Magnetosphere-Ionosphere Energy Interchange in the Electron Diffuse Aurora

NASA Technical Reports Server (NTRS)

Khazanov, George V.; Glocer, Alex; Himwich, E. W.

2014-01-01

The diffuse aurora has recently been shown to be a major contributor of energy flux into the Earth's ionosphere. Therefore, a comprehensive theoretical analysis is required to understand its role in energy redistribution in the coupled ionosphere-magnetosphere system. In previous theoretical descriptions of precipitated magnetospheric electrons (E is approximately 1 keV), the major focus has been the ionization and excitation rates of the neutral atmosphere and the energy deposition rate to thermal ionospheric electrons. However, these precipitating electrons will also produce secondary electrons via impact ionization of the neutral atmosphere. This paper presents the solution of the Boltzman-Landau kinetic equation that uniformly describes the entire electron distribution function in the diffuse aurora, including the affiliated production of secondary electrons (E greater than 600 eV) and their ionosphere-magnetosphere coupling processes. In this article, we discuss for the first time how diffuse electron precipitation into the atmosphere and the associated secondary electron production participate in ionosphere-magnetosphere energy redistribution.

A tutorial solution to scattering of radiation in a thin atmosphere bounded below by a diffusely reflecting, absorbing surface

NASA Technical Reports Server (NTRS)

Buglia, J. J.

1982-01-01

A simple tutorial method, based on a photon tracking procedure, is described to determine the spherical albedo for a thin atmosphere overlying a reflecting surface. This procedure is used to provide a physical structure with which to interpret the more detailed but highly mathematical analyses presented. The final equations are shown to be in good numerical agreement with more exact solutions for thin atmospheres.

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Dispersion of aerosol particles in the atmosphere: Fukushima

NASA Astrophysics Data System (ADS)

Haszpra, Tímea; Lagzi, István; Tél, Tamás

2013-04-01

Investigation of dispersion and deposition of aerosol particles in the atmosphere is an essential issue, because they have an effect on the biosphere and atmosphere. Moreover, aerosol particles have different transport properties and chemical and physical transformations in the atmosphere compared to gas phase air pollutants. The motion of a particle is described by a set of ordinary differential equations. The large-scale dynamics in the horizontal direction can be described by the equations of passive scalar advection, but in the vertical direction a well-defined terminal velocity should be taken into account as a term added to the vertical wind component. In the planetary boundary layer turbulent diffusion has an important role in the particle dispersion, which is taken into account by adding stochastic terms to the deterministic equations above. Wet deposition is also an essential process in the lower levels of the atmosphere, however, its precise parameterization is a challenge. For the simulations the wind field and other necessary data were taken from the ECMWF ERA-Interim database. In the case of the Fukushima Daiichi nuclear disaster (March-April 2011) radioactive aerosol particles were also released in the planetary boundary layer. Simulations (included the continuous and varying emission from the nuclear power plant) will be presented for the period of 14-23 March. Results show that wet deposition also has to be taken into consideration in the lower levels of the atmosphere. Furthermore, dynamical system characteristics are evaluated for the aerosol particle dynamics. The escape rate of particles was estimated both with and without turbulent diffusion, and in both cases when there was no wet deposition and also when wet deposition was taken into consideration.

Deterministic chaos in atmospheric radon dynamics

NASA Astrophysics Data System (ADS)

Cuculeanu, Vasile; Lupu, Alexandru

2001-08-01

The correlation dimension and Lyapunov exponents have been calculated for two time series of atmospheric radon daughter concentrations obtained from four daily measurements during the period 1993-1996. A number of about 6000 activity concentration values of 222Rn and 220Rn daughters have been used. The measuring method is based on aerosol collection on filters. In order to determine the filter activity, a low background gross beta measuring device with Geiger-Müller counter tubes in anticoincidence was used. The small noninteger value of the correlation dimension (≃2.2) and the existence of a positive Lyapunov exponent prove that deterministic chaos is present in the time series of atmospheric 220Rn daughters. This shows that a simple diffusion equation with a parameterized turbulent diffusion coefficient is insufficient for describing the dynamics in the near-ground layer where turbulence is not fully developed and coherent structures dominate. The analysis of 222Rn series confirms that the dynamics of the boundary layer cannot be described by a system of ordinary differential equations with a low number of independent variables.

Computation of diffuse sky irradiance from multidirectional radiance measurements

NASA Technical Reports Server (NTRS)

Ahmad, Suraiya P.; Middleton, Elizabeth M.; Deering, Donald W.

1987-01-01

Accurate determination of the diffuse solar spectral irradiance directly above the land surface is important in characterizing the reflectance properties of these surfaces, especially vegetation canopies. This determination is also needed to infer the net radiation budget of the earth-atmosphere system above these surfaces. An algorithm is developed here for the computation of hemispheric diffuse irradiance using the measurements from an instrument called PARABOLA, which rapidly measures upwelling and downwelling radiances in three selected wavelength bands. The validity of the algorithm is established from simulations. The standard reference data set of diffuse radiances of Dave (1978), obtained by solving the radiative transfer equation numerically for realistic atmospheric models, is used to simulate PARABOLA radiances. Hemispheric diffuse irradiance is estimated from a subset of simulated radiances by using the algorithm described. The algorithm is validated by comparing the estimated diffuse irradiance with the true diffuse irradiance of the standard data set. The validations include sensitivity studies for two wavelength bands (visible, 0.65-0.67 micron; near infrared, 0.81-0.84 micron), different atmospheric conditions, solar elevations, and surface reflectances. In most cases the hemispheric diffuse irradiance computed from simulated PARABOLA radiances and the true irradiance obtained from radiative transfer calculations agree within 1-2 percent. This technique can be applied to other sampling instruments designed to estimate hemispheric diffuse sky irradiance.

DREAM3D simulations of inner-belt dynamics

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

Cunningham, Gregory Scott

2015-05-26

A 1973 paper by Lyons and Thorne explains the two-belt structure for electrons in the inner magnetosphere as a balance between inward radial diffusion and loss to the atmosphere, where the loss to the atmosphere is enabled by pitch-angle scattering from Coulomb and wave-particle interactions. In the 1973 paper, equilibrium solutions to a decoupled set of 1D radial diffusion equations, one for each value of the first invariant of motion, μ, were computed to produce the equilibrium two-belt structure. Each 1D radial diffusion equation incorporated an L-and μ-dependent `lifetime' due to the Coulomb and wave-particle interactions. This decoupling of themore » problem is appropriate under the assumption that radial diffusion is slow in comparison to pitch-angle scattering. However, for some values of μ and L the lifetime associated with pitch-angle scattering is comparable to the timescale associated with radial diffusion, suggesting that the true equilibrium solutions might reflect `coupled modes' involving pitch-angle scattering and radial diffusion and thus requiring a 3D diffusion model. In the work we show here, we have computed the equilibrium solutions using our 3D diffusion model, DREAM3D, that allows for such coupling. We find that the 3D equilibrium solutions are quite similar to the solutions shown in the 1973 paper when we use the same physical models for radial diffusion and pitch-angle scattering from hiss. However, we show that the equilibrium solutions are quite sensitive to various aspects of the physics model employed in the 1973 paper that can be improved, suggesting that additional work needs to be done to understand the two-belt structure.« less

Sound propagation in urban areas: a periodic disposition of buildings.

PubMed

Picaut, J; Hardy, J; Simon, L

1999-10-01

A numerical simulation of background noise propagation is performed for a network of hexagonal buildings. The obtained results suggest that the prediction of background noise in urban spaces is possible by means of a modified diffusion equation using two parameters: the diffusion coefficient that expresses the spreading out of noise resulting from diffuse scattering and multiple reflections by buildings, and an attenuation term accounting for the wall absorption, atmospheric attenuation, and absorption by the open top. The dependence of the diffusion coefficient with geometrical shapes and the diffusive nature of the buildings are investigated in the case of a periodic disposition of hexagonal buildings.

Segregation of isotopes of heavy metals due to light-induced drift: results and problems

NASA Astrophysics Data System (ADS)

Sapar, A.; Aret, A.; Poolamäe, R.; Sapar, L.

2008-04-01

Atutov and Shalagin (1988) proposed light-induced drift (LID) as a physically well understandable mechanism to explain the formation of isotopic anomalies observed in CP stars. We have generalized the theory of LID and applied it to diffusion of heavy elements and their isotopes in quiescent atmospheres of CP stars. Diffusional segregation of isotopes of chemical elements is described by the equations of continuity and diffusion velocity. Computations of evolutionary sequences for the abundances of mercury isotopes in several model atmospheres have been made, using the Fortran 90 program SMART composed by the authors. Results confirm predominant role of LID in separation of isotopes.

Estimation of Downwind Concentration of Airborne Effluents Discharged in the Neighbourhood of Buildings.

ERIC Educational Resources Information Center

Barry, P. J.

Air flow in the neighborhood of buildings is briefly described and compared with that assumed for the usual atmospheric diffusion equations. The literature is reviewed and empirical formulae which have been proposed are listed and compared. (RH)

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

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

de Almeida, Valmor F.

In this work, a phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equationmore » and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.« less

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

DOE PAGES

de Almeida, Valmor F.

2017-04-19

In this work, a phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equationmore » and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.« less

Solutions for Reacting and Nonreacting Viscous Shock Layers with Multicomponent Diffusion and Mass Injection. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Moss, J. N.

1971-01-01

Numerical solutions are presented for the viscous shocklayer equations where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium. Also the effects of the diffusion model, surface catalyticity, and mass injection on surface transport and flow parameters are considered. The equilibrium calculations for air species using multicomponent: diffusion provide solutions previously unavailable. The viscous shock-layer equations are solved by using an implicit finite-difference scheme. The flow is treated as a mixture of inert and thermally perfect species. Also the flow is assumed to be in vibrational equilibrium. All calculations are for a 45 deg hyperboloid. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented showing the effects of the chemical models; diffusion models; surface catalyticity; and mass injection of air, water, and ablation products on heat transfer; skin friction; shock stand-off distance; wall pressure distribution; and tangential velocity, temperature, and species profiles.

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.

Turbulent diffusion with memories and intrinsic shear

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1974-01-01

The first part of the present theory is devoted to the derivation of a Fokker-Planck equation. The eddies smaller than the hydrodynamic scale of the diffusion cloud form a diffusivity, while the inhomogeneous, bigger eddies give rise to a nonuniform migratory drift. This introduces an eddy-induced shear which reflects on the large-scale diffusion. The eddy-induced shear does not require the presence of a permanent wind shear and is intrinsic to the diffusion. Secondly, a transport theory of diffusivity is developed by the method of repeated-cascade and is based upon a relaxation of a chain of memories with decreasing information. The full range of diffusion consists of inertia, composite, and shear subranges, for which variance and eddy diffusivities are predicted. The coefficients are evaluated. Comparison with experiments in the upper atmosphere and oceans is made.

Diffusion scrubber-ion chromatography for the measurement of trace levels of atmospheric HCl

NASA Astrophysics Data System (ADS)

Lindgren, Per F.

A diffusion scrubber-ion chromatographic (DS-IC) instrument has been characterized and employed for the measurement of trace levels of gaseous HCl in the atmosphere. The instrument operates with a temporal resolution of 5 min and the detection limit is estimated to be 5 pptv. Collection efficiencies for HCl with two identical diffusion scrubbers were 28±2% and 20±2%, respectively, at a sampling flow rate of 2 SLPM. Instrument response decreases with increased relative humidity. An equation, correction factor=2.45 × 10 -7 × %r.h 3 + 1.00, is used to correct for the relative humidity dependency. The instrument was tested in ambient air studies by measuring background mixing ratios between 0.02 and 0.5 ppbv at a suburban sampling site. Calibration of the instrument was carried out with a novel source of gaseous HCl based on sublimation of ammonium chloride.

Multi-Scale Modeling and the Eddy-Diffusivity/Mass-Flux (EDMF) Parameterization

NASA Astrophysics Data System (ADS)

Teixeira, J.

2015-12-01

Turbulence and convection play a fundamental role in many key weather and climate science topics. Unfortunately, current atmospheric models cannot explicitly resolve most turbulent and convective flow. Because of this fact, turbulence and convection in the atmosphere has to be parameterized - i.e. equations describing the dynamical evolution of the statistical properties of turbulence and convection motions have to be devised. Recently a variety of different models have been developed that attempt at simulating the atmosphere using variable resolution. A key problem however is that parameterizations are in general not explicitly aware of the resolution - the scale awareness problem. In this context, we will present and discuss a specific approach, the Eddy-Diffusivity/Mass-Flux (EDMF) parameterization, that not only is in itself a multi-scale parameterization but it is also particularly well suited to deal with the scale-awareness problems that plague current variable-resolution models. It does so by representing small-scale turbulence using a classic Eddy-Diffusivity (ED) method, and the larger-scale (boundary layer and tropospheric-scale) eddies as a variety of plumes using the Mass-Flux (MF) concept.

Anisotropic Turbulence Models for Acoustic Propagation Through the Neutral Atmospheric Surface Layer

DTIC Science & Technology

1998-02-01

and Brost (1984). †Specific means per unit mass. 2 Observations Top-Down Approach Bottom-Up Approach Equations for the energy spectra Equations for...R. A. Brost (1984): Top-down and bottom-up diffusion of a scalar in the convective boundary layer. J. Atmos. Sci., 41, 102–112. 62 Distribution 63...Agency Attn W21 Longbothum 9800 Savage Rd FT George G Meade MD 20755-6000 TACOM Attn AMSTA-TR-R E Shalis Mail Stop 263 Warren MI 48090 US Army

Vertical distribution of ozone: a new method of determination using satellite measurements.

PubMed

Aruga, T; Igarashi, T

1976-01-01

A new method to determine the vertical distribution of atmospheric ozone over a wide range from the spectral measurement of backscattered solar uv radiation is proposed. Equations for the diffuse reflection in an inhomogeneous atmosphere are introduced, and some theoretical approximations are discussed. An inversion equation is formulated in such a way that the change of radiance at each wavelength, caused by the minute relative increment of ozone density at each altitude, is obtained exactly. The equation is solved by an iterative procedure using the weight function obtained in this work. The results of computer simulation indicate that the ozone distribution from the mesopause to the tropopause can be determined, and that although it is impossible to suggest exactly the complicated profile with fine structure, the smoothed ozone distribution and the total content can be determined with almost the same accuracy as the accuracies of measurement and theoretical calculation of the spectral intensity.

Inverse atmospheric radiative transfer problems - A nonlinear minimization search method of solution. [aerosol pollution monitoring

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1976-01-01

The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.

A model of the atmospheric metal deposition by cosmic dust particles

NASA Astrophysics Data System (ADS)

McNeil, W. J.

1993-11-01

We have developed a model of the deposition of meteoric metals in Earth's atmosphere. The model takes as input the total mass influx of material to the Earth and calculates the deposition rate at all altitudes through solution of the drag and subliminal equations in a Monte Carlo-type computation. The diffusion equation is then solved to give steady state concentration of complexes of specific metal species and kinetics are added to calculate the concentration of individual complexes. Concentrating on sodium, we calculate the Na(D) nightglow predicted by the model, and by introduction of seasonal variations in lower tropospheric ozone based on experimental results, we are able to duplicate the seasonal variation of mid-latitude nightglow data.

DCMIP2016: a review of non-hydrostatic dynamical core design and intercomparison of participating models

NASA Astrophysics Data System (ADS)

Ullrich, Paul A.; Jablonowski, Christiane; Kent, James; Lauritzen, Peter H.; Nair, Ramachandran; Reed, Kevin A.; Zarzycki, Colin M.; Hall, David M.; Dazlich, Don; Heikes, Ross; Konor, Celal; Randall, David; Dubos, Thomas; Meurdesoif, Yann; Chen, Xi; Harris, Lucas; Kühnlein, Christian; Lee, Vivian; Qaddouri, Abdessamad; Girard, Claude; Giorgetta, Marco; Reinert, Daniel; Klemp, Joseph; Park, Sang-Hun; Skamarock, William; Miura, Hiroaki; Ohno, Tomoki; Yoshida, Ryuji; Walko, Robert; Reinecke, Alex; Viner, Kevin

2017-12-01

Atmospheric dynamical cores are a fundamental component of global atmospheric modeling systems and are responsible for capturing the dynamical behavior of the Earth's atmosphere via numerical integration of the Navier-Stokes equations. These systems have existed in one form or another for over half of a century, with the earliest discretizations having now evolved into a complex ecosystem of algorithms and computational strategies. In essence, no two dynamical cores are alike, and their individual successes suggest that no perfect model exists. To better understand modern dynamical cores, this paper aims to provide a comprehensive review of 11 non-hydrostatic dynamical cores, drawn from modeling centers and groups that participated in the 2016 Dynamical Core Model Intercomparison Project (DCMIP) workshop and summer school. This review includes a choice of model grid, variable placement, vertical coordinate, prognostic equations, temporal discretization, and the diffusion, stabilization, filters, and fixers employed by each system.

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

NASA Astrophysics Data System (ADS)

Gupta, A.; Sharan, M.

2017-12-01

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

Marangoni Convection during Free Electron Laser Nitriding of Titanium

NASA Astrophysics Data System (ADS)

Höche, Daniel; Müller, Sven; Rapin, Gerd; Shinn, Michelle; Remdt, Elvira; Gubisch, Maik; Schaaf, Peter

2009-08-01

Pure titanium was treated by free electron laser (FEL) radiation in a nitrogen atmosphere. As a result, nitrogen diffusion occurs and a TiN coating was synthesized. Local gradients of interfacial tension due to the local heating lead to a Marangoni convection, which determines the track properties. Because of the experimental inaccessibility of time-dependent occurrences, finite element calculations were performed, to determine the physical processes such as heat transfer, melt flow, and mass transport. In order to calculate the surface deformation of the gas-liquid interface, the level set approach was used. The equations were modified and coupled with heat-transfer and diffusion equations. The process was characterized by dimensionless numbers such as the Reynolds, Peclet, and capillary numbers, to obtain more information about the acting forces and the coating development. Moreover, the nitrogen distribution was calculated using the corresponding transport equation. The simulations were compared with cross-sectional micrographs of the treated titanium sheets and checked for their validity. Finally, the process presented is discussed and compared with similar laser treatments.

Middle atmosphere dynamical sources of the semiannual oscillation in the thermosphere and ionosphere

NASA Astrophysics Data System (ADS)

Jones, M.; Emmert, J. T.; Drob, D. P.; Siskind, D. E.

