherical Macroions in Solution: A Coarse-grained Molecular Dynamics Study

NASA Astrophysics Data System (ADS)

Liu, Zhuonan; Liu, Tianbo; Tsige, Mesfin

2015-03-01

Macroions (such as polyoxometalates) in solution can form a stable hollow spherical super-molecular structure called blackberry when they have moderate surface charge density and size (1-10 nm). Depending on the surface charge density of macroions, the size of the blackberry can be from 20 to more than 100 nm. Other macroions such as dendrimers can also self-assemble into similar super-molecular structure in solution. Existing theories such as Debye-Hückel and DLVO theories cannot explain this phenomenon and we are not aware of any other theory that can explain this. Previous studies using all-atom Molecular Dynamics simulations have shown identical macroions forming oligomers mediated by counterions. Due to the limitations in all-atom simulation and available computational capabilities, these studies handled only small systems with simple macroions, leading to less conclusive but still relevant results on the self-assembly behavior. To overcome these limitations, in this work large-scale coarse-grained modeling of macroions in solution is used. In order to understand the origin of the attractive force that is responsible for the self-assembly of macroions, different types of macroions in different solution conditions are studied. This work was supported by NSF Grant DMR0847580.

Improving CMD Areal Density Analysis: Algorithms and Strategies

NASA Astrophysics Data System (ADS)

Wilson, R. E.

2014-06-01

Essential ideas, successes, and difficulties of Areal Density Analysis (ADA) for color-magnitude diagrams (CMD¡¯s) of resolved stellar populations are examined, with explanation of various algorithms and strategies for optimal performance. A CMDgeneration program computes theoretical datasets with simulated observational error and a solution program inverts the problem by the method of Differential Corrections (DC) so as to compute parameter values from observed magnitudes and colors, with standard error estimates and correlation coefficients. ADA promises not only impersonal results, but also significant saving of labor, especially where a given dataset is analyzed with several evolution models. Observational errors and multiple star systems, along with various single star characteristics and phenomena, are modeled directly via the Functional Statistics Algorithm (FSA). Unlike Monte Carlo, FSA is not dependent on a random number generator. Discussions include difficulties and overall requirements, such as need for fast evolutionary computation and realization of goals within machine memory limits. Degradation of results due to influence of pixelization on derivatives, Initial Mass Function (IMF) quantization, IMF steepness, low Areal Densities (A ), and large variation in A are reduced or eliminated through a variety of schemes that are explained sufficiently for general application. The Levenberg-Marquardt and MMS algorithms for improvement of solution convergence are contained within the DC program. An example of convergence, which typically is very good, is shown in tabular form. A number of theoretical and practical solution issues are discussed, as are prospects for further development.

A composition joint PDF method for the modeling of spray flames

NASA Technical Reports Server (NTRS)

Raju, M. S.

1995-01-01

This viewgraph presentation discusses an extension of the probability density function (PDF) method to the modeling of spray flames to evaluate the limitations and capabilities of this method in the modeling of gas-turbine combustor flows. The comparisons show that the general features of the flowfield are correctly predicted by the present solution procedure. The present solution appears to provide a better representation of the temperature field, particularly, in the reverse-velocity zone. The overpredictions in the centerline velocity could be attributed to the following reasons: (1) the use of k-epsilon turbulence model is known to be less precise in highly swirling flows and (2) the swirl number used here is reported to be estimated rather than measured.

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

NASA Technical Reports Server (NTRS)

Woronowicz, Michael

2016-01-01

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

Coupled Leidenfrost states as a monodisperse granular clock

NASA Astrophysics Data System (ADS)

Liu, Rui; Yang, Mingcheng; Chen, Ke; Hou, Meiying; To, Kiwing

2016-08-01

Using an event-driven molecular dynamics simulation, we show that simple monodisperse granular beads confined in coupled columns may oscillate as a different type of granular clock. To trigger this oscillation, the system needs to be driven against gravity into a density-inverted state, with a high-density clustering phase supported from below by a gaslike low-density phase (Leidenfrost effect) in each column. Our analysis reveals that the density-inverted structure and the relaxation dynamics between the phases can amplify any small asymmetry between the columns, and lead to a giant oscillation. The oscillation occurs only for an intermediate range of the coupling strength, and the corresponding phase diagram can be universally described with a characteristic height of the density-inverted structure. A minimal two-phase model is proposed and a linear stability analysis shows that the triggering mechanism of the oscillation can be explained as a switchable two-parameter Andronov-Hopf bifurcation. Numerical solutions of the model also reproduce similar oscillatory dynamics to the simulation results.

Observation of number-density-dependent growth of plasmonic nanobubbles

NASA Astrophysics Data System (ADS)

Nakajima, Takashi; Wang, Xiaolong; Chatterjee, Souvik; Sakka, Tetsuo

2016-06-01

Interaction dynamics of laser pulses and nanoparticles are of great interest in recent years. In many cases, laser-nanoparticle interactions result in the formation of plasmonic nanobubbles, and the dynamics of nanoparticles and nanobubbles are inseparable. So far, very little attention has been paid to the number density. Here we report the first observation of number-density-dependent growth of plasmonic nanobubbles. Our results show that the nanobubbles growth depends (does not depend) on the number density at high (low) laser fluence, although the inter-particle distance in the solution is as long as 14-30 μm. This cannot be explained by the existing physical picture, and we propose a new model which takes into account the pressure waves arising from nanoparticles. The numerical results based on this model agree well with the experimental results. Our findings imply that the number density can be a new doorknob to control laser-nanobubble as well as laser-nanoparticle interactions.

Observation of number-density-dependent growth of plasmonic nanobubbles.

PubMed

Nakajima, Takashi; Wang, Xiaolong; Chatterjee, Souvik; Sakka, Tetsuo

2016-06-29

Interaction dynamics of laser pulses and nanoparticles are of great interest in recent years. In many cases, laser-nanoparticle interactions result in the formation of plasmonic nanobubbles, and the dynamics of nanoparticles and nanobubbles are inseparable. So far, very little attention has been paid to the number density. Here we report the first observation of number-density-dependent growth of plasmonic nanobubbles. Our results show that the nanobubbles growth depends (does not depend) on the number density at high (low) laser fluence, although the inter-particle distance in the solution is as long as 14-30 μm. This cannot be explained by the existing physical picture, and we propose a new model which takes into account the pressure waves arising from nanoparticles. The numerical results based on this model agree well with the experimental results. Our findings imply that the number density can be a new doorknob to control laser-nanobubble as well as laser-nanoparticle interactions.

Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model.

PubMed

Schuss, Z; Nadler, B; Eisenberg, R S

2001-09-01

Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is what and how to average. In this paper, we average a Langevin model of ionic motion in a bulk solution and protein channel. The main result is a coupled system of averaged Poisson and Nernst-Planck equations (CPNP) involving conditional and unconditional charge densities and conditional potentials. The resulting NP equations contain the averaged force on a single ion, which is the sum of two components. The first component is the gradient of a conditional electric potential that is the solution of Poisson's equation with conditional and permanent charge densities and boundary conditions of the applied voltage. The second component is the self-induced force on an ion due to surface charges induced only by that ion at dielectric interfaces. The ion induces surface polarization charge that exerts a significant force on the ion itself, not present in earlier PNP equations. The proposed CPNP system is not complete, however, because the electric potential satisfies Poisson's equation with conditional charge densities, conditioned on the location of an ion, while the NP equations contain unconditional densities. The conditional densities are closely related to the well-studied pair-correlation functions of equilibrium statistical mechanics. We examine a specific closure relation, which on the one hand replaces the conditional charge densities by the unconditional ones in the Poisson equation, and on the other hand replaces the self-induced force in the NP equation by an effective self-induced force. This effective self-induced force is nearly zero in the baths but is approximately equal to the self-induced force in and near the channel. The charge densities in the NP equations are interpreted as time averages over long times of the motion of a quasiparticle that diffuses with the same diffusion coefficient as that of a real ion, but is driven by the averaged force. In this way, continuum equations with averaged charge densities and mean-fields can be used to describe permeation through a protein channel.

STABILITY OF A CYLINDRICAL SOLUTE-SOLVENT INTERFACE: EFFECT OF GEOMETRY, ELECTROSTATICS, AND HYDRODYNAMICS.

PubMed

Li, B O; Sun, Hui; Zhou, Shenggao

The solute-solvent interface that separates biological molecules from their surrounding aqueous solvent characterizes the conformation and dynamics of such molecules. In this work, we construct a solvent fluid dielectric boundary model for the solvation of charged molecules and apply it to study the stability of a model cylindrical solute-solvent interface. The motion of the solute-solvent interface is defined to be the same as that of solvent fluid at the interface. The solvent fluid is assumed to be incompressible and is described by the Stokes equation. The solute is modeled simply by the ideal-gas law. All the viscous force, hydrostatic pressure, solute-solvent van der Waals interaction, surface tension, and electrostatic force are balanced at the solute-solvent interface. We model the electrostatics by Poisson's equation in which the solute-solvent interface is treated as a dielectric boundary that separates the low-dielectric solute from the high-dielectric solvent. For a cylindrical geometry, we find multiple cylindrically shaped equilibrium interfaces that describe polymodal (e.g., dry and wet) states of hydration of an underlying molecular system. These steady-state solutions exhibit bifurcation behavior with respect to the charge density. For their linearized systems, we use the projection method to solve the fluid equation and find the dispersion relation. Our asymptotic analysis shows that, for large wavenumbers, the decay rate is proportional to wavenumber with the proportionality half of the ratio of surface tension to solvent viscosity, indicating that the solvent viscosity does affect the stability of a solute-solvent interface. Consequences of our analysis in the context of biomolecular interactions are discussed.

On the global well-posedness theory for a class of PDE models for criminal activity

NASA Astrophysics Data System (ADS)

Rodríguez, N.

2013-10-01

We study a class of ‘reaction-advection-diffusion’ system of partial differential equations, which can be taken as basic models for criminal activity. This class of models are based on routine activity theory and other theories, such as the ‘repeat and near-repeat victimization effect’ and were first introduced in Short et al. (2008) [11]. In these models the criminal density is advected by a velocity field that depends on a scalar field, which measures the appeal to commit a crime. We refer to this scalar field as the attractiveness field. We prove local well-posedness of solutions for the general class of models. Furthermore, we prove global well-posedness of solutions to a fully-parabolic system with a velocity field that depends logarithmically on the attractiveness field. Our final result is the global well-posedness of solutions the fully-parabolic system with velocity field that depends linearly on the attractiveness field for small initial mass.

An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows

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

Snider, D.M.; O`Rourke, P.J.; Andrews, M.J.

1997-06-01

A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles,more » with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.« less

Hypergeometric Equation in Modeling Relativistic Isotropic Sphere

NASA Astrophysics Data System (ADS)

Thirukkanesh, S.; Ragel, F. C.

2014-04-01

We study the Einstein system of equations in static spherically symmetric spacetimes. We obtained classes of exact solutions to the Einstein system by transforming the condition for pressure isotropy to a hypergeometric equation choosing a rational form for one of the gravitational potentials. The solutions are given in simple form that is a desirable requisite to study the behavior of relativistic compact objects in detail. A physical analysis indicate that our models satisfy all the fundamental requirements of realistic star and match smoothly with the exterior Schwarzschild metric. The derived masses and densities are consistent with the previously reported experimental and theoretical studies describing strange stars. The models satisfy the standard energy conditions required by normal matter.

Galactic civilizations: Population dynamics and interstellar diffusion

NASA Technical Reports Server (NTRS)

Newman, W. I.; Sagan, C.

1978-01-01

The interstellar diffusion of galactic civilizations is reexamined by potential theory; both numerical and analytical solutions are derived for the nonlinear partial differential equations which specify a range of relevant models, drawn from blast wave physics, soil science, and, especially, population biology. An essential feature of these models is that, for all civilizations, population growth must be limited by the carrying capacity of the environment. Dispersal is fundamentally a diffusion process; a density-dependent diffusivity describes interstellar emigration. Two models are considered: the first describing zero population growth (ZPG), and the second which also includes local growth and saturation of a planetary population, and for which an asymptotic traveling wave solution is found.

Trapping of Neutrinos in Extremely Compact Stars and the Influence of Brane Tension on This Process

NASA Astrophysics Data System (ADS)

Stuchlík, Zdenäěk; Hladík, Jan; Urbanec, Martin

We present estimates on the efficiency of neutrino trapping in brany extremely compact stars, using the simplest model with uniform distribution of energy density, assuming massless neutrinos and uniform distribution of neutrino emissivity. Computation have been done for two different uniform-density stellar solution in the Randall-Sundrum II type braneworld, namely with the Reissner-Nordström-type of geometry and the second one, derived by Germani and Maartens.1

Electrostatic Debye layer formed at a plasma-liquid interface

NASA Astrophysics Data System (ADS)

Rumbach, Paul; Clarke, Jean Pierre; Go, David B.

2017-05-01

We construct an analytic model for the electrostatic Debye layer formed at a plasma-liquid interface by combining the Gouy-Chapman theory for the liquid with a simple parabolic band model for the plasma sheath. The model predicts a nonlinear scaling between the plasma current density and the solution ionic strength, and we confirmed this behavior with measurements using a liquid-anode plasma. Plots of the measured current density as a function of ionic strength collapse the data and curve fits yield a plasma electron density of ˜1019m-3 and an electric field of ˜104V /m on the liquid side of the interface. Because our theory is based firmly on fundamental physics, we believe it can be widely applied to many emerging technologies involving the interaction of low-temperature, nonequilibrium plasma with aqueous media, including plasma medicine and various plasma chemical synthesis techniques.

Coherent pulses in the diffusive transport of charged particles`

NASA Technical Reports Server (NTRS)

Kota, J.

1994-01-01

We present exact solutions to the diffusive transport of charged particles following impulsive injection for a simple model of scattering. A modified, two-parameter relaxation-time model is considered that simulates the low rate of scattering through perpendicular pitch-angle. Scattering is taken to be isotropic within each of the foward- and backward-pointing hemispheres, respectively, but, at the same time, a reduced rate of sccattering is assumed from one hemisphere to the other one. By applying a technique of Fourier- and Laplace-transform, the inverse transformation can be performed and exact solutions can be reached. By contrast with the first, and so far only exact solutions of Federov and Shakov, this wider class of solutions gives rise to coherent pulses to appear. The present work addresses omnidirectional densities for isotropic injection from an instantaneous and localized source. The dispersion relations are briefly discussed. We find, for this particular model, two diffusive models to exist up to a certain limiting wavenumber. The corresponding eigenvalues are real at the lowest wavenumbers. Complex eigenvalues, which are responsible for coherent pulses, appear at higher wavenumbers.

Solute transport along a single fracture in a porous rock: a simple analytical solution and its extension for modeling velocity dispersion

NASA Astrophysics Data System (ADS)

Liu, Longcheng; Neretnieks, Ivars; Shahkarami, Pirouz; Meng, Shuo; Moreno, Luis

2018-02-01

A simple and robust solution is developed for the problem of solute transport along a single fracture in a porous rock. The solution is referred to as the solution to the single-flow-path model and takes the form of a convolution of two functions. The first function is the probability density function of residence-time distribution of a conservative solute in the fracture-only system as if the rock matrix is impermeable. The second function is the response of the fracture-matrix system to the input source when Fickian-type dispersion is completely neglected; thus, the effects of Fickian-type dispersion and matrix diffusion have been decoupled. It is also found that the solution can be understood in a way in line with the concept of velocity dispersion in fractured rocks. The solution is therefore extended into more general cases to also account for velocity variation between the channels. This leads to a development of the multi-channel model followed by detailed statistical descriptions of channel properties and sensitivity analysis of the model upon changes in the model key parameters. The simulation results obtained by the multi-channel model in this study fairly well agree with what is often observed in field experiments—i.e. the unchanged Peclet number with distance, which cannot be predicted by the classical advection-dispersion equation. In light of the findings from the aforementioned analysis, it is suggested that forced-gradient experiments can result in considerably different estimates of dispersivity compared to what can be found in natural-gradient systems for typical channel widths.

Effects of LiDAR point density and landscape context on estimates of urban forest biomass

NASA Astrophysics Data System (ADS)

Singh, Kunwar K.; Chen, Gang; McCarter, James B.; Meentemeyer, Ross K.

2015-03-01

Light Detection and Ranging (LiDAR) data is being increasingly used as an effective alternative to conventional optical remote sensing to accurately estimate aboveground forest biomass ranging from individual tree to stand levels. Recent advancements in LiDAR technology have resulted in higher point densities and improved data accuracies accompanied by challenges for procuring and processing voluminous LiDAR data for large-area assessments. Reducing point density lowers data acquisition costs and overcomes computational challenges for large-area forest assessments. However, how does lower point density impact the accuracy of biomass estimation in forests containing a great level of anthropogenic disturbance? We evaluate the effects of LiDAR point density on the biomass estimation of remnant forests in the rapidly urbanizing region of Charlotte, North Carolina, USA. We used multiple linear regression to establish a statistical relationship between field-measured biomass and predictor variables derived from LiDAR data with varying densities. We compared the estimation accuracies between a general Urban Forest type and three Forest Type models (evergreen, deciduous, and mixed) and quantified the degree to which landscape context influenced biomass estimation. The explained biomass variance of the Urban Forest model, using adjusted R2, was consistent across the reduced point densities, with the highest difference of 11.5% between the 100% and 1% point densities. The combined estimates of Forest Type biomass models outperformed the Urban Forest models at the representative point densities (100% and 40%). The Urban Forest biomass model with development density of 125 m radius produced the highest adjusted R2 (0.83 and 0.82 at 100% and 40% LiDAR point densities, respectively) and the lowest RMSE values, highlighting a distance impact of development on biomass estimation. Our evaluation suggests that reducing LiDAR point density is a viable solution to regional-scale forest assessment without compromising the accuracy of biomass estimates, and these estimates can be further improved using development density.

Self-similar perturbations of a Friedmann universe

NASA Technical Reports Server (NTRS)

Carr, Bernard J.; Yahil, Amos

1990-01-01

The present analysis of spherically symmetric self-similar solutions to the Einstein equations gives attention to those solutions that are asymptotically k = 0 Friedmann at large z values, and possess finite but perturbed density at the origin. Such solutions represent nonlinear density fluctuations which grow at the same rate as the universe's particle horizon. The overdense solutions span only a narrow range of parameters, and resemble static isothermal gas spheres just within the sonic point; the underdense solutions may have arbitrarily low density at the origin while exhibiting a unique relationship between amplitude and scale. Their relevance to large-scale void formation is considered.

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.

Approximating the nonlinear density dependence of electron transport coefficients and scattering rates across the gas-liquid interface

NASA Astrophysics Data System (ADS)

Garland, N. A.; Boyle, G. J.; Cocks, D. G.; White, R. D.

2018-02-01

This study reviews the neutral density dependence of electron transport in gases and liquids and develops a method to determine the nonlinear medium density dependence of electron transport coefficients and scattering rates required for modeling transport in the vicinity of gas-liquid interfaces. The method has its foundations in Blanc’s law for gas-mixtures and adapts the theory of Garland et al (2017 Plasma Sources Sci. Technol. 26) to extract electron transport data across the gas-liquid transition region using known data from the gas and liquid phases only. The method is systematically benchmarked against multi-term Boltzmann equation solutions for Percus-Yevick model liquids. Application to atomic liquids highlights the utility and accuracy of the derived method.

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

NASA Astrophysics Data System (ADS)

Shi, Bingren

2010-10-01

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

Confinement of anomalous liquids in nanoporous matrices.

PubMed

Strekalova, Elena G; Luo, Jiayuan; Stanley, H Eugene; Franzese, Giancarlo; Buldyrev, Sergey V

2012-09-07

Using molecular dynamics simulations, we investigate the effects of different nanoconfinements on complex liquids-e.g., colloids or protein solutions-with density anomalies and a liquid-liquid phase transition (LLPT). In all the confinements, we find a strong depletion effect with a large increase in liquid density near the confining surface. If the nanoconfinement is modeled by an ordered matrix of nanoparticles, we find that the anomalies are preserved. On the contrary, if the confinement is modeled by a disordered matrix of nanoparticles, we find a drastically different phase diagram: the LLPT shifts to lower pressures and temperatures, and the anomalies become weaker, as the disorder increases. We find that the density heterogeneities induced by the disordered matrix are responsible for the weakening of the LLPT and the disappearance of the anomalies.

Torsion as a source of expansion in a Bianchi type-I universe in the self-consistent Einstein-Cartan theory of a perfect fluid with spin density

NASA Technical Reports Server (NTRS)

Bradas, James C.; Fennelly, Alphonsus J.; Smalley, Larry L.

1987-01-01

It is shown that a generalized (or 'power law') inflationary phase arises naturally and inevitably in a simple (Bianchi type-I) anisotropic cosmological model in the self-consistent Einstein-Cartan gravitation theory with the improved stress-energy-momentum tensor with the spin density of Ray and Smalley (1982, 1983). This is made explicit by an analytical solution of the field equations of motion of the fluid variables. The inflation is caused by the angular kinetic energy density due to spin. The model further elucidates the relationship between fluid vorticity, the angular velocity of the inertially dragged tetrads, and the precession of the principal axes of the shear ellipsoid. Shear is not effective in damping the inflation.