2017-01-01

The strong global semiannual oscillation (SAO) in thermospheric density has been observed for five decades, but definitive knowledge of its source has been elusive. We use the National Center of Atmospheric Research thermosphere-ionosphere-mesosphere electrodynamics general circulation model (TIME-GCM) to study how middle atmospheric dynamics generate the SAO in the thermosphere-ionosphere (T-I). The "standard" TIME-GCM simulates, from first principles, SAOs in thermospheric mass density and ionospheric total electron content that agree well with observed climatological variations. Diagnosis of the globally averaged continuity equation for atomic oxygen ([O]) shows that the T-I SAO originates in the upper mesosphere, where an SAO in [O] is forced by nonlinear, resolved-scale variations in the advective, net tidal, and diffusive transport of O. Contrary to earlier hypotheses, TIME-GCM simulations demonstrate that intra-annually varying eddy diffusion by breaking gravity waves may not be the primary driver of the T-I SAO: A pronounced SAO is produced without parameterized gravity waves.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

Steady state model for the thermal regimes of shells of airships and hot air balloons

NASA Astrophysics Data System (ADS)

Luchev, Oleg A.

1992-10-01

A steady state model of the temperature regime of airships and hot air balloons shells is developed. The model includes three governing equations: the equation of the temperature field of airships or balloons shell, the integral equation for the radiative fluxes on the internal surface of the shell, and the integral equation for the natural convective heat exchange between the shell and the internal gas. In the model the following radiative fluxes on the shell external surface are considered: the direct and the earth reflected solar radiation, the diffuse solar radiation, the infrared radiation of the earth surface and that of the atmosphere. For the calculations of the infrared external radiation the model of the plane layer of the atmosphere is used. The convective heat transfer on the external surface of the shell is considered for the cases of the forced and the natural convection. To solve the mentioned set of the equations the numerical iterative procedure is developed. The model and the numerical procedure are used for the simulation study of the temperature fields of an airship shell under the forced and the natural convective heat transfer.

Groups in the radiative transfer theory

NASA Astrophysics Data System (ADS)

Nikoghossian, Arthur

2016-11-01

The paper presents a group-theoretical description of radiation transfer in inhomogeneous and multi-component atmospheres with the plane-parallel geometry. It summarizes and generalizes the results obtained recently by the author for some standard transfer problems of astrophysical interest with allowance of the angle and frequency distributions of the radiation field. We introduce the concept of composition groups for media with different optical and physical properties. Group representations are derived for two possible cases of illumination of a composite finite atmosphere. An algorithm for determining the reflectance and transmittance of inhomogeneous and multi-component atmospheres is described. The group theory is applied also to determining the field of radiation inside an inhomogeneous atmosphere. The concept of a group of optical depth translations is introduced. The developed theory is illustrated with the problem of radiation diffusion with partial frequency distribution assuming that the inhomogeneity is due to depth-variation of the scattering coefficient. It is shown that once reflectance and transmittance of a medium are determined, the internal field of radiation in the source-free atmosphere is found without solving any new equations. The transfer problems for a semi-infinite atmosphere and an atmosphere with internal sources of energy are discussed. The developed theory allows to derive summation laws for the mean number of scattering events underwent by the photons in the course of diffusion in the atmosphere.

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

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

Ho, C.-L.; Lee, C.-C., E-mail: chieh.no27@gmail.com

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

Parameterization of planetary wave breaking in the middle atmosphere

NASA Technical Reports Server (NTRS)

Garcia, Rolando R.

1991-01-01

A parameterization of planetary wave breaking in the middle atmosphere has been developed and tested in a numerical model which includes governing equations for a single wave and the zonal-mean state. The parameterization is based on the assumption that wave breaking represents a steady-state equilibrium between the flux of wave activity and its dissipation by nonlinear processes, and that the latter can be represented as linear damping of the primary wave. With this and the additional assumption that the effect of breaking is to prevent further amplitude growth, the required dissipation rate is readily obtained from the steady-state equation for wave activity; diffusivity coefficients then follow from the dissipation rate. The assumptions made in the derivation are equivalent to those commonly used in parameterizations for gravity wave breaking, but the formulation in terms of wave activity helps highlight the central role of the wave group velocity in determining the dissipation rate. Comparison of model results with nonlinear calculations of wave breaking and with diagnostic determinations of stratospheric diffusion coefficients reveals remarkably good agreement, and suggests that the parameterization could be useful for simulating inexpensively, but realistically, the effects of planetary wave transport.

Optoenergy storage and random walks assisted broadband amplification in Er3+-doped (Pb,La)(Zr,Ti)O3 disordered ceramics.

PubMed

Xu, Long; Zhao, Hua; Xu, Caixia; Zhang, Siqi; Zou, Yingyin K; Zhang, Jingwen

2014-02-01

A broadband optical amplification was observed and investigated in Er3+-doped electrostrictive ceramics of lanthanum-modified lead zirconate titanate under a corona atmosphere. The ceramic structure change caused by UV light, electric field, and random walks originated from the diffusive process in intrinsically disordered materials may all contribute to the optical amplification and the associated energy storage. Discussion based on optical energy storage and diffusive equations was given to explain the findings. Those experiments performed made it possible to study random walks and optical amplification in transparent ceramics materials.

Excitation of the Magnetospheric Cavity

DTIC Science & Technology

2007-06-16

gyrofrequency of 880 kHz at the ground at the equator, and uses a diffusive equilibrium model [ Angerami and Thomas, 1964] to calculate charged particle...significantly damped [Smith and Angerami , 1968; Edgar, 1976; Gurnett and Inan, 1988], resonantly interacting with, and pitch angle scattering...2429, 1999. Angerami , J. J., and J. O. Thomas, Studies of planetary Atmospheres, 1, The distribution of electrons and ions in the Earth’s

The Martian climate and energy balance models with CO2/H2O atmospheres

NASA Technical Reports Server (NTRS)

Hoffert, M. I.

1986-01-01

The analysis begins with a seasonal energy balance model (EBM) for Mars. This is used to compute surface temperature versus x = sin(latitude) and time over the seasonal cycle. The core model also computes the evolving boundaries of the CO2 icecaps, net sublimational/condensation rates, and the resulting seasonal pressure wave. Model results are compared with surface temperature and pressure history data at Viking lander sites, indicating fairly good agreement when meridional heat transport is represented by a thermal diffusion coefficient D approx. 0.015 W/sq. m/K. Condensational wind distributions are also computed. An analytic model of Martian wind circulation is then proposed, as an extension of the EMB, which incorporates vertical wind profiles containing an x-dependent function evaluated by substitution in the equation defining the diffusion coefficient. This leads to a parameterization of D(x) and of the meridional circulation which recovers the high surface winds predicted by dynamic Mars atmosphere models (approx. 10 m/sec). Peak diffusion coefficients, D approx. 0.6 w/sq m/K, are found over strong Hadley zones - some 40 times larger than those of high-latitude baroclinic eddies. When the wind parameterization is used to find streamline patterns over Martian seasons, the resulting picture shows overturning hemispheric Hadley cells crossing the equator during solstices, and attaining peak intensities during the south summer dust storm season, while condensational winds are most important near the polar caps.

Hourly global and diffuse radiation of Lagos, Nigeria-correlation with some atmospheric parameters

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

Chendo, M.A.C.; Maduekwe, A.A.L.

1994-03-01

The influence of four climatic parameters on the hourly diffuse fraction in Lagos, Nigeria, has been studied. Using data for two years, new correlations were established. The standard error of the Liu and Jordan-type equation was reduced by 12.83% when solar elevation, ambient temperature, and relative humidity were used together as predictor variables for the entire data set. Ambient temperature and relative humidity proved to be very important variables for predicting the diffuse fraction of the solar radiation passing through the humid atmosphere of the coastal and tropic city of Lagos. Seasonal analysis carried out with the data showed improvementsmore » on the standard errors for the new seasonal correlations. In the case of the dry season, the improvement was 18.37%, whole for the wet season, this was 12.37%. Comparison with existing correlations showed that the performance of the one parameter model (namely K[sub t]), of Orgill and Hollands and Reindl, Beckman, and Duffie were very different from the Liu and Jordan-type model obtained for Lagos.« less

A new paradigm for predicting zonal-mean climate and climate change

NASA Astrophysics Data System (ADS)

Armour, K.; Roe, G.; Donohoe, A.; Siler, N.; Markle, B. R.; Liu, X.; Feldl, N.; Battisti, D. S.; Frierson, D. M.

2016-12-01

How will the pole-to-equator temperature gradient, or large-scale patterns of precipitation, change under global warming? Answering such questions typically involves numerical simulations with comprehensive general circulation models (GCMs) that represent the complexities of climate forcing, radiative feedbacks, and atmosphere and ocean dynamics. Yet, our understanding of these predictions hinges on our ability to explain them through the lens of simple models and physical theories. Here we present evidence that zonal-mean climate, and its changes, can be understood in terms of a moist energy balance model that represents atmospheric heat transport as a simple diffusion of latent and sensible heat (as a down-gradient transport of moist static energy, with a diffusivity coefficient that is nearly constant with latitude). We show that the theoretical underpinnings of this model derive from the principle of maximum entropy production; that its predictions are empirically supported by atmospheric reanalyses; and that it successfully predicts the behavior of a hierarchy of climate models - from a gray radiation aquaplanet moist GCM, to comprehensive GCMs participating in CMIP5. As an example of the power of this paradigm, we show that, given only patterns of local radiative feedbacks and climate forcing, the moist energy balance model accurately predicts the evolution of zonal-mean temperature and atmospheric heat transport as simulated by the CMIP5 ensemble. These results suggest that, despite all of its dynamical complexity, the atmosphere essentially responds to energy imbalances by simply diffusing latent and sensible heat down-gradient; this principle appears to explain zonal-mean climate and its changes under global warming.

Sucrose diffusion in aqueous solution

PubMed Central

Murray, Benjamin J.

2016-01-01

The diffusion of sugar in aqueous solution is important both in nature and in technological applications, yet measurements of diffusion coefficients at low water content are scarce. We report directly measured sucrose diffusion coefficients in aqueous solution. Our technique utilises a Raman isotope tracer method to monitor the diffusion of non-deuterated and deuterated sucrose across a boundary between the two aqueous solutions. At a water activity of 0.4 (equivalent to 90 wt% sucrose) at room temperature, the diffusion coefficient of sucrose was determined to be approximately four orders of magnitude smaller than that of water in the same material. Using literature viscosity data, we show that, although inappropriate for the prediction of water diffusion, the Stokes–Einstein equation works well for predicting sucrose diffusion under the conditions studied. As well as providing information of importance to the fundamental understanding of diffusion in binary solutions, these data have technological, pharmaceutical and medical implications, for example in cryopreservation. Moreover, in the atmosphere, slow organic diffusion may have important implications for aerosol growth, chemistry and evaporation, where processes may be limited by the inability of a molecule to diffuse between the bulk and the surface of a particle. PMID:27364512

Finite-element numerical modeling of atmospheric turbulent boundary layer

NASA Technical Reports Server (NTRS)

Lee, H. N.; Kao, S. K.

1979-01-01

A dynamic turbulent boundary-layer model in the neutral atmosphere is constructed, using a dynamic turbulent equation of the eddy viscosity coefficient for momentum derived from the relationship among the turbulent dissipation rate, the turbulent kinetic energy and the eddy viscosity coefficient, with aid of the turbulent second-order closure scheme. A finite-element technique was used for the numerical integration. In preliminary results, the behavior of the neutral planetary boundary layer agrees well with the available data and with the existing elaborate turbulent models, using a finite-difference scheme. The proposed dynamic formulation of the eddy viscosity coefficient for momentum is particularly attractive and can provide a viable alternative approach to study atmospheric turbulence, diffusion and air pollution.

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

PubMed

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

Tropical atmospheric circulations with humidity effects.

PubMed

Hsia, Chun-Hsiung; Lin, Chang-Shou; Ma, Tian; Wang, Shouhong

2015-01-08

The main objective of this article is to study the effect of the moisture on the planetary scale atmospheric circulation over the tropics. The modelling we adopt is the Boussinesq equations coupled with a diffusive equation of humidity, and the humidity-dependent heat source is modelled by a linear approximation of the humidity. The rigorous mathematical analysis is carried out using the dynamic transition theory. In particular, we obtain mixed transitions, also known as random transitions, as described in Ma & Wang (2010 Discrete Contin. Dyn. Syst. 26 , 1399-1417. (doi:10.3934/dcds.2010.26.1399); 2011 Adv. Atmos. Sci. 28 , 612-622. (doi:10.1007/s00376-010-9089-0)). The analysis also indicates the need to include turbulent friction terms in the model to obtain correct convection scales for the large-scale tropical atmospheric circulations, leading in particular to the right critical temperature gradient and the length scale for the Walker circulation. In short, the analysis shows that the effect of moisture lowers the magnitude of the critical thermal Rayleigh number and does not change the essential characteristics of dynamical behaviour of the system.

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

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

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

A Unified Theory for the Great Plains Nocturnal Low-Level Jet

NASA Astrophysics Data System (ADS)

Shapiro, A.; Fedorovich, E.; Rahimi, S.

2014-12-01

The nocturnal low-level jet (LLJ) is a warm-season atmospheric boundary layer phenomenon common to the Great Plains of the United States and other places worldwide, typically in regions east of mountain ranges. Low-level jets develop around sunset in fair weather conditions conducive to strong radiational cooling, reach peak intensity in the pre-dawn hours, and then dissipate with the onset of daytime convective mixing. In this study we consider the LLJ as a diurnal oscillation of a stably stratified atmosphere overlying a planar slope on the rotating Earth. The oscillations arise from diurnal cycles in both the heating of the slope (mechanism proposed by Holton in 1967) and the turbulent mixing (mechanism proposed by Blackadar in 1957). The governing equations are the equations of motion, incompressibility condition, and thermal energy in the Boussinesq approximation, with turbulent heat and momentum exchange parameterized through spatially constant but diurnally varying turbulent diffusion coefficients (diffusivities). Analytical solutions are obtained for diffusivities with piecewise constant waveforms (step-changes at sunrise and sunset) and slope temperatures/buoyancies with piecewise linear waveforms (saw-tooth function with minimum at sunrise and maximum before sunset). The jet characteristics are governed by eleven parameters: slope angle, Coriolis parameter, environmental buoyancy frequency, geostrophic wind strength, daytime and nighttime diffusivities, maximum (daytime) and minimum (nighttime) slope buoyancies, duration of daylight, lag time between peak slope buoyancy and sunset, and a Newtonian cooling time scale. An exploration of the parameter space yields results that are broadly consistent with findings particular to the Holton and Blackadar theories, and agree with climatological observations, for example, that stronger jets tend to occur over slopes of 0.15-0.25 degrees characteristic of the Great Plains. The solutions also yield intriguing predictions that peak jet strength increases with attenuation of the minimum surface buoyancy, and that the single most important parameter determining jet height is the nighttime diffusivity, with weaker nightime diffusion associated with smaller jet heights. These and other highlights will be discussed in the presentation.

Numerical simulation of the generation of reactive oxygen and nitrogen species (RONS) in water by atmospheric-pressure plasmas and their effects on Escherichia coli (E. coli)

NASA Astrophysics Data System (ADS)

Ikuse, Kazumasa; Hamaguchi, Satoshi

2016-09-01

We have used two types of numerical simulations to examine biological effects of reactive oxygen and nitrogen species (RONS) generated in water by an atmospheric-pressure plasma (APP) that irradiates the water surface. One is numerical simulation for the generation and transport of RONS in water based on the reaction-diffusion-advection equations coupled with Poisson equation. The rate constants, mobilities, and diffusion coefficients used in the equations are obtained from the literature. The gaseous species are given as boundary conditions and time evolution of the concentrations of chemical species in pure water is solved numerically as functions of the depth in one dimension. Although it is not clear how living organisms respond to such exogenous RONS, we also use numerical simulation for metabolic reactions of Escherichia coli (E. coli) and examine possible effects of such RONS on an in-silico model organism. The computation model is based on the flux balance analysis (FBA), where the fluxes of the metabolites in a biological system are evaluated in steady state, i.e., under the assumption that the fluxes do not change in time. The fluxes are determined with liner programming to maximize the growth rate of the bacteria under the given conditions. Although FBA cannot be directly applied to dynamical responses of metabolic reactions, the simulation still gives insight into the biological reactions to exogenous chemical species generated by an APP. Partially supported by JSPS Grants-in-Aid for Scientific Research.

Quadrupole terms in the Maxwell equations: Debye-Hückel theory in quadrupolarizable solvent and self-salting-out of electrolytes.

PubMed

Slavchov, Radomir I

2014-04-28

If the molecules of a given solvent possess significant quadrupolar moment, the macroscopic Maxwell equations must involve the contribution of the density of the quadrupolar moment to the electric displacement field. This modifies the Poisson-Boltzmann equation and all consequences from it. In this work, the structure of the diffuse atmosphere around an ion dissolved in quadrupolarizable medium is analyzed by solving the quadrupolar variant of the Coulomb-Ampere's law of electrostatics. The results are compared to the classical Debye-Hückel theory. The quadrupolar version of the Debye-Hückel potential of a point charge is finite even in r = 0. The ion-quadrupole interaction yields a significant expansion of the diffuse atmosphere of the ion and, thus, it decreases the Debye-Hückel energy. In addition, since the dielectric permittivity of the electrolyte solutions depends strongly on concentration, the Born energy of the dissolved ions alters with concentration, which has a considerable contribution to the activity coefficient γ± known as the self-salting-out effect. The quadrupolarizability of the medium damps strongly the self-salting-out of the electrolyte, and thus it affects additionally γ±. Comparison with experimental data for γ± for various electrolytes allows for the estimation of the quadrupolar length of water: LQ ≈ 2 Å, in good agreement with previous assessments. The effect of quadrupolarizability is especially important in non-aqueous solutions. Data for the activity of NaBr in methanol is used to determine the quadrupolarizability of methanol with good accuracy.

DREAM3D simulations of inner-belt dynamics

NASA Astrophysics Data System (ADS)

Cunningham, G.

2015-12-01

A 1973 paper by Lyons and Thorne explains the two-belt structure for electrons in the inner magnetosphere as a balance between inward radial diffusion and loss to the atmosphere due to pitch-angle scattering from Coulomb and VLF wave-particle interactions. In this paper, equilibrium solutions to a set of 1D radial diffusion equations, one for each value of the first invariant of motion, μ, were computed to produce the equilibrium structure. Each diffusion equation incorporated an L- and μ-dependent `lifetime' due to the Coulomb and wave-particle interactions. This model is appropriate under the assumption that radial diffusion is slow in comparison to pitch-angle scattering, and that there is no acceleration caused by the VLF wave-particle interactions. We have revisited this model using our DREAM3D 3D diffusion code, which allows the user to explicitly model the diffusion in pitch-angle and momentum rather than using a lifetime. We find that a) replacing the lifetimes with an explicit model of pitch-angle diffusion, thus allowing for coupling between radial and pitch-angle diffusion, affects the equilibrium structure, and b) over the long time scales needed to reach equilibrium, significant acceleration due to VLF wave particle interactions takes place due to the 'cross-terms' in pitch-angle and momentum and the sharp gradient in the equilibrium pitch-angle distributions. We also find that the equilibrium solutions are quite sensitive to various aspects of the physics model employed in the 1973 paper that can be improved, suggesting that additional work needs to be done to fully understand the equilibirum nature of the trapped electron radiation belts.

Investigating Whistler Mode Wave Diffusion Coefficients at Mars

NASA Astrophysics Data System (ADS)

Shane, A. D.; Liemohn, M. W.; Xu, S.; Florie, C.

2017-12-01

Observations of electron pitch angle distributions have suggested collisions are not the only pitch angle scattering process occurring in the Martian ionosphere. This unknown scattering process is causing high energy electrons (>100 eV) to become isotropized. Whistler mode waves are one pitch angle scattering mechanism known to preferentially scatter high energy electrons in certain plasma regimes. The distribution of whistler mode wave diffusion coefficients are dependent on the background magnetic field strength and thermal electron density, as well as the frequency and wave normal angle of the wave. We have solved for the whistler mode wave diffusion coefficients using the quasi-linear diffusion equations and have integrated them into a superthermal electron transport (STET) model. Preliminary runs have produced results that qualitatively match the observed electron pitch angle distributions at Mars. We performed parametric sweeps over magnetic field, thermal electron density, wave frequency, and wave normal angle to understand the relationship between the plasma parameters and the diffusion coefficient distributions, but also to investigate what regimes whistler mode waves scatter only high energy electrons. Increasing the magnetic field strength and lowering the thermal electron density shifts the distribution of diffusion coefficients toward higher energies and lower pitch angles. We have created an algorithm to identify Mars Atmosphere Volatile and EvolutioN (MAVEN) observations of high energy isotropic pitch angle distributions in the Martian ionosphere. We are able to map these distributions at Mars, and compare the conditions under which these are observed at Mars with the results of our parametric sweeps. Lastly, we will also look at each term in the kinetic diffusion equation to determine if the energy and mixed diffusion coefficients are important enough to incorporate into STET as well.

Cellular Automata for Spatiotemporal Pattern Formation from Reaction-Diffusion Partial Differential Equations

NASA Astrophysics Data System (ADS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.

Hypervelocity atmospheric flight: Real gas flow fields

NASA Technical Reports Server (NTRS)

Howe, John T.

1990-01-01

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that were reduced to a relatively compact set of equations of a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-averaged behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equation a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. For hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates, chemical nonequilibrium is considered and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

Hypervelocity atmospheric flight: Real gas flow fields

NASA Technical Reports Server (NTRS)

Howe, John T.

1989-01-01

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that have been reduced to a relatively compact set of equations in a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-average behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equations a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. Hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates chemical nonequilibrium is considered, and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

Hadley cell dynamics of a cold and virtually dry Snowball Earth atmosphere

NASA Astrophysics Data System (ADS)

Voigt, Aiko; Held, Isaac; Marotzke, Jochem

2010-05-01

We use the full-physics atmospheric general circulation model ECHAM5 to investigate a cold and virtually dry Snowball Earth atmosphere that results from specifying sea ice as the surface boundary condition everywhere, corresponding to a frozen aquaplanet, while keeping total solar irradiance at its present-day value of 1365 Wm-2. The aim of this study is the investigation of the zonal-mean circulation of a Snowball Earth atmosphere, which, due to missing moisture, might constitute an ideal though yet unexplored testbed for theories of atmospheric dynamics. To ease comparison with theories, incoming solar insolation follows permanent equinox conditions with disabled diurnal cycle. The meridional circulation consists of a thermally direct cell extending from the equator to 45 N/S with ascent in the equatorial region, and a weak thermally indirect cell with descent between 45 and 65 N/S and ascent in the polar region. The former cell corresponds to the present-day Earth's Hadley cell, while the latter can be viewed as an eddy-driven Ferrell cell; the present-day Earth's direct polar cell is missing. The Hadley cell itself is subdivided into a vigorous cell confined to the troposphere and a weak deep cell reaching well into the stratosphere. The dynamics of the vigorous Snowball Earth Hadley cell differ substantially from the dynamics of the present-day Hadley cell. The zonal momentum balance shows that in the poleward branch of the vigorous Hadley cell, mean flow meridional advection of absolute vorticity is not only balanced by eddy momentum flux convergence but also by vertical diffusion. Inside the poleward branch, eddies are more important in the upper part and vertical diffusion is more important in the lower part. Vertical diffusion also contributes to the meridional momentum balance as it decelerates the vigorous Hadley cell by downgradient momentum mixing between its poleward and equatorward branch. Zonal winds, therefore, are not in thermal wind balance in the vigorous Hadley cell. Suppressing vertical momentum diffusion above 870 hPa results in a doubling of the vigorous Hadley cell strength. Simulations where we only suppress either vertical diffusion of zonal or meridional momentum show that this doubling can be understood from the decelerating effect of vertical diffusion in the meridional momentum balance. Comparing our simulations with theories, we conclude that neither the axisymmetric Hadley cell model of Held & Hou (1980) nor the eddy-permitting model of T. Schneider et al. (2005, 2006, 2008) are applicable to a Snowball Earth atmosphere since both assume an inviscid upper Hadley cell branch.

Transformed Fourier and Fick equations for the control of heat and mass diffusion

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

Guenneau, S.; Petiteau, D.; Zerrad, M.

We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves,more » the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.« less

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.

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

Some Properties of the Fractional Equation of Continuity and the Fractional Diffusion Equation

NASA Astrophysics Data System (ADS)

Fukunaga, Masataka

2006-05-01

The fractional equation of continuity (FEC) and the fractional diffusion equation (FDE) show peculiar behaviors that are in the opposite sense to those expected from the equation of continuity and the diffusion equation, respectively. The behaviors are interpreted in terms of the memory effect of the fractional time derivatives included in the equations. Some examples are given by solutions of the FDE.

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

DIFFUSE AURORA ON GANYMEDE DRIVEN BY ELECTROSTATIC WAVES

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

Singhal, R. P.; Tripathi, A. K.; Halder, S.

The role of electrostatic electron cyclotron harmonic (ECH) waves in producing diffuse auroral emission O i 1356 Å on Ganymede is investigated. Electron precipitation flux entering the atmosphere of Ganymede due to pitch-angle diffusion by ECH waves into the atmospheric loss-cone is calculated. The analytical yield spectrum approach for electron energy degradation in gases is used for calculating diffuse auroral intensities. It is found that calculated O i 1356 Å intensity resulting from the precipitation of magnetospheric electrons observed near Ganymede is insufficient to account for the observed diffuse auroral intensity. This is in agreement with estimates made in earliermore » works. Heating and acceleration of ambient electrons by ECH wave turbulence near the magnetic equator on the field line connecting Ganymede and Jupiter are considered. Two electron distribution functions are used to simulate the heating effect by ECH waves. Use of a Maxwellian distribution with temperature 100 eV can produce about 50–70 Rayleigh O i 1356 Å intensities, and the kappa distribution with characteristic energy 50 eV also gives rise to intensities with similar magnitude. Numerical experiments are performed to study the effect of ECH wave spectral intensity profile, ECH wave amplitude, and temperature/characteristic energy of electron distribution functions on the calculated diffuse auroral intensities. The proposed missions, joint NASA/ESA Jupiter Icy Moon Explorer and the present JUNO mission to Jupiter, would provide new data to constrain the ECH wave and other physical parameters near Ganymede. These should help confirm the findings of the present study.« less

Mesoscale atmospheric modeling for emergency response

NASA Astrophysics Data System (ADS)

Osteen, B. L.; Fast, J. D.

Atmospheric transport models for emergency response have traditionally utilized meteorological fields interpolated from sparse data to predict contaminant transport. Often these fields are adjusted to satisfy constraints derived from the governing equations of geophysical fluid dynamics, e.g. mass continuity. Gaussian concentration distributions or stochastic models are then used to represent turbulent diffusion of a contaminant in the diagnosed meteorological fields. The popularity of these models derives from their relative simplicity, ability to make reasonable short-term predictions, and, most important, execution speed. The ability to generate a transport prediction for an accidental release from the Savannah River Site in a time frame which will allow protective action to be taken is essential in an emergency response operation.

Diffusion Coefficients from Molecular Dynamics Simulations in Binary and Ternary Mixtures

NASA Astrophysics Data System (ADS)

Liu, Xin; Schnell, Sondre K.; Simon, Jean-Marc; Krüger, Peter; Bedeaux, Dick; Kjelstrup, Signe; Bardow, André; Vlugt, Thijs J. H.

2013-07-01

Multicomponent diffusion in liquids is ubiquitous in (bio)chemical processes. It has gained considerable and increasing interest as it is often the rate limiting step in a process. In this paper, we review methods for calculating diffusion coefficients from molecular simulation and predictive engineering models. The main achievements of our research during the past years can be summarized as follows: (1) we introduced a consistent method for computing Fick diffusion coefficients using equilibrium molecular dynamics simulations; (2) we developed a multicomponent Darken equation for the description of the concentration dependence of Maxwell-Stefan diffusivities. In the case of infinite dilution, the multicomponent Darken equation provides an expression for [InlineEquation not available: see fulltext.] which can be used to parametrize the generalized Vignes equation; and (3) a predictive model for self-diffusivities was proposed for the parametrization of the multicomponent Darken equation. This equation accurately describes the concentration dependence of self-diffusivities in weakly associating systems. With these methods, a sound framework for the prediction of mutual diffusion in liquids is achieved.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Instability of turing patterns in reaction-diffusion-ODE systems.

PubMed

Marciniak-Czochra, Anna; Karch, Grzegorz; Suzuki, Kanako

2017-02-01

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

Effects of pressure and fuel dilution on coflow laminar methane-air diffusion flames: A computational and experimental study

NASA Astrophysics Data System (ADS)

Cao, Su; Ma, Bin; Giassi, Davide; Bennett, Beth Anne V.; Long, Marshall B.; Smooke, Mitchell D.

2018-03-01

In this study, the influence of pressure and fuel dilution on the structure and geometry of coflow laminar methane-air diffusion flames is examined. A series of methane-fuelled, nitrogen-diluted flames has been investigated both computationally and experimentally, with pressure ranging from 1.0 to 2.7 atm and CH4 mole fraction ranging from 0.50 to 0.65. Computationally, the MC-Smooth vorticity-velocity formulation was employed to describe the reactive gaseous mixture, and soot evolution was modelled by sectional aerosol equations. The governing equations and boundary conditions were discretised on a two-dimensional computational domain by finite differences, and the resulting set of fully coupled, strongly nonlinear equations was solved simultaneously at all points using a damped, modified Newton's method. Experimentally, chemiluminescence measurements of CH* were taken to determine its relative concentration profile and the structure of the flame front. A thin-filament ratio pyrometry method using a colour digital camera was employed to determine the temperature profiles of the non-sooty, atmospheric pressure flames, while soot volume fraction was quantified, after evaluation of soot temperature, through an absolute light calibration using a thermocouple. For a broad spectrum of flames in atmospheric and elevated pressures, the computed and measured flame quantities were examined to characterise the influence of pressure and fuel dilution, and the major conclusions were as follows: (1) maximum temperature increases with increasing pressure or CH4 concentration; (2) lift-off height decreases significantly with increasing pressure, modified flame length is roughly independent of pressure, and flame radius decreases with pressure approximately as P-1/2; and (3) pressure and fuel stream dilution significantly affect the spatial distribution and the peak value of the soot volume fraction.

Diurnal forcing of planetary atmospheres

NASA Technical Reports Server (NTRS)

Houben, Howard C.

1991-01-01

A free convection parameterization has been introduced into the Mars Planetary Boundary Layer Model (MPBL). Previously, the model would fail to generate turbulence under conditions of zero wind shear, even when statically unstable. This in turn resulted in erroneous results at the equator, for example, when the lack of Coriolis forcing allowed zero wind conditions. The underlying cause of these failures was the level 2 second-order turbulence closure scheme which derived diffusivities as algebraic functions of the Richardson number (the ratio of static stability to wind shear). In the previous formulation, the diffusivities were scaled by the wind shear--a convenient parameter since it is non-negative. This was the drawback that all diffusivities are zero under conditions of zero shear (viz., the free convection case). The new scheme tests for the condition of zero shear in conjunction with static instability and recalculates the diffusivities using a static stability scaling. The results for a simulation of the equatorial boundary layer at autumnal equinox are presented. (Note that after some wind shear is generated, the model reverts to the traditional diffusivity calculation.)

Experimental studies and model analysis of noble gas fractionation in low-permeability porous media

NASA Astrophysics Data System (ADS)

Ding, Xin; Mack Kennedy, B.; Molins, Sergi; Kneafsey, Timothy; Evans, William C.

2017-05-01

Gas flow through the vadose zone from sources at depth involves fractionation effects that can obscure the nature of transport and even the identity of the source. Transport processes are particularly complex in low permeability media but as shown in this study, can be elucidated by measuring the atmospheric noble gases. A series of laboratory column experiments was conducted to evaluate the movement of noble gas from the atmosphere into soil in the presence of a net efflux of CO2, a process that leads to fractionation of the noble gases from their atmospheric abundance ratios. The column packings were designed to simulate natural sedimentary deposition by interlayering low permeability ceramic plates and high permeability beach sand. Gas samples were collected at different depths at CO2 fluxes high enough to cause extreme fractionation of the noble gases (4He/36Ar > 20 times the air ratio). The experimental noble gas fractionation-depth profiles were in good agreement with those predicted by the dusty gas (DG) model, demonstrating the applicability of the DG model across a broad spectrum of environmental conditions. A governing equation based on the dusty gas model was developed to specifically describe noble gas fractionation at each depth that is controlled by the binary diffusion coefficient, Knudsen diffusion coefficient and the ratio of total advection flux to total flux. Finally, the governing equation was used to derive the noble gas fractionation pattern and illustrate how it is influenced by soil CO2 flux, sedimentary sequence, thickness of each sedimentary layer and each layer's physical parameters. Three potential applications of noble gas fractionation are provided: evaluating soil attributes in the path of gas flow from a source at depth to the atmosphere, testing leakage through low permeability barriers used to isolate buried waste, and tracking biological methanogenesis and methane oxidation associated with hydrocarbon degradation.

Background-Error Correlation Model Based on the Implicit Solution of a Diffusion Equation

DTIC Science & Technology

2010-01-01

1 Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation Matthew J. Carrier* and Hans Ngodock...4. TITLE AND SUBTITLE Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation 5a. CONTRACT NUMBER 5b. GRANT...2001), which sought to model error correlations based on the explicit solution of a generalized diffusion equation. The implicit solution is

Causes of plasma column contraction in surface-wave-driven discharges in argon at atmospheric pressure

NASA Astrophysics Data System (ADS)

Ridenti, Marco Antonio; de Amorim, Jayr; Dal Pino, Arnaldo; Guerra, Vasco; Petrov, George

2018-01-01

In this work we compute the main features of a surface-wave-driven plasma in argon at atmospheric pressure in view of a better understanding of the contraction phenomenon. We include the detailed chemical kinetics dynamics of Ar and solve the mass conservation equations of the relevant neutral excited and charged species. The gas temperature radial profile is calculated by means of the thermal diffusion equation. The electric field radial profile is calculated directly from the numerical solution of the Maxwell equations assuming the surface wave to be propagating in the TM00 mode. The problem is considered to be radially symmetrical, the axial variations are neglected, and the equations are solved in a self-consistent fashion. We probe the model results considering three scenarios: (i) the electron energy distribution function (EEDF) is calculated by means of the Boltzmann equation; (ii) the EEDF is considered to be Maxwellian; (iii) the dissociative recombination is excluded from the chemical kinetics dynamics, but the nonequilibrium EEDF is preserved. From this analysis, the dissociative recombination is shown to be the leading mechanism in the constriction of surface-wave plasmas. The results are compared with mass spectrometry measurements of the radial density profile of the ions Ar+ and Ar2+. An explanation is proposed for the trends seen by Thomson scattering diagnostics that shows a substantial increase of electron temperature towards the plasma borders where the electron density is small.

Numerical evaluation of static-chamber measurements of soil-atmospheric gas exchange--Identification of physical processes

USGS Publications Warehouse

Healy, Richard W.; Striegl, Robert G.; Russell, Thomas F.; Hutchinson, Gordon L.; Livingston, Gerald P.

1996-01-01

The exchange of gases between soil and atmosphere is an important process that affects atmospheric chemistry and therefore climate. The static-chamber method is the most commonly used technique for estimating the rate of that exchange. We examined the method under hypothetical field conditions where diffusion was the only mechanism for gas transport and the atmosphere outside the chamber was maintained at a fixed concentration. Analytical and numerical solutions to the soil gas diffusion equation in one and three dimensions demonstrated that gas flux density to a static chamber deployed on the soil surface was less in magnitude than the ambient exchange rate in the absence of the chamber. This discrepancy, which increased with chamber deployment time and air-filled porosity of soil, is attributed to two physical factors: distortion of the soil gas concentration gradient (the magnitude was decreased in the vertical component and increased in the radial component) and the slow transport rate of diffusion relative to mixing within the chamber. Instantaneous flux density to a chamber decreased continuously with time; steepest decreases occurred so quickly following deployment and in response to such slight changes in mean chamber headspace concentration that they would likely go undetected by most field procedures. Adverse influences of these factors were reduced by mixing the chamber headspace, minimizing deployment time, maximizing the height and radius of the chamber, and pushing the rim of the chamber into the soil. Nonlinear models were superior to a linear regression model for estimating flux densities from mean headspace concentrations, suggesting that linearity of headspace concentration with time was not necessarily a good indicator of measurement accuracy.

Snow Micro-Structure Model

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

Micah Johnson, Andrew Slaughter

PIKA is a MOOSE-based application for modeling micro-structure evolution of seasonal snow. The model will be useful for environmental, atmospheric, and climate scientists. Possible applications include application to energy balance models, ice sheet modeling, and avalanche forecasting. The model implements physics from published, peer-reviewed articles. The main purpose is to foster university and laboratory collaboration to build a larger multi-scale snow model using MOOSE. The main feature of the code is that it is implemented using the MOOSE framework, thus making features such as multiphysics coupling, adaptive mesh refinement, and parallel scalability native to the application. PIKA implements three equations:more » the phase-field equation for tracking the evolution of the ice-air interface within seasonal snow at the grain-scale; the heat equation for computing the temperature of both the ice and air within the snow; and the mass transport equation for monitoring the diffusion of water vapor in the pore space of the snow.« less

Diffusion of Charged Species in Liquids

NASA Astrophysics Data System (ADS)

Del Río, J. A.; Whitaker, S.

2016-11-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids.

PubMed

Del Río, J A; Whitaker, S

2016-11-04

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids

PubMed Central

del Río, J. A.; Whitaker, S.

2016-01-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases. PMID:27811959

GCM simulations of cold dry Snowball Earth atmospheres

NASA Astrophysics Data System (ADS)

Voigt, A.; Held, I.; Marotzke, J.