A 3-D Coupled CFD-DSMC Solution Method With Application to the Mars Sample Return Orbiter

NASA Technical Reports Server (NTRS)

Glass, Christopher E.; Gnoffo, Peter A.

2000-01-01

A method to obtain coupled Computational Fluid Dynamics-Direct Simulation Monte Carlo (CFD-DSMC), 3-D flow field solutions for highly blunt bodies at low incidence is presented and applied to one concept of the Mars Sample Return Orbiter vehicle as a demonstration of the technique. CFD is used to solve the high-density blunt forebody flow defining an inflow boundary condition for a DSMC solution of the afterbody wake flow. By combining the two techniques in flow regions where most applicable, the entire mixed flow field is modeled in an appropriate manner.

Cosmology in Mirror Twin Higgs and neutrino masses

NASA Astrophysics Data System (ADS)

Chacko, Zackaria; Craig, Nathaniel; Fox, Patrick J.; Harnik, Roni

2017-07-01

We explore a simple solution to the cosmological challenges of the original Mirror Twin Higgs (MTH) model that leads to interesting implications for experiment. We consider theories in which both the standard model and mirror neutrinos acquire masses through the familiar seesaw mechanism, but with a low right-handed neutrino mass scale of order a few GeV. In these νMTH models, the right-handed neutrinos leave the thermal bath while still relativistic. As the universe expands, these particles eventually become nonrelativistic, and come to dominate the energy density of the universe before decaying. Decays to standard model states are preferred, with the result that the visible sector is left at a higher temperature than the twin sector. Consequently the contribution of the twin sector to the radiation density in the early universe is suppressed, allowing the current bounds on this scenario to be satisfied. However, the energy density in twin radiation remains large enough to be discovered in future cosmic microwave background experiments. In addition, the twin neutrinos are significantly heavier than their standard model counterparts, resulting in a sizable contribution to the overall mass density in neutrinos that can be detected in upcoming experiments designed to probe the large scale structure of the universe.

Gradient flow of O(N) nonlinear sigma model at large N

DOE PAGES

Aoki, Sinya; Kikuchi, Kengo; Onogi, Tetsuya

2015-04-28

Here, we study the gradient flow equation for the O(N) nonlinear sigma model in two dimensions at large N. We parameterize solution of the field at flow time t in powers of bare fields by introducing the coefficient function X n for the n-th power term (n = 1, 3, ··· ). Reducing the flow equation by keeping only the contributions at leading order in large N, we obtain a set of equations for X n ’s, which can be solved iteratively starting from n = 1. For n = 1 case, we find an explicit form of the exactmore » solution. Using this solution, we show that the two point function at finite flow time t is finite. As an application, we obtain the non-perturbative running coupling defined from the energy density. We also discuss the solution for n = 3 case.« less

Numerical investigation of coupled density-driven flow and hydrogeochemical processes below playas

NASA Astrophysics Data System (ADS)

Hamann, Enrico; Post, Vincent; Kohfahl, Claus; Prommer, Henning; Simmons, Craig T.

2015-11-01

Numerical modeling approaches with varying complexity were explored to investigate coupled groundwater flow and geochemical processes in saline basins. Long-term model simulations of a playa system gain insights into the complex feedback mechanisms between density-driven flow and the spatiotemporal patterns of precipitating evaporites and evolving brines. Using a reactive multicomponent transport model approach, the simulations reproduced, for the first time in a numerical study, the evaporite precipitation sequences frequently observed in saline basins ("bull's eyes"). Playa-specific flow, evapoconcentration, and chemical divides were found to be the primary controls for the location of evaporites formed, and the resulting brine chemistry. Comparative simulations with the computationally far less demanding surrogate single-species transport models showed that these were still able to replicate the major flow patterns obtained by the more complex reactive transport simulations. However, the simulated degree of salinization was clearly lower than in reactive multicomponent transport simulations. For example, in the late stages of the simulations, when the brine becomes halite-saturated, the nonreactive simulation overestimated the solute mass by almost 20%. The simulations highlight the importance of the consideration of reactive transport processes for understanding and quantifying geochemical patterns, concentrations of individual dissolved solutes, and evaporite evolution.

Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density

NASA Astrophysics Data System (ADS)

Jiang, Li; Liu, Jie; Zhang, Jianzhong; Feng, Zhibing

2017-12-01

Variable-density sources have been paid more attention in gravity modeling. We conduct the computation of gravity gradient tensor of given mass sources with variable density in this paper. 3D rectangular prisms, as simple building blocks, can be used to approximate well 3D irregular-shaped sources. A polynomial function of depth can represent flexibly the complicated density variations in each prism. Hence, we derive the analytic expressions in closed form for computing all components of the gravity gradient tensor due to a 3D right rectangular prism with an arbitrary-order polynomial density function of depth. The singularity of the expressions is analyzed. The singular points distribute at the corners of the prism or on some of the lines through the edges of the prism in the lower semi-space containing the prism. The expressions are validated, and their numerical stability is also evaluated through numerical tests. The numerical examples with variable-density prism and basin models show that the expressions within their range of numerical stability are superior in computational accuracy and efficiency to the common solution that sums up the effects of a collection of uniform subprisms, and provide an effective method for computing gravity gradient tensor of 3D irregular-shaped sources with complicated density variation. In addition, the tensor computed with variable density is different in magnitude from that with constant density. It demonstrates the importance of the gravity gradient tensor modeling with variable density.

Density and viscosity of some partially carbonated aqueous alkanolamine solutions and their blends

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

Weiland, R.H.; Dingman, J.C.; Cronin, D.B.

1998-05-01

Very little information is available concerning the effect of acid gas loading on the physical properties of amine-treating solutions flowing through the absorption and regeneration columns used in gas processing. The densities and viscosities of partially carbonated monoethanolamine (MEA), diethanolamine (DEA), and N-methyldiethanolamine (MDEA) solutions were measured at 298 K. With increasing carbon dioxide loadings, significant increases in both density and viscosity were observed. These results were combined with literature data to produce correlations for alkanolamine solution density and viscosity as a function of amine concentration, carbon dioxide loading, and temperature. The resulting single-amine correlations were used to predict themore » densities and viscosities of DEA + MDEA and MEA + MDEA blends. Predictions are compared with data measured for these blends.« less

Charged Analogues of Henning Knutsen Type Solutions in General Relativity

NASA Astrophysics Data System (ADS)

Gupta, Y. K.; Kumar, Sachin; Pratibha

2011-11-01

In the present article, we have found charged analogues of Henning Knutsen's interior solutions which join smoothly to the Reissner-Nordstrom metric at the pressure free interface. The solutions are singularity free and analyzed numerically with respect to pressure, energy-density and charge-density in details. The solutions so obtained also present the generalization of A.L. Mehra's solutions.

On the Eikonal equation in the pedestrian flow problem

NASA Astrophysics Data System (ADS)

Felcman, J.; Kubera, P.

2017-07-01

We consider the Pedestrian Flow Equations (PFEs) as the coupled system formed by the Eikonal equation and the first order hyperbolic system with the source term. The hyperbolic system consists of the continuity equation and momentum equation of fluid dynamics. Specifying the social and pressure forces in the momentum equation we come to the assumption that each pedestrian is trying to move in a desired direction (e.g. to the exit in the panic situation) with a desired velocity, where his velocity and the direction of movement depend on the density of pedestrians in his neighborhood. In [1] we used the model, where the desired direction of movement is given by the solution of the Eikonal equation (more precisely by the gradient of the solution). Here we avoid the solution of the Eikonal equation, which is the novelty of the paper. Based on the fact that the solution of the Eikonal equation has the meaning of the shortest time to reach the exit, we define explicitly such a function in the framework of the Dijkstra's algorithm for the shortest path in the graph. This is done at the discrete level of the solution. As the graph we use the underlying triangulation, where the norm of each edge is density depending and has the dimension of the time. The numerical examples of the solution of the PFEs with and without the solution of the Eikonal equation are presented.

Use of a chemical equilibrium model to describe surface properties and uptake of cadmium, strontium, and lead by Chlorella (UTEX 252)

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

Hassett, J.M.

1988-01-01

Metal-aquatic biota interactions are important in both natural and engineered systems. In this study, the uptake of cadmium, strontium and lead by the unicellular green alga Chlorella (UTEX 252) was investigated. Variables included metal concentration, pH, and ionic strength. Data gathered included dry weights (mg/l), cell counts (cells/ml), electrophoretic mobilities (EPMs, {mu}m/sec/V/cm) of metal-free and metal-exposed cells, and metal uptake - difference in concentration in filtrate of cell-metal and cell-free metal solutions. Derived data included cell volumes and surface area, uptake on a {mu}M/m{sup 2} basis, {zeta}-potentials, diffuse layer potentials and charge densities. Typical uptake values were 1.1, 5.2, andmore » 6 {mu}M/m{sup 2} for Cd, Pb, and Sr, respectively, from solutions of pH 6, ionic strength 0.02M, and metal concentration 10{sup {minus}4} M. Cell EPMs were insensitive to metal; under certain conditions, however, (pM > 4, pH > 8), cadmium exposed cells exhibited a reversal in surface charge from negative to positive. The chemical equilibrium model MINEQL1 + STANFORD was used to model algal surface properties and metal uptake. Input data included site pK, density, and {Delta}pK, estimated from EPM-pH data. The model described surface properties of Chlorella (UTEX 252) as judged by a close fit of {zeta}-potentials and model-derived diffuse layer potentials. Metal uptake was modelled by adjusting site density and/or metal-surface site equilibrium constants. Attempts to model surface properties and metal uptake simultaneously were not successful.« less

An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

NASA Astrophysics Data System (ADS)

Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

An upwind space-time conservation element and solution element (CE/SE) scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme.

Uniformly rotating, axisymmetric, and triaxial quark stars in general relativity

NASA Astrophysics Data System (ADS)

Zhou, Enping; Tsokaros, Antonios; Rezzolla, Luciano; Xu, Renxin; Uryū, Kōji

2018-01-01

Quasiequilibrium models of uniformly rotating axisymmetric and triaxial quark stars are computed in a general-relativistic gravity scenario. The Isenberg-Wilson-Mathews (IWM) formulation is employed and the Compact Object Calculator (cocal) code is extended to treat rotating stars with finite surface density and new equations of state (EOSs). Besides the MIT bag model for quark matter which is composed of deconfined quarks, we examine a new EOS proposed by Lai and Xu that is based on quark clustering and results in a stiff EOS that can support masses up to 3.3 M⊙ in the case we considered. We perform convergence tests for our new code to evaluate the effect of finite surface density in the accuracy of our solutions and construct sequences of solutions for both small and high compactness. The onset of secular instability due to viscous dissipation is identified and possible implications are discussed. An estimate of the gravitational wave amplitude and luminosity based on quadrupole formulas is presented and comparison with neutron stars is discussed.

Oxygen Reduction Reaction on Ag(111) in Alkaline Solution: A Combined Density Functional Theory and Kinetic Monte Carlo Study

DOE PAGES

Liu, Shizhong; White, Michael G.; Liu, Ping

2018-01-25

We reported a detailed mechanistic study of the oxygen reduction reaction (ORR) on the model Ag(111) surface in alkaline solution by using density functional theory (DFT) and Kinetic Monte Carlo (KMC) simulations, in which multiple pathways involving either 2 e - or 4 e - mechanisms were included. The theoretical modelling presented here is able to reproduce the experimentally measured polarization curves in both low and high potential regions. An electrochemical 4 e - network including both a chemisorbed water (*H 2O)-mediated 4 e - associative pathway and the conventional associative pathway was identified to dominate the ORR mechanism. Onmore » the basis of the mechanistic understanding derived from these calculations, the ways to promote the ORR on Ag(111) were provided, including facilitating *OH removal, **O 2 reduction by *H 2O, and suppressing **O 2 desorption. Finally, the origin of the different ORR behaviors of Ag(111) and Pt(111) was also discussed in detail.« less

Oxygen Reduction Reaction on Ag(111) in Alkaline Solution: A Combined Density Functional Theory and Kinetic Monte Carlo Study

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

Liu, Shizhong; White, Michael G.; Liu, Ping

We reported a detailed mechanistic study of the oxygen reduction reaction (ORR) on the model Ag(111) surface in alkaline solution by using density functional theory (DFT) and Kinetic Monte Carlo (KMC) simulations, in which multiple pathways involving either 2 e - or 4 e - mechanisms were included. The theoretical modelling presented here is able to reproduce the experimentally measured polarization curves in both low and high potential regions. An electrochemical 4 e - network including both a chemisorbed water (*H 2O)-mediated 4 e - associative pathway and the conventional associative pathway was identified to dominate the ORR mechanism. Onmore » the basis of the mechanistic understanding derived from these calculations, the ways to promote the ORR on Ag(111) were provided, including facilitating *OH removal, **O 2 reduction by *H 2O, and suppressing **O 2 desorption. Finally, the origin of the different ORR behaviors of Ag(111) and Pt(111) was also discussed in detail.« less

Well behaved parametric class of relativistic charged fluid ball in general relativity

NASA Astrophysics Data System (ADS)

Pant, Neeraj

2011-04-01

The paper presents a class of interior solutions of Einstein-Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0≤ K≤42) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ b =2×1014 g/cm3. Corresponding to K=2 and X=0.30, the maximum mass of the star comes out to be 4.96 M Θ with linear dimension 34.16 km and central redshift and surface redshift 2.1033 and 0.683 respectively. In absence of the charge we are left behind with the well behaved fourth model of Durgapal (J. Phys., A, Math. Gen. 15:2637, 1982).

Comparative Validation of Realtime Solar Wind Forecasting Using the UCSD Heliospheric Tomography Model

NASA Technical Reports Server (NTRS)

MacNeice, Peter; Taktakishvili, Alexandra; Jackson, Bernard; Clover, John; Bisi, Mario; Odstrcil, Dusan

2011-01-01

The University of California, San Diego 3D Heliospheric Tomography Model reconstructs the evolution of heliospheric structures, and can make forecasts of solar wind density and velocity up to 72 hours in the future. The latest model version, installed and running in realtime at the Community Coordinated Modeling Center(CCMC), analyzes scintillations of meter wavelength radio point sources recorded by the Solar-Terrestrial Environment Laboratory(STELab) together with realtime measurements of solar wind speed and density recorded by the Advanced Composition Explorer(ACE) Solar Wind Electron Proton Alpha Monitor(SWEPAM).The solution is reconstructed using tomographic techniques and a simple kinematic wind model. Since installation, the CCMC has been recording the model forecasts and comparing them with ACE measurements, and with forecasts made using other heliospheric models hosted by the CCMC. We report the preliminary results of this validation work and comparison with alternative models.

Flow and Transport in Highly Heterogeneous Porous Formations: Numerical Experiments Performed Using the Analytic Element Method

NASA Astrophysics Data System (ADS)

Jankovic, I.

2002-05-01

Flow and transport in porous formations are analyzed using numerical simulations. Hydraulic conductivity is treated as a spatial random function characterized by a probability density function and a two-point covariance function. Simulations are performed for a multi-indicator conductivity structure developed by Gedeon Dagan (personal communication). This conductivity structure contains inhomogeneities (inclusions) of elliptical and ellipsoidal geometry that are embedded in a homogeneous background. By varying the distribution of sizes and conductivities of inclusions, any probability density function and two-point covariance may be reproduced. The multi-indicator structure is selected since it yields simple approximate transport solutions (Aldo Fiori, personal communication) and accurate numerical solutions (based on the Analytic Element Method). The dispersion is examined for two conceptual models. Both models are based on the multi-indicator conductivity structure. The first model is designed to examine dispersion in aquifers with continuously varying conductivity. The inclusions in this model cover as much area/volume of the porous formation as possible. The second model is designed for aquifers that contain clay/sand/gravel lenses embedded in otherwise homogeneous background. The dispersion in both aquifer types is simulated numerically. Simulation results are compared to those obtained using simple approximate solutions. In order to infer transport statistics that are representative of an infinite domain using the numerical experiments, the inclusions are placed in a domain that was shaped as a large ellipse (2D) and a large spheroid (3D) that were submerged in an unbounded homogeneous medium. On a large scale, the large body of inclusions behaves like a single large inhomogeneity. The analytic solution for a uniform flow past the single inhomogeneity of such geometry yields uniform velocity inside the domain. The velocity differs from that at infinity and can be used to infer the effective conductivity of the medium. As many as 100,000 inhomogeneities are placed inside the domain for 2D simulations. Simulations in 3D were limited to 50,000 inclusions. A large number of simulations was conducted on a massively parallel supercomputer cluster at the Center for Computational Research, University at Buffalo. Simulations range from mildly heterogeneous formations to highly heterogeneous formations (variance of the logarithm of conductivity equal to 10) and from sparsely populated systems to systems where inhomogeneities cover 95% of the volume. Particles are released and tracked inside the core of constant mean velocity. Following the particle tracking, various medium, flow, and transport statistics are computed. These include: spatial moments of particle positions, probability density function of hydraulic conductivity and each component of velocity, their two-point covariance function in the direction of flow and normal to it, covariance of Lagrangean velocities, and probability density function of travel times to various break-through locations. Following the analytic nature of the flow solution, all the results are presented in dimensionless forms. For example, the dispersion coefficients are made dimensionless with respect to the mean velocity and size of inhomogeneities. Detailed results will be presented and compared to well known first-order results and the results that are based on simple approximate transport solutions of Aldo Fiori.

Buoyancy-induced mixing during wash and elution steps in expanded bed adsorption.

PubMed

Fee, C J; Liten, A D

2001-01-01

Buoyancy-induced mixing occurs during expanded bed adsorption processes when the feed stream entering the bottom of the system has a lower density than that of the fluid above it. In the absence of a headspace, mixing in the expanded bed can be modeled as a single, well-mixed vessel, with first-order dynamics. In the presence of a headspace, the system exhibits second-order dynamics for the densities typically encountered in protein chromatography, and can be modeled as two well-mixed vessels (the expanded bed and the headspace) arranged in series. In this paper, the mixing dynamics of the expanded bed are described and a mathematical model of the system is presented. Experimental measurements of density changes during the dilution of sucrose and salt solutions in a STREAMLINE 25 column are presented. These show excellent agreement with predictions using the model. A number of strategies for wash and elution in expanded mode, both in the presence and absence of headspace, are discussed.

Global strong solutions to the one-dimensional heat-conductive model for planar non-resistive magnetohydrodynamics with large data

NASA Astrophysics Data System (ADS)

Li, Yang

2018-06-01

In this paper, we consider the initial-boundary value problem to the one-dimensional compressible heat-conductive model for planar non-resistive magnetohydrodynamics. By making full use of the effective viscous flux and an analogue, together with the structure of the equations, global existence and uniqueness of strong solutions are obtained on condition that the initial density is bounded below away from vacuum and the heat conductivity coefficient κ satisfies the growth condition κ _1(1+θ^{α })≤ κ (θ)≤ κ _2(1+θ^{α }),\\quad { for some }0< α < ∞, with κ _1,κ _2 being positive constants. Moreover, global solvability of strong solutions is shown with the initial vacuum. The results are obtained without any smallness restriction to the initial data.

A bioconvection model for a squeezing flow of nanofluid between parallel plates in the presence of gyrotactic microorganisms

NASA Astrophysics Data System (ADS)

Bin-Mohsin, Bandar; Ahmed, Naveed; Adnan; Khan, Umar; Tauseef Mohyud-Din, Syed

2017-04-01

This article deals with the bioconvection flow in a parallel-plate channel. The plates are parallel and the flowing fluid is saturated with nanoparticles, and water is considered as a base fluid because microorganisms can survive only in water. A highly nonlinear and coupled system of partial differential equations presenting the model of bioconvection flow between parallel plates is reduced to a nonlinear and coupled system (nondimensional bioconvection flow model) of ordinary differential equations with the help of feasible nondimensional variables. In order to find the convergent solution of the system, a semi-analytical technique is utilized called variation of parameters method (VPM). Numerical solution is also computed and the Runge-Kutta scheme of fourth order is employed for this purpose. Comparison between these solutions has been made on the domain of interest and found to be in excellent agreement. Also, influence of various parameters has been discussed for the nondimensional velocity, temperature, concentration and density of the motile microorganisms both for suction and injection cases. Almost inconsequential influence of thermophoretic and Brownian motion parameters on the temperature field is observed. An interesting variation are inspected for the density of the motile microorganisms due to the varying bioconvection parameter in suction and injection cases. At the end, we make some concluding remarks in the light of this article.