2009-12-01

We use the full-physics atmospheric general circulation model ECHAM5 to investigate cold and virtually dry Snowball Earth atmospheres. These result from specifying sea ice as the surface boundary condition everywhere, corresponding to a frozen aquaplanet, while keeping total solar irradiance at its present-day value of 1365 Wm-2 and setting atmospheric carbon dioxide to 300 ppmv. Here, we present four simulations corresponding to the four possible combinations of enabled or disabled diurnal and seasonal cycles. The aim of this study is twofold. First, we focus on the zonal-mean circulation of Snowball Earth atmospheres, which, due to missing moisture, might constitute an ideal though yet unexplored testbed for theories of atmospheric dynamics. Second, we investigate tropical surface temperatures with an emphasis on the impact of the diurnal and seasonal cycles. This will indicate whether the presence of the diurnal or seasonal cycle would facilitate or anticipate the escape from Snowball Earth conditions when total solar irradiance or atmospheric CO2 levels were increased. The dynamics of the tropical circulation in Snowball Earth atmospheres differs substantially from that in the modern atmosphere. The analysis of the mean zonal momentum budget reveals that the mean flow meridional advection of absolute vorticity is primarily balanced by vertical diffusion of zonal momentum. The contribution of eddies is found to be even smaller than the contribution of mean flow vertical advection of zonal momentum, the latter being usually neglected in theories for the Hadley circulation, at least in its upper tropospheric branch. Suppressing vertical diffusion of horizontal momentum above 850 hPa leads to a stronger Hadley circulation. This behaviour cannot be understood from axisymmetric models of the atmosphere, nor idealized atmospheric general circulation models, which both predict a weakening of the Hadley circulation when the vertical viscosity is decreased globally. We find that enabling the diurnal cycle does not change tropical annual-mean surface temperatures but significantly strengthens the Hadley circulation, which increases by 33% for equinoctial and by 50% during solstitial insolation conditions compared to simulations without diurnal cycle. Including the seasonal cycle results in a ''reversed'' annual-mean Hadley circulation with subsiding motion at the equator and ascending motion around 15N/S, a manifestation of the extreme seasonality of Snowball Earth atmospheres due to the low thermal inertia of the sea-ice surface. The impact of the seasonal cycle on the tropical annual-mean surface is a straightforward consequence of changes in insolation distribution: as annual-mean incoming shortwave radiation at the equator reduces by 18 Wm-2 for enabled seasonal cycle, tropical annual-mean surface temperatures decrease from 221 K to 217 K.

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

Computational Aerothermodynamics in Aeroassist Applications

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2001-01-01

Aeroassisted planetary entry uses atmospheric drag to decelerate spacecraft from super-orbital to orbital or suborbital velocities. Numerical simulation of flow fields surrounding these spacecraft during hypersonic atmospheric entry is required to define aerothermal loads. The severe compression in the shock layer in front of the vehicle and subsequent, rapid expansion into the wake are characterized by high temperature, thermo-chemical nonequilibrium processes. Implicit algorithms required for efficient, stable computation of the governing equations involving disparate time scales of convection, diffusion, chemical reactions, and thermal relaxation are discussed. Robust point-implicit strategies are utilized in the initialization phase; less robust but more efficient line-implicit strategies are applied in the endgame. Applications to ballutes (balloon-like decelerators) in the atmospheres of Venus, Mars, Titan, Saturn, and Neptune and a Mars Sample Return Orbiter (MSRO) are featured. Examples are discussed where time-accurate simulation is required to achieve a steady-state solution.

Prediction of stream volatilization coefficients

USGS Publications Warehouse

Rathbun, Ronald E.

1990-01-01

Equations are developed for predicting the liquid-film and gas-film reference-substance parameters for quantifying volatilization of organic solutes from streams. Molecular weight and molecular-diffusion coefficients of the solute are used as correlating parameters. Equations for predicting molecular-diffusion coefficients of organic solutes in water and air are developed, with molecular weight and molal volume as parameters. Mean absolute errors of prediction for diffusion coefficients in water are 9.97% for the molecular-weight equation, 6.45% for the molal-volume equation. The mean absolute error for the diffusion coefficient in air is 5.79% for the molal-volume equation. Molecular weight is not a satisfactory correlating parameter for diffusion in air because two equations are necessary to describe the values in the data set. The best predictive equation for the liquid-film reference-substance parameter has a mean absolute error of 5.74%, with molal volume as the correlating parameter. The best equation for the gas-film parameter has a mean absolute error of 7.80%, with molecular weight as the correlating parameter.

Causal Diffusion and the Survival of Charge Fluctuations

NASA Astrophysics Data System (ADS)

Abdel-Aziz, Mohamed; Gavin, Sean

2004-10-01

Diffusion may obliterate fluctuation signals of the QCD phase transition in nuclear collisions at SPS and RHIC energies. We propose a hyperbolic diffusion equation to study the dissipation of net charge fluctuations [1]. This equation is needed in a relativistic context, because the classic parabolic diffusion equation violates causality. We find that causality substantially limits the extent to which diffusion can dissipate these fluctuations. [1] M. Abdel-Aziz and S. Gavin, nucl-th/0404058

Improvement of a device for detection and characterization of certain atmospheric pollutants. Final report. Perfectionnement d'un appareillage de detection et de caracterisation de certains pollutants atmospheriques

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

Tesseyre, Y.

The study allowed development of an original measuring system for mobility, involving simultaneously a repulsive electrical field and a continuous gas flow. It made it possible to define a model to calculate ionic transparency of grates, taking into account electrical fields below and above them, ion mobility, speed of gas flow and geometric transparency. Calculation of the electrical field proceeded in a plane-plane system, taking into account the space load and diffusion; a graphic method was developed to determine the field, thus avoiding numerical integration of the diffusion equation. The tracings of the mobility spectra obtained in different gases mademore » it possible to determine characteristic discrete mobility values comparable to those observed by other more sophisticated systems for measuring mobilities, such as the flight time systems. Detection of pollutants in weak concentration in dry air was shown. However, the presence of water vapor in the air forms agglomerates around the ions formed, reducing resolution of the system and making it less applicable under normal atmospheric conditions.« less

Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane

NASA Astrophysics Data System (ADS)

Hu, Wenjie; Duan, Yueliang

2018-04-01

We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.

FRACTIONAL PEARSON DIFFUSIONS.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-07-15

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.

A nonlinear equation for ionic diffusion in a strong binary electrolyte

PubMed Central

Ghosal, Sandip; Chen, Zhen

2010-01-01

The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176

An Ab Initio and Kinetic Monte Carlo Simulation Study of Lithium Ion Diffusion on Graphene

PubMed Central

Zhong, Kehua; Yang, Yanmin; Xu, Guigui; Zhang, Jian-Min; Huang, Zhigao

2017-01-01

The Li+ diffusion coefficients in Li+-adsorbed graphene systems were determined by combining first-principle calculations based on density functional theory with Kinetic Monte Carlo simulations. The calculated results indicate that the interactions between Li ions have a very important influence on lithium diffusion. Based on energy barriers directly obtained from first-principle calculations for single-Li+ and two-Li+ adsorbed systems, a new equation predicting energy barriers with more than two Li ions was deduced. Furthermore, it is found that the temperature dependence of Li+ diffusion coefficients fits well to the Arrhenius equation, rather than meeting the equation from electrochemical impedance spectroscopy applied to estimate experimental diffusion coefficients. Moreover, the calculated results also reveal that Li+ concentration dependence of diffusion coefficients roughly fits to the equation from electrochemical impedance spectroscopy in a low concentration region; however, it seriously deviates from the equation in a high concentration region. So, the equation from electrochemical impedance spectroscopy technique could not be simply used to estimate the Li+ diffusion coefficient for all Li+-adsorbed graphene systems with various Li+ concentrations. Our work suggests that interactions between Li ions, and among Li ion and host atoms will influence the Li+ diffusion, which determines that the Li+ intercalation dependence of Li+ diffusion coefficient should be changed and complex. PMID:28773122

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Radiative transfer calculated from a Markov chain formalism

NASA Technical Reports Server (NTRS)

Esposito, L. W.; House, L. L.

1978-01-01

The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

Effects of curved midline and varying width on the description of the effective diffusivity of Brownian particles

NASA Astrophysics Data System (ADS)

Chávez, Yoshua; Chacón-Acosta, Guillermo; Dagdug, Leonardo

2018-05-01

Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick–Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet–Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick–Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.

A local heat transfer analysis of lava cooling in the atmosphere: application to thermal diffusion-dominated lava flows

NASA Astrophysics Data System (ADS)

Neri, Augusto

1998-05-01

The local cooling process of thermal diffusion-dominated lava flows in the atmosphere was studied by a transient, one-dimensional heat transfer model taking into account the most relevant processes governing its behavior. Thermal diffusion-dominated lava flows include any type of flow in which the conductive-diffusive contribution in the energy equation largely overcomes the convective terms. This type of condition is supposed to be satisfied, during more or less extended periods of time, for a wide range of lava flows characterized by very low flow-rates, such as slabby and toothpaste pahoehoe, spongy pahoehoe, flow at the transition pahoehoe-aa, and flows from ephemeral vents. The analysis can be useful for the understanding of the effect of crust formation on the thermal insulation of the lava interior and, if integrated with adequate flow models, for the explanation of local features and morphologies of lava flows. The study is particularly aimed at a better knowledge of the complex non-linear heat transfer mechanisms that control lava cooling in the atmosphere and at the estimation of the most important parameters affecting the global heat transfer coefficient during the solidification process. The three fundamental heat transfer mechanisms with the atmosphere, that is radiation, natural convection, and forced convection by the wind, were modeled, whereas conduction and heat generation due to crystallization were considered within the lava. The magma was represented as a vesiculated binary melt with a given liquidus and solidus temperature and with the possible presence of a eutectic. The effects of different morphological features of the surface were investigated through a simplified description of their geometry. Model results allow both study of the formation in time of the crust and the thermal mushy layer underlying it, and a description of the behavior of the temperature distribution inside the lava as well as radiative and convective fluxes to the atmosphere. The analysis, performed by using parameters typical of Etnean lavas, particularly focuses on the non-intuitive relations between superficial cooling effects and inner temperature distribution as a function of the major variables involved in the cooling process. Results integrate recent modelings and measurements of the cooling process of Hawaiian pahoehoe flow lobes by Hon et al. (1994) and Keszthelyi and Denlinger (1996) and highlight the critical role played by surface morphology, lava thermal properties, and crystallization dynamics. Furthermore, the reported description of the various heat fluxes between lava and atmosphere can be extended to any other type of lava flows in which atmospheric cooling is involved.

A simulation of the atmospheric cloud physics laboratory to aid in its design and the design of the experiments within the laboratory

NASA Technical Reports Server (NTRS)

Winchester, L. W., Jr.

1980-01-01

Using the finite difference method with overrelaxation, numerical solutions of the steady-state vorticity transport equation were obtained for a continuous flow diffusion chamber of the Hudson-Squires type. The calculation neglected the effects due to temperature, gravity, and saturation. The size and shape of the manifold used to inject the aerosol laden flow were varied to obtain a design which would improve the performance of the chamber from strictly low Reynolds number (less than 20) fluid dynamical considerations.

An atmospheric pressure flow reactor: Gas phase kinetics and mechanism in tropospheric conditions without wall effects

NASA Technical Reports Server (NTRS)

Koontz, Steven L.; Davis, Dennis D.; Hansen, Merrill

1988-01-01

A new type of gas phase flow reactor, designed to permit the study of gas phase reactions near 1 atm of pressure, is described. A general solution to the flow/diffusion/reaction equations describing reactor performance under pseudo-first-order kinetic conditions is presented along with a discussion of critical reactor parameters and reactor limitations. The results of numerical simulations of the reactions of ozone with monomethylhydrazine and hydrazine are discussed, and performance data from a prototype flow reactor are presented.

General PFG signal attenuation expressions for anisotropic anomalous diffusion by modified-Bloch equations

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-05-01

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) anomalous diffusion is complicated, especially in the anisotropic case where limited research has been reported. A general PFG signal attenuation expression, including the finite gradient pulse (FGPW) effect for free general anisotropic fractional diffusion { 0 < α , β ≤ 2 } based on the fractional derivative, has not been obtained, where α and β are time and space derivative orders. It is essential to derive a general PFG signal attenuation expression including the FGPW effect for PFG anisotropic anomalous diffusion research. In this paper, two recently developed modified-Bloch equations, the fractal differential modified-Bloch equation and the fractional integral modified-Bloch equation, were extended to obtain general PFG signal attenuation expressions for anisotropic anomalous diffusion. Various cases of PFG anisotropic anomalous diffusion were investigated, including coupled and uncoupled anisotropic anomalous diffusion. The continuous-time random walk (CTRW) simulation was also carried out to support the theoretical results. The theory and the CTRW simulation agree with each other. The obtained signal attenuation expressions and the three-dimensional fractional modified-Bloch equations are important for analyzing PFG anisotropic anomalous diffusion in NMR and MRI.

A parallel algorithm for nonlinear convection-diffusion equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1990-01-01

A parallel algorithm for the efficient solution of nonlinear time-dependent convection-diffusion equations with small parameter on the diffusion term is presented. The method is based on a physically motivated domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. The method is suitable for the solution of problems arising in the simulation of fluid dynamics. Experimental results for a nonlinear equation in two-dimensions are presented.

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights

NASA Astrophysics Data System (ADS)

Chechkin, A. V.; Gonchar, V. Yu.; Gorenflo, R.; Korabel, N.; Sokolov, I. M.

2008-08-01

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order. Such equations were introduced in A. V. Chechkin, R. Gorenflo, and I. Sokolov [Phys. Rev. E 66, 046129 (2002)] for the description of the processes getting more anomalous in the course of time (decelerating subdiffusion and accelerating superdiffusion). Here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time, which we call, respectively, accelerating subdiffusion and decelerating superdiffusion. For the former process, by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time. For the latter process we demonstrate by a particular example how the power-law truncated Lévy stable distribution evolves in time to the distribution with power-law asymptotics and Gaussian shape in the central part. The special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics.

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

Heavy-tailed fractional Pearson diffusions.

PubMed

Leonenko, N N; Papić, I; Sikorskii, A; Šuvak, N

2017-11-01

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.

Feynman-Kac equations for reaction and diffusion processes

NASA Astrophysics Data System (ADS)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Ezz-Eldien, Samer S.

2013-10-01

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

The exit-time problem for a Markov jump process

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

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

NASA Astrophysics Data System (ADS)

Frank, T. D.

2008-02-01

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

A Three-Wave Model of the Stratosphere with Coupled Dynamics, Radiation and Photochemistry. Appendix M

NASA Technical Reports Server (NTRS)

Shia, Run-Lie; Zhou, Shuntai; Ko, Malcolm K. W.; Sze, Nien-Dak; Salstein, David; Cady-Pereira, Karen

1997-01-01

A zonal mean chemistry transport model (2-D CTM) coupled with a semi-spectral dynamical model is used to simulate the distributions of trace gases in the present day atmosphere. The zonal-mean and eddy equations for the velocity and the geopotential height are solved in the semi-spectral dynamical model. The residual mean circulation is derived from these dynamical variables and used to advect the chemical species in the 2- D CTM. Based on a linearized wave transport equation, the eddy diffusion coefficients for chemical tracers are expressed in terms of the amplitude, frequency and growth rate of dynamical waves; local chemical loss rates; and a time constant parameterizing small scale mixing. The contributions to eddy flux are from the time varying wave amplitude (transient eddy), chemical reactions (chemical eddy) and small scale mixing. In spite of the high truncation in the dynamical module (only three longest waves are resolved), the model has simulated many observed characteristics of stratospheric dynamics and distribution of chemical species including ozone. Compared with the values commonly used in 2-D CTMs, the eddy diffusion coefficients for chemical species calculated in this model are smaller, especially in the subtropics. It is also found that the chemical eddy diffusion has only a small effects in determining the distribution of most slow species, including ozone in the stratosphere.

Diffusion Influenced Adsorption Kinetics.

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.

Analytical solutions of the space-time fractional Telegraph and advection-diffusion equations

NASA Astrophysics Data System (ADS)

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

2018-02-01

The aim of this paper is to develop a fractional derivative model of energetic particle transport for both uniform and non-uniform large-scale magnetic field by studying the fractional Telegraph equation and the fractional advection-diffusion equation. Analytical solutions of the space-time fractional Telegraph equation and space-time fractional advection-diffusion equation are obtained by use of the Caputo fractional derivative and the Laplace-Fourier technique. The solutions are given in terms of Fox's H function. As an illustration they are applied to the case of solar energetic particles.

Some New Lidar Equations for Laser Pulses Scattered Back from Optically Thick Media Such as Clouds, Dense Aerosol Plumes, Sea Ice, Snow, and Turbid Coastal Waters

NASA Technical Reports Server (NTRS)

Davis, Anthony B.

2013-01-01

I survey the theoretical foundations of the slowly-but-surely emerging field of multiple scattering lidar, which has already found applications in atmospheric and cryospheric optics that I also discuss. In multiple scattering lidar, returned pulses are stretched far beyond recognition, and there is no longer a one-to-one connection between range and return-trip timing. Moreover, one can exploit the radial profile of the diffuse radiance field excited by the laser source that, by its very nature, is highly concentrated in space and collimated in direction. One needs, however, a new class of lidar equations to explore this new phenomenology. A very useful set is derived from radiative diffusion theory, which is found at the opposite asymptotic limit of radiative transfer theory than the conventional (single-scattering) limit used to derive the standard lidar equation. In particular, one can use it to show that, even if the simple time-of-flight-to-range connection is irretrievably lost, multiply-scattered lidar light can be used to restore a unique profiling capability with coarser resolution but much deeper penetration into a wide variety of optical thick media in nature. Several new applications are proposed, including a laser bathymetry technique that should work for highly turbid coastal waters.

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations

NASA Astrophysics Data System (ADS)

Lin, Zeng; Wang, Dongdong

2017-10-01

Due to the nonlocal property of the fractional derivative, the finite element analysis of fractional diffusion equation often leads to a dense and non-symmetric stiffness matrix, in contrast to the conventional finite element formulation with a particularly desirable symmetric and banded stiffness matrix structure for the typical diffusion equation. This work first proposes a finite element formulation that preserves the symmetry and banded stiffness matrix characteristics for the fractional diffusion equation. The key point of the proposed formulation is the symmetric weak form construction through introducing a fractional weight function. It turns out that the stiffness part of the present formulation is identical to its counterpart of the finite element method for the conventional diffusion equation and thus the stiffness matrix formulation becomes trivial. Meanwhile, the fractional derivative effect in the discrete formulation is completely transferred to the force vector, which is obviously much easier and efficient to compute than the dense fractional derivative stiffness matrix. Subsequently, it is further shown that for the general fractional advection-diffusion-reaction equation, the symmetric and banded structure can also be maintained for the diffusion stiffness matrix, although the total stiffness matrix is not symmetric in this case. More importantly, it is demonstrated that under certain conditions this symmetric diffusion stiffness matrix formulation is capable of producing very favorable numerical solutions in comparison with the conventional non-symmetric diffusion stiffness matrix finite element formulation. The effectiveness of the proposed methodology is illustrated through a series of numerical examples.

Measurement and Modeling of Water-Vapor Diffusion in Elastomers with Impact in Humidity and Vacuum Measurements

NASA Astrophysics Data System (ADS)

Šetina, Janez; Sefa, Makfir; Erjavec, Bojan; Hudoklin, Domen

2013-03-01

The dynamics of water-vapor dissolution in Viton O-rings is measured with a gravimetric method using a precise mass comparator. A sample gasket was degassed in high vacuum for a sufficiently long period to remove more than 99 % of the dissolved water vapor. After that, it was exposed to the ambient atmosphere with a controlled temperature, and relative humidity and water-vapor uptake curves were measured gravimetrically with a precise balance. The dynamics of a water-vapor release into vacuum from another sample that was previously saturated with water vapor at room temperature was determined. The sample was placed in a vacuum outgassing rate measurement apparatus. The time dependence of the evolved water vapor was calculated by integrating the measured outgassing rate. The physical process of water absorption can be described by the diffusion equation. The geometry of the samples required solving the diffusion equation in cylindrical coordinates. This was done numerically using a finite-difference method. As a result of the modeling, room temperature values of the diffusion constant D, the solubility s, and the permeability K = D× s of water vapor in the sample material (Viton A-401C) were obtained. For sample 1, we obtained D = 8.0 × 10 ^{-8} cm2 {\\cdot } s^{-1} and s = 6.5 × 10^{-7} g {\\cdot } cm^-3 Pa^{-1}, while for sample 2, D = 3.0 × 10^{-7} cm2 s^{-1} and s = 3.5 × 10^{-7} g {\\cdot } cm^{-3} {\\cdot } Pa^{-1}.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

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

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

S{sub 2}SA preconditioning for the S{sub n} equations with strictly non negative spatial discretization

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

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-07-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S{sub n} transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use amore » linear diffusion equation has important implications for preconditioning the S{sub n} equations with a strictly non negative spatial discretization in multiple dimensions. (authors)« less

An elemental mercury diffusion coefficient for natural waters determined by molecular dynamics simulation.

PubMed

Kuss, Joachim; Holzmann, Jörg; Ludwig, Ralf

2009-05-01

Mercury is a priority pollutant as its mobility between the hydrosphere and the atmosphere threatens the biosphere globally. The air-water gas transfer of elemental mercury (Hg0) is controlled by its diffusion through the water-side boundary layer and thus by its diffusion coefficient, D(Hg), the value of which, however, has not been established. Here, the diffusion of Hg0 in water was modeled by molecular dynamics (MD) simulation and the diffusion coefficient subsequently determined. Therefore the movement of either Hg(0) or xenon and 1000 model water molecules (TIP4P-Ew) were traced for time spans of 50 ns. The modeled D(Xe) of the monatomic noble gas agreed well with measured data; thus, MD simulation was assumed to be a reliable approach to determine D(Hg) for monatomic Hg(0) as well. Accordingly, Hg(0) diffusion was then simulated for freshwater and seawater, and the data were well-described by the equation of Eyring. The activation energies for the diffusion of Hg0 in freshwater was 17.0 kJ mol(-1) and in seawater 17.8 kJ mol(-1). The newly determined D(Hg) is clearly lower than the one previously used for an oceanic mercury budget. Thus, its incorporation into the model should lead to lower estimates of global ocean mercury emissions.

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

2D Lattice Boltzmann Simulation Of Chemical Reactions Within Rayleigh-Bénard And Poiseuille-Bénard Convection Systems

NASA Astrophysics Data System (ADS)

Amaya-Ventura, Gilberto; Rodríguez-Romo, Suemi

2011-09-01

This paper deals with the computational simulation of the reaction-diffusion-advection phenomena emerging in Rayleigh-Bénard (RB) and Poiseuille-Bénard reactive convection systems. We use the Boussinesq's approximation for buoyancy forces and the Lattice Boltzmann method (LBM). The first kinetic mesoscopic model proposed here is based on the discrete Boltzmann equation needed to solve the momentum balance coupled with buoyancy forces. Then, a second lattice Boltzmann algorithm is applied to solve the reaction-diffusion-advection equation to calculate the evolution of the chemical species concentration. We use a reactive system composed by nitrous oxide (so call laughing gas) in air as an example; its spatio-temporal decomposition is calculated. Two cases are considered, a rectangular enclosed cavity and an open channel. The simulations are performed at low Reynolds numbers and in a steady state between the first and second thermo-hydrodynamic instabilities. The results presented here, for the thermo-hydrodynamic behavior, are in good agreement with experimental data; while our| chemical kinetics simulation yields expected results. Some applications of our approach are related to chemical reactors and atmospheric phenomena, among others.

Results of a zonally truncated three-dimensional model of the Venus middle atmosphere

NASA Technical Reports Server (NTRS)

Newman, M.

1992-01-01

Although the equatorial rotational speed of the solid surface of Venus is only 4 m s(exp-1), the atmospheric rotational speed reaches a maximum of approximately 100 m s(exp-1) near the equatorial cloud top level (65 to 70 km). This phenomenon, known as superrotation, is the central dynamical problem of the Venus atmosphere. We report here the results of numerical simulations aimed at clarifying the mechanism for maintaining the equatorial cloud top rotation. Maintenance of an equatorial rotational speed maximum above the surface requires waves or eddies that systematically transport angular momentum against its zonal mean gradient. The zonally symmetric Hadley circulation is driven thermally and acts to reduce the rotational speed at the equatorial cloud top level; thus wave or eddy transport must counter this tendency as well as friction. Planetary waves arising from horizontal shear instability of the zonal flow (barotropic instability) could maintain the equatorial rotation by transporting angular momentum horizontally from midlatitudes toward the equator. Alternatively, vertically propagating waves could provide the required momentum source. The relative motion between the rotating atmosphere and the pattern of solar heating, which as a maximum where solar radiation is absorbed near the cloud tops, drives diurnal and semidiurnal thermal tides that propagate vertically away from the cloud top level. The effect of this wave propagation is to transport momentum toward the cloud top level at low latitudes and accelerate the mean zonal flow there. We employ a semispectral primitive equation model with a zonal mean flow and zonal wavenumbers 1 and 2. These waves correspond to the diurnal and semidiurnal tides, but they can also be excited by barotropic or baroclinic instability. Waves of higher wavenumbers and interactions between the waves are neglected. Symmetry about the equator is assumed, so the model applies to one hemisphere and covers the altitude range 30 to 110 km. Horizontal resolution is 1.5 deg latitude, and vertical resolution is 1.5 km. Solar and thermal infrared heating, based on Venus observations and calculations drive the model flow. Dissipation is accomplished mainly by Rayleigh friction, chosen to produce strong dissipation above 85 km in order to absorb upward propagating waves and limit extreme flow velocities there, yet to give very weak Rayleigh friction below 70 km; results in the cloud layer do not appear to be sensitive to the Rayleigh friction. The model also has weak vertical diffusion, and very weak horizontal diffusion, which has a smoothing effect on the flow only at the two grid points nearest the pole.

On the anisotropic advection-diffusion equation with time dependent coefficients

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

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE PAGES

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

2017-02-01

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

The role of partial ionization effects in the chromosphere

PubMed Central

Martínez-Sykora, Juan; De Pontieu, Bart; Hansteen, Viggo; Carlsson, Mats

2015-01-01

The energy for the coronal heating must be provided from the convection zone. However, the amount and the method by which this energy is transferred into the corona depend on the properties of the lower atmosphere and the corona itself. We review: (i) how the energy could be built in the lower solar atmosphere, (ii) how this energy is transferred through the solar atmosphere, and (iii) how the energy is finally dissipated in the chromosphere and/or corona. Any mechanism of energy transport has to deal with the various physical processes in the lower atmosphere. We will focus on a physical process that seems to be highly important in the chromosphere and not deeply studied until recently: the ion–neutral interaction effects in the chromosphere. We review the relevance and the role of the partial ionization in the chromosphere and show that this process actually impacts considerably the outer solar atmosphere. We include analysis of our 2.5D radiative magnetohydrodynamic simulations with the Bifrost code (Gudiksen et al. 2011 Astron. Astrophys. 531, A154 (doi:10.1051/0004-6361/201116520)) including the partial ionization effects on the chromosphere and corona and thermal conduction along magnetic field lines. The photosphere, chromosphere and transition region are partially ionized and the interaction between ionized particles and neutral particles has important consequences on the magneto-thermodynamics of these layers. The partial ionization effects are treated using generalized Ohm's law, i.e. we consider the Hall term and the ambipolar diffusion (Pedersen dissipation) in the induction equation. The interaction between the different species affects the modelled atmosphere as follows: (i) the ambipolar diffusion dissipates magnetic energy and increases the minimum temperature in the chromosphere and (ii) the upper chromosphere may get heated and expanded over a greater range of heights. These processes reveal appreciable differences between the modelled atmospheres of simulations with and without ion–neutral interaction effects. PMID:25897096

Ground-water age and atmospheric tracers: Simulation studies and analysis of field data from the Mirror Lake site, New Hampshire

USGS Publications Warehouse

Goode, Daniel J.

1998-01-01

The use of environmental tracers in characterization of ground-water systems is investigated through mathematical modeling of ground-water age and atmospheric tracer transport, and by a field study at the Mirror Lake site, New Hampshire. Theory is presented for modeling ground-water age using the advective-dispersive transport equation. The transport equation includes a zero-order source of unit strength, corresponding to the rate of aging, and can accommodate matrix diffusion and other exchange processes. The effect of temperature fluctuations and layered soils on transport of atmospheric gases to the water table is investigated using a one-dimensional numerical model of chlorofluorocarbon (CFC-11) transport. The nonlinear relation between temperature and Henry's Law coefficient (reflecting air/water phase partitioning) can cause the apparent recharge temperature to be elevated above the annual mean temperature where the water table is shallow. In addition, fine-grained soils can isolate the air phase in the unsaturated zone from the atmosphere. At the USGS' Mirror Lake, New Hampshire fractured-rock research site CFC concentrations near the water table are depleted where dissolved oxygen is low. CFC-11 and CFC-113 are completely absent under anaerobic conditions, while CFC-12 is as low as one-third of modern concentrations. Anaerobic biodegradation apparently consumes CFC's near the water table at this site. One area of active degradation appears to be associated with streamflow loss to ground water. Soil gas concentrations are generally close to atmospheric levels, although some spatial correlation is observed between depleted concentrations of CFC-11 and CFC-113 in soil gas and water-table samples. Results of unsaturated-zone monitoring indicate that recharge occurs throughout the year in the watershed, even during summer evapotranspiration periods, and that seasonal temperature fluctuations occur as much as 5 meters below land surface. Application of ground-water age and CFC-11 transport models to the large-scale ground-water system at Mirror Lake illustrates the similarities between age and chemical transport. Generally, bedrock porosities required to match observed apparent ages from CFC concentrations are high relative to porosities measured on cores. Although matrix diffusion has no effect on steady-state age, it can significantly reduce CFC concentrations in fractured rock in which the effective porosity is low.

Thermal radiation from large bolides and impact plumes

NASA Astrophysics Data System (ADS)

Svetsov, V.; Shuvalov, V.

2017-09-01

Numerical simulations of the impacts of asteroids and comets from 20 m to 3 km in diameter have been carried out and thermal radiation fluxes on the ground and luminous efficiencies of the impacts have been calculated. It was assumed that the cosmic objects have no strength, deform, fragment, and vaporize in the atmosphere. After the impact on the ground, formation of craters and plumes was simulated taking into account internal friction of destroyed rocks and a wake formed in the atmosphere. The equations of radiative transfer, added to the equations of gas dynamics, were used in the approximation of radiative heat diffusion or, if the Rosseland optical depth of a radiating volume of gas and vapor was less than unity, in the approximation of volume emission. Radiation fluxes on the Earth's surface were calculated by integrating the equation of radiative transfer along rays passing through a luminous area. Direct thermal radiation from fireballs and impact plumes produced by asteroids and comets larger than 50 m in diameter is dangerous for people, animals, plants, economic objects. Forest fires can be ignited on the ground within a radius of roughly 1000 times the body's diameter (for diameters of the order or smaller than 1 km), 50-m-diameter bodies can ignite forest fires within a radius of up to 40 km and 3-km asteroids - within 1700 km.

Three-dimensional stochastic modeling of radiation belts in adiabatic invariant coordinates

NASA Astrophysics Data System (ADS)

Zheng, Liheng; Chan, Anthony A.; Albert, Jay M.; Elkington, Scot R.; Koller, Josef; Horne, Richard B.; Glauert, Sarah A.; Meredith, Nigel P.

2014-09-01

A 3-D model for solving the radiation belt diffusion equation in adiabatic invariant coordinates has been developed and tested. The model, named Radbelt Electron Model, obtains a probabilistic solution by solving a set of Itô stochastic differential equations that are mathematically equivalent to the diffusion equation. This method is capable of solving diffusion equations with a full 3-D diffusion tensor, including the radial-local cross diffusion components. The correct form of the boundary condition at equatorial pitch angle α0=90° is also derived. The model is applied to a simulation of the October 2002 storm event. At α0 near 90°, our results are quantitatively consistent with GPS observations of phase space density (PSD) increases, suggesting dominance of radial diffusion; at smaller α0, the observed PSD increases are overestimated by the model, possibly due to the α0-independent radial diffusion coefficients, or to insufficient electron loss in the model, or both. Statistical analysis of the stochastic processes provides further insights into the diffusion processes, showing distinctive electron source distributions with and without local acceleration.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-01-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-06-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

A moving mesh finite difference method for equilibrium radiation diffusion equations

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

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

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

2017-07-27

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy.more » Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.« less

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

PubMed Central

Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

2012-01-01

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

Examining Changes in Radioxenon Isotope Activity Ratios during Subsurface Transport

NASA Astrophysics Data System (ADS)

Annewandter, R.

2013-12-01

The Non-Proliferation Experiment (NPE) has demonstrated and modelled the usefulness of barometric pumping induced soil gas sampling during On-Site inspections. Gas transport has been widely studied with different numerical codes. However, gas transport of all radioxenons in the post-detonation regime and their possible fractionation is still neglected in the open literature. Atmospheric concentrations of the radioxenons Xe-135, Xe-133m, Xe-133 and Xe-131m can be used to discriminate between civilian releases (nuclear power plants or medical isotope facilities), and nuclear explosion sources. It is based on the isotopic activity ratio method. Yet it is not clear whether subsurface migration of the radioxenons, with eventual release into the atmosphere, can affect the activity ratios due to fractionation. Fractionation can be caused by different diffusivities due to mass differences between the radioxenons. A previous study showed surface arrival time of a chemically inert gaseous tracer is affected by its diffusivity. They observed detectable amount for SF6 50 days after detonation and 375 days for He-3. They predict 50 and 80 days for Xe-133 and Ar-37 respectively. Cyclical changes in atmospheric pressure can drive subsurface gas transport. This barometric pumping phenomenon causes an oscillatoric flow in upward trending fractures which, combined with diffusion into the porous matrix, leads to a net transport of gaseous components - a ratcheting effect. We use a general purpose reservoir simulator (Complex System Modelling Platform, CSMP++) which has been applied in a range of fields such as deep geothermal systems, three-phase black oil simulations , fracture propagation in fractured, porous media, Navier-Stokes pore-scale modelling among others. It is specifically designed to account for structurally complex geologic situation of fractured, porous media. Parabolic differential equations are solved by a continuous Galerkin finite-element method, hyperbolic differential equations by a complementary finite volume method. The parabolic and hyperbolic problem can be solved separately using the operator-splitting method (Implicit Pressure Explicit Saturation, IMPES). The resulting system of linear equations is solved by the algebraic multigrid library SAMG, developed at the Fraunhofer Institute for Algorithms and Scientific Computing. CSMP++ is developed at Montan University of Leoben, ETH Zuerich, Imperial College London and Heriot-Watt University in Edinburgh. To date, there has been no research investigating how subsurface transport impacts isotope activity ratios. The isotopic activity ratio method can be used to discriminate between civil release or nuclear explosion sources. This study examines possible fractionation of Xe-135, Xe-133m, Xe-133, Xe-131m during barometric pumping-driven subsurface migration, which can affect surface arrival times and isotopic activity ratios. Surface arrival times for the Noble gases Kr-81, Kr-85 and Ar-39 are also calculated.

THOR: an open-source exo-GCM

NASA Astrophysics Data System (ADS)

Grosheintz, Luc; Mendonça, João; Käppeli, Roger; Lukas Grimm, Simon; Mishra, Siddhartha; Heng, Kevin

2015-12-01

In this talk, I will present THOR, the first fully conservative, GPU-accelerated exo-GCM (general circulation model) on a nearly uniform, global grid that treats shocks and is non-hydrostatic. THOR will be freely available to the community as a standard tool.Unlike most GCMs THOR solves the full, non-hydrostatic Euler equations instead of the primitive equations. The equations are solved on a global three-dimensional icosahedral grid by a second order Finite Volume Method (FVM). Icosahedral grids are nearly uniform refinements of an icosahedron. We've implemented three different versions of this grid. FVM conserves the prognostic variables (density, momentum and energy) exactly and doesn't require a diffusion term (artificial viscosity) in the Euler equations to stabilize our solver. Historically FVM was designed to treat discontinuities correctly. Hence it excels at resolving shocks, including those present in hot exoplanetary atmospheres.Atmospheres are generally in near hydrostatic equilibrium. We therefore implement a well-balancing technique recently developed at the ETH Zurich. This well-balancing ensures that our FVM maintains hydrostatic equilibrium to machine precision. Better yet, it is able to resolve pressure perturbations from this equilibrium as small as one part in 100'000. It is important to realize that these perturbations are significantly smaller than the truncation error of the same scheme without well-balancing. If during the course of the simulation (due to forcing) the atmosphere becomes non-hydrostatic, our solver continues to function correctly.THOR just passed an important mile stone. We've implemented the explicit part of the solver. The explicit solver is useful to study instabilities or local problems on relatively short time scales. I'll show some nice properties of the explicit THOR. An explicit solver is not appropriate for climate study because the time step is limited by the sound speed. Therefore, we are working on the first fully implicit GCM. By ESS3, I hope to present results for the advection equation.THOR is part of the Exoclimes Simulation Platform (ESP), a set of open-source community codes for simulating and understanding the atmospheres of exoplanets. The ESP also includes tools for radiative transfer and retrieval (HELIOS), an opacity calculator (HELIOS-K), and a chemical kinetics solver (VULCAN). We expect to publicly release an initial version of THOR in 2016 on www.exoclime.org.

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2001-01-01

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

Design and laboratory testing of a chamber device to measure total flux of volatile organic compounds from the unsaturated zone under natural conditions.