Inflation in a closed universe

NASA Astrophysics Data System (ADS)

Ratra, Bharat

2017-11-01

To derive a power spectrum for energy density inhomogeneities in a closed universe, we study a spatially-closed inflation-modified hot big bang model whose evolutionary history is divided into three epochs: an early slowly-rolling scalar field inflation epoch and the usual radiation and nonrelativistic matter epochs. (For our purposes it is not necessary to consider a final dark energy dominated epoch.) We derive general solutions of the relativistic linear perturbation equations in each epoch. The constants of integration in the inflation epoch solutions are determined from de Sitter invariant quantum-mechanical initial conditions in the Lorentzian section of the inflating closed de Sitter space derived from Hawking's prescription that the quantum state of the universe only include field configurations that are regular on the Euclidean (de Sitter) sphere section. The constants of integration in the radiation and matter epoch solutions are determined from joining conditions derived by requiring that the linear perturbation equations remain nonsingular at the transitions between epochs. The matter epoch power spectrum of gauge-invariant energy density inhomogeneities is not a power law, and depends on spatial wave number in the way expected for a generalization to the closed model of the standard flat-space scale-invariant power spectrum. The power spectrum we derive appears to differ from a number of other closed inflation model power spectra derived assuming different (presumably non de Sitter invariant) initial conditions.

Interpretation of scrape-off layer profile evolution and first-wall ion flux statistics on JET using a stochastic framework based on fillamentary motion

NASA Astrophysics Data System (ADS)

Walkden, N. R.; Wynn, A.; Militello, F.; Lipschultz, B.; Matthews, G.; Guillemaut, C.; Harrison, J.; Moulton, D.; Contributors, JET

2017-08-01

This paper presents the use of a novel modelling technique based around intermittent transport due to filament motion, to interpret experimental profile and fluctuation data in the scrape-off layer (SOL) of JET during the onset and evolution of a density profile shoulder. A baseline case is established, prior to shoulder formation, and the stochastic model is shown to be capable of simultaneously matching the time averaged profile measurement as well as the PDF shape and autocorrelation function from the ion-saturation current time series at the outer wall. Aspects of the stochastic model are then varied with the aim of producing a profile shoulder with statistical measurements consistent with experiment. This is achieved through a strong localised reduction in the density sink acting on the filaments within the model. The required reduction of the density sink occurs over a highly localised region with the timescale of the density sink increased by a factor of 25. This alone is found to be insufficient to model the expansion and flattening of the shoulder region as the density increases, which requires additional changes within the stochastic model. An example is found which includes both a reduction in the density sink and filament acceleration and provides a consistent match to the experimental data as the shoulder expands, though the uniqueness of this solution can not be guaranteed. Within the context of the stochastic model, this implies that the localised reduction in the density sink can trigger shoulder formation, but additional physics is required to explain the subsequent evolution of the profile.

Uniqueness of a solution of a steady state photochemical problem: Applications to Mars

NASA Technical Reports Server (NTRS)

Krasnopolsky, Vladimir A.

1995-01-01

Based on the conservation of chemical elements in chemical reactions, a rule is proved that the number of boundary conditions given by densities and/or nonzero velocities should not be less than the number of chemical elements in the system, and the boundary conditions for species given by densities and velocities should include all elements in the system. Applications of this rule to Mars are considered. It is shown that the problem of the CO2-H2O chemistry in the lower and middle atmosphere of Mars, say, in the range of 0-80 km does not have a unique solution, if only CO2 and H2O densities are given at the lower boundary, and the remaining boundary conditions are fluxes. Two examples of models of this type are discussed. Two models of the photochemistry of the Martian atmosphere, with and without nitrogen chemistry, are considered. The oxygen nonthermal escape ratio of 1.2 x 10(exp 8)/cu cm/s is given at 240 km and is balanced with the total hydrogen escape rate within an uncertainty of 1% for both models. Both models fit the measured O2 and CO mixing ratios, the O3 abundance, and the O2 1.27-micrometer dayglow almost within the uncertainties of the measured values, though the model without nitrogen chemistry fits better. The importance of nitrogen chemistry in the lower and middle atmosphere of Mars depends on a fine balance between production of NO and N in the upper atmosphere which is not known within the required accuracy.

Viscous entrainment on hairy surfaces

NASA Astrophysics Data System (ADS)

Nasto, Alice; Brun, P.-T.; Hosoi, A. E.

2018-02-01

Nectar-drinking bats and honeybees have tongues covered with hairlike structures, enhancing their ability to take up viscous nectar by dipping. Using a combination of model experiments and theory, we explore the physical mechanisms that govern viscous entrainment in a hairy texture. Hairy surfaces are fabricated using laser cut molds and casting samples with polydimethylsiloxane (PDMS) elastomer. We model the liquid trapped within the texture using a Darcy-Brinkmann-like approach and derive the drainage flow solution. The amount of fluid that is entrained is dependent on the viscosity of the fluid, the density of the hairs, and the withdrawal speed. Both experiments and theory reveal an optimal hair density to maximize fluid uptake.

Visualization and simulation of density driven convection in porous media using magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Montague, James A.; Pinder, George F.; Gonyea, Jay V.; Hipko, Scott; Watts, Richard

2018-05-01

Magnetic resonance imaging is used to observe solute transport in a 40 cm long, 26 cm diameter sand column that contained a central core of low permeability silica surrounded by higher permeability well-sorted sand. Low concentrations (2.9 g/L) of Magnevist, a gadolinium based contrast agent, produce density driven convection within the column when it starts in an unstable state. The unstable state, for this experiment, exists when higher density contrast agent is present above the lower density water. We implement a numerical model in OpenFOAM to reproduce the observed fluid flow and transport from a density difference of 0.3%. The experimental results demonstrate the usefulness of magnetic resonance imaging in observing three-dimensional gravity-driven convective-dispersive transport behaviors in medium scale experiments.

New Type of the Interface Evolution in the Richtmyer-Meshkov Instability

NASA Technical Reports Server (NTRS)

Abarzhi, S. I.; Herrmann, M.

2003-01-01

We performed systematic theoretical and numerical studies of the nonlinear large-scale coherent dynamics in the Richtmyer-Meshkov instability for fluids with contrast densities. Our simulations modeled the interface dynamics for compressible and viscous uids. For a two-fluid system we observed that in the nonlinear regime of the instability the bubble velocity decays and its surface attens, and the attening is accompanied by slight oscillations. We found the theoretical solution for the system of conservation laws, describing the principal influence of the density ratio on the motion of the nonlinear bubble. The solution has no adjustable parameters, and shows that the attening of the bubble front is a distinct property universal for all values of the density ratio. This property follows from the fact that the RM bubbles decelerate. The theoretical and numerical results validate each other, describe the new type of the bubble front evolution in RMI, and identify the bubble curvature as important and sensitive diagnostic parameter.

Electrodeposition and codeposition under low gravity/nonconvecting conditions

NASA Technical Reports Server (NTRS)

Riley, Clyde; Coble, H. Dwain; Loo, Boon; Benson, Brian; Abi-Akar, Hind

1987-01-01

An experimental electrodeposition system was developed for modeling the behavior of inert particles codepositing in an electroplating matrix under low-gravity conditions. The device consists of a Co-electrodeposition cell operating in a convectionless mode (cathode over anode) and containing polystyrene particles with density approximating that of the electroplating solution. Data were obtained in shielded cells at 1 g, and the experiment was duplicated at 0.01 g on a KC-135 flight. No difference was found between convection-free bench experiments and the 0.01 g KC-135 experiments with 0.0900 M CuSO4. Codeposition experiments using 11.8-micron matched-density polystyrene spheres in 1 M CoSO4 have revealed that a noticeable particle gradient is created as the solution density mismatches in the vicinity of the cathode; gentle stirring was required to maintain a homogeneous particle suspension. Cr3C2 dust, which readily disperses at 1 g, tended to coagulate into spherical globules at 0.01 g, when stirred.

Universal core model for multiple-gate field-effect transistors with short channel and quantum mechanical effects

NASA Astrophysics Data System (ADS)

Shin, Yong Hyeon; Bae, Min Soo; Park, Chuntaek; Park, Joung Won; Park, Hyunwoo; Lee, Yong Ju; Yun, Ilgu

2018-06-01

A universal core model for multiple-gate (MG) field-effect transistors (FETs) with short channel effects (SCEs) and quantum mechanical effects (QMEs) is proposed. By using a Young’s approximation based solution for one-dimensional Poisson’s equations the total inversion charge density (Q inv ) in the channel is modeled for double-gate (DG) and surrounding-gate SG (SG) FETs, following which a universal charge model is derived based on the similarity of the solutions, including for quadruple-gate (QG) FETs. For triple-gate (TG) FETs, the average of DG and QG FETs are used. A SCEs model is also proposed considering the potential difference between the channel’s surface and center. Finally, a QMEs model for MG FETs is developed using the quantum correction compact model. The proposed universal core model is validated on commercially available three-dimensional ATLAS numerical simulations.

Multimodal, high-dimensional, model-based, Bayesian inverse problems with applications in biomechanics

NASA Astrophysics Data System (ADS)

Franck, I. M.; Koutsourelakis, P. S.

2017-01-01

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of unknown (latent) variables is high. This is the setting in many problems in computational physics where forward models with nonlinear PDEs are used and the parameters to be calibrated involve spatio-temporarily varying coefficients, which upon discretization give rise to a high-dimensional vector of unknowns. One of the consequences of the well-documented ill-posedness of inverse problems is the possibility of multiple solutions. While such information is contained in the posterior density in Bayesian formulations, the discovery of a single mode, let alone multiple, poses a formidable computational task. The goal of the present paper is two-fold. On one hand, we propose approximate, adaptive inference strategies using mixture densities to capture multi-modal posteriors. On the other, we extend our work in [1] with regard to effective dimensionality reduction techniques that reveal low-dimensional subspaces where the posterior variance is mostly concentrated. We validate the proposed model by employing Importance Sampling which confirms that the bias introduced is small and can be efficiently corrected if the analyst wishes to do so. We demonstrate the performance of the proposed strategy in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical diagnosis. The discovery of multiple modes (solutions) in such problems is critical in achieving the diagnostic objectives.

Effects of Convection Electric Fields on Modeled Plasmaspheric Densities and ccc Temperatures

NASA Technical Reports Server (NTRS)

Comfort, Richard H.; Richards, Phil G.; Liao, Jin-Hua; Craven, Paul D.

1998-01-01

This paper examines the effects of convection electric fields on plasmaspheric H+, O+, He+, and N+ densities and electron and ion temperatures. These effects are studied with the aid of the Field Line Interhemispheric Plasma (FLIP) model, which has recently been extended to include the effects of ExB drifts. The FLIP model solves the continuity and momentum equations for the major ion species as well as the energy equations for ions and electrons along entire drifting flux tubes from 100 km altitude in the northern hemisphere to 100 km altitude in the southern hemisphere. Electron heating in the ionosphere and plasmasphere is provided by the solution of two-stream equations for photoelectrons. The dawn-dusk electric field imposed by the solar wind causes changes in plasmaspheric density and temperature as the plasma drifts onto flux tubes having different volumes. In an idealized convection model, outward drifts in the afternoon cause decreases in the plasmasphere density and temperature while inward drifts in the evening cause increases in plasmasphere density and temperature. In this paper we examine the effects of convection electric fields on the rate of refilling of flux tubes and investigate the hypothesis that convection electric fields are responsible for the unusually high evening electron temperatures and the post-midnight density maxima often observed in the winter ionosphere above Millstone Hill.

Options for refractive index and viscosity matching to study variable density flows

NASA Astrophysics Data System (ADS)

Clément, Simon A.; Guillemain, Anaïs; McCleney, Amy B.; Bardet, Philippe M.

2018-02-01

Variable density flows are often studied by mixing two miscible aqueous solutions of different densities. To perform optical diagnostics in such environments, the refractive index of the fluids must be matched, which can be achieved by carefully choosing the two solutes and the concentration of the solutions. To separate the effects of buoyancy forces and viscosity variations, it is desirable to match the viscosity of the two solutions in addition to their refractive index. In this manuscript, several pairs of index matched fluids are compared in terms of viscosity matching, monetary cost, and practical use. Two fluid pairs are studied in detail, with two aqueous solutions (binary solutions of water and a salt or alcohol) mixed into a ternary solution. In each case: an aqueous solution of isopropanol mixed with an aqueous solution of sodium chloride (NaCl) and an aqueous solution of glycerol mixed with an aqueous solution of sodium sulfate (Na_2SO_4). The first fluid pair allows reaching high-density differences at low cost, but brings a large difference in dynamic viscosity. The second allows matching dynamic viscosity and refractive index simultaneously, at reasonable cost. For each of these four solutes, the density, kinematic viscosity, and refractive index are measured versus concentration and temperature, as well as wavelength for the refractive index. To investigate non-linear effects when two index-matched, binary solutions are mixed, the ternary solutions formed are also analyzed. Results show that density and refractive index follow a linear variation with concentration. However, the viscosity of the isopropanol and NaCl pair deviates from the linear law and has to be considered. Empirical correlations and their coefficients are given to create index-matched fluids at a chosen temperature and wavelength. Finally, the effectiveness of the refractive index matching is illustrated with particle image velocimetry measurements performed for a buoyant jet in a linearly stratified environment. The creation of the index-matched solutions and linear stratification in a large-scale experimental facility are detailed, as well as the practical challenges to obtain precise refractive index matching.

SUTRA: A model for 2D or 3D saturated-unsaturated, variable-density ground-water flow with solute or energy transport

USGS Publications Warehouse

Voss, Clifford I.; Provost, A.M.

2002-01-01

SUTRA (Saturated-Unsaturated Transport) is a computer program that simulates fluid movement and the transport of either energy or dissolved substances in a subsurface environment. This upgraded version of SUTRA adds the capability for three-dimensional simulation to the former code (Voss, 1984), which allowed only two-dimensional simulation. The code employs a two- or three-dimensional finite-element and finite-difference method to approximate the governing equations that describe the two interdependent processes that are simulated: 1) fluid density-dependent saturated or unsaturated ground-water flow; and 2) either (a) transport of a solute in the ground water, in which the solute may be subject to: equilibrium adsorption on the porous matrix, and both first-order and zero-order production or decay; or (b) transport of thermal energy in the ground water and solid matrix of the aquifer. SUTRA may also be used to simulate simpler subsets of the above processes. A flow-direction-dependent dispersion process for anisotropic media is also provided by the code and is introduced in this report. As the primary calculated result, SUTRA provides fluid pressures and either solute concentrations or temperatures, as they vary with time, everywhere in the simulated subsurface system. SUTRA flow simulation may be employed for two-dimensional (2D) areal, cross sectional and three-dimensional (3D) modeling of saturated ground-water flow systems, and for cross sectional and 3D modeling of unsaturated zone flow. Solute-transport simulation using SUTRA may be employed to model natural or man-induced chemical-species transport including processes of solute sorption, production, and decay. For example, it may be applied to analyze ground-water contaminant transport problems and aquifer restoration designs. In addition, solute-transport simulation with SUTRA may be used for modeling of variable-density leachate movement, and for cross sectional modeling of saltwater intrusion in aquifers at near-well or regional scales, with either dispersed or relatively sharp transition zones between freshwater and saltwater. SUTRA energy-transport simulation may be employed to model thermal regimes in aquifers, subsurface heat conduction, aquifer thermal-energy storage systems, geothermal reservoirs, thermal pollution of aquifers, and natural hydrogeologic convection systems. Mesh construction, which is quite flexible for arbitrary geometries, employs quadrilateral finite elements in 2D Cartesian or radial-cylindrical coordinate systems, and hexahedral finite elements in 3D systems. 3D meshes are currently restricted to be logically rectangular; in other words, they are similar to deformable finite-difference-style grids. Permeabilities may be anisotropic and may vary in both direction and magnitude throughout the system, as may most other aquifer and fluid properties. Boundary conditions, sources and sinks may be time dependent. A number of input data checks are made to verify the input data set. An option is available for storing intermediate results and restarting a simulation at the intermediate time. Output options include fluid velocities, fluid mass and solute mass or energy budgets, and time-varying observations at points in the system. Both the mathematical basis for SUTRA and the program structure are highly general, and are modularized to allow for straightforward addition of new methods or processes to the simulation. The FORTRAN-90 coding stresses clarity and modularity rather than efficiency, providing easy access for later modifications.

Biological adaptive control model: a mechanical analogue of multi-factorial bone density adaptation.

PubMed

Davidson, Peter L; Milburn, Peter D; Wilson, Barry D

2004-03-21

The mechanism of how bone adapts to every day demands needs to be better understood to gain insight into situations in which the musculoskeletal system is perturbed. This paper offers a novel multi-factorial mathematical model of bone density adaptation which combines previous single-factor models in a single adaptation system as a means of gaining this insight. Unique aspects of the model include provision for interaction between factors and an estimation of the relative contribution of each factor. This interacting system is considered analogous to a Newtonian mechanical system and the governing response equation is derived as a linear version of the adaptation process. The transient solution to sudden environmental change is found to be exponential or oscillatory depending on the balance between cellular activation and deactivation frequencies.

Solvable Hydrodynamics of Quantum Integrable Systems

NASA Astrophysics Data System (ADS)

Bulchandani, Vir B.; Vasseur, Romain; Karrasch, Christoph; Moore, Joel E.

2017-12-01

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudomomenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudomomentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.

Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

NASA Astrophysics Data System (ADS)

Steinacker, Harold C.

2018-02-01

We present simple solutions of IKKT-type matrix models that can be viewed as quantized homogeneous and isotropic cosmological space-times, with finite density of microstates and a regular Big Bang (BB). The BB arises from a signature change of the effective metric on a fuzzy brane embedded in Lorentzian target space, in the presence of a quantized 4-volume form. The Hubble parameter is singular at the BB, and becomes small at late times. There is no singularity from the target space point of view, and the brane is Euclidean "before" the BB. Both recollapsing and expanding universe solutions are obtained, depending on the mass parameters.

Global Well-Posedness and Decay Rates of Strong Solutions to a Non-Conservative Compressible Two-Fluid Model

NASA Astrophysics Data System (ADS)

Evje, Steinar; Wang, Wenjun; Wen, Huanyao

2016-09-01

In this paper, we consider a compressible two-fluid model with constant viscosity coefficients and unequal pressure functions {P^+neq P^-}. As mentioned in the seminal work by Bresch, Desjardins, et al. (Arch Rational Mech Anal 196:599-629, 2010) for the compressible two-fluid model, where {P^+=P^-} (common pressure) is used and capillarity effects are accounted for in terms of a third-order derivative of density, the case of constant viscosity coefficients cannot be handled in their settings. Besides, their analysis relies on a special choice for the density-dependent viscosity [refer also to another reference (Commun Math Phys 309:737-755, 2012) by Bresch, Huang and Li for a study of the same model in one dimension but without capillarity effects]. In this work, we obtain the global solution and its optimal decay rate (in time) with constant viscosity coefficients and some smallness assumptions. In particular, capillary pressure is taken into account in the sense that {Δ P=P^+ - P^-=fneq 0} where the difference function {f} is assumed to be a strictly decreasing function near the equilibrium relative to the fluid corresponding to {P^-}. This assumption plays an key role in the analysis and appears to have an essential stabilization effect on the model in question.

Density functional study on the structural and thermodynamic properties of aqueous DNA-electrolyte solution in the framework of cell model.

PubMed

Wang, Ke; Yu, Yang-Xin; Gao, Guang-Hua

2008-05-14

A density functional theory (DFT) in the framework of cell model is proposed to calculate the structural and thermodynamic properties of aqueous DNA-electrolyte solution with finite DNA concentrations. The hard-sphere contribution to the excess Helmholtz energy functional is derived from the modified fundamental measure theory, and the electrostatic interaction is evaluated through a quadratic functional Taylor expansion around a uniform fluid. The electroneutrality in the cell leads to a variational equation with a constraint. Since the reference fluid is selected to be a bulk phase, the Lagrange multiplier proves to be the potential drop across the cell boundary (Donnan potential). The ion profiles and electrostatic potential profiles in the cell are calculated from the present DFT-cell model. Our DFT-cell model gives better prediction of ion profiles than the Poisson-Boltzmann (PB)- or modified PB-cell models when compared to the molecular simulation data. The effects of polyelectrolyte concentration, ion size, and added-salt concentration on the electrostatic potential difference between the DNA surface and the cell boundary are investigated. The expression of osmotic coefficient is derived from the general formula of grand potential. The osmotic coefficients predicted by the DFT are lower than the PB results and are closer to the simulation results and experimental data.

Monte Carlo simulation and equation of state for flexible charged hard-sphere chain fluids: polyampholyte and polyelectrolyte solutions.

PubMed

Jiang, Hao; Adidharma, Hertanto

2014-11-07

The thermodynamic modeling of flexible charged hard-sphere chains representing polyampholyte or polyelectrolyte molecules in solution is considered. The excess Helmholtz energy and osmotic coefficients of solutions containing short polyampholyte and the osmotic coefficients of solutions containing short polyelectrolytes are determined by performing canonical and isobaric-isothermal Monte Carlo simulations. A new equation of state based on the thermodynamic perturbation theory is also proposed for flexible charged hard-sphere chains. For the modeling of such chains, the use of solely the structure information of monomer fluid for calculating the chain contribution is found to be insufficient and more detailed structure information must therefore be considered. Two approaches, i.e., the dimer and dimer-monomer approaches, are explored to obtain the contribution of the chain formation to the Helmholtz energy. By comparing with the simulation results, the equation of state with either the dimer or dimer-monomer approach accurately predicts the excess Helmholtz energy and osmotic coefficients of polyampholyte and polyelectrolyte solutions except at very low density. It also well captures the effect of temperature on the thermodynamic properties of these solutions.

Mixing of two solutions combined by gravity drainage.

PubMed

Leuptow, R M; Smith, K; Mockros, L F

1995-01-01

A variety of medical therapies require the mixing of solutions from two separate bags before use. One scenario for the mixing is to drain the solution from one bag into the other by gravity through a short connecting tube. The degree of mixing in the lower bag depends on the relative densities of the two solutions, the geometry of the two bags and the connecting tube, and the placement of the connecting tube. Solutions with densities differing by as much as 12% were mixed by draining the solution from an upper bag into a lower bag for a particular geometric configuration. The two solutions had different electrical conductivities, and the conductivity of the combined solution as it exited from the lower bag was used as a measure of the effectiveness of mixing. When the more dense solution was drained from the upper bag into the less dense solution in a lower bag, mixing was very effective. The incoming jet of high density solution entrained the low density solution. Flow visualization indicated that the incoming jet penetrated to the bottom of the lower bag, and resulting large vortical structures enhanced mixing. When the less dense solution was drained from the upper bag into the more dense solution in the lower bag mixing was less effective. The buoyancy force reduced the momentum of the incoming jet such that it did not penetrate to the bottom of the lower bag, resulting in stratification of the solutions.

Measuring the Density of a Sugar Solution: A General Chemistry Experiment Using a Student-Prepared Unknown

ERIC Educational Resources Information Center

Peterson, Karen I.

2008-01-01

The experiment developed in this article addresses the concept of equipment calibration for reducing systematic error. It also suggests simple student-prepared sucrose solutions for which accurate densities are known, but not readily available to students. Densities are measured with simple glassware that has been calibrated using the density of…

Study of laser cooling in deep optical lattice: two-level quantum model

NASA Astrophysics Data System (ADS)

Prudnikov, O. N.; Il'enkov, R. Ya.; Taichenachev, A. V.; Yudin, V. I.; Rasel, E. M.

2018-01-01

We study a possibility of laser cooling of 24Mg atoms in deep optical lattice formed by intense off-resonant laser field in a presence of cooling field resonant to narrow (3s3s) 1 S 0 → (3s3p)3 P 1 (λ = 457 nm) optical transition. For description of laser cooling with taking into account quantum recoil effects we consider two quantum models. The first one is based on direct numerical solution of quantum kinetic equation for atom density matrix and the second one is simplified model based on decomposition of atom density matrix over vibration states in the lattice wells. We search cooling field intensity and detuning for minimum cooling energy and fast laser cooling.

Drinking with a hairy tongue: viscous entrainment by dipping hairy surfaces

NASA Astrophysics Data System (ADS)

Nasto, Alice; Brun, Pierre-Thomas; Alvarado, José; Bush, John; Hosoi, Anette

2016-11-01

Nectar-drinking bats have tongues covered with hair-like papillae, enhancing their ability to take up viscous nectar by dipping. Using a combination of model experiments and theory reminiscent of Landau-Levich-Derjaguin dip coating, we rationalize this mechanism of viscous entrainment in a hairy texture. For the model experiments, hairy surfaces are fabricated using laser cut molds and casting samples with PDMS elastomer. Modeling the liquid trapped within the texture using a Darcy-Brinkman like approach, we derive the drainage flow solution. The amount of fluid that is entrained is dependent on the viscosity of the fluid, the density of the hairs, and the dipping speed. We find that there is an optimal hair density to maximize fluid uptake.

Kinetic Theory and Fast Wind Observations of the Electron Strahl

NASA Astrophysics Data System (ADS)

Horaites, Konstantinos; Boldyrev, Stanislav; Wilson, Lynn B., III; Viñas, Adolfo F.; Merka, Jan

2017-10-01

Measurements of the electron velocity distribution function (eVDF) in the solar wind exhibit a high-energy, field-aligned beam of electrons, known as the ``strahl''. We develop a kinetic model for the strahl population, based on the solution of the electron drift-kinetic equation at heliospheric distances where the plasma density, temperature, and the strength of the magnetic field decline as power-laws of the distance along a magnetic flux tube. We compare our model with the eVDF measured by the Wind satellite's SWE strahl detector. The model is successful at predicting the angular width of the strahl for the Wind data at 1 AU, in particular, the scaling of the width with particle energy and background density.

Theoretical calculations of Electron Paramagnetic Resonance parameters of liquid phase Orotic acid radical

NASA Astrophysics Data System (ADS)

Sarikaya, Ebru Karakaş; Dereli, Ömer

2017-02-01

To obtain liquid phase molecular structure, conformational analysis of Orotic acid was performed and six conformers were determined. For these conformations, eight possible radicals were modelled by using Density Functional Theory computations with respect to molecular structure. Electron Paramagnetic Resonance parameters of these model radicals were calculated and then they were compared with the experimental ones. Geometry optimizations of the molecule and modeled radicals were performed using Becke's three-parameter hybrid-exchange functional combined with the Lee-Yang-Parr correlation functional of Density Functional Theory and 6-311++G(d,p) basis sets in p-dioxane solution. Because Orotic acid can be mutagenic in mammalian somatic cells and it is also mutagenic for bacteria and yeast, it has been studied.

Dynamics of stochastic SEIS epidemic model with varying population size

NASA Astrophysics Data System (ADS)

Liu, Jiamin; Wei, Fengying

2016-12-01

We introduce the stochasticity into a deterministic model which has state variables susceptible-exposed-infected with varying population size in this paper. The infected individuals could return into susceptible compartment after recovering. We show that the stochastic model possesses a unique global solution under building up a suitable Lyapunov function and using generalized Itô's formula. The densities of the exposed and infected tend to extinction when some conditions are being valid. Moreover, the conditions of persistence to a global solution are derived when the parameters are subject to some simple criteria. The stochastic model admits a stationary distribution around the endemic equilibrium, which means that the disease will prevail. To check the validity of the main results, numerical simulations are demonstrated as end of this contribution.

Quantum dynamics in continuum for proton transport II: Variational solvent-solute interface.

PubMed

Chen, Duan; Chen, Zhan; Wei, Guo-Wei

2012-01-01

Proton transport plays an important role in biological energy transduction and sensory systems. Therefore, it has attracted much attention in biological science and biomedical engineering in the past few decades. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins involving continuum, atomic, and quantum descriptions, assisted with the evolution, formation, and visualization of membrane channel surfaces. We describe proton dynamics quantum mechanically via a new density functional theory based on the Boltzmann statistics, while implicitly model numerous solvent molecules as a dielectric continuum to reduce the number of degrees of freedom. The density of all other ions in the solvent is assumed to obey the Boltzmann distribution in a dynamic manner. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic scale. A variational solute-solvent interface is designed to separate the explicit molecule and implicit solvent regions. We formulate a total free-energy functional to put proton kinetic and potential energies, the free energy of all other ions, and the polar and nonpolar energies of the whole system on an equal footing. The variational principle is employed to derive coupled governing equations for the proton transport system. Generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation, and generalized Kohn-Sham equation are obtained from the present variational framework. The variational solvent-solute interface is generated and visualized to facilitate the multiscale discrete/continuum/quantum descriptions. Theoretical formulations for the proton density and conductance are constructed based on fundamental laws of physics. A number of mathematical algorithms, including the Dirichlet-to-Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The gramicidin A channel is used to validate the performance of the proposed proton transport model and demonstrate the efficiency of the proposed mathematical algorithms. The proton channel conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and confirms the proposed model. Copyright © 2011 John Wiley & Sons, Ltd.

Spectral Density of Laser Beam Scintillation in Wind Turbulence. Part 1; Theory

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1997-01-01

The temporal spectral density of the log-amplitude scintillation of a laser beam wave due to a spatially dependent vector-valued crosswind (deterministic as well as random) is evaluated. The path weighting functions for normalized spectral moments are derived, and offer a potential new technique for estimating the wind velocity profile. The Tatarskii-Klyatskin stochastic propagation equation for the Markov turbulence model is used with the solution approximated by the Rytov method. The Taylor 'frozen-in' hypothesis is assumed for the dependence of the refractive index on the wind velocity, and the Kolmogorov spectral density is used for the refractive index field.

3D ELECTRON DENSITY DISTRIBUTIONS IN THE SOLAR CORONA DURING SOLAR MINIMA: ASSESSMENT FOR MORE REALISTIC SOLAR WIND MODELING

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

Patoul, Judith de; Foullon, Claire; Riley, Pete, E-mail: j.depatoul@exeter.ac.uk, E-mail: c.foullon@exeter.ac.uk, E-mail: rileype@saic.com

Knowledge of the electron density distribution in the solar corona put constraints on the magnetic field configurations for coronal modeling and on initial conditions for solar wind modeling. We work with polarized SOHO/LASCO-C2 images from the last two recent minima of solar activity (1996–1997 and 2008–2010), devoid of coronal mass ejections. The goals are to derive the 4D electron density distributions in the corona by applying a newly developed time-dependent tomographic reconstruction method and to compare the results between the two solar minima and with two magnetohydrodynamic models. First, we confirm that the values of the density distribution in thermodynamic models aremore » more realistic than in polytropic ones. The tomography provides more accurate distributions in the polar regions, and we find that the density in tomographic and thermodynamic solutions varies with the solar cycle in both polar and equatorial regions. Second, we find that the highest-density structures do not always correspond to the predicted large-scale heliospheric current sheet or its helmet streamer but can follow the locations of pseudo-streamers. We deduce that tomography offers reliable density distributions in the corona, reproducing the slow time evolution of coronal structures, without prior knowledge of the coronal magnetic field over a full rotation. Finally, we suggest that the highest-density structures show a differential rotation well above the surface depending on how they are magnetically connected to the surface. Such valuable information on the rotation of large-scale structures could help to connect the sources of the solar wind to their in situ counterparts in future missions such as Solar Orbiter and Solar Probe Plus.« less

Molecular density functional theory of water describing hydrophobicity at short and long length scales

NASA Astrophysics Data System (ADS)

Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel

2013-10-01

We present an extension of our recently introduced molecular density functional theory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619 (2013)] to the solvation of hydrophobic solutes of various sizes, going from angstroms to nanometers. The theory is based on the quadratic expansion of the excess free energy in terms of two classical density fields: the particle density and the multipolar polarization density. Its implementation requires as input a molecular model of water and three measurable bulk properties, namely, the structure factor and the k-dependent longitudinal and transverse dielectric susceptibilities. The fine three-dimensional water structure around small hydrophobic molecules is found to be well reproduced. In contrast, the computed solvation free-energies appear overestimated and do not exhibit the correct qualitative behavior when the hydrophobic solute is grown in size. These shortcomings are corrected, in the spirit of the Lum-Chandler-Weeks theory, by complementing the functional with a truncated hard-sphere functional acting beyond quadratic order in density, and making the resulting functional compatible with the Van-der-Waals theory of liquid-vapor coexistence at long range. Compared to available molecular simulations, the approach yields reasonable solvation structure and free energy of hard or soft spheres of increasing size, with a correct qualitative transition from a volume-driven to a surface-driven regime at the nanometer scale.

Hydration of an apolar solute in a two-dimensional waterlike lattice fluid

NASA Astrophysics Data System (ADS)

Buzano, C.; de Stefanis, E.; Pretti, M.

2005-05-01

In a previous work, we investigated a two-dimensional lattice-fluid model, displaying some waterlike thermodynamic anomalies. The model, defined on a triangular lattice, is now extended to aqueous solutions with apolar species. Water molecules are of the “Mercedes Benz” type, i.e., they possess a D3 (equilateral triangle) symmetry, with three equivalent bonding arms. Bond formation depends both on orientation and local density. The insertion of inert molecules displays typical signatures of hydrophobic hydration: large positive transfer free energy, large negative transfer entropy (at low temperature), strong temperature dependence of the transfer enthalpy and entropy, i.e., large (positive) transfer heat capacity. Model properties are derived by a generalized first order approximation on a triangle cluster.

Hydration of an apolar solute in a two-dimensional waterlike lattice fluid.

PubMed

Buzano, C; De Stefanis, E; Pretti, M

2005-05-01

In a previous work, we investigated a two-dimensional lattice-fluid model, displaying some waterlike thermodynamic anomalies. The model, defined on a triangular lattice, is now extended to aqueous solutions with apolar species. Water molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three equivalent bonding arms. Bond formation depends both on orientation and local density. The insertion of inert molecules displays typical signatures of hydrophobic hydration: large positive transfer free energy, large negative transfer entropy (at low temperature), strong temperature dependence of the transfer enthalpy and entropy, i.e., large (positive) transfer heat capacity. Model properties are derived by a generalized first order approximation on a triangle cluster.

Optical and Transport Properties of Energetic Materials

NASA Astrophysics Data System (ADS)

Choi, Chang Sun

1990-01-01

The densities of Hydroxyl ammonium nitrate (HAN) based fast reacting liquids were measured as a function of pressure (up to 4.83 kbars) at several temperatures and the results of density measurements were fit to the Tait equation. Also the shear viscosities of this liquid were measured as a function of both pressure and temperature. The free volume model was applied to explain behavior of the shear viscosity with the assumption that only the reference temperature (T_0) in the Fulcher (1925), WLF (Williams, Landel, and Ferry) and Angell equations depends on pressure. The general relation to predict viscosity of this liquid at any temperature and pressure was derived and the difference between expected and measured values are about 5%. The phase diagrams of the HAN solution, Triethanol ammonium nitrate (TEAN) solution and LP-1845 were obtained through Differential Scanning Calorimetry (DSC) measurements. The TEAN solution has a eutectic temperature in the vicinity of 260^circK. The measured phase diagrams are in good agreement with the calculated phase diagrams. The TEAN solutions show a large supercooling effect. Some phase separation was observed in the TEAN solutions and this separation was believed to be due to eutectic composition of the TEAN solution. The expected freezing temperature of LP-1845 was almost the same with the calculated T_0 from the viscosity data. Raman spectra from the HAN solution, TEAN solution and LP-1845 were measured. Every peak in the spectra was assigned. These solutions show various interactions, such as ion-ion pairing and ion-water interaction. The strongest peak was a NO_3^- symmetric stretch mode at 1050 cm^{-1}. The time correlation functions were calculated from the Raman spectra of the 1050 cm^{-1} peak. The correlation time, which can be calculated from the linewidth, become shorter with decreasing temperatures and with increasing concentrations. The Kubo's stochastic theory explains the correlation functions very well if the solution is relatively dilute. The pressure dependence of the reaction rate was estimated by using the density data and Raman peak shift data.

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

Bae, Kyu Jung; Baer, Howard; Serce, Hasan

The supersymmetrized DFSZ axion model is highly motivated not only because it offers solutions to both the gauge hierarchy and strong CP problems, but also because it provides a solution to the SUSY μ-problem which naturally allows for a Little Hierarchy. We compute the expected mixed axion-neutralino dark matter abundance for the SUSY DFSZ axion model in two benchmark cases—a natural SUSY model with a standard neutralino underabundance (SUA) and an mSUGRA/CMSSM model with a standard overabundance (SOA). Our computation implements coupled Boltzmann equations which track the radiation density along with neutralino, axion, axion CO (produced via coherent oscillations), saxion,more » saxion CO, axino and gravitino densities. In the SUSY DFSZ model, axions, axinos and saxions go through the process of freeze-in—in contrast to freeze-out or out-of-equilibrium production as in the SUSY KSVZ model—resulting in thermal yields which are largely independent of the re-heat temperature. We find the SUA case with suppressed saxion-axion couplings (ξ=0) only admits solutions for PQ breaking scale f{sub a}∼< 6× 10{sup 12} GeV where the bulk of parameter space tends to be axion-dominated. For SUA with allowed saxion-axion couplings (ξ =1), then f{sub a} values up to ∼ 10{sup 14} GeV are allowed. For the SOA case, almost all of SUSY DFSZ parameter space is disallowed by a combination of overproduction of dark matter, overproduction of dark radiation or violation of BBN constraints. An exception occurs at very large f{sub a}∼ 10{sup 15}–10{sup 16} GeV where large entropy dilution from CO-produced saxions leads to allowed models.« less

Comparison of precision orbit derived density estimates for CHAMP and GRACE satellites

NASA Astrophysics Data System (ADS)

Fattig, Eric Dale

Current atmospheric density models cannot adequately represent the density variations observed by satellites in Low Earth Orbit (LEO). Using an optimal orbit determination process, precision orbit ephemerides (POE) are used as measurement data to generate corrections to density values obtained from existing atmospheric models. Densities obtained using these corrections are then compared to density data derived from the onboard accelerometers of satellites, specifically the CHAMP and GRACE satellites. This comparison takes two forms, cross correlation analysis and root mean square analysis. The densities obtained from the POE method are nearly always superior to the empirical models, both in matching the trends observed by the accelerometer (cross correlation), and the magnitudes of the accelerometer derived density (root mean square). In addition, this method consistently produces better results than those achieved by the High Accuracy Satellite Drag Model (HASDM). For satellites orbiting Earth that pass through Earth's upper atmosphere, drag is the primary source of uncertainty in orbit determination and prediction. Variations in density, which are often not modeled or are inaccurately modeled, cause difficulty in properly calculating the drag acting on a satellite. These density variations are the result of many factors; however, the Sun is the main driver in upper atmospheric density changes. The Sun influences the densities in Earth's atmosphere through solar heating of the atmosphere, as well as through geomagnetic heating resulting from the solar wind. Data are examined for fourteen hour time spans between November 2004 and July 2009 for both the CHAMP and GRACE satellites. This data spans all available levels of solar and geomagnetic activity, which does not include data in the elevated and high solar activity bins due to the nature of the solar cycle. Density solutions are generated from corrections to five different baseline atmospheric models, as well as nine combinations of density and ballistic coefficient correlated half-lives. These half-lives are varied among values of 1.8, 18, and 180 minutes. A total of forty-five sets of results emerge from the orbit determination process for all combinations of baseline density model and half-lives. Each time period is examined for both CHAMP and GRACE-A, and the results are analyzed. Results are averaged from all solutions periods for 2004--2007. In addition, results are averaged after binning according to solar and geomagnetic activity levels. For any given day in this period, a ballistic coefficient correlated half-life of 1.8 minutes yields the best correlation and root mean square values for both CHAMP and GRACE. For CHAMP, a density correlated half-life of 18 minutes is best for higher levels of solar and geomagnetic activity, while for lower levels 180 minutes is usually superior. For GRACE, 180 minutes is nearly always best. The three Jacchia-based atmospheric models yield very similar results. The CIRA 1972 or Jacchia 1971 models as baseline consistently produce the best results for both satellites, though results obtained for Jacchia-Roberts are very similar to the other Jacchia-based models. Data are examined in a similar manner for the extended solar minimum period during 2008 and 2009, albeit with a much smaller sampling of data. With the exception of some atypical results, similar combinations of half-lives and baseline atmospheric model produce the best results. A greater sampling of data will aid in characterizing density in a period of especially low solar activity. In general, cross correlation values for CHAMP and GRACE revealed that the POE method matched trends observed by the accelerometers very well. However, one period of time deviated from this trend for the GRACE-A satellite. Between late October 2005 and January 2006, correlations for GRACE-A were very low. Special examination of the surrounding months revealed the extent of time this period covered. Half-life and baseline model combinations that produced the best results during this time were similar to those during normal periods. Plotting these periods revealed very short period density variations in the accelerometer that could not be reproduced by the empirical models, HASDM, or the POE method. Finally, densities produced using precision orbit data for the GRACE-B satellite were shown to be nearly indistinguishable from those produced by GRACE-A. Plots of the densities produced for both satellites during the same time periods revealed this fact. Multiple days were examined covering all possible ranges of solar and geomagnetic activity. In addition, the period in which GRACE-A correlations were low was studied. No significant differences existed between GRACE-A and GRACE-B for all of the days examined.

The role of adequate reference materials in density measurements in hemodialysis

NASA Astrophysics Data System (ADS)

Furtado, A.; Moutinho, J.; Moura, S.; Oliveira, F.; Filipe, E.

2015-02-01

In hemodialysis, oscillation-type density meters are used to measure the density of the acid component of the dialysate solutions used in the treatment of kidney patients. An incorrect density determination of this solution used in hemodialysis treatments can cause several and adverse events to patients. Therefore, despite the Fresenius Medical Care (FME) tight control of the density meters calibration results, this study shows the benefits of mimic the matrix usually measured to produce suitable reference materials for the density meter calibrations.