PubMed

Tillman, Fred D; Smith, James A

2004-11-01

To determine if an aquifer contaminated with volatile organic compounds (VOCs) has potential for natural remediation, all natural processes affecting the fate and transport of VOCs in the subsurface must be identified and quantified. This research addresses the quantification of air-phase volatile organic compounds (VOCs) leaving the unsaturated zone soil gas and entering the atmosphere-including the additional flux provided by advective soil-gas movement induced by barometric pumping. A simple and easy-to-use device for measuring VOC flux under natural conditions is presented. The vertical flux chamber (VFC) was designed using numerical simulations and evaluated in the laboratory. Mass-balance numerical simulations based on continuously stirred tank reactor equations (CSTR) provided information on flux measurement performance of several sampling configurations with the final chamber configuration measuring greater than 96% of model-simulated fluxes. A laboratory device was constructed to evaluate the flux chamber under both diffusion-only and advection-plus-diffusion transport conditions. The flux chamber measured an average of 82% of 15 diffusion-only fluxes and an average of 95% of 15 additional advection-plus-diffusion flux experiments. The vertical flux chamber has the capability of providing reliable measurement of VOC flux from the unsaturated zone under both diffusion and advection transport conditions.

Numerical simulation of supersonic water vapor jet impinging on a flat plate

NASA Astrophysics Data System (ADS)

Kuzuu, Kazuto; Aono, Junya; Shima, Eiji

2012-11-01

We investigated supersonic water vapor jet impinging on a flat plate through numerical simulation. This simulation is for estimating heating effect of a reusable sounding rocket during vertical landing. The jet from the rocket bottom is supersonic, M=2 to 3, high temperature, T=2000K, and over-expanded. Atmospheric condition is a stationary standard air. The simulation is base on the full Navier-Stokes equations, and the flow is numerically solved by an unstructured compressible flow solver, in-house code LS-FLOW-RG. In this solver, the transport properties of muti-species gas and mass conservation equations of those species are considered. We employed DDES method as a turbulence model. For verification and validation, we also carried out a simulation under the condition of air, and compared with the experimental data. Agreement between our results and the experimental data are satisfactory. Through this simulation, we calculated the flow under some exit pressure conditions, and discuss the effects of pressure ratio on flow structures, heat transfer and so on. Furthermore, we also investigated diffusion effects of water vapor, and we confirmed that these phenomena are generated by the interaction of atmospheric air and affects the heat transfer to the surrounding environment.

Solution of the nonlinear Poisson-Boltzmann equation: Application to ionic diffusion in cementitious materials

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

Arnold, J.; Kosson, D.S., E-mail: david.s.kosson@vanderbilt.edu; Garrabrants, A.

2013-02-15

A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.

Hydrodynamic escape from planetary atmospheres

NASA Astrophysics Data System (ADS)

Tian, Feng

Hydrodynamic escape is an important process in the formation and evolution of planetary atmospheres. Due to the existence of a singularity point near the transonic point, it is difficult to find transonic steady state solutions by solving the time-independent hydrodynamic equations. In addition to that, most previous works assume that all energy driving the escape flow is deposited in one narrow layer. This assumption not only results in less accurate solutions to the hydrodynamic escape problem, but also makes it difficult to include other chemical and physical processes in the hydrodynamic escape models. In this work, a numerical model describing the transonic hydrodynamic escape from planetary atmospheres is developed. A robust solution technique is used to solve the time dependent hydrodynamic equations. The method has been validated in an isothermal atmosphere where an analytical solution is available. The hydrodynamic model is applied to 3 cases: hydrogen escape from small orbit extrasolar planets, hydrogen escape from a hydrogen rich early Earth's atmosphere, and nitrogen/methane escape from Pluto's atmosphere. Results of simulations on extrasolar planets are in good agreement with the observations of the transiting extrasolar planet HD209458b. Hydrodynamic escape of hydrogen from other hypothetical close-in extrasolar planets are simulated and the influence of hydrogen escape on the long-term evolution of these extrasolar planets are discussed. Simulations on early Earth suggest that hydrodynamic escape of hydrogen from a hydrogen rich early Earth's atmosphere is about two orders magnitude slower than the diffusion limited escape rate. A hydrogen rich early Earth's atmosphere could have been maintained by the balance between the hydrogen escape and the supply of hydrogen into the atmosphere by volcanic outgassing. Origin of life may have occurred in the organic soup ocean created by the efficient formation of prebiotic molecules in the hydrogen rich early Earth's atmosphere. Simulations show that hydrodynamic escape of nitrogen from Pluto is able to remove a ~3 km layer of ice over the age of the solar system. The escape flux of neutral nitrogen may interact with the solar wind at Pluto's orbit and may be detected by the New Horizon mission.

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

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

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalousmore » diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.« less

Examining Changes in Radioxenon Isotope Activity Ratios during Subsurface Transport

NASA Astrophysics Data System (ADS)

Annewandter, Robert

2014-05-01

The Non-Proliferation Experiment (NPE) has demonstrated and modelled the usefulness of barometric pumping induced gas transport and subsequent soil gas sampling during On-Site inspections. Generally, gas transport has been widely studied with different numerical codes. However, gas transport of radioxenons and radioiodines in the post-detonation regime and their possible fractionation is still neglected in the open peer-reviewed literature. Atmospheric concentrations of the radioxenons Xe-135, Xe-133m, Xe-133 and Xe-131m can be used to discriminate between civilian releases (nuclear power plants or medical isotope facilities), and nuclear explosion sources. It is based on the multiple isotopic activity ratio method. Yet it is not clear whether subsurface migration of the radionuclides, with eventual release into the atmosphere, can affect the activity ratios due to fractionation. Fractionation can be caused by different mass diffusivities due to mass differences between the radionuclides. Cyclical changes in atmospheric pressure can drive subsurface gas transport. This barometric pumping phenomenon causes an oscillatoric flow in upward trending fractures or highly conductive faults which, combined with diffusion into the porous matrix, leads to a net transport of gaseous components - a so-called ratcheting effect. We use a general purpose reservoir simulator (Complex System Modelling Platform, CSMP++) which is recognized by the oil industry as leading in Discrete Fracture-Matrix (DFM) simulations. It has been applied in a range of fields such as deep geothermal systems, three-phase black oil simulations, fracture propagation in fractured, porous media, and Navier-Stokes pore-scale modelling among others. It is specifically designed to account for structurally complex geologic situation of fractured, porous media. Parabolic differential equations are solved by a continuous Galerkin finite-element method, hyperbolic differential equations by a complementary finite volume method. The parabolic and hyperbolic problem can be solved separately by operator-splitting. The resulting system of linear equations is solved by the algebraic multigrid library SAMG, developed at the Fraunhofer Institute for Algorithms and Scientific Computing, Germany. CSMP++ is developed at Montan University of Leoben, ETH Zuerich, Imperial College London and Heriot-Watt University in Edinburgh. This study examines barometric pumping-driven subsurface transport of Xe-135, Xe-133m, Xe-133, Xe-131m including I-131, I-133 and I-135 on arrival times and isotopic activity ratios. This work was funded by the CTBTO Research Award for Young Scientist and Engineers (2013).

Projecting diffusion along the normal bundle of a plane curve

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

Valero-Valdés, Carlos; Herrera-Guzmán, Rafael

2014-05-15

The purpose of this paper is to provide new formulas for the effective diffusion coefficient of a generalized Fick-Jacob's equation obtained by projecting the two-dimensional diffusion equation along the normal directions of an arbitrary curve on the plane.

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

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1994-01-01

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

Fractional diffusion on bounded domains

DOE PAGES

Defterli, Ozlem; D'Elia, Marta; Du, Qiang; ...

2015-03-13

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

Mathematics of thermal diffusion in an exponential temperature field

NASA Astrophysics Data System (ADS)

Zhang, Yaqi; Bai, Wenyu; Diebold, Gerald J.

2018-04-01

The Ludwig-Soret effect, also known as thermal diffusion, refers to the separation of gas, liquid, or solid mixtures in a temperature gradient. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fractions. Here solutions to the nonlinear differential equation for a binary mixture are discussed for an externally imposed, exponential temperature field. The equation of motion for the separation without the effects of mass diffusion is reduced to a Hamiltonian pair from which spatial distributions of the components of the mixture are found. Analytical calculations with boundary effects included show shock formation. The results of numerical calculations of the equation of motion that include both thermal and mass diffusion are given.

OH density measured by PLIF in a nanosecond atmospheric pressure diffuse discharge in humid air under steep high voltage pulses

NASA Astrophysics Data System (ADS)

Ouaras, K.; Magne, L.; Pasquiers, S.; Tardiveau, P.; Jeanney, P.; Bournonville, B.

2018-04-01

The spatiotemporal distributions of the OH radical density are measured using planar laser induced fluorescence in the afterglow of a nanosecond diffuse discharge at atmospheric pressure in humid air. The diffuse discharge is generated between a pin and a grounded plate electrodes within a gap of 18 mm. The high voltage pulse applied to the pin ranges from 65 to 85 kV with a rise time of 2 ns. The specific electrical energy transferred to the gas ranges from 5 to 40 J l‑1. The influence of H2O concentration is studied from 0.5% to 1.5%. An absolute calibration of OH density is performed using a six-level transient rate equation model to simulate the dynamics of OH excitation by the laser, taking into account collisional processes during the optical pumping and the fluorescence. Rayleigh scattering measurements are used to achieve the geometrical part of the calibration. A local maximum of OH density is found in the pin area whatever the operating conditions. For 85 kV and 1% of H2O, this peak reaches a value of 2.0 × 1016 cm‑3 corresponding to 8% of H2O dissociation. The temporal decay of the spatially averaged OH density is found to be similar as in the afterglow of a homogeneous photo-triggered discharge for which a self-consistent modeling is done. These tools are then used to bring discussion elements on OH kinetics.

Double diffusivity model under stochastic forcing

NASA Astrophysics Data System (ADS)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real-life fluctuating environments.

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki

2010-11-01

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

Fractional-calculus diffusion equation

PubMed Central

2010-01-01

Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

Simulation of tracer dispersion from elevated and surface releases in complex terrain

NASA Astrophysics Data System (ADS)

Hernández, J. F.; Cremades, L.; Baldasano, J. M.

A new version of an advanced mesoscale dispersion modeling system for simulating passive air pollutant dispersion in the real atmospheric planetary boundary layer (PBL), is presented. The system comprises a diagnostic mass-consistent meteorological model and a Lagrangian particle dispersion model (LADISMO). The former version of LADISMO, developed according to Zannetti (Air pollution modelling, 1990), was based on the Monte Carlo technique and included calculation of higher-order moments of vertical random forcing for convective conditions. Its ability to simulate complex flow dispersion has been stated in a previous paper (Hernández et al. 1995, Atmospheric Environment, 29A, 1331-1341). The new version follows Thomson's scheme (1984, Q. Jl Roy. Met. Soc.110, 1107-1120). It is also based on Langevin equation and follows the ideas given by Brusasca et al. (1992, Atmospheric Environment26A, 707-723) and Anfossi et al. (1992, Nuovo Cemento 15c, 139-158). The model is used to simulate the dispersion and predict the ground level concentration (g.l.c.) of a tracer (SF 6) released from both an elevated source ( case a) and a ground level source ( case b) in a highly complex mountainous terrain during neutral and synoptically dominated conditions ( case a) and light and apparently stable conditions ( case b). The last case is considered as being a specially difficult task to simulate. In fact, few works have reported situations with valley drainage flows in complex terrains and real stable atmospheric conditions with weak winds. The model assumes that nearly calm situations associated to strong stability and air stagnation, make the lowest layers of PBL poorly diffusive (Brusasca et al., 1992, Atmospheric Environment26A, 707-723). Model results are verified against experimental data from Guardo-90 tracer experiments, an intensive field campaign conducted in the Carrion river valley (Northern Spain) to study atmospheric diffusion within a steep walled valley in mountainous terrain (Ibarra, 1992, Energia, No. 1, 74-85).

Hemoglobin encapsulation in vesicles retards NO and CO binding and O2 release when perfused through narrow gas-permeable tubes.

PubMed

Sakai, Hiromi; Okuda, Naoto; Sato, Atsushi; Yamaue, Tatsuya; Takeoka, Shinji; Tsuchida, Eishun

2010-03-01

Intravenous administration of cell-free Hb induces vasoconstriction and circulatory disorders, presumably because of the intrinsic affinities to endogenous nitric oxide (NO) and carbon monoxide (CO) as vasorelaxation factors and because of the facilitated O(2) release that might induce autoregulatory vasoconstriction. We examined these gas reactions when Hb-containing solutions of four kinds were perfused through artificial narrow tubes at a practical Hb concentration (10 g/dl). Purified Hb solution, polymerized bovine Hb (Poly(B)Hb), encapsulated Hb [Hb-vesicles (HbV), 279 nm], and red blood cells (RBCs) were perfused through a gas-permeable narrow tube (25 microm inner diameter) at 1 mm/s centerline velocity. The level of reactions was determined microscopically based on the visible-light absorption spectrum of Hb. When the tube was immersed in NO and CO atmospheres, both NO binding and CO binding of deoxygenated Hb (deoxy-Hb) and Poly(B)Hb in the tube was faster than those of HbV and RBCs, and HbV and RBCs showed almost identical binding rates. When the tube was immersed in a N(2) atmosphere, oxygenated Hb and Poly(B)Hb showed much faster O(2) release than did HbV and RBCs. Poly(B)Hb showed a faster reaction than Hb because of the lower O(2) affinity of Poly(B)Hb than Hb. The diffusion process of the particles was simulated using Navier-Stokes and Maxwell-Stefan equations. Results clarified that small Hb (6 nm) diffuses laterally and mixes rapidly. However, the large-dimension HbV shows no such rapid diffusion. The purely physicochemical differences in diffusivity of the particles and the resulting reactivity with gas molecules are one factor inducing biological vasoconstriction of Hb-based oxygen carriers.

Atmospheric dispersion of natural carbon dioxide emissions on Vulcano Island, Italy

NASA Astrophysics Data System (ADS)

Granieri, D.; Carapezza, M. L.; Barberi, F.; Ranaldi, M.; Ricci, T.; Tarchini, L.

2014-07-01

La Fossa quiescent volcano and its surrounding area on the Island of Vulcano (Italy) are characterized by intensive, persistent degassing through both fumaroles and diffuse soil emissions. Periodic degassing crises occur, with marked increase in temperature and steam and gas output (mostly CO2) from crater fumaroles and in CO2 soil diffuse emission from the crater area as well as from the volcano flanks and base. The gas hazard of the most inhabited part of the island, Vulcano Porto, was investigated by simulating the CO2 dispersion in the atmosphere under different wind conditions. The DISGAS (DISpersion of GAS) code, an Eulerian model based on advection-diffusion equations, was used together with the mass-consistent Diagnostic Wind Model. Numerical simulations were validated by measurements of air CO2 concentration inside the village and along the crater's rim by means of a Soil CO2 Automatic Station and a Tunable Diode Laser device. The results show that in the village of Vulcano Porto, the CO2 air concentration is mostly due to local soil degassing, while the contribution from the crater gas emission is negligible at the breathing height for humans and always remains well below the lowest indoor CO2 concentration threshold recommended by the health authorities (1000 ppm). Outdoor excess CO2 maxima up to 200 ppm above local background CO2 air concentration are estimated in the center of the village and up to 100 ppm in other zones. However, in some ground excavations or in basements the health code threshold can be exceeded. In the crater area, because of the combined effect of fumaroles and diffuse soil emissions, CO2 air concentrations can reach 5000-7000 ppm in low-wind conditions and pose a health hazard for visitors.

Uncertainty for calculating transport on Titan: A probabilistic description of bimolecular diffusion parameters

NASA Astrophysics Data System (ADS)

Plessis, S.; McDougall, D.; Mandt, K.; Greathouse, T.; Luspay-Kuti, A.

2015-11-01

Bimolecular diffusion coefficients are important parameters used by atmospheric models to calculate altitude profiles of minor constituents in an atmosphere. Unfortunately, laboratory measurements of these coefficients were never conducted at temperature conditions relevant to the atmosphere of Titan. Here we conduct a detailed uncertainty analysis of the bimolecular diffusion coefficient parameters as applied to Titan's upper atmosphere to provide a better understanding of the impact of uncertainty for this parameter on models. Because temperature and pressure conditions are much lower than the laboratory conditions in which bimolecular diffusion parameters were measured, we apply a Bayesian framework, a problem-agnostic framework, to determine parameter estimates and associated uncertainties. We solve the Bayesian calibration problem using the open-source QUESO library which also performs a propagation of uncertainties in the calibrated parameters to temperature and pressure conditions observed in Titan's upper atmosphere. Our results show that, after propagating uncertainty through the Massman model, the uncertainty in molecular diffusion is highly correlated to temperature and we observe no noticeable correlation with pressure. We propagate the calibrated molecular diffusion estimate and associated uncertainty to obtain an estimate with uncertainty due to bimolecular diffusion for the methane molar fraction as a function of altitude. Results show that the uncertainty in methane abundance due to molecular diffusion is in general small compared to eddy diffusion and the chemical kinetics description. However, methane abundance is most sensitive to uncertainty in molecular diffusion above 1200 km where the errors are nontrivial and could have important implications for scientific research based on diffusion models in this altitude range.

An asymptotic induced numerical method for the convection-diffusion-reaction equation

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.; Sorensen, Danny C.

1988-01-01

A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.

A new Eulerian model for viscous and heat conducting compressible flows

NASA Astrophysics Data System (ADS)

Svärd, Magnus

2018-09-01

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the Lagrangian derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely Eulerian framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.

Analytical solution of the nonlinear diffusion equation

NASA Astrophysics Data System (ADS)

Shanker Dubey, Ravi; Goswami, Pranay

2018-05-01

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

Lee wave breaking region: the map of instability development scenarios

NASA Astrophysics Data System (ADS)

Yakovenko, S. N.

2017-10-01

Numerical study of a stably stratified flow above the two-dimensional cosine-shaped obstacle has been performed by DNS and LES. These methods were implemented to solve the three-dimensional Navier-Stokes equations in the Boussinesq approximation, together with by the scalar diffusion equation. The results of scanning in the wide ranges of physical parameters (Reynolds and Prandtl/Schmidt numbers relating to laboratory experiment cases and atmospheric or oceanic situations) are presented for instability and turbulence development scenarios in the overturning internal lee waves. The latter is generated by the obstacle in a flow with the constant inflow values of velocity and stable density gradient. Evolution of lee-wave breaking is explored by visualization of velocity and scalar (density) fields, and the analysis of spectra. Based on the numerical simulation results, the power-law dependence on Reynolds number is demonstrated for the wavelength of the most unstable perturbation.

Large-scale Atmospheric Transport Processes

NASA Technical Reports Server (NTRS)

Plumb, R. Alan

2004-01-01

Continuing earlier work, we continued an investigation of the seasonal behavior of the edges of the stratospheric surf zone. These edges form a barrier between the rapidly mixed surf zone and the relatively isolated tropics. In collaboration with Dr Lynn Sparling at GSFC, we used a statistical analysis of HALOE and CLAES trace gas data from UARS to identify and locate these edges during each UARS observing period. We found that the edges on both sides of the equator are present all year (a fact that is important for conceptual models of stratospheric transport), though that on the summer side of the equator is much less sharp than the winter edge. The edges migrate seasonally into the summer hemisphere. Their location also shows influence of the QBO, together with the SAO at higher altitudes. Comparisons with effective diffusivities, and the edge locations, suggest that the edge is sustained by surf zone entrainment during winter, but by the residual circulation during summer.

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

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

Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form ismore » based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.« less

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

DOE PAGES

Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick; ...

2017-02-21

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form ismore » based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.« less

The effective boundary conditions and their lifespan of the logistic diffusion equation on a coated body

NASA Astrophysics Data System (ADS)

Li, Huicong; Wang, Xuefeng; Wu, Yanxia

2014-11-01

We consider the logistic diffusion equation on a bounded domain, which has two components with a thin coating surrounding a body. The diffusion tensor is isotropic on the body, and anisotropic on the coating. The size of the diffusion tensor on these components may be very different; within the coating, the diffusion rates in the normal and tangent directions may be in different scales. We find effective boundary conditions (EBCs) that are approximately satisfied by the solution of the diffusion equation on the boundary of the body. We also prove that the lifespan of each EBC, which measures how long the EBC remains effective, is infinite. The EBCs enable us to see clearly the effect of the coating and ease the difficult task of solving the PDE in a thin region with a small diffusion tensor. The motivation of the mathematics includes a nature reserve surrounded by a buffer zone.

Worst case prediction of additives migration from polystyrene for food safety purposes: a model update.

PubMed

Martínez-López, Brais; Gontard, Nathalie; Peyron, Stéphane

2018-03-01

A reliable prediction of migration levels of plastic additives into food requires a robust estimation of diffusivity. Predictive modelling of diffusivity as recommended by the EU commission is carried out using a semi-empirical equation that relies on two polymer-dependent parameters. These parameters were determined for the polymers most used by packaging industry (LLDPE, HDPE, PP, PET, PS, HIPS) from the diffusivity data available at that time. In the specific case of general purpose polystyrene, the diffusivity data published since then shows that the use of the equation with the original parameters results in systematic underestimation of diffusivity. The goal of this study was therefore, to propose an update of the aforementioned parameters for PS on the basis of up to date diffusivity data, so the equation can be used for a reasoned overestimation of diffusivity.

Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods

DTIC Science & Technology

2002-05-06

reaction- diffusion equation is a difficult problem in analysis that will not be addressed here. Errors will also arise from numerically approx solutions to...the ODEs. When comparing the approximate solution to actual reaction- diffusion systems found in nature, we must also take into account errors that...

Three-pattern decomposition of global atmospheric circulation: part II—dynamical equations of horizontal, meridional and zonal circulations

NASA Astrophysics Data System (ADS)

Hu, Shujuan; Cheng, Jianbo; Xu, Ming; Chou, Jifan

2018-04-01

The three-pattern decomposition of global atmospheric circulation (TPDGAC) partitions three-dimensional (3D) atmospheric circulation into horizontal, meridional and zonal components to study the 3D structures of global atmospheric circulation. This paper incorporates the three-pattern decomposition model (TPDM) into primitive equations of atmospheric dynamics and establishes a new set of dynamical equations of the horizontal, meridional and zonal circulations in which the operator properties are studied and energy conservation laws are preserved, as in the primitive equations. The physical significance of the newly established equations is demonstrated. Our findings reveal that the new equations are essentially the 3D vorticity equations of atmosphere and that the time evolution rules of the horizontal, meridional and zonal circulations can be described from the perspective of 3D vorticity evolution. The new set of dynamical equations includes decomposed expressions that can be used to explore the source terms of large-scale atmospheric circulation variations. A simplified model is presented to demonstrate the potential applications of the new equations for studying the dynamics of the Rossby, Hadley and Walker circulations. The model shows that the horizontal air temperature anomaly gradient (ATAG) induces changes in meridional and zonal circulations and promotes the baroclinic evolution of the horizontal circulation. The simplified model also indicates that the absolute vorticity of the horizontal circulation is not conserved, and its changes can be described by changes in the vertical vorticities of the meridional and zonal circulations. Moreover, the thermodynamic equation shows that the induced meridional and zonal circulations and advection transport by the horizontal circulation in turn cause a redistribution of the air temperature. The simplified model reveals the fundamental rules between the evolution of the air temperature and the horizontal, meridional and zonal components of global atmospheric circulation.

Thermospheric wind effects on the global distribution of helium in the earth's upper atmosphere. Ph.D. Thesis - Michigan Univ., Ann Arbor

NASA Technical Reports Server (NTRS)

Reber, C. A.

1973-01-01

The momentum and continuity equations for a minor gas are combined with the momentum equation for the major constituents to obtain the time dependent continuity equation for the minor species reflecting a wind field in the background gas. This equation is used to study the distributions of helium and argon at times of low, medium, and high solar activity for a variety of latitudinal-seasonal wind cells. For helium, the exospheric return flow at the higher thermospheric temperatures dominates the distribution to the extent that much larger latitudinal gradients can be maintained during periods of low solar activity than during periods of high activity. By comparison to the exospheric flow, the smoothing effect of horizontal diffusion is almost negligible. The latitudinal variation of helium observed by satellite mass spectrometers can be reproduced by the effect of a wind system of air rising in the summer hemisphere, flowing across the equator with speeds on the order of 100 to 200 m/sec, and descending in the winter hemisphere. Argon, being heavier than the mean mass in the lower thermosphere, reacts oppositely to helium in that it is enhanced in the summer hemisphere and depleted in the winter.

Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

NASA Astrophysics Data System (ADS)

Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

2018-04-01

Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

Exact Solutions of Coupled Multispecies Linear Reaction–Diffusion Equations on a Uniformly Growing Domain

PubMed Central

Simpson, Matthew J.; Sharp, Jesse A.; Morrow, Liam C.; Baker, Ruth E.

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit. PMID:26407013

Exact Solutions of Coupled Multispecies Linear Reaction-Diffusion Equations on a Uniformly Growing Domain.

PubMed

Simpson, Matthew J; Sharp, Jesse A; Morrow, Liam C; Baker, Ruth E

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Hydrogen calibration of GD-spectrometer using Zr-1Nb alloy

NASA Astrophysics Data System (ADS)

Mikhaylov, Andrey A.; Priamushko, Tatiana S.; Babikhina, Maria N.; Kudiiarov, Victor N.; Heller, Rene; Laptev, Roman S.; Lider, Andrey M.

2018-02-01

To study the hydrogen distribution in Zr-1Nb alloy (Э110 alloy) GD-OES was applied in this work. Qualitative analysis needs the standard samples with hydrogen. However, the standard samples with high concentrations of hydrogen in the zirconium alloy which would meet the requirements of the shape, size are absent. In this work method of Zr + H calibration samples production was performed at the first time. Automated Complex Gas Reaction Controller was used for samples hydrogenation. To calculate the parameters of post-hydrogenation incubation of the samples in an inert gas atmosphere the diffusion equations were used. Absolute hydrogen concentrations in the samples were determined by melting in the inert gas atmosphere using RHEN602 analyzer (LECO Company). Hydrogen distribution was studied using nuclear reaction analysis (HZDR, Dresden, Germany). RF GD-OES was used for calibration. The depth of the craters was measured with the help of a Hommel-Etamic profilometer by Jenoptik, Germany.

An accurate computational method for the diffusion regime verification

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-04-01

The diffusion regime (sub-diffusive, standard, or super-diffusive) is defined by the order of the derivative in the corresponding transport equation. We develop an accurate computational method for the direct estimation of the diffusion regime. The method is based on the derivative order estimation using the asymptotic analytic solutions of the diffusion equation with the integer order and the time-fractional derivatives. The robustness and the computational cheapness of the proposed method are verified using the experimental methane and methyl alcohol transport kinetics through the catalyst pellet.

Control of reaction-diffusion equations on time-evolving manifolds.

PubMed

Rossi, Francesco; Duteil, Nastassia Pouradier; Yakoby, Nir; Piccoli, Benedetto

2016-12-01

Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such signal. Meanwhile, the diffusion of the signal is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the signal and the change of the shapes. In this paper, we introduce a mathematical model to investigate such coupling. The shape is given by a manifold, that varies in time as the result of a deformation given by a transport equation. The signal is represented by a density, diffusing on the manifold via a diffusion equation. We show the non-commutativity of the transport and diffusion evolution by introducing a new concept of Lie bracket between the diffusion and the transport operator. We also provide numerical simulations showing this phenomenon.

An idealised study of the effects of small scales on chemistry in a two-dimensional turbulent flow.

NASA Astrophysics Data System (ADS)

Chaalal, F. Ait; Bartello, P.; Bourqui, M.

2009-04-01

The non-linear nature of stratospheric chemical reactions makes them sensitive to mixing and diffusion. Most stratospheric Climate-Chemistry Models neglect the effects of sub-grid flow structures on chemistry. Several previous studies have pointed out that such unresolved small scales could significantly affect the chemistry. However this problem has not been thoroughly studied from a theoretical point of view. To fulfill this gap, we investigate the interactions between advection, diffusion and chemistry for a simple bimolecular reaction between two initially unmixed reactants, within the framework of two-dimensional isotropic and homogenous turbulence. This is a highly simplified representation of quasi-isentropic mixing in the stratosphere. Our goal here is to describe and understand how the production rate of the product species is affected by the size of the smallest scales of the tracer field, as determined by the tracer diffusion coefficient ΰ. The spatial average of the prognostic equation for the product's concentration involves the covariance of the reactants. The time evolution of this covariance depends in turn on a dissipative term, and on second and third order chemical terms. The set of equations is not closed and any finite resolution model would need a parameterization of the dissipation and a closure hypothesis on the chemical terms. To study these terms, we perform ensembles of direct numerical simulations using a pseudo-spectral two-dimensional periodic model. The ensembles span different initial conditions of the flow and different tracer diffusion coefficients ΰ. Our results show a strong dependence of the total production on the diffusion coefficient. This production scales like ΰp(t) , where p(t) is a positive decreasing function of time. This scaling is very similar to the one found by Tan et al. (1998) for atmospheric flows on the deactivation of chlorine by nitrogen oxide at the southern edge of the winter time polar vortex. Furthermore, the time derivative of the reactants' covariance is found to be only very weakly dependent on the chemical reaction rate, for both slow and fast chemistries compared to the advection. The variations of the dissipation and of the chemical terms with the reaction speed compensate each other. As a consequence, the calculation of the product's concentration using the covariance of the dissipation without chemistry is a good approximation of the effect of diffusion with chemistry. Reference Tan, DGH; Haynes, PH; MacKenzie, AR; et al., Effects of fluid-dynamical stirring and mixing on the deactivation of stratospheric chlorine, Journal of Geophysical Research-Atmospheres, Volume: 103 Issue: D1 Pages: 1585-1605 (1998).

Fractional Number Operator and Associated Fractional Diffusion Equations

NASA Astrophysics Data System (ADS)

Rguigui, Hafedh

2018-03-01

In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

PubMed Central

Vázquez, J. L.

2010-01-01

The goal of this paper is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It relies on the identification of the optimal constants in some related Hardy–Poincaré inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities, and rates for nonlinear diffusion equations. PMID:20823259

Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations

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

Zhou Tao, E-mail: tzhou@lsec.cc.ac.c; Tang Tao, E-mail: ttang@hkbu.edu.h

2010-11-01

In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266-281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.

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.

Stress, deformation and diffusion interactions in solids - A simulation study

NASA Astrophysics Data System (ADS)

Fischer, F. D.; Svoboda, J.

2015-05-01

Equations of diffusion treated in the frame of Manning's concept, are completed by equations for generation/annihilation of vacancies at non-ideal sources and sinks, by conservation laws, by equations for generation of an eigenstrain state and by a strain-stress analysis. The stress-deformation-diffusion interactions are demonstrated on the evolution of a diffusion couple consisting of two thin layers of different chemical composition forming a free-standing plate without external loading. The equations are solved for different material parameters represented by the values of diffusion coefficients of individual components and by the intensity of sources and sinks for vacancies. The results of simulations indicate that for low intensity of sources and sinks for vacancies a significant eigenstress state can develop and the interdiffusion process is slowed down. For high intensity of sources and sinks for vacancies a significant eigenstrain state can develop and the eigenstress state quickly relaxes. If the difference in the diffusion coefficients of individual components is high, then the intensity of sources and sinks for vacancies influences the interdiffusion process considerably. For such systems their description only by diffusion coefficients is insufficient and must be completed by a microstructure characterization.

A double medium model for diffusion in fluid-bearing rock

NASA Astrophysics Data System (ADS)

Wang, H. F.

1993-09-01

The concept of a double porosity medium to model fluid flow in fractured rock has been applied to model diffusion in rock containing a small amount of a continuous fluid phase that surrounds small volume elements of the solid matrix. The model quantifies the relative role of diffusion in the fluid and solid phases of the rock. The fluid is the fast diffusion path, but the solid contains the volumetrically significant amount of the diffusing species. The double medium model consists of two coupled differential equations. One equation is the diffusion equation for the fluid concentration; it contains a source term for change in the average concentration of the diffusing species in the solid matrix. The second equation represents the assumption that the change in average concentration in a solid element is proportional to the difference between the average concentration in the solid and the concentration in the fluid times the solid-fluid partition coefficient. The double medium model is shown to apply to laboratory data on iron diffusion in fluid-bearing dunite and to measured oxygen isotope ratios at marble-metagranite contacts. In both examples, concentration profiles are calculated for diffusion taking place at constant temperature, where a boundary value changes suddenly and is subsequently held constant. Knowledge of solid diffusivities can set a lower bound to the length of time over which diffusion occurs, but only the product of effective fluid diffusivity and time is constrained for times longer than the characteristic solid diffusion time. The double medium results approach a local, grain-scale equilibrium model for times that are large relative to the time constant for solid diffusion.

The influence of vertical sorbed phase transport on the fate of organic chemicals in surface soils.

PubMed

McLachlan, Michael S; Czub, Gertje; Wania, Frank

2002-11-15

Gaseous exchange between surface soil and the atmosphere is an important process in the environmental fate of many chemicals. It was hypothesized that this process is influenced by vertical transport of chemicals sorbed to soil particles. Vertical sorbed phase transport in surface soils occurs by many processes such as bioturbation, cryoturbation, and erosion into cracks formed by soil drying. The solution of the advection/diffusion equation proposed by Jury et al. to describe organic chemical fate in a uniformly contaminated surface soil was modified to include vertical sorbed phase transport This process was modeled using a sorbed phase diffusion coefficient, the value of which was derived from soil carbon mass balances in the literature. The effective diffusivity of the chemical in a typical soil was greater in the modified model than in the model without sorbed phase transport for compounds with log K(OW) > 2 and log K(OA) > 6. Within this chemical partitioning space, the rate of volatilization from the surface soil was larger in the modified model than in the original model by up to a factor of 65. The volatilization rate was insensitive to the value of the sorbed phase diffusion coefficient throughout much of this chemical partitioning space, indicating that the surface soil layer was essentially well-mixed and that the mass transfer coefficient was determined by diffusion through the atmospheric boundary layer only. When this process was included in a non-steady-state regional multimedia chemical fate model running with a generic emissions scenario to air, the predicted soil concentrations increased by upto a factor of 25,whilethe air concentrations decreased by as much as a factor of approximately 3. Vertical sorbed phase transport in the soil thus has a major impact on predicted air and soil concentrations, the state of equilibrium, and the direction and magnitude of the chemical flux between air and soil. It is a key process influencing the environmental fate of persistent organic pollutants (POPs).

Diffusion in the special theory of relativity.

PubMed

Herrmann, Joachim

2009-11-01

The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane

NASA Astrophysics Data System (ADS)

Abd-El-Malek, Mina B.; Kassem, Magda M.; Meky, Mohammed L. M.

2002-03-01

The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.

Dynamics and Chemistry in Jovian Atmospheres: 2D Hydrodynamical Simulations

NASA Astrophysics Data System (ADS)

Bordwell, B. R.; Brown, B. P.; Oishi, J.

2016-12-01

A key component of our understanding of the formation and evolution of planetary systems is chemical composition. Problematically, however, in the atmospheres of cooler gas giants, dynamics on the same timescale as chemical reactions pull molecular abundances out of thermochemical equilibrium. These disequilibrium abundances are treated using what is known as the "quench" approximation, based upon the mixing length theory of convection. The validity of this approximation is questionable, though, as the atmospheres of gas giants encompass two distinct dynamic regimes: convective and radiative. To resolve this issue, we conduct 2D hydrodynamical simulations using the state-of-the-art pseudospectral simulation framework Dedalus. In these simulations, we solve the fully compressible equations of fluid motion in a local slab geometry that mimics the structure of a planetary atmosphere (convective zone underlying a radiative zone). Through the inclusion of passive tracers, we explore the transport properties of both regimes, and assess the validity of the classical eddy diffusion parameterization. With the addition of active tracers, we examine the interactions between dynamical and chemical processes, and generate prescriptions for the observational community. By providing insight into mixing and feedback mechanisms in Jovian atmospheres, this research lays a solid foundation for future global simulations and the construction of physically-sound models for current and future observations.

Ionic conduction and self-diffusion near infinitesimal concentration in lithium salt-organic solvent electrolytes

NASA Astrophysics Data System (ADS)

Aihara, Yuichi; Sugimoto, Kyoko; Price, William S.; Hayamizu, Kikuko

2000-08-01

The Debye-Hückel-Onsager and Nernst-Einstein equations, which are based on two different conceptual approaches, constitute the most widely used equations for relating ionic conduction to ionic mobility. However, both of these classical (simple) equations are predictive of ionic conductivity only at very low salt concentrations. In the present work the ionic conductivity of four organic solvent-lithium salt-based electrolytes were measured. These experimental conductivity values were then contrasted with theoretical values calculated using the translational diffusion (also known as self-diffusion or intradiffusion) coefficients of all of the species present obtained using pulsed-gradient spin-echo (1H, 19F and 7Li) nuclear magnetic resonance self-diffusion measurements. The experimental results verified the applicability of both theoretical approaches at very low salt concentrations for these particular systems as well as helping to clarify the reasons for the divergence between theory and experiment. In particular, it was found that the correspondence between the Debye-Hückel-Onsager equation and experimental values could be improved by using the measured solvent self-diffusion values to correct for salt-induced changes in the solution viscosity. The concentration dependence of the self-diffusion coefficients is discussed in terms of the Jones-Dole equation.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Obstructions to Existence in Fast-Diffusion Equations

NASA Astrophysics Data System (ADS)

Rodriguez, Ana; Vazquez, Juan L.