Lithium-Based High Energy Density Flow Batteries

NASA Technical Reports Server (NTRS)

Bugga, Ratnakumar V. (Inventor); West, William C. (Inventor); Kindler, Andrew (Inventor); Smart, Marshall C. (Inventor)

2014-01-01

Systems and methods in accordance with embodiments of the invention implement a lithium-based high energy density flow battery. In one embodiment, a lithium-based high energy density flow battery includes a first anodic conductive solution that includes a lithium polyaromatic hydrocarbon complex dissolved in a solvent, a second cathodic conductive solution that includes a cathodic complex dissolved in a solvent, a solid lithium ion conductor disposed so as to separate the first solution from the second solution, such that the first conductive solution, the second conductive solution, and the solid lithium ionic conductor define a circuit, where when the circuit is closed, lithium from the lithium polyaromatic hydrocarbon complex in the first conductive solution dissociates from the lithium polyaromatic hydrocarbon complex, migrates through the solid lithium ionic conductor, and associates with the cathodic complex of the second conductive solution, and a current is generated.

Self-consistent many-electron theory of electron work functions and surface potential characteristics for selected metals

NASA Technical Reports Server (NTRS)

Smith, J. R.

1969-01-01

Electron work functions, surface potentials, and electron number density distributions and electric fields in the surface region of 26 metals were calculated from first principles within the free electron model. Calculation proceeded from an expression of the total energy as a functional of the electron number density, including exchange and correlation energies, as well as a first inhomogeneity term. The self-consistent solution was obtained via a variational procedure. Surface barriers were due principally to many-body effects; dipole barriers were small only for some alkali metals, becoming quite large for the transition metals. Surface energies were inadequately described by this model, which neglects atomistic effects. Reasonable results were obtained for electron work functions and surface potential characteristics, maximum electron densities varying by a factor of over 60.

An Application of the H-Function to Curve-Fitting and Density Estimation.

DTIC Science & Technology

1983-12-01

equations into a model that is linear in its coefficients. Nonlinear least squares estimation is a relatively new area developed to accomodate models which...to converge on a solution (10:9-10). For the simple linear model and when general assump- tions are made, the Gauss-Markov theorem states that the...distribution. For example, if the analyst wants to model the time between arrivals to a queue for a computer simulation, he infers the true probability

Stratified flows with variable density: mathematical modelling and numerical challenges.

NASA Astrophysics Data System (ADS)

Murillo, Javier; Navas-Montilla, Adrian

2017-04-01

Stratified flows appear in a wide variety of fundamental problems in hydrological and geophysical sciences. They may involve from hyperconcentrated floods carrying sediment causing collapse, landslides and debris flows, to suspended material in turbidity currents where turbulence is a key process. Also, in stratified flows variable horizontal density is present. Depending on the case, density varies according to the volumetric concentration of different components or species that can represent transported or suspended materials or soluble substances. Multilayer approaches based on the shallow water equations provide suitable models but are not free from difficulties when moving to the numerical resolution of the governing equations. Considering the variety of temporal and spatial scales, transfer of mass and energy among layers may strongly differ from one case to another. As a consequence, in order to provide accurate solutions, very high order methods of proved quality are demanded. Under these complex scenarios it is necessary to observe that the numerical solution provides the expected order of accuracy but also converges to the physically based solution, which is not an easy task. To this purpose, this work will focus in the use of Energy balanced augmented solvers, in particular, the Augmented Roe Flux ADER scheme. References: J. Murillo , P. García-Navarro, Wave Riemann description of friction terms in unsteady shallow flows: Application to water and mud/debris floods. J. Comput. Phys. 231 (2012) 1963-2001. J. Murillo B. Latorre, P. García-Navarro. A Riemann solver for unsteady computation of 2D shallow flows with variable density. J. Comput. Phys.231 (2012) 4775-4807. A. Navas-Montilla, J. Murillo, Energy balanced numerical schemes with very high order. The Augmented Roe Flux ADER scheme. Application to the shallow water equations, J. Comput. Phys. 290 (2015) 188-218. A. Navas-Montilla, J. Murillo, Asymptotically and exactly energy balanced augmented flux-ADER schemes with application to hyperbolic conservation laws with geometric source terms, J. Comput. Phys. 317 (2016) 108-147. J. Murillo and A. Navas-Montilla, A comprehensive explanation and exercise of the source terms in hyperbolic systems using Roe type solutions. Application to the 1D-2D shallow water equations, Advances in Water Resources 98 (2016) 70-96.

Transcranial Electrical Neuromodulation Based on the Reciprocity Principle

PubMed Central

Fernández-Corazza, Mariano; Turovets, Sergei; Luu, Phan; Anderson, Erik; Tucker, Don

2016-01-01

A key challenge in multi-electrode transcranial electrical stimulation (TES) or transcranial direct current stimulation (tDCS) is to find a current injection pattern that delivers the necessary current density at a target and minimizes it in the rest of the head, which is mathematically modeled as an optimization problem. Such an optimization with the Least Squares (LS) or Linearly Constrained Minimum Variance (LCMV) algorithms is generally computationally expensive and requires multiple independent current sources. Based on the reciprocity principle in electroencephalography (EEG) and TES, it could be possible to find the optimal TES patterns quickly whenever the solution of the forward EEG problem is available for a brain region of interest. Here, we investigate the reciprocity principle as a guideline for finding optimal current injection patterns in TES that comply with safety constraints. We define four different trial cortical targets in a detailed seven-tissue finite element head model, and analyze the performance of the reciprocity family of TES methods in terms of electrode density, targeting error, focality, intensity, and directionality using the LS and LCMV solutions as the reference standards. It is found that the reciprocity algorithms show good performance comparable to the LCMV and LS solutions. Comparing the 128 and 256 electrode cases, we found that use of greater electrode density improves focality, directionality, and intensity parameters. The results show that reciprocity principle can be used to quickly determine optimal current injection patterns in TES and help to simplify TES protocols that are consistent with hardware and software availability and with safety constraints. PMID:27303311

Transcranial Electrical Neuromodulation Based on the Reciprocity Principle.

PubMed

Fernández-Corazza, Mariano; Turovets, Sergei; Luu, Phan; Anderson, Erik; Tucker, Don

2016-01-01

A key challenge in multi-electrode transcranial electrical stimulation (TES) or transcranial direct current stimulation (tDCS) is to find a current injection pattern that delivers the necessary current density at a target and minimizes it in the rest of the head, which is mathematically modeled as an optimization problem. Such an optimization with the Least Squares (LS) or Linearly Constrained Minimum Variance (LCMV) algorithms is generally computationally expensive and requires multiple independent current sources. Based on the reciprocity principle in electroencephalography (EEG) and TES, it could be possible to find the optimal TES patterns quickly whenever the solution of the forward EEG problem is available for a brain region of interest. Here, we investigate the reciprocity principle as a guideline for finding optimal current injection patterns in TES that comply with safety constraints. We define four different trial cortical targets in a detailed seven-tissue finite element head model, and analyze the performance of the reciprocity family of TES methods in terms of electrode density, targeting error, focality, intensity, and directionality using the LS and LCMV solutions as the reference standards. It is found that the reciprocity algorithms show good performance comparable to the LCMV and LS solutions. Comparing the 128 and 256 electrode cases, we found that use of greater electrode density improves focality, directionality, and intensity parameters. The results show that reciprocity principle can be used to quickly determine optimal current injection patterns in TES and help to simplify TES protocols that are consistent with hardware and software availability and with safety constraints.

Coupled metal partitioning dynamics and toxicodynamics at biointerfaces: a theory beyond the biotic ligand model framework.

PubMed

Duval, Jérôme F L

2016-04-14

A mechanistic understanding of the processes governing metal toxicity to microorganisms (bacteria, algae) calls for an adequate formulation of metal partitioning at biointerfaces during cell exposure. This includes the account of metal transport dynamics from bulk solution to biomembrane and the kinetics of metal internalisation, both potentially controlling the intracellular and surface metal fractions that originate cell growth inhibition. A theoretical rationale is developed here for such coupled toxicodynamics and interfacial metal partitioning dynamics under non-complexing medium conditions with integration of the defining cell electrostatic properties. The formalism explicitly considers intertwined metal adsorption at the biointerface, intracellular metal excretion, cell growth and metal depletion from bulk solution. The theory is derived under relevant steady-state metal transport conditions on the basis of coupled Nernst-Planck equation and continuous logistic equation modified to include metal-induced cell growth inhibition and cell size changes. Computational examples are discussed to identify limitations of the classical Biotic Ligand Model (BLM) in evaluating metal toxicity over time. In particular, BLM is shown to severely underestimate metal toxicity depending on cell exposure time, metal internalisation kinetics, cell surface electrostatics and initial cell density. Analytical expressions are provided for the interfacial metal concentration profiles in the limit where cell-growth is completely inhibited. A rigorous relationship between time-dependent cell density and metal concentrations at the biosurface and in bulk solution is further provided, which unifies previous equations formulated by Best and Duval under constant cell density and cell size conditions. The theory is sufficiently flexible to adapt to toxicity scenarios with involved cell survival-death processes.

Multicore runup simulation by under water avalanche using two-layer 1D shallow water equations

NASA Astrophysics Data System (ADS)

Bagustara, B. A. R. H.; Simanjuntak, C. A.; Gunawan, P. H.

2018-03-01

The increasing of layers in shallow water equations (SWE) produces more dynamic model than the one-layer SWE model. The two-layer 1D SWE model has different density for each layer. This model becomes more dynamic and natural, for instance in the ocean, the density of water will decreasing from the bottom to the surface. Here, the source-centered hydro-static reconstruction (SCHR) numerical scheme will be used to approximate the solution of two-layer 1D SWE model, since this scheme is proved to satisfy the mathematical properties for shallow water equation. Additionally in this paper, the algorithm of SCHR is adapted to the multicore architecture. The simulation of runup by under water avalanche is elaborated here. The results show that the runup is depend on the ratio of density of each layers. Moreover by using grid sizes Nx = 8000, the speedup and efficiency by 2 threads are obtained 1.74779 times and 87.3896 % respectively. Nevertheless, by 4 threads the speedup and efficiency are obtained 2.93132 times and 73.2830 % respectively by similar number of grid sizes Nx = 8000.

Theoretical and lidar studies of the density response of the mesospheric sodium layer to gravity wave perturbations

NASA Technical Reports Server (NTRS)

Shelton, J. D.; Gardner, C. S.

1981-01-01

The density response of atmospheric layers to gravity waves is developed in two forms, an exact solution and a perturbation series solution. The degree of nonlinearity in the layer density response is described by the series solution whereas the exact solution gives insight into the nature of the responses. Density perturbation in an atmospheric layer are shown to be substantially greater than the atmospheric density perturbation associated with the propagation of a gravity wave. Because of the density gradients present in atmospheric layers, interesting effects were observed such as a phase reversal in the linear layer response which occurs near the layer peak. Once the layer response is understood, the sodium layer can be used as a tracer of atmospheric wave motions. A two dimensional digital signal processing technique was developed. Both spatial and temporal filtering are utilized to enhance the resolution by decreasing shot noise by more han 10 dB. Many of the features associated with a layer density response to gravity waves were observed in high resolution density profiles of the mesospheric sodium layer. These include nonlinearities as well as the phase reversal in the linear layer response.

Electrochemical current noise on aluminum microelectrodes

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

Isaac, J.W.; Hebert, K.R.

1999-02-01

Aluminum disk microelectrodes were used to investigate electrochemical current noise in pH 8.8 borate buffer. The current noise spectra, expressed in terms of the current spectral density, had a characteristic two-plateau structure in the experimental bandwidth of 0.05--50 Hz, were potential-independent, and increased proportionally to electrode area. Injection of NaCl solution near the electrode surface, at potentials below that of the onset of pitting corrosion, caused 0.1--1 Hz current fluctuations to appear. From the frequency and area dependence of the current spectral density in the chloride-free solution, it was concluded that the noise arose from a number of discrete, approximatelymore » evenly distributed voltage noise sources positioned electrically in series with the inner barrier layer of the oxide film. A mathematical model for the current noise was developed which described a physical mechanism for noise production based on fluctuations in the widths of cracks or pores in the outer part of the surface film. The model was consistent with the observed area and frequency dependence of the current spectral density, suggesting that the physical process it described is a possible mechanism of noise generation. It could not be determined whether the noise sources were isolated defects or flaws, or pores in an outer precipitated portion of the oxide film.« less

A singularity free analytical solution of artificial satellite motion with drag

NASA Technical Reports Server (NTRS)

Mueller, A.

1978-01-01

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

A two-fluid model of the solar wind

NASA Technical Reports Server (NTRS)

Sandbaek, O.; Leer, E.; Holzer, T. E.

1992-01-01

A method is presented for the integration of the two-fluid solar-wind equations which is applicable to a wide variety of coronal base densities and temperatures. The method involves proton heat conduction, and may be applied to coronal base conditions for which subsonic-supersonic solar wind solutions exist.

Effects of LiDAR point density and landscape context on the retrieval of urban forest biomass

NASA Astrophysics Data System (ADS)

Singh, K. K.; Chen, G.; McCarter, J. B.; Meentemeyer, R. K.

2014-12-01

Light Detection and Ranging (LiDAR), as an alternative to conventional optical remote sensing, is being increasingly used to accurately estimate aboveground forest biomass ranging from individual tree to stand levels. Recent advancements in LiDAR technology have resulted in higher point densities and better data accuracies, which however pose challenges to the procurement and processing of LiDAR data for large-area assessments. Reducing point density cuts data acquisition costs and overcome computational challenges for broad-scale forest management. However, how does that impact the accuracy of biomass estimation in an urban environment containing a great level of anthropogenic disturbances? The main goal of this study is to evaluate the effects of LiDAR point density on the biomass estimation of remnant forests in the rapidly urbanizing regions of Charlotte, North Carolina, USA. We used multiple linear regression to establish the statistical relationship between field-measured biomass and predictor variables (PVs) derived from LiDAR point clouds with varying densities. We compared the estimation accuracies between the general Urban Forest models (no discrimination of forest type) and the Forest Type models (evergreen, deciduous, and mixed), which was followed by quantifying the degree to which landscape context influenced biomass estimation. The explained biomass variance of Urban Forest models, adjusted R2, was fairly consistent across the reduced point densities with the highest difference of 11.5% between the 100% and 1% point densities. The combined estimates of Forest Type biomass models outperformed the Urban Forest models using two representative point densities (100% and 40%). The Urban Forest biomass model with development density of 125 m radius produced the highest adjusted R2 (0.83 and 0.82 at 100% and 40% LiDAR point densities, respectively) and the lowest RMSE values, signifying the distance impact of development on biomass estimation. Our evaluation suggests that reducing LiDAR point density is a viable solution to regional-scale forest biomass assessment without compromising the accuracy of estimation, which may further be improved using development density.

The Receptacle Model of Salting-In by Tetramethylammonium Ions

PubMed Central

Hribar–Lee, Barbara; Dill, Ken A.; Vlachy, Vojko

2010-01-01

Water is a poor solvent for nonpolar solutes. Water containing ions is an even poorer solvent. According to standard terminology, the tendency of salts to precipitate oils from water is called salting-out. However, interestingly, some salt ions, such as tetramethylammonium (TMA), cause instead the salting-in of hydrophobic solutes. Even more puzzling, there is a systematic dependence on solute size. TMA causes the salting-out of small hydrophobes and the salting-in of larger nonpolar solutes. We study these effects using NPT Monte Carlo simulations of the MB + dipole model of water, which was previously shown to account for hydrophobic effects and ion solubilities in water. The present model gives a structural interpretation for the thermodynamics of salting-in. The TMA structure allows deep penetration by a first shell of waters, the dipoles of which interact electrostatically with the ion. This first water shell sets up a second water shell that is shaped to act as a receptacle that binds the nonpolar solute. In this way, a nonpolar solute can actually bind more tightly to the TMA ion than to another hydrophobe, leading to the increased solubility and salting-in. Such structuring may also explain why molecular ions do not follow the same charge density series’ as atomic ions do. PMID:21028768

Receptacle model of salting-in by tetramethylammonium ions.

PubMed

Hribar-Lee, Barbara; Dill, Ken A; Vlachy, Vojko

2010-11-25

Water is a poor solvent for nonpolar solutes. Water containing ions is an even poorer solvent. According to standard terminology, the tendency of salts to precipitate oils from water is called salting-out. However, interestingly, some salt ions, such as tetramethylammonium (TMA), cause instead the salting-in of hydrophobic solutes. Even more puzzling, there is a systematic dependence on solute size. TMA causes the salting-out of small hydrophobes and the salting-in of larger nonpolar solutes. We study these effects using NPT Monte Carlo simulations of the Mercedes-Benz (MB) + dipole model of water, which was previously shown to account for hydrophobic effects and ion solubilities in water. The present model gives a structural interpretation for the thermodynamics of salting-in. The TMA structure allows deep penetration by a first shell of waters, the dipoles of which interact electrostatically with the ion. This first water shell sets up a second water shell that is shaped to act as a receptacle that binds the nonpolar solute. In this way, a nonpolar solute can actually bind more tightly to the TMA ion than to another hydrophobe, leading to the increased solubility and salting-in. Such structuring may also explain why molecular ions do not follow the same charge density series as atomic ions do.

3D electron density distributions in the solar corona during solar minima: assessment for more realistic solar wind modeling

NASA Astrophysics Data System (ADS)

de Patoul, J.; Foullon, C.; Riley, P.

2015-12-01

Knowledge of the electron density distribution in the solar corona put constraints on the magnetic field configurations for coronal modeling, and on initial conditions for solar wind modeling. We work with polarized SOHO/LASCO-C2 images from the last two recent minima of solar activity (1996-1997 and 2008-2010), devoid of coronal mass ejections. We derive the 4D electron density distributions in the corona by applying a newly developed time-dependent tomographic reconstruction method. First we compare the density distributions obtained from tomography with magnetohydrodynamic (MHD) solutions. The tomography provides more accurate distributions of electron densities in the polar regions, and we find that the observed density varies with the solar cycle in both polar and equatorial regions. Second, we find that the highest-density structures do not always correspond to the predicted large-scale heliospheric current sheet or its helmet streamer but can follow the locations of pseudo-streamers. We conclude that tomography offers reliable density distribution in the corona, reproducing the slow time evolution of coronal structures, without prior knowledge of the coronal magnetic field over a full rotation. Finally, we suggest that the highest-density structures show a differential rotation well above the surface depending on how it is magnetically connected to the surface. Such valuable information on the rotation of large-scale structures could help to connect the sources of the solar wind to their in-situ counterparts in future missions such as Solar Orbiter and Solar Probe Plus. This research combined with the MHD coronal modeling efforts has the potential to increase the reliability for future space weather forecasting.

Simple model of sickle hemogloblin

NASA Astrophysics Data System (ADS)

Shiryayev, Andrey; Li, Xiaofei; Gunton, J. D.

2006-07-01

A microscopic model is proposed for the interactions between sickle hemoglobin molecules based on information from the protein data bank. A solution of this model, however, requires accurate estimates of the interaction parameters which are currently unavailable. Therefore, as a first step toward a molecular understanding of the nucleation mechanisms in sickle hemoglobin, a Monte Carlo simulation of a simplified two patch model is carried out. A gradual transition from monomers to one dimensional chains is observed as one varies the density of molecules at fixed temperature, somewhat similar to the transition from monomers to polymer fibers in sickle hemoglobin molecules in solution. An observed competition between chain formation and crystallization for the model is also discussed. The results of the simulation of the equation of state are shown to be in excellent agreement with a theory for a model of globular proteins, for the case of two interacting sites.

Numerical solution of a multi-ion one-potential model for electroosmotic flow in two-dimensional rectangular microchannels.

PubMed

Van Theemsche, Achim; Deconinck, Johan; Van den Bossche, Bart; Bortels, Leslie

2002-10-01

A new more general numerical model for the simulation of electrokinetic flow in rectangular microchannels is presented. The model is based on the dilute solution model and the Navier-Stokes equations and has been implemented in a finite-element-based C++ code. The model includes the ion distribution in the Helmholtz double layer and considers only one single electrical' potential field variable throughout the domain. On a charged surface(s) the surface charge density, which is proportional to the local electrical field, is imposed. The zeta potential results, then, from this boundary condition and depends on concentrations, temperature, ion valence, molecular diffusion coefficients, and geometric conditions. Validation cases show that the model predicts accurately known analytical results, also for geometries having dimensions comparable to the Debye length. As a final study, the electro-osmotic flow in a controlled cross channel is investigated.

A three-dimensional, time-dependent model of Mobile Bay

NASA Technical Reports Server (NTRS)

Pitts, F. H.; Farmer, R. C.

1976-01-01

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.

Mixing parametrizations for ocean climate modelling

NASA Astrophysics Data System (ADS)

Gusev, Anatoly; Moshonkin, Sergey; Diansky, Nikolay; Zalesny, Vladimir

2016-04-01

The algorithm is presented of splitting the total evolutionary equations for the turbulence kinetic energy (TKE) and turbulence dissipation frequency (TDF), which is used to parameterize the viscosity and diffusion coefficients in ocean circulation models. The turbulence model equations are split into the stages of transport-diffusion and generation-dissipation. For the generation-dissipation stage, the following schemes are implemented: the explicit-implicit numerical scheme, analytical solution and the asymptotic behavior of the analytical solutions. The experiments were performed with different mixing parameterizations for the modelling of Arctic and the Atlantic climate decadal variability with the eddy-permitting circulation model INMOM (Institute of Numerical Mathematics Ocean Model) using vertical grid refinement in the zone of fully developed turbulence. The proposed model with the split equations for turbulence characteristics is similar to the contemporary differential turbulence models, concerning the physical formulations. At the same time, its algorithm has high enough computational efficiency. Parameterizations with using the split turbulence model make it possible to obtain more adequate structure of temperature and salinity at decadal timescales, compared to the simpler Pacanowski-Philander (PP) turbulence parameterization. Parameterizations with using analytical solution or numerical scheme at the generation-dissipation step of the turbulence model leads to better representation of ocean climate than the faster parameterization using the asymptotic behavior of the analytical solution. At the same time, the computational efficiency left almost unchanged relative to the simple PP parameterization. Usage of PP parametrization in the circulation model leads to realistic simulation of density and circulation with violation of T,S-relationships. This error is majorly avoided with using the proposed parameterizations containing the split turbulence model. The high sensitivity of the eddy-permitting circulation model to the definition of mixing is revealed, which is associated with significant changes of density fields in the upper baroclinic ocean layer over the total considered area. For instance, usage of the turbulence parameterization instead of PP algorithm leads to increasing circulation velocity in the Gulf Stream and North Atlantic Current, as well as the subpolar cyclonic gyre in the North Atlantic and Beaufort Gyre in the Arctic basin are reproduced more realistically. Consideration of the Prandtl number as a function of the Richardson number significantly increases the modelling quality. The research was supported by the Russian Foundation for Basic Research (grant № 16-05-00534) and the Council on the Russian Federation President Grants (grant № MK-3241.2015.5)

Formalism for calculation of polymer-solvent-mediated potential

NASA Astrophysics Data System (ADS)

Zhou, Shiqi

2006-07-01

A simple theoretical approach is proposed for calculation of a solvent-mediated potential (SMP) between two colloid particles immersed in a polymer solvent bath in which the polymer is modeled as a chain with intramolecular degrees of freedom. The present recipe is only concerned with the estimation of the density profile of a polymer site around a single solute colloid particle instead of two solute colloid particles separated by a varying distance as done in existing calculational methods for polymer-SMP. Therefore the present recipe is far simpler for numerical implementation than the existing methods. The resultant predictions for the polymer-SMP and polymer solvent-mediated mean force (polymer-SMMF) are in very good agreement with available simulation data. With the present recipe, change tendencies of the contact value and second virial coefficiency of the SMP as a function of size ratio between the colloid particle and polymer site, the number of sites per chain, and the polymer concentration are investigated in detail. The metastable critical polymer concentration as a function of size ratio and the number of sites per chain is also reported for the first time. To yield the numerical solution of the present recipe at less than 1min on a personal computer, a rapid and accurate algorithm for the numerical solution of the classical density functional theory is proposed to supply rapid and accurate estimation of the density profile of the polymer site as an input into the present formalism.

Light propagation in Swiss-cheese cosmologies

NASA Astrophysics Data System (ADS)

Szybka, Sebastian J.

2011-08-01

We study the effect of inhomogeneities on light propagation. The Sachs equations are solved numerically in the Swiss-cheese models with inhomogeneities modeled by the Lemaître-Tolman solutions. Our results imply that, within the models we study, inhomogeneities may partially mimic the accelerated expansion of the Universe provided the light propagates through regions with lower than the average density. The effect of inhomogeneities is small and full randomization of the photons’ trajectories reduces it to an insignificant level.

Exploring the uncertainty in attributing sediment contributions in fingerprinting studies due to uncertainty in determining element concentrations in source areas.

NASA Astrophysics Data System (ADS)

Gomez, Jose Alfonso; Owens, Phillip N.; Koiter, Alex J.; Lobb, David

2016-04-01

One of the major sources of uncertainty in attributing sediment sources in fingerprinting studies is the uncertainty in determining the concentrations of the elements used in the mixing model due to the variability of the concentrations of these elements in the source materials (e.g., Kraushaar et al., 2015). The uncertainty in determining the "true" concentration of a given element in each one of the source areas depends on several factors, among them the spatial variability of that element, the sampling procedure and sampling density. Researchers have limited control over these factors, and usually sampling density tends to be sparse, limited by time and the resources available. Monte Carlo analysis has been used regularly in fingerprinting studies to explore the probable solutions within the measured variability of the elements in the source areas, providing an appraisal of the probability of the different solutions (e.g., Collins et al., 2012). This problem can be considered analogous to the propagation of uncertainty in hydrologic models due to uncertainty in the determination of the values of the model parameters, and there are many examples of Monte Carlo analysis of this uncertainty (e.g., Freeze, 1980; Gómez et al., 2001). Some of these model analyses rely on the simulation of "virtual" situations that were calibrated from parameter values found in the literature, with the purpose of providing insight about the response of the model to different configurations of input parameters. This approach - evaluating the answer for a "virtual" problem whose solution could be known in advance - might be useful in evaluating the propagation of uncertainty in mixing models in sediment fingerprinting studies. In this communication, we present the preliminary results of an on-going study evaluating the effect of variability of element concentrations in source materials, sampling density, and the number of elements included in the mixing models. For this study a virtual catchment was constructed, composed by three sub-catchments each of 500 x 500 m size. We assumed that there was no selectivity in sediment detachment or transport. A numerical excercise was performed considering these variables: 1) variability of element concentration: three levels with CVs of 20 %, 50 % and 80 %; 2) sampling density: 10, 25 and 50 "samples" per sub-catchment and element; and 3) number of elements included in the mixing model: two (determined), and five (overdetermined). This resulted in a total of 18 (3 x 3 x 2) possible combinations. The five fingerprinting elements considered in the study were: C, N, 40K, Al and Pavail, and their average values, taken from the literature, were: sub-catchment 1: 4.0 %, 0.35 %, 0.50 ppm, 5.0 ppm, 1.42 ppm, respectively; sub-catchment 2: 2.0 %, 0.18 %, 0.20 ppm, 10.0 ppm, 0.20 ppm, respectively; and sub-catchment 3: 1.0 %, 0.06 %, 1.0 ppm, 16.0 ppm, 7.8 ppm, respectively. For each sub-catchment, three maps of the spatial distribution of each element was generated using the random generator of Mejia and Rodriguez-Iturbe (1974) as described in Freeze (1980), using the average value and the three different CVs defined above. Each map for each source area and property was generated for a 100 x 100 square grid, each grid cell being 5 m x 5 m. Maps were randomly generated for each property and source area. In doing so, we did not consider the possibility of cross correlation among properties. Spatial autocorrelation was assumed to be weak. The reason for generating the maps was to create a "virtual" situation where all the element concentration values at each point are known. Simultaneously, we arbitrarily determined the percentage of sediment coming from sub-catchments. These values were 30 %, 10 % and 60 %, for sub-catchments 1, 2 and 3, respectively. Using these values, we determined the element concentrations in the sediment. The exercise consisted of creating different sampling strategies in a virtual environment to determine an average value for each of the different maps of element concentration and sub-catchment, under different sampling densities: 200 different average values for the "high" sampling density (average of 50 samples); 400 different average values for the "medium" sampling density (average of 25 samples); and 1,000 different average values for the "low" sampling density (average of 10 samples). All these combinations of possible values of element concentrations in the source areas were solved for the concentration in the sediment already determined for the "true" solution using limSolve (Soetaert et al., 2014) in R language. The sediment source solutions found for the different situations and values were analyzed in order to: 1) evaluate the uncertainty in the sediment source attribution; and 2) explore strategies to detect the most probable solutions that might lead to improved methods for constructing the most robust mixing models. Preliminary results on these will be presented and discussed in this communication. Key words: sediment, fingerprinting, uncertainty, variability, mixing model. References Collins, A.L., Zhang, Y., McChesney, D., Walling, D.E., Haley, S.M., Smith, P. 2012. Sediment source tracing in a lowland agricultural catchment in southern England using a modified procedure combining statistical analysis and numerical modelling. Science of the Total Environment 414: 301-317. Freeze, R.A. 1980. A stochastic-conceptual analysis of rainfall-runoff processes on a hillslope. Water Resources Research 16: 391-408.

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

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

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

2016-12-20

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

Visualization and simulation of density driven convection in porous media using magnetic resonance imaging.

PubMed

Montague, James A; Pinder, George F; Gonyea, Jay V; Hipko, Scott; Watts, Richard

2018-05-01

Magnetic resonance imaging is used to observe solute transport in a 40cm long, 26cm diameter sand column that contained a central core of low permeability silica surrounded by higher permeability well-sorted sand. Low concentrations (2.9g/L) of Magnevist, a gadolinium based contrast agent, produce density driven convection within the column when it starts in an unstable state. The unstable state, for this experiment, exists when higher density contrast agent is present above the lower density water. We implement a numerical model in OpenFOAM to reproduce the observed fluid flow and transport from a density difference of 0.3%. The experimental results demonstrate the usefulness of magnetic resonance imaging in observing three-dimensional gravity-driven convective-dispersive transport behaviors in medium scale experiments. Copyright © 2017 Elsevier B.V. All rights reserved.

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

NASA Astrophysics Data System (ADS)

Pan, E.; Chen, J. Y.; Bevis, M.; Bordoni, A.; Barletta, V. R.; Molavi Tabrizi, A.

2015-12-01

We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.

The role of the attractive and the repulsive interactions in the nonpolar solvation dynamics in simple fluids from the gas-like to the liquid-like densities

NASA Astrophysics Data System (ADS)

Yamaguchi, T.; Kimura, Y.; Hirota, N.

1999-09-01

We have performed molecular dynamics (MD) simulations of the nonpolar solvation dynamics in simple fluids composed of particles interacting through the Lennard-Jones (LJ) 12-6 potential or its repulsive part. The attractive or the repulsive part of the solute-solvent interaction is assumed to change on the excitation of a solute. We have followed the transition energy fluctuation of the solute by the equilibrium simulation. The division of the LJ potential followed the method of WCA [J. W. Weeks, D. Chandler, and H. C. Andersen, J. Chem. Phys. 54, 5237 (1971)]. We have surveyed over a wide solvent density region from gas-like to liquid-like densities at the constant temperature. When the attractive part changes, the relaxation becomes faster with an increase of the solvent density. This result contradicts with previous theories that treat the nonpolar solvation dynamics in terms of the diffusion of solvent particles. The time scale of the initial part of the relaxation is well correlated with the static fluctuation divided by the static average, which suggests the importance of the curvature of the free energy surface in the initial part of the solvation. When the repulsive part changes, the initial part of the relaxation is almost density independent, determined by the binary motion between solute and solvent. It is consistent with the result that the static fluctuation is almost proportional to the static average, which indicates the absence of the static correlation between solvent particles. On the other hand, the solvation correlation function shows rather complicated density dependence at the longer time scale. In the case of the binary mixture solvent, the relaxation time is inversely proportional to the diffusion coefficient. On the basis of the nonpolar solvation dynamics, the validity of the isolated binary collision model for the vibrational energy relaxation is also discussed, and the recent hydrodynamic theory on the vibrational energy relaxation [B. J. Cherayil and M. D. Feyer, J. Chem. Phys. 107, 7642 (1997)] is critically examined.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

On the Five-Moment Hamburger Maximum Entropy Reconstruction

NASA Astrophysics Data System (ADS)

Summy, D. P.; Pullin, D. I.

2018-05-01

We consider the Maximum Entropy Reconstruction (MER) as a solution to the five-moment truncated Hamburger moment problem in one dimension. In the case of five monomial moment constraints, the probability density function (PDF) of the MER takes the form of the exponential of a quartic polynomial. This implies a possible bimodal structure in regions of moment space. An analytical model is developed for the MER PDF applicable near a known singular line in a centered, two-component, third- and fourth-order moment (μ _3 , μ _4 ) space, consistent with the general problem of five moments. The model consists of the superposition of a perturbed, centered Gaussian PDF and a small-amplitude packet of PDF-density, called the outlying moment packet (OMP), sitting far from the mean. Asymptotic solutions are obtained which predict the shape of the perturbed Gaussian and both the amplitude and position on the real line of the OMP. The asymptotic solutions show that the presence of the OMP gives rise to an MER solution that is singular along a line in (μ _3 , μ _4 ) space emanating from, but not including, the point representing a standard normal distribution, or thermodynamic equilibrium. We use this analysis of the OMP to develop a numerical regularization of the MER, creating a procedure we call the Hybrid MER (HMER). Compared with the MER, the HMER is a significant improvement in terms of robustness and efficiency while preserving accuracy in its prediction of other important distribution features, such as higher order moments.

External intermittency prediction using AMR solutions of RANS turbulence and transported PDF models

NASA Astrophysics Data System (ADS)

Olivieri, D. A.; Fairweather, M.; Falle, S. A. E. G.

2011-12-01

External intermittency in turbulent round jets is predicted using a Reynolds-averaged Navier-Stokes modelling approach coupled to solutions of the transported probability density function (pdf) equation for scalar variables. Solutions to the descriptive equations are obtained using a finite-volume method, combined with an adaptive mesh refinement algorithm, applied in both physical and compositional space. This method contrasts with conventional approaches to solving the transported pdf equation which generally employ Monte Carlo techniques. Intermittency-modified eddy viscosity and second-moment turbulence closures are used to accommodate the effects of intermittency on the flow field, with the influence of intermittency also included, through modifications to the mixing model, in the transported pdf equation. Predictions of the overall model are compared with experimental data on the velocity and scalar fields in a round jet, as well as against measurements of intermittency profiles and scalar pdfs in a number of flows, with good agreement obtained. For the cases considered, predictions based on the second-moment turbulence closure are clearly superior, although both turbulence models give realistic predictions of the bimodal scalar pdfs observed experimentally.

Inverse square law isothermal property in relativistic charged static distributions

NASA Astrophysics Data System (ADS)

Hansraj, Sudan; Qwabe, Nkululeko

2017-12-01

We analyze the impact of the inverse square law fall-off of the energy density in a charged isotropic spherically symmetric fluid. Initially, we impose a linear barotropic equation of state p = αρ but this leads to an intractable differential equation. Next, we consider the neutral isothermal metric of Saslaw et al. [Phys. Rev. D 13, 471 (1996)] in an electric field and the usual inverse square law of energy density and pressure results thus preserving the equation of state. Additionally, we discard a linear equation of state and endeavor to find new classes of solutions with the inverse square law fall-off of density. Certain prescribed forms of the spatial and temporal gravitational forms result in new exact solutions. An interesting result that emerges is that while isothermal fluid spheres are unbounded in the neutral case, this is not so when charge is involved. Indeed it was found that barotropic equations of state exist and hypersurfaces of vanishing pressure exist establishing a boundary in practically all models. One model was studied in depth and found to satisfy other elementary requirements for physical admissibility such as a subluminal sound speed as well as gravitational surface redshifts smaller than 2. Buchdahl [Acta Phys. Pol. B 10, 673 (1965)], Böhmer and Harko [Gen. Relat. Gravit. 39, 757 (2007)] and Andréasson [Commum. Math. Phys. 198, 507 (2009)] mass-radius bounds were also found to be satisfied. Graphical plots utilizing constants selected from the boundary conditions established that the model displayed characteristics consistent with physically viable models.

Development and validation of a turbulent-mix model for variable-density and compressible flows.

PubMed

Banerjee, Arindam; Gore, Robert A; Andrews, Malcolm J

2010-10-01

The modeling of buoyancy driven turbulent flows is considered in conjunction with an advanced statistical turbulence model referred to as the BHR (Besnard-Harlow-Rauenzahn) k-S-a model. The BHR k-S-a model is focused on variable-density and compressible flows such as Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) driven mixing. The BHR k-S-a turbulence mix model has been implemented in the RAGE hydro-code, and model constants are evaluated based on analytical self-similar solutions of the model equations. The results are then compared with a large test database available from experiments and direct numerical simulations (DNS) of RT, RM, and KH driven mixing. Furthermore, we describe research to understand how the BHR k-S-a turbulence model operates over a range of moderate to high Reynolds number buoyancy driven flows, with a goal of placing the modeling of buoyancy driven turbulent flows at the same level of development as that of single phase shear flows.

Influence of Mean-Density Gradient on Small-Scale Turbulence Noise

NASA Technical Reports Server (NTRS)

Khavaran, Abbas

2000-01-01

A physics-based methodology is described to predict jet-mixing noise due to small-scale turbulence. Both self- and shear-noise source teens of Lilley's equation are modeled and the far-field aerodynamic noise is expressed as an integral over the jet volume of the source multiplied by an appropriate Green's function which accounts for source convection and mean-flow refraction. Our primary interest here is to include transverse gradients of the mean density in the source modeling. It is shown that, in addition to the usual quadrupole type sources which scale to the fourth-power of the acoustic wave number, additional dipole and monopole sources are present that scale to lower powers of wave number. Various two-point correlations are modeled and an approximate solution to noise spectra due to multipole sources of various orders is developed. Mean flow and turbulence information is provided through RANS-k(epsilon) solution. Numerical results are presented for a subsonic jet at a range of temperatures and Mach numbers. Predictions indicated a decrease in high frequency noise with added heat, while changes in the low frequency noise depend on jet velocity and observer angle.

Method for the separation of high impact polystyrene (HIPS) and acrylonitrile butadiene styrene (ABS) plastics

DOEpatents

Jody, Bassam J.; Arman, Bayram; Karvelas, Dimitrios E.; Pomykala, Jr., Joseph A.; Daniels, Edward J.

1997-01-01

An improved method is provided for separating acrylonitrile butadiene styrene (ABS) and high impact polystyrene (HIPS) plastics from each other. The ABS and HIPS plastics are shredded to provide a selected particle size. The shredded particles of the ABS and HIPS plastics are applied to a solution having a solution density in a predefined range between 1.055 gm/cm.sup.3 and 1.07 gm/cm.sup.3, a predefined surface tension in a range between 22 dynes/cm to 40 dynes/cm and a pH in the range of 1.77 and 2.05. In accordance with a feature of the invention, the novel method is provided for separating ABS and HIPS, two solid thermoplastics which have similar densities by selectively modifying the effective density of the HIPS using a binary solution with the appropriate properties, such as pH, density and surface tension, such as a solution of acetic acid and water or a quaternary solution having the appropriate density, surface tension, and pH.

Absorption features in the quasar HS 1603 + 3820 II. Distance to the absorber obtained from photoionisation modelling

NASA Astrophysics Data System (ADS)

Różańska, A.; Nikołajuk, M.; Czerny, B.; Dobrzycki, A.; Hryniewicz, K.; Bechtold, J.; Ebeling, H.

2014-04-01

We present the photoionisation modelling of the intrinsic absorber in the bright quasar HS 1603 + 3820. We constructed the broad-band spectral energy distribution using the optical/UV/X-ray observations from different instruments as inputs for the photoionisation calculations. The spectra from the Keck telescope show extremely high CIV to HI ratios, for the first absorber in system A, named A1. This value, together with high column density of CIV ion, place strong constraints on the photoionisation model. We used two photoionisation codes to derive the hydrogen number density at the cloud illuminated surface. By estimating bolometric luminosity of HS 1603 + 3820 using the typical formula for quasars, we calculated the distance to A1. We could find one photoionization solution, by assuming either a constant density cloud (which was modelled using CLOUDY), or a stratified cloud (which was modelled using TITAN), as well as the solar abundances. This model explained both the ionic column density of CIV and the high CIV to HI ratio. The location of A1 is 0.1 pc, and it is situated even closer to the nucleus than the possible location of the Broad Line Region in this object. The upper limit of the distance is sensitive to the adopted covering factor and the carbon abundance. Photoionisation modelling always prefers dense clouds with the number density n0 = 1010 - 1012 cm-3, which explains intrinsic absorption in HS 1603 + 3820. This number density is of the same order as that in the disk atmosphere at the implied distance of A1. Therefore, our results show that the disk wind that escapes from the outermost accretion disk atmosphere can build up dense absorber in quasars.

Solute drag in polycrystalline materials: Derivation and numerical analysis of a variational model for the effect of solute on the motion of boundaries and junctions during coarsening

NASA Astrophysics Data System (ADS)

Wilson, Seth Robert

A mathematical model that results in an expression for the local acceleration of a network of sharp interfaces interacting with an ambient solute field is proposed. This expression comprises a first-order differential equation for the local velocity that, given the appropriate initial conditions, may be used to predict the subsequent time evolution of the system, including non-steady state absorption and desorption of solute. Evolution equations for both interfaces and the junction of interfaces are derived by maximizing a functional approximating the rate at which the local Gibbs free energy density decreases, as a function of the local solute content and the instantaneous velocity. The model has been formulated in three dimensions, and non-equilibrium effects such as grain boundary diffusion, solute gradients, and time-dependant segregation are taken into account. As a consequence of this model, it is shown that both interfaces and the junctions between interfaces obey evolution equations that closely resemble Newton's second law. In particular, the concept of "thrust" in variable-mass systems is shown to have a direct analog in solute-interface interaction. Numerical analysis of the equations that result reveals that a double cusp catastrophe governs the behavior of the solute-interface system, for which trajectories that include hysteresis, slip-stick motion, and jerky motion are all conceivable. The geometry of the cusp catastrophe is quantified, and a number of relations between physical parameters and system behavior are consequently predicted.

Upscaling heterogeneity in aquifer reactivity via exposure-time concept: forward model.

PubMed

Seeboonruang, Uma; Ginn, Timothy R

2006-03-20

Reactive properties of aquifer solid phase materials play an important role in solute fate and transport in the natural subsurface on time scales ranging from years in contaminant remediation to millennia in dynamics of aqueous geochemistry. Quantitative tools for dealing with the impact of natural heterogeneity in solid phase reactivity on solute fate and transport are limited. Here we describe the use of a structural variable to keep track of solute flux exposure to reactive surfaces. With this approach, we develop a non-reactive tracer model that is useful for determining the signature of multi-scale reactive solid heterogeneity in terms of solute flux distributions at the field scale, given realizations of three-dimensional reactive site density fields. First, a governing Eulerian equation for the non-reactive tracer model is determined by an upscaling technique in which it is found that the exposure time of solution to reactive surface areas evolves via both a macroscopic velocity and a macroscopic dispersion in the artificial dimension of exposure time. Second, we focus on the Lagrangian approach in the context of a streamtube ensemble and demonstrate the use of the distribution of solute flux over the exposure time dimension in modeling two-dimensional transport of a solute undergoing simplified linear reversible reactions, in hypothetical conditions following prior laboratory experiments. The distribution of solute flux over exposure time in a given case is a signature of the impact of heterogeneous aquifer reactivity coupled with a particular physical heterogeneity, boundary conditions, and hydraulic gradient. Rigorous application of this approach in a simulation sense is limited here to linear kinetically controlled reactions.

Stability analysis of wall driven nanofluid flow through a tube

NASA Astrophysics Data System (ADS)

Hossain, M. Mainul; Khan, M. A. H.

2017-06-01

Wall driven incompressible viscous fluid flow with nanoparticles through a tube is considered where two different nanofluids (Cu-water, SiO2-water) are used separately. Flow becomes gradually unstable due to movement of wall and existence of nanoparticles. However, Reynolds number, volume fraction and density ratio are responsible for flow instability. The mathematical model of the problem is constructed and solved by means of series solution method. Special type Hermite-Padé approximation method is used to improve the series solution. The critical point for Reynolds number, volume fraction and density ratio are determined and described using approximation technique and bifurcation diagram for both nanofluids. Moreover, Interaction between these three numbers and their effect on velocity profile are discussed. To indicate the nanofluid which is more effective for flow stability is our major concerned.

Relativistic stars in degenerate higher-order scalar-tensor theories after GW170817

NASA Astrophysics Data System (ADS)

Kobayashi, Tsutomu; Hiramatsu, Takashi

2018-05-01

We study relativistic stars in degenerate higher-order scalar-tensor theories that evade the constraint on the speed of gravitational waves imposed by GW170817. It is shown that the exterior metric is given by the usual Schwarzschild solution if the lower order Horndeski terms are ignored in the Lagrangian and a shift symmetry is assumed. However, this class of theories exhibits partial breaking of Vainshtein screening in the stellar interior and thus modifies the structure of a star. Employing a simple concrete model, we show that for high-density stars the mass-radius relation is altered significantly even if the parameters are chosen so that only a tiny correction is expected in the Newtonian regime. We also find that, depending on the parameters, there is a maximum central density above which solutions cease to exist.

Gravastars with higher dimensional spacetimes

NASA Astrophysics Data System (ADS)

Ghosh, Shounak; Ray, Saibal; Rahaman, Farook; Guha, B. K.

2018-07-01

We present a new model of gravastar in the higher dimensional Einsteinian spacetime including Einstein's cosmological constant Λ. Following Mazur and Mottola (2001, 2004) we design the star with three specific regions, as follows: (I) Interior region, (II) Intermediate thin spherical shell and (III) Exterior region. The pressure within the interior region is equal to the negative matter density which provides a repulsive force over the shell. This thin shell is formed by ultra relativistic plasma, where the pressure is directly proportional to the matter-energy density which does counter balance the repulsive force from the interior whereas the exterior region is completely vacuum assumed to be de Sitter spacetime which can be described by the generalized Schwarzschild solution. With this specification we find out a set of exact non-singular and stable solutions of the gravastar which seems physically very interesting and reasonable.

Mechanism and models for zinc metal morphology in alkaline media

NASA Technical Reports Server (NTRS)

May, C. E.; Kautz, H. E.

1981-01-01

Based on experimental observations, a mechanism is presented to explain existence of the different morphologies of electrodeposited zinc in alkaline solution. The high current density dendrites appear to be due to more rapid growth on the nonbasal crystallographic planes than on the basal plane. The low current density moss apparently results from dissolution from the nonbasal planes at low cathodic voltages. Electrochemical models were sought which would produce such a phenomenon. The fundamental plating mechanism alone accounts only for different rates on different planes, not for zinc dissolution from a plane in the cathodic region. Fourteen models were explored; two models were in accord with the proposed mechanism. One involves rapid disproportionation of the zinc +1 species on the nonbasal planes. The other involves a redox reaction (corrosion) between the zinc-zincate and hydrogen-water systems.

From the Highly Compressible Navier-Stokes Equations to Fast Diffusion and Porous Media Equations, Existence of Global Weak Solution for the Quasi-Solutions

NASA Astrophysics Data System (ADS)

Haspot, Boris

2016-06-01

We consider the compressible Navier-Stokes equations for viscous and barotropic fluids with density dependent viscosity. The aim is to investigate mathematical properties of solutions of the Navier-Stokes equations using solutions of the pressureless Navier-Stokes equations, that we call quasi solutions. This regime corresponds to the limit of highly compressible flows. In this paper we are interested in proving the announced result in Haspot (Proceedings of the 14th international conference on hyperbolic problems held in Padova, pp 667-674, 2014) concerning the existence of global weak solution for the quasi-solutions, we also observe that for some choice of initial data (irrotationnal) the quasi solutions verify the porous media, the heat equation or the fast diffusion equations in function of the structure of the viscosity coefficients. In particular it implies that it exists classical quasi-solutions in the sense that they are {C^{∞}} on {(0,T)× {R}N} for any {T > 0}. Finally we show the convergence of the global weak solution of compressible Navier-Stokes equations to the quasi solutions in the case of a vanishing pressure limit process. In particular for highly compressible equations the speed of propagation of the density is quasi finite when the viscosity corresponds to {μ(ρ)=ρ^{α}} with {α > 1}. Furthermore the density is not far from converging asymptotically in time to the Barrenblatt solution of mass the initial density {ρ0}.

Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description

NASA Astrophysics Data System (ADS)

Bauer, Sebastian; Mathias, Gerald; Tavan, Paul

2014-03-01

We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ɛ(r) is close to one everywhere inside the protein. The Gaussian widths σi of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σi. A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by comparison with so-called generalized Born methods. A follow-up paper describes how the method enables Hamiltonian, efficient, and accurate MM molecular dynamics simulations of proteins in dielectric solvent continua.

Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description.

PubMed

Bauer, Sebastian; Mathias, Gerald; Tavan, Paul

2014-03-14

We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σ(i) of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σ(i). A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by comparison with so-called generalized Born methods. A follow-up paper describes how the method enables Hamiltonian, efficient, and accurate MM molecular dynamics simulations of proteins in dielectric solvent continua.

Changes in apparent molar water volume and DKP solubility yield insights on the Hofmeister effect.

PubMed

Payumo, Alexander Y; Huijon, R Michael; Mansfield, Deauna D; Belk, Laurel M; Bui, Annie K; Knight, Anne E; Eggers, Daryl K

2011-12-15

This study examines the properties of a 4 × 2 matrix of aqueous cations and anions at concentrations up to 8.0 M. The apparent molar water volume, as calculated by subtracting the mass and volume of the ions from the corresponding solution density, was found to exceed the molar volume of ice in many concentrated electrolyte solutions, underscoring the nonideal behavior of these systems. The solvent properties of water were also analyzed by measuring the solubility of diketopiperazine (DKP) in 2.000 M salt solutions prepared from the same ion combinations. Solution rankings for DKP solubility were found to parallel the Hofmeister series for both cations and anions, whereas molar water volume concurred with the cation series only. The results are discussed within the framework of a desolvation energy model that attributes solute-specific changes in equilibria to solute-dependent changes in the free energy of bulk water.

Changes in Apparent Molar Water Volume and DKP Solubility Yield Insights on the Hofmeister Effect

PubMed Central

Payumo, Alexander Y.; Huijon, R. Michael; Mansfield, Deauna D.; Belk, Laurel M.; Bui, Annie K.; Knight, Anne E.; Eggers, Daryl K.

2011-01-01

This study examines the properties of a 4 × 2 matrix of aqueous cations and anions at concentrations up to 8.0 M. The apparent molar water volume, as calculated by subtracting the mass and volume of the ions from the corresponding solution density, was found to exceed the molar volume of ice in many concentrated electrolyte solutions, underscoring the non-ideal behavior of these systems. The solvent properties of water were also analyzed by measuring the solubility of diketopiperazine (DKP) in 2.000 M salt solutions prepared from the same ion combinations. Solution rankings for DKP solubility were found to parallel the Hofmeister series for both cations and anions, whereas molar water volume concurred with the cation series only. The results are discussed within the framework of a desolvation energy model that attributes solute-specific changes in equilibria to solute-dependent changes in the free energy of bulk water. PMID:22029390

Modeling of Density-Dependent Flow based on the Thermodynamically Constrained Averaging Theory

NASA Astrophysics Data System (ADS)

Weigand, T. M.; Schultz, P. B.; Kelley, C. T.; Miller, C. T.; Gray, W. G.

2016-12-01

The thermodynamically constrained averaging theory (TCAT) has been used to formulate general classes of porous medium models, including new models for density-dependent 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 a diffusion that arises from gradients associated with pressure and activity and the ability to describe both high and low concentration displacement. The TCAT model is presented and closure relations for the TCAT model are postulated based on microscale averages and a parameter estimation is performed on a subset of the experimental data. Due to the sharpness of the fronts, an adaptive moving mesh technique was used to ensure grid independent solutions within the run time constraints. The optimized parameters are then used for forward simulations and compared to the set of experimental data not used for the parameter estimation.

Heat transfer to and from vegetated surfaces - An analytical method for the bulk exchange coefficients

NASA Technical Reports Server (NTRS)

Massman, William J.

1987-01-01

The semianalytical model outlined in a previous study (Massman, 1987) to describe momentum exchange between the atmosphere and vegetated surfaces is extended to include the exchange of heat. The methods employed are based on one-dimensional turbulent diffusivities, and use analytical solutions to the steady-state diffusion equation. The model is used to assess the influence that the canopy foliage structure and density, the wind profile structure within the canopy, and the shelter factor can have upon the inverse surface Stanton number (kB exp -1), as well as to explore the consequences of introducing a scalar displacement height which can be different from the momentum displacement height. In general, the triangular foliage area density function gives results which agree more closely with observations than that for constant foliage area density. The intended application of this work is for parameterizing the bulk aerodynamic resistances for heat and momentum exchange for use within large-scale models of plant-atmosphere exchanges.

Electric field mill network products to improve detection of the lightning hazard

NASA Technical Reports Server (NTRS)

Maier, Launa M.

1987-01-01

An electric field mill network has been used at Kennedy Space Center for over 10 years as part of the thunderstorm detection system. Several algorithms are currently available to improve the informational output of the electric field mill data. The charge distributions of roughly 50 percent of all lightning can be modeled as if they reduced the charged cloud by a point charge or a point dipole. Using these models, the spatial differences in the lightning induced electric field changes, and a least squares algorithm to obtain an optimum solution, the three-dimensional locations of the lightning charge centers can be located. During the lifetime of a thunderstorm, dynamically induced charging, modeled as a current source, can be located spatially with measurements of Maxwell current density. The electric field mills can be used to calculate the Maxwell current density at times when it is equal to the displacement current density. These improvements will produce more accurate assessments of the potential electrical activity, identify active cells, and forecast thunderstorm termination.

Mathematical assessment of the role of temperature and rainfall on mosquito population dynamics.

PubMed

Abdelrazec, Ahmed; Gumel, Abba B

2017-05-01

A new stage-structured model for the population dynamics of the mosquito (a major vector for numerous vector-borne diseases), which takes the form of a deterministic system of non-autonomous nonlinear differential equations, is designed and used to study the effect of variability in temperature and rainfall on mosquito abundance in a community. Two functional forms of eggs oviposition rate, namely the Verhulst-Pearl logistic and Maynard-Smith-Slatkin functions, are used. Rigorous analysis of the autonomous version of the model shows that, for any of the oviposition functions considered, the trivial equilibrium of the model is locally- and globally-asymptotically stable if a certain vectorial threshold quantity is less than unity. Conditions for the existence and global asymptotic stability of the non-trivial equilibrium solutions of the model are also derived. The model is shown to undergo a Hopf bifurcation under certain conditions (and that increased density-dependent competition in larval mortality reduces the likelihood of such bifurcation). The analyses reveal that the Maynard-Smith-Slatkin oviposition function sustains more oscillations than the Verhulst-Pearl logistic function (hence, it is more suited, from ecological viewpoint, for modeling the egg oviposition process). The non-autonomous model is shown to have a globally-asymptotically stable trivial periodic solution, for each of the oviposition functions, when the associated reproduction threshold is less than unity. Furthermore, this model, in the absence of density-dependent mortality rate for larvae, has a unique and globally-asymptotically stable periodic solution under certain conditions. Numerical simulations of the non-autonomous model, using mosquito surveillance and weather data from the Peel region of Ontario, Canada, show a peak mosquito abundance for temperature and rainfall values in the range [Formula: see text]C and [15-35] mm, respectively. These ranges are recorded in the Peel region between July and August (hence, this study suggests that anti-mosquito control effects should be intensified during this period).

PHAST Version 2-A Program for Simulating Groundwater Flow, Solute Transport, and Multicomponent Geochemical Reactions

USGS Publications Warehouse

Parkhurst, David L.; Kipp, Kenneth L.; Charlton, Scott R.

2010-01-01

The computer program PHAST (PHREEQC And HST3D) simulates multicomponent, reactive solute transport in three-dimensional saturated groundwater flow systems. PHAST is a versatile groundwater flow and solute-transport simulator with capabilities to model a wide range of equilibrium and kinetic geochemical reactions. The flow and transport calculations are based on a modified version of HST3D that is restricted to constant fluid density and constant temperature. The geochemical reactions are simulated with the geochemical model PHREEQC, which is embedded in PHAST. Major enhancements in PHAST Version 2 allow spatial data to be defined in a combination of map and grid coordinate systems, independent of a specific model grid (without node-by-node input). At run time, aquifer properties are interpolated from the spatial data to the model grid; regridding requires only redefinition of the grid without modification of the spatial data. PHAST is applicable to the study of natural and contaminated groundwater systems at a variety of scales ranging from laboratory experiments to local and regional field scales. PHAST can be used in studies of migration of nutrients, inorganic and organic contaminants, and radionuclides; in projects such as aquifer storage and recovery or engineered remediation; and in investigations of the natural rock/water interactions in aquifers. PHAST is not appropriate for unsaturated-zone flow, multiphase flow, or density-dependent flow. A variety of boundary conditions are available in PHAST to simulate flow and transport, including specified-head, flux (specified-flux), and leaky (head-dependent) conditions, as well as the special cases of rivers, drains, and wells. Chemical reactions in PHAST include (1) homogeneous equilibria using an ion-association or Pitzer specific interaction thermodynamic model; (2) heterogeneous equilibria between the aqueous solution and minerals, ion exchange sites, surface complexation sites, solid solutions, and gases; and (3) kinetic reactions with rates that are a function of solution composition. The aqueous model (elements, chemical reactions, and equilibrium constants), minerals, exchangers, surfaces, gases, kinetic reactants, and rate expressions may be defined or modified by the user. A number of options are available to save results of simulations to output files. The data may be saved in three formats: a format suitable for viewing with a text editor; a format suitable for exporting to spreadsheets and postprocessing programs; and in Hierarchical Data Format (HDF), which is a compressed binary format. Data in the HDF file can be visualized on Windows computers with the program Model Viewer and extracted with the utility program PHASTHDF; both programs are distributed with PHAST.

Real-Time Communication Support for Underwater Acoustic Sensor Networks †.

PubMed

Santos, Rodrigo; Orozco, Javier; Micheletto, Matias; Ochoa, Sergio F; Meseguer, Roc; Millan, Pere; Molina, And Carlos

2017-07-14

Underwater sensor networks represent an important and promising field of research due to the large diversity of underwater ubiquitous applications that can be supported by these networks, e.g., systems that deliver tsunami and oil spill warnings, or monitor submarine ecosystems. Most of these monitoring and warning systems require real-time communication in wide area networks that have a low density of nodes. The underwater communication medium involved in these networks is very harsh and imposes strong restrictions to the communication process. In this scenario, the real-time transmission of information is done mainly using acoustic signals, since the network nodes are not physically close. The features of the communication scenario and the requirements of the communication process represent major challenges for designers of both, communication protocols and monitoring and warning systems. The lack of models to represent these networks is the main stumbling block for the proliferation of underwater ubiquitous systems. This paper presents a real-time communication model for underwater acoustic sensor networks (UW-ASN) that are designed to cover wide areas with a low density of nodes, using any-to-any communication. This model is analytic, considers two solution approaches for scheduling the real-time messages, and provides a time-constraint analysis for the network performance. Using this model, the designers of protocols and underwater ubiquitous systems can quickly prototype and evaluate their solutions in an evolving way, in order to determine the best solution to the problem being addressed. The suitability of the proposal is illustrated with a case study that shows the performance of a UW-ASN under several initial conditions. This is the first analytic model for representing real-time communication in this type of network, and therefore, it opens the door for the development of underwater ubiquitous systems for several application scenarios.

Real-Time Communication Support for Underwater Acoustic Sensor Networks †

PubMed Central

Santos, Rodrigo; Orozco, Javier; Micheletto, Matias

2017-01-01

Underwater sensor networks represent an important and promising field of research due to the large diversity of underwater ubiquitous applications that can be supported by these networks, e.g., systems that deliver tsunami and oil spill warnings, or monitor submarine ecosystems. Most of these monitoring and warning systems require real-time communication in wide area networks that have a low density of nodes. The underwater communication medium involved in these networks is very harsh and imposes strong restrictions to the communication process. In this scenario, the real-time transmission of information is done mainly using acoustic signals, since the network nodes are not physically close. The features of the communication scenario and the requirements of the communication process represent major challenges for designers of both, communication protocols and monitoring and warning systems. The lack of models to represent these networks is the main stumbling block for the proliferation of underwater ubiquitous systems. This paper presents a real-time communication model for underwater acoustic sensor networks (UW-ASN) that are designed to cover wide areas with a low density of nodes, using any-to-any communication. This model is analytic, considers two solution approaches for scheduling the real-time messages, and provides a time-constraint analysis for the network performance. Using this model, the designers of protocols and underwater ubiquitous systems can quickly prototype and evaluate their solutions in an evolving way, in order to determine the best solution to the problem being addressed. The suitability of the proposal is illustrated with a case study that shows the performance of a UW-ASN under several initial conditions. This is the first analytic model for representing real-time communication in this type of network, and therefore, it opens the door for the development of underwater ubiquitous systems for several application scenarios. PMID:28708093

The short range anion-H interaction is the driving force for crystal formation of ions in water.

PubMed

Alejandre, José; Chapela, Gustavo A; Bresme, Fernando; Hansen, Jean-Pierre

2009-05-07

The crystal formation of NaCl in water is studied by extensive molecular dynamics simulations. Ionic solutions at room temperature and various concentrations are studied using the SPC/E and TIP4P/2005 water models and seven force fields of NaCl. Most force fields of pure NaCl fail to reproduce the experimental density of the crystal, and in solution some favor dissociation at saturated conditions, while others favor crystal formation at low concentration. A new force field of NaCl is proposed, which reproduces the experimental phase diagram in the solid, liquid, and vapor regions. This force field overestimates the solubility of NaCl in water at saturation conditions when used with standard Lorentz-Berthelot combining rules for the ion-water pair potentials. It is shown that precipitation of ions is driven by the short range interaction between Cl-H pairs, a term which is generally missing in the simulation of ionic solutions. The effects of intramolecular flexibility of water on the solubility of NaCl ions are analyzed and is found to be small compared to rigid models. A flexible water model, extending the rigid SPC/E, is proposed, which incorporates Lennard-Jones interactions centered on the hydrogen atoms. This force field gives liquid-vapor coexisting densities and surface tensions in better agreement with experimental data than the rigid SPC/E model. The Cl-H, Na-O, and Cl-O pair distribution functions of the rigid and flexible models agree well with experiment. The predicted concentration dependence of the electric conductivity is in fair agreement with available experimental data.

Cosmology with a stiff matter era

NASA Astrophysics Data System (ADS)

Chavanis, Pierre-Henri

2015-11-01

We consider the possibility that the Universe is made of a dark fluid described by a quadratic equation of state P =K ρ2 , where ρ is the rest-mass density and K is a constant. The energy density ɛ =ρ c2+K ρ2 is the sum of two terms: a rest-mass term ρ c2 that mimics "dark matter" (P =0 ) and an internal energy term u =K ρ2=P that mimics a "stiff fluid" (P =ɛ ) in which the speed of sound is equal to the speed of light. In the early universe, the internal energy dominates and the dark fluid behaves as a stiff fluid (P ˜ɛ , ɛ ∝a-6). In the late universe, the rest-mass energy dominates and the dark fluid behaves as pressureless dark matter (P ≃0 , ɛ ∝a-3). We provide a simple analytical solution of the Friedmann equations for a universe undergoing a stiff matter era, a dark matter era, and a dark energy era due to the cosmological constant. This analytical solution generalizes the Einstein-de Sitter solution describing the dark matter era, and the Λ CDM model describing the dark matter era and the dark energy era. Historically, the possibility of a primordial stiff matter era first appeared in the cosmological model of Zel'dovich where the primordial universe is assumed to be made of a cold gas of baryons. A primordial stiff matter era also occurs in recent cosmological models where dark matter is made of relativistic self-gravitating Bose-Einstein condensates (BECs). When the internal energy of the dark fluid mimicking stiff matter is positive, the primordial universe is singular like in the standard big bang theory. It expands from an initial state with a vanishing scale factor and an infinite density. We consider the possibility that the internal energy of the dark fluid is negative (while, of course, its total energy density is positive), so that it mimics anti-stiff matter. This happens, for example, when the BECs have an attractive self-interaction with a negative scattering length. In that case, the primordial universe is nonsingular and bouncing like in loop quantum cosmology. At t =0 , the scale factor is finite and the energy density is equal to zero. The universe first has a phantom behavior where the energy density increases with the scale factor, then a normal behavior where the energy density decreases with the scale factor. For the sake of generality, we consider a cosmological constant of arbitrary sign. When the cosmological constant is positive, the Universe asymptotically reaches a de Sitter regime where the scale factor increases exponentially rapidly with time. This can account for the accelerating expansion of the Universe that we observe at present. When the cosmological constant is negative (anti-de Sitter), the evolution of the Universe is cyclic. Therefore, depending on the sign of the internal energy of the dark fluid and on the sign of the cosmological constant, we obtain analytical solutions of the Friedmann equations describing singular and nonsingular expanding, bouncing, or cyclic universes.

A three-dimensional, finite element model for coastal and estuarine circulation

USGS Publications Warehouse

Walters, R.A.

1992-01-01

This paper describes the development and application of a three-dimensional model for coastal and estuarine circulation. The model uses a harmonic expansion in time and a finite element discretization in space. All nonlinear terms are retained, including quadratic bottom stress, advection and wave transport (continuity nonlinearity). The equations are solved as a global and a local problem, where the global problem is the solution of the wave equation formulation of the shallow water equations, and the local problem is the solution of the momentum equation for the vertical velocity profile. These equations are coupled to the advection-diffusion equation for salt so that density gradient forcing is included in the momentum equations. The model is applied to a study of Delaware Bay, U.S.A., where salinity intrusion is the primary focus. ?? 1991.

Transit-time and age distributions for nonlinear time-dependent compartmental systems.

PubMed

Metzler, Holger; Müller, Markus; Sierra, Carlos A

2018-02-06

Many processes in nature are modeled using compartmental systems (reservoir/pool/box systems). Usually, they are expressed as a set of first-order differential equations describing the transfer of matter across a network of compartments. The concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions. Until now, explicit formulas for transit-time and age distributions of nonlinear time-dependent compartmental systems were not available. We compute densities for these types of systems under the assumption of well-mixed compartments. Assuming that a solution of the nonlinear system is available at least numerically, we show how to construct a linear time-dependent system with the same solution trajectory. We demonstrate how to exploit this solution to compute transit-time and age distributions in dependence on given start values and initial age distributions. Furthermore, we derive equations for the time evolution of quantiles and moments of the age distributions. Our results generalize available density formulas for the linear time-independent case and mean-age formulas for the linear time-dependent case. As an example, we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time-dependent input signal which represents fossil fuel additions. We derive time-dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business-as-usual scenario.

Phase-field-crystal study of solute trapping

NASA Astrophysics Data System (ADS)

Humadi, Harith; Hoyt, Jeffrey J.; Provatas, Nikolas

2013-02-01

In this study we have incorporated two time scales into the phase-field-crystal model of a binary alloy to explore different solute trapping properties as a function of crystal-melt interface velocity. With only diffusive dynamics, we demonstrate that the segregation coefficient, K as a function of velocity for a binary alloy is consistent with the model of Kaplan and Aziz where K approaches unity in the limit of infinite velocity. However, with the introduction of wavelike dynamics in both the density and concentration fields, the trapping follows the kinetics proposed by Sobolev [Phys. Lett. A10.1016/0375-9601(95)00084-G 199, 383 (1995)], where complete trapping occurs at a finite velocity.

Local existence of solutions to the Euler-Poisson system, including densities without compact support

NASA Astrophysics Data System (ADS)

Brauer, Uwe; Karp, Lavi

2018-01-01

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for γ = 6/5. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.

Density fluctuations in aqueous solution of ionic liquid with lower critical solution temperature: Mixture of tetrabutylphosphonium trifluoroacetate and water

NASA Astrophysics Data System (ADS)

Nitta, Ayako; Morita, Takeshi; Saita, Shohei; Kohno, Yuki; Ohno, Hiroyuki; Nishikawa, Keiko

2015-05-01

Aqueous solutions of tetrabutylphosphonium trifluoroacetate ([P4444]CF3COO) exhibit a LCST-type phase transition with the critical point near 0.025 in mole fraction of [P4444]CF3COO at T = 302 K. The phase behavior of [P4444]CF3COO-water mixtures was investigated by evaluating their density fluctuations, which provide quantitative descriptions of the mixing states of the solutions. The concentration dependence of the density fluctuations was investigated at 293 and 301 K for the mixtures without distinguishing the components and for the individual components ([P4444]CF3COO and water). A drastic change in the mixing state was observed for the solution when the critical point was approached.

Molecular dynamics study on glycolic acid in the physiological salt solution

NASA Astrophysics Data System (ADS)

Matsunaga, S.

2018-05-01

Molecular dynamics (MD) study on glycolic acid in the physiological salt solution has been performed, which is a model of a biofuel cell. The structure and charge distribution of glycolic acid in aqueous solution used in MD is beforehand optimized by Gaussian09 utilizing the density functional theory. MD is performed in the NTV constant condition, i.e. the number of particles, temperature, and volume of MD cell are definite. The structure difference of the glycolic acid and oxalic acid is detected by the water distribution around the molecules using the pair distribution functions, gij(r), and the frequency dependent diffusion coefficients, Di(ν). The anomalous dielectric constant of the solution, i.e. about 12 times larger than that of water, has been obtained, which may be attributed to the ion pair formation in the solution.

Automated MAD and MIR structure solution

PubMed Central

Terwilliger, Thomas C.; Berendzen, Joel

1999-01-01

Obtaining an electron-density map from X-ray diffraction data can be difficult and time-consuming even after the data have been collected, largely because MIR and MAD structure determinations currently require many subjective evaluations of the qualities of trial heavy-atom partial structures before a correct heavy-atom solution is obtained. A set of criteria for evaluating the quality of heavy-atom partial solutions in macromolecular crystallography have been developed. These have allowed the conversion of the crystal structure-solution process into an optimization problem and have allowed its automation. The SOLVE software has been used to solve MAD data sets with as many as 52 selenium sites in the asymmetric unit. The automated structure-solution process developed is a major step towards the fully automated structure-determination, model-building and refinement procedure which is needed for genomic scale structure determinations. PMID:10089316

A Mathematical Model of Solute Coupled Water Transport in Toad Intestine Incorporating Recirculation of the Actively Transported Solute

PubMed Central

Larsen, Erik Hviid; Sørensen, Jakob Balslev; Sørensen, Jens Nørkær

2000-01-01

A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2–4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241–251), computations predict that 60–80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model generates pseudo-solvent drag. The associated flux-ratio equation is derived. PMID:10919860

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.

The Jeffcott equations in nonlinear rotordynamics

NASA Technical Reports Server (NTRS)

Zalik, R. A.

1987-01-01

The Jeffcott equations are a system of coupled differential equations representing the behavior of a rotating shaft. This is a simple model which allows investigation of the basic dynamic behavior of rotating machinery. Nolinearities can be introduced by taking into consideration deadband, side force, and rubbing, among others. The properties of the solutions of the Jeffcott equations with deadband are studied. In particular, it is shown how bounds for the solution of these equations can be obtained from bounds for the solutions of the linearized equations. By studying the behavior of the Fourier transforms of the solutions, we are also able to predict the onset of destructive vibrations. These conclusions are verified by means of numerical solutions of the equations, and of power spectrum density (PSD) plots. This study offers insight into a possible detection method to determine pump stability margins during flight and hot fire tests, and was motivated by the need to explain a phenomenon observed in the development phase of the cryogenic pumps of the Space Shuttle, during hot fire ground testing; namely, the appearance of vibrations at frequencies that could not be accounted for by means of linear models.

Nonperturbative parton distributions and the proton spin problem

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

Simonov, Yu. A., E-mail: simonov@itep.ru

2016-05-15

The Lorentz contracted form of the static wave functions is used to calculate the valence parton distributions for mesons and baryons, boosting the rest frame solutions of the path integral Hamiltonian. It is argued that nonperturbative parton densities are due to excitedmultigluon baryon states. A simplemodel is proposed for these states ensuring realistic behavior of valence and sea quarks and gluon parton densities at Q{sup 2} = 10 (GeV/c){sup 2}. Applying the same model to the proton spin problem one obtains Σ{sub 3} = 0.18 for the same Q{sup 2}.

X-Ray Wind Tomography of IGR J17252-3616

NASA Astrophysics Data System (ADS)

Manousakis, Antonios; Walter, Roland

2010-07-01

IGR J17252-3616, a highly absorbed High Mass X-ray Binary (HMXB) with Hydrogen column density NH~(2-4)×1023 cm-2, has been observed with XMM-Newton for about one month. Observations were scheduled in order to cover the orbital-phase space as much as possible. IGR J17252-3616 shows a varying column density NH and Fe Kα line when fit with simple phenomenological models. A refined orbital solution can be derived. Spectral timing analysis allows derivation of the wind properties of the massive star.

Hydration shell parameters of aqueous alcohols: THz excess absorption and packing density.

PubMed

Matvejev, V; Zizi, M; Stiens, J

2012-12-06

Solvation in water requires minimizing the perturbations in its hydrogen bonded network. Hence solutes distort water molecular motions in a surrounding domain, forming a molecule-specific hydration shell. The properties of those hydration shells impact the structure and function of the solubilized molecules, both at the single molecule and at higher order levels. The size of the hydration shell and the picoseconds time-scale water dynamics retardation are revealed by terahertz (THz) absorption coefficient measurements. Room-temperature absorption coefficient at f = 0.28 [THz] is measured as a function of alcohol concentration in aqueous methanol, ethanol, 1,2-propanol, and 1-butanol solutions. Highly diluted alcohol measurements and enhanced overall measurement accuracy are achieved with a THz absorption measurement technique of nL-volume liquids in a capillary tube. In the absorption analysis, bulk and interfacial molecular domains of water and alcohol are considered. THz ideal and excess absorption coefficients are defined in accordance with thermodynamics mixing formulations. The parameter extraction method is developed based on a THz excess absorption model and hydrated solute molecule packing density representation. First, the hydration shell size is deduced from the hydrated solute packing densities at two specific THz excess absorption nonlinearity points: at infinite alcohol dilution (IAD) and at the THz excess absorption extremum (EAE). Consequently, interfacial water and alcohol molecular domain absorptions are deduced from the THz excess absorption model. The hydration shell sizes obtained at the THz excess absorption extremum are in excellent agreement with other reports. The hydration shells of methanol, ethanol, 1- and 2-propanol consist of 13.97, 22.94, 22.99, and 31.10 water molecules, respectively. The hydration shell water absorption is on average 0.774 ± 0.028 times the bulk water absorption. The hydration shell parameters might shed light on hydration dynamics of biomolecules.

Crustal thickness inversions from recent Mars Reconnaissance Orbiter gravity solutions

NASA Astrophysics Data System (ADS)

Neumann, Gregory; Zuber, Maria T.; Lemoine, Frank; Neumann, Gregory A.; Smith, David E.

Recent Mars Reconnaissance Orbiter gravity solutions from low-altitude tracking of MRO, together with previous spacecraft, have dramatically improved correlation with MOLA topography at spherical harmonic degrees up to 95. We present several updated models of crustal thickness. These models are calculated to fit the Bouguer potential anomaly following the assumptions in Neumann et al. 2004, with much weaker a priori constraints applied to the topographic corrections and the downward continuation to the martian mantle. These models are available via anonymous ftp to "ftp://lepftp.gsfc.nasa.gov/pub/exports/tharsis/marscrust3". The higher-resolution models improve on those we produced in 2004-2005. They are appropriate for modeling impacts as small as 300 km diameter, and for processes related to the hemispheric dichotomy boundary. We discuss in particular the assumption of quasi-uniform crustal density and its likely failure in volcanic regions.

Imaging the density distributions at the regional scale using full waveform and gravity data inversion - Application to the Pyrenees

NASA Astrophysics Data System (ADS)

Martin, Roland; Chevrot, Sébastien; Wang, Yi; Spangenberg, Hannah; Goubet, Marie; Monteiller, Vadim; Komatitsch, Dimitri; Seoane, Lucia; Dufréchou, Grégory

2017-04-01

We present a hybrid inversion method that allows us to image density distributions at the regional scale using both seismic and gravity data. One main goal is to obtain densities and seismic wave velocities (P and S) in the lithosphere with a fine resolution to get important constraints on the mineralogic composition and thermal state of the lithosphere. In the context of the Pyrenees (located between Spain and France), accurate Vp and Vs seismic velocity models are computed first on a 3D spectral element grid at the scale of the Pyrenees by inverting teleseismic full waveforms. In a second step, Vp velocities are mapped to densities using empirical relations to build an a priori density model. BGI and BRGM Bouguer gravity anomaly data sets are then inverted on the same 3D spectral element grid as the Vp model at a resolution of 1-2 km by using high-order numerical integration formulae. Solutions are compared to those obtained using classical semi-analytical techniques. This procedure opens the possibility to invert both teleseismic and gravity data on the same finite-element grid. It can handle topography of the free surface in the same spectral-element distorted mesh that is used to solve the wave equation, without performing extra interpolations between different grids and models. WGS84 curvature, SRTM or ETOPO1 topographies are used.

On the Gause predator-prey model with a refuge: a fresh look at the history.

PubMed

Křivan, Vlastimil

2011-04-07

This article re-analyses a prey-predator model with a refuge introduced by one of the founders of population ecology Gause and his co-workers to explain discrepancies between their observations and predictions of the Lotka-Volterra prey-predator model. They replaced the linear functional response used by Lotka and Volterra by a saturating functional response with a discontinuity at a critical prey density. At concentrations below this critical density prey were effectively in a refuge while at a higher densities they were available to predators. Thus, their functional response was of the Holling type III. They analyzed this model and predicted existence of a limit cycle in predator-prey dynamics. In this article I show that their model is ill posed, because trajectories are not well defined. Using the Filippov method, I define and analyze solutions of the Gause model. I show that depending on parameter values, there are three possibilities: (1) trajectories converge to a limit cycle, as predicted by Gause, (2) trajectories converge to an equilibrium, or (3) the prey population escapes predator control and grows to infinity. Copyright © 2011 Elsevier Ltd. All rights reserved.

Multiphasic modeling of charged solute transport across articular cartilage: Application of multi-zone finite-bath model.

PubMed

Arbabi, Vahid; Pouran, Behdad; Weinans, Harrie; Zadpoor, Amir A

2016-06-14

Charged and uncharged solutes penetrate through cartilage to maintain the metabolic function of chondrocytes and to possibly restore or further breakdown the cartilage tissue in different stages of osteoarthritis. In this study the transport of charged solutes across the various zones of cartilage was quantified, taken into account the physicochemical interactions between the solute and the cartilage constituents. A multiphasic finite-bath finite element (FE) model was developed to simulate equine cartilage diffusion experiments that used a negatively charged contrast agent (ioxaglate) in combination with serial micro-computed tomography (micro-CT) to measure the diffusion. By comparing the FE model with the experimental data both the diffusion coefficient of ioxaglate and the fixed charge density (FCD) were obtained. In the multiphasic model, cartilage was divided into multiple (three) zones to help understand how diffusion coefficient and FCD vary across cartilage thickness. The direct effects of charged solute-FCD interaction on diffusion were investigated by comparing the diffusion coefficients derived from the multiphasic and biphasic-solute models. We found a relationship between the FCD obtained by the multiphasic model and ioxaglate partitioning obtained from micro-CT experiments. Using our multi-zone multiphasic model, diffusion coefficient of the superficial zone was up to ten-fold higher than that of the middle zone, while the FCD of the middle zone was up to almost two-fold higher than that of the superficial zone. In conclusion, the developed finite-bath multiphasic model provides us with a non-destructive method by which we could obtain both diffusion coefficient and FCD of different cartilage zones. The outcomes of the current work will also help understand how charge of the bath affects the diffusion of a charged molecule and also predict the diffusion behavior of a charged solute across articular cartilage. Copyright © 2016 Elsevier Ltd. All rights reserved.

Excited atoms in the free-burning Ar arc: treatment of the resonance radiation

NASA Astrophysics Data System (ADS)

Golubovskii, Yu; Kalanov, D.; Gortschakow, S.; Baeva, M.; Uhrlandt, D.

2016-11-01

The collisional-radiative model with an emphasis on the accurate treatment of the resonance radiation transport is developed and applied to the free-burning Ar arc plasma. This model allows for analysis of the influence of resonance radiation on the spatial density profiles of the atoms in different excited states. The comparison of the radial density profiles obtained using an effective transition probability approximation with the results of the accurate solution demonstrates the distinct impact of transport on the profiles and absolute densities of the excited atoms, especially in the arc fringes. The departures from the Saha-Boltzmann equilibrium distributions, caused by different radiative transitions, are analyzed. For the case of the DC arc, the local thermodynamic equilibrium (LTE) state holds close to the arc axis, while strong deviations from the equilibrium state on the periphery occur. In the intermediate radial positions the conditions of partial LTE are fulfilled.

The specific purpose Monte Carlo code McENL for simulating the response of epithermal neutron lifetime well logging tools

NASA Astrophysics Data System (ADS)

Prettyman, T. H.; Gardner, R. P.; Verghese, K.

1993-08-01

A new specific purpose Monte Carlo code called McENL for modeling the time response of epithermal neutron lifetime tools is described. The weight windows technique, employing splitting and Russian roulette, is used with an automated importance function based on the solution of an adjoint diffusion model to improve the code efficiency. Complete composition and density correlated sampling is also included in the code, and can be used to study the effect on tool response of small variations in the formation, borehole, or logging tool composition and density. An illustration of the latter application is given for the density of a thermal neutron filter. McENL was benchmarked against test-pit data for the Mobil pulsed neutron porosity tool and was found to be very accurate. Results of the experimental validation and details of code performance are presented.

Compact stars in the non-minimally coupled electromagnetic fields to gravity

NASA Astrophysics Data System (ADS)

Sert, Özcan

2018-03-01

We investigate the gravitational models with the non-minimal Y(R)F^2 coupled electromagnetic fields to gravity, in order to describe charged compact stars, where Y( R) denotes a function of the Ricci curvature scalar R and F^2 denotes the Maxwell invariant term. We determine two parameter family of exact spherically symmetric static solutions and the corresponding non-minimal model without assuming any relation between energy density of matter and pressure. We give the mass-radius, electric charge-radius ratios and surface gravitational redshift which are obtained by the boundary conditions. We reach a wide range of possibilities for the parameters k and α in these solutions. Lastly we show that the models can describe the compact stars even in the more simple case α =3.

The Neural Basis of Insight Problem Solving: An Event-Related Potential Study

ERIC Educational Resources Information Center

Qiu, Jiang; Li, Hong; Yang, Dong; Luo, Yuejia; Li, Ying; Wu, Zhenzhen; Zhang, Qinglin

2008-01-01

The electrophysiological correlates of successful insight problem solving (Chinese logogriphs) were studied in 18 healthy subjects using high-density event-related potentials (ERPs). A new experimental paradigm (learning-testing model) was adopted in order to make subjects find a solution on their own initiative rather than receive an answer…

POWER DENSITY, FIELD INTENSITY, AND CARRIER FREQUENCY DETERMINANTS OF RF-ENERGY-INDUCED CALCIUM-ION EFFLUX FROM BRAIN TISSUE

EPA Science Inventory

To explain a carrier frequency dependence reported for radiofrequency (RF)-induced calcium-ion efflux from brain tissue, a chick-brain hemisphere bathed in buffer solution is modeled as a sphere within the uniform field of the incident electromagnetic wave. Calculations on a sphe...