The study of nonlinear diffusion equations produces a number of peculiar phenomena not present in the standard linear theory. Thus, in the sub-field of very fast diffusion it is known that the Cauchy problem can be ill-posed, either because of non-uniqueness, or because of non-existence of solutions with small data. The equations we consider take the general form ut=( D( u, ux) ux) x or its several-dimension analogue. Fast diffusion means that D→∞ at some values of the arguments, typically as u→0 or ux→0. Here, we describe two different types of non-existence phenomena. Some fast-diffusion equations with very singular D do not allow for solutions with sign changes, while other equations admit only monotone solutions, no oscillations being allowed. The examples we give for both types of anomaly are closely related. The most typical examples are vt=( vx/∣ v∣) x and ut= uxx/∣ ux∣. For these equations, we investigate what happens to the Cauchy problem when we take incompatible initial data and perform a standard regularization. It is shown that the limit gives rise to an initial layer where the data become admissible (positive or monotone, respectively), followed by a standard evolution for all t>0, once the obstruction has been removed.

A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics

ERIC Educational Resources Information Center

Spayd, Kimberly; Puckett, James

2016-01-01

This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical…

A third-order computational method for numerical fluxes to guarantee nonnegative difference coefficients for advection-diffusion equations in a semi-conservative form

NASA Astrophysics Data System (ADS)

Sakai, K.; Watabe, D.; Minamidani, T.; Zhang, G. S.

2012-10-01

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations in a semi-conservative form, in which there exist two kinds of numerical fluxes at a cell surface and these two fluxes are not always coincident in non-uniform velocity fields. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter. We extend the present method into multi-dimensional equations. Numerical experiments for advection-diffusion equations showed nonoscillatory solutions.

Global Regularity and Time Decay for the 2D Magnetohydrodynamic Equations with Fractional Dissipation and Partial Magnetic Diffusion

NASA Astrophysics Data System (ADS)

Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong

2018-05-01

This paper focuses on a system of the 2D magnetohydrodynamic (MHD) equations with the kinematic dissipation given by the fractional operator (-Δ )^α and the magnetic diffusion by partial Laplacian. We are able to show that this system with any α >0 always possesses a unique global smooth solution when the initial data is sufficiently smooth. In addition, we make a detailed study on the large-time behavior of these smooth solutions and obtain optimal large-time decay rates. Since the magnetic diffusion is only partial here, some classical tools such as the maximal regularity property for the 2D heat operator can no longer be applied. A key observation on the structure of the MHD equations allows us to get around the difficulties due to the lack of full Laplacian magnetic diffusion. The results presented here are the sharpest on the global regularity problem for the 2D MHD equations with only partial magnetic diffusion.

Wind-Tunnel Modeling of Flow Diffusion over an Urban Complex.

DTIC Science & Technology

URBAN AREAS, *ATMOSPHERIC MOTION, *AIR POLLUTION, ATMOSPHERIC MOTION, WIND TUNNEL MODELS, HEAT, DIFFUSION , TURBULENT BOUNDARY LAYER, WIND, SKIN FRICTION, MATHEMATICAL MODELS, URBAN PLANNING, INDIANA.

Fisher equation for anisotropic diffusion: simulating South American human dispersals.

PubMed

Martino, Luis A; Osella, Ana; Dorso, Claudio; Lanata, José L

2007-09-01

The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal.

Viscous regularization of the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations

DOE PAGES

Delchini, Marc O.; Ragusa, Jean C.; Ferguson, Jim

2017-02-17

A viscous regularization technique, based on the local entropy residual, was proposed by Delchini et al. (2015) to stabilize the nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations using an artificial viscosity technique. This viscous regularization is modulated by the local entropy production and is consistent with the entropy minimum principle. However, Delchini et al. (2015) only based their work on the hyperbolic parts of the Grey Radiation-Hydrodynamic equations and thus omitted the relaxation and diffusion terms present in the material energy and radiation energy equations. Here in this paper, we extend the theoretical grounds for the method and derive an entropy minimum principlemore » for the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations. This further strengthens the applicability of the entropy viscosity method as a stabilization technique for radiation-hydrodynamic shock simulations. Radiative shock calculations using constant and temperature-dependent opacities are compared against semi-analytical reference solutions, and we present a procedure to perform spatial convergence studies of such simulations.« less

Localization and Ballistic Diffusion for the Tempered Fractional Brownian-Langevin Motion

NASA Astrophysics Data System (ADS)

Chen, Yao; Wang, Xudong; Deng, Weihua

2017-10-01

This paper discusses the tempered fractional Brownian motion (tfBm), its ergodicity, and the derivation of the corresponding Fokker-Planck equation. Then we introduce the generalized Langevin equation with the tempered fractional Gaussian noise for a free particle, called tempered fractional Langevin equation (tfLe). While the tfBm displays localization diffusion for the long time limit and for the short time its mean squared displacement (MSD) has the asymptotic form t^{2H}, we show that the asymptotic form of the MSD of the tfLe transits from t^2 (ballistic diffusion for short time) to t^{2-2H}, and then to t^2 (again ballistic diffusion for long time). On the other hand, the overdamped tfLe has the transition of the diffusion type from t^{2-2H} to t^2 (ballistic diffusion). The tfLe with harmonic potential is also considered.

A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal

NASA Astrophysics Data System (ADS)

Zhou, Zhenyu; Guo, Zhichang; Zhang, Dazhi; Wu, Boying

2018-04-01

Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona-Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.

Nature of self-diffusion in two-dimensional fluids

NASA Astrophysics Data System (ADS)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; Talkner, Peter; Kidera, Akinori; Lee, Eok Kyun

2017-12-01

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(t\\sqrt{{ln}t}), however with a rescaled time.

Dimensional reduction of a general advection–diffusion equation in 2D channels

NASA Astrophysics Data System (ADS)

Kalinay, Pavol; Slanina, František

2018-06-01

Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x. Unlike the previous specific cases, the presented procedure enables us to find the one-dimensional description of the confined diffusion even for non-conservative (vortex) forces, e.g. caused by flowing solvent dragging the particles. We show that the result is again the generalized Fick–Jacobs equation. Despite of non existing scalar potential in the case of vortex forces, the effective one-dimensional scalar potential, as well as the corresponding quasi-equilibrium and the effective diffusion coefficient can be always found.

Diffusion of liquid polystyrene into glassy poly(phenylene oxide) characterized by DSC

NASA Astrophysics Data System (ADS)

Li, Linling; Wang, Xiaoliang; Zhou, Dongshan; Xue, Gi

2013-03-01

We report a diffusion study on the polystyrene/poly(phenylene oxide) (PS/PPO) mixture consisted by the PS and PPO nanoparticles. Diffusion of liquid PS into glassy PPO (l-PS/g-PPO) is promoted by annealing the PS/PPO mixture at several temperatures below Tg of the PPO. By tracing the Tgs of the PS-rich domain behind the diffusion front using DSC, we get the relationships of PS weight fractions and diffusion front advances with the elapsed diffusion times at different diffusion temperatures using the Gordon-Taylor equation and core-shell model. We find that the plots of weight fraction of PS vs. elapsed diffusion times at different temperatures can be converted to a master curve by Time-Temperature superposition, and the shift factors obey the Arrhenius equation. Besides, the diffusion front advances of l-PS into g-PPO show an excellent agreement with the t1/2 scaling law at the beginning of the diffusion process, and the diffusion coefficients of different diffusion temperatures also obey the Arrhenius equation. We believe the diffusion mechanism for l-PS/g-PPO should be the Fickean law rather than the Case II, though there are departures of original linearity at longer diffusion times due to the limited liquid supply system. Diffusion of liquid polystyrene into glassy poly(phenylene oxide) characterized by DSC

Two-dimensional Radiative Magnetohydrodynamic Simulations of Partial Ionization in the Chromosphere. II. Dynamics and Energetics of the Low Solar Atmosphere

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

Martínez-Sykora, Juan; Pontieu, Bart De; Hansteen, Viggo H.

2017-09-20

We investigate the effects of interactions between ions and neutrals on the chromosphere and overlying corona using 2.5D radiative MHD simulations with the Bifrost code. We have extended the code capabilities implementing ion–neutral interaction effects using the generalized Ohm’s law, i.e., we include the Hall term and the ambipolar diffusion (Pedersen dissipation) in the induction equation. Our models span from the upper convection zone to the corona, with the photosphere, chromosphere, and transition region partially ionized. Our simulations reveal that the interactions between ionized particles and neutral particles have important consequences for the magnetothermodynamics of these modeled layers: (1) ambipolarmore » diffusion increases the temperature in the chromosphere; (2) sporadically the horizontal magnetic field in the photosphere is diffused into the chromosphere, due to the large ambipolar diffusion; (3) ambipolar diffusion concentrates electrical currents, leading to more violent jets and reconnection processes, resulting in (3a) the formation of longer and faster spicules, (3b) heating of plasma during the spicule evolution, and (3c) decoupling of the plasma and magnetic field in spicules. Our results indicate that ambipolar diffusion is a critical ingredient for understanding the magnetothermodynamic properties in the chromosphere and transition region. The numerical simulations have been made publicly available, similar to previous Bifrost simulations. This will allow the community to study realistic numerical simulations with a wider range of magnetic field configurations and physics modules than previously possible.« less

Two-dimensional Radiative Magnetohydrodynamic Simulations of Partial Ionization in the Chromosphere. II. Dynamics and Energetics of the Low Solar Atmosphere

NASA Astrophysics Data System (ADS)

Martínez-Sykora, Juan; De Pontieu, Bart; Carlsson, Mats; Hansteen, Viggo H.; Nóbrega-Siverio, Daniel; Gudiksen, Boris V.

2017-09-01

We investigate the effects of interactions between ions and neutrals on the chromosphere and overlying corona using 2.5D radiative MHD simulations with the Bifrost code. We have extended the code capabilities implementing ion-neutral interaction effects using the generalized Ohm’s law, I.e., we include the Hall term and the ambipolar diffusion (Pedersen dissipation) in the induction equation. Our models span from the upper convection zone to the corona, with the photosphere, chromosphere, and transition region partially ionized. Our simulations reveal that the interactions between ionized particles and neutral particles have important consequences for the magnetothermodynamics of these modeled layers: (1) ambipolar diffusion increases the temperature in the chromosphere; (2) sporadically the horizontal magnetic field in the photosphere is diffused into the chromosphere, due to the large ambipolar diffusion; (3) ambipolar diffusion concentrates electrical currents, leading to more violent jets and reconnection processes, resulting in (3a) the formation of longer and faster spicules, (3b) heating of plasma during the spicule evolution, and (3c) decoupling of the plasma and magnetic field in spicules. Our results indicate that ambipolar diffusion is a critical ingredient for understanding the magnetothermodynamic properties in the chromosphere and transition region. The numerical simulations have been made publicly available, similar to previous Bifrost simulations. This will allow the community to study realistic numerical simulations with a wider range of magnetic field configurations and physics modules than previously possible.

Vapor Transport Within the Thermal Diffusion Cloud Chamber

NASA Technical Reports Server (NTRS)

Ferguson, Frank T.; Heist, Richard H.; Nuth, Joseph A., III

2000-01-01

A review of the equations used to determine the 1-D vapor transport in the thermal diffusion cloud chamber (TDCC) is presented. These equations closely follow those of the classical Stefan tube problem in which there is transport of a volatile species through a noncondensible, carrier gas. In both cases, the very plausible assumption is made that the background gas is stagnant. Unfortunately, this assumption results in a convective flux which is inconsistent with the momentum and continuity equations for both systems. The approximation permits derivation of an analytical solution for the concentration profile in the Stefan tube, but there is no computational advantage in the case of the TDCC. Furthermore, the degree of supersaturation is a sensitive function of the concentration profile in the TD CC and the stagnant background gas approximation can make a dramatic difference in the calculated supersaturation. In this work, the equations typically used with a TDCC are compared with very general transport equations describing the 1-D diffusion of the volatile species. Whereas no pressure dependence is predicted with the typical equations, a strong pressure dependence is present with the more general equations given in this work. The predicted behavior is consistent with observations in diffusion cloud experiments. It appears that the new equations may account for much of the pressure dependence noted in TDCC experiments, but a comparison between the new equations and previously obtained experimental data are needed for verification.

Modeling studies of gas movement and moisture migration at Yucca Mountain, Nevada

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

Tsang, Y.W.; Pruess, K.

1991-06-01

Modeling studies on moisture redistribution processes that are mediated by gas phase flow and diffusion have been carried out. The problem addressed is the effect of a lowered humidity of the soil gas at the land surface on moisture removal from Yucca Mountain, the potential site for a high-level nuclear waste repository. At the land surface, humid formation gas contacts much drier atmospheric air. Near this contact, the humidity of the soil gas may be considerably lower than at greater depth, where the authors expect equilibrium with the liquid phase and close to 100% humidity. The lower relative humidity ofmore » the soil gas may be modeled by imposing, at the land surface, an additional negative capillary suction corresponding to vapor pressure lowering according to Kelvin`s Equation, thus providing a driving force for the upward movement of moisture in both the vapor and liquid phases. Sensitivity studies show that moisture removal from Yucca Mountain arising from the lowered-relative-humidity boundary condition is controlled by vapor diffusion. There is much experimental evidence in the soil literature that diffusion of vapor is enhanced due to pore-level phase change effects by a few orders of magnitude. Modeling results presented here will account for this enhancement in vapor diffusion.« less

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

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

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE PAGES

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

2016-07-26

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Ionic Channels as Natural Nanodevices

DTIC Science & Technology

2006-05-01

introduce the numerical techniques required to simulate charge transport in ion channels. [1] Using Poisson- Nernst -Planck-type (PNP) equations ...Eisenberg. 2003. Ionic diffusion through protein channels: from molecular description to continuum equations . Nanotech 2003, 3: 439-442. 4...Nadler, B., Schuss, Z., Singer, A., and R. S. Eisenberg. 2004. Ionic diffusion through confined geometries: from Langevin equations to partial

Feynman-Kac equation for anomalous processes with space- and time-dependent forces

NASA Astrophysics Data System (ADS)

Cairoli, Andrea; Baule, Adrian

2017-04-01

Functionals of a stochastic process Y(t) model many physical time-extensive observables, for instance particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the celebrated Feynman-Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is non-Brownian, e.g. an anomalous diffusive process, generalizations of the Feynman-Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is directly related to the memory kernel appearing in the generalized Feynman-Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in numerous experiments on biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman-Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are of particular relevance for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. An additional aim of this paper is to provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a subordinated process.

FDM study of ion exchange diffusion equation in glass

NASA Astrophysics Data System (ADS)

Zhou, Zigang; Yang, Yongjia; Wang, Qiang; Sun, Guangchun

2009-05-01

Ion-exchange technique in glass was developed to fabricate gradient refractive index optical devices. In this paper, the Finite Difference Method(FDM), which is used for the solution of ion-diffusion equation, is reported. This method transforms continual diffusion equation to separate difference equation. It unitizes the matrix of MATLAB program to solve the iteration process. The collation results under square boundary condition show that it gets a more accurate numerical solution. Compared to experiment data, the relative error is less than 0.2%. Furthermore, it has simply operation and kinds of output solutions. This method can provide better results for border-proliferation of the hexagonal and the channel devices too.

Gas-induced friction and diffusion of rigid rotors

NASA Astrophysics Data System (ADS)

Martinetz, Lukas; Hornberger, Klaus; Stickler, Benjamin A.

2018-05-01

We derive the Boltzmann equation for the rotranslational dynamics of an arbitrary convex rigid body in a rarefied gas. It yields as a limiting case the Fokker-Planck equation accounting for friction, diffusion, and nonconservative drift forces and torques. We provide the rotranslational friction and diffusion tensors for specular and diffuse reflection off particles with spherical, cylindrical, and cuboidal shape, and show that the theory describes thermalization, photophoresis, and the inverse Magnus effect in the free molecular regime.

Back-exchange: a novel approach to quantifying oxygen diffusion and surface exchange in ambient atmospheres.

PubMed

Cooper, Samuel J; Niania, Mathew; Hoffmann, Franca; Kilner, John A

2017-05-17

A novel two-step Isotopic Exchange (IE) technique has been developed to investigate the influence of oxygen containing components of ambient air (such as H 2 O and CO 2 ) on the effective surface exchange coefficient (k*) of a common mixed ionic electronic conductor material. The two step 'back-exchange' technique was used to introduce a tracer diffusion profile, which was subsequently measured using Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS). The isotopic fraction of oxygen in a dense sample as a function of distance from the surface, before and after the second exchange step, could then be used to determine the surface exchange coefficient in each atmosphere. A new analytical solution was found to the diffusion equation in a semi-infinite domain with a variable surface exchange boundary, for the special case where D* and k* are constant for all exchange steps. This solution validated the results of a numerical, Crank-Nicolson type finite-difference simulation, which was used to extract the parameters from the experimental data. When modelling electrodes, D* and k* are important input parameters, which significantly impact performance. In this study La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3-δ (LSCF6428) was investigated and it was found that the rate of exchange was increased by around 250% in ambient air compared to high purity oxygen at the same pO 2 . The three experiments performed in this study were used to validate the back-exchange approach and show its utility.

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 Simple, Analytical Model of Collisionless Magnetic Reconnection in a Pair Plasma

NASA Technical Reports Server (NTRS)

Hesse, Michael; Zenitani, Seiji; Kuznetova, Masha; Klimas, Alex

2011-01-01

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region, and to impart thermal energy to the plasma by means of quasi-viscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative, procedure. The solutions show expected features such as dominance of enthalpy flux in the reconnection outflow, as well as combination of adiabatic and quasi-viscous heating. Furthermore, the model predicts a maximum reconnection electric field of E(sup *)=0.4, normalized to the parameters at the inflow edge of the diffusion region.

A simple, analytical model of collisionless magnetic reconnection in a pair plasma

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

Hesse, Michael; Zenitani, Seiji; Kuznetsova, Masha

2009-10-15

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region and to impart thermal energy to the plasma by means of quasiviscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative procedure. The solutions show expected features such as dominance of enthalpymore » flux in the reconnection outflow, as well as combination of adiabatic and quasiviscous heating. Furthermore, the model predicts a maximum reconnection electric field of E{sup *}=0.4, normalized to the parameters at the inflow edge of the diffusion region.« less

Comparison of fluid neutral models for one-dimensional plasma edge modeling with a finite volume solution of the Boltzmann equation

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

Horsten, N., E-mail: niels.horsten@kuleuven.be; Baelmans, M.; Dekeyser, W.

2016-01-15

We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assumingmore » equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition for the fluid models: one based on a diffusion approximation and the other assuming a truncated Chapman-Enskog distribution. The pressure-diffusion model predicts the plasma sources very well. The diffusion boundary condition gives slightly better results overall. Although including an energy equation still improves the results, the assumption of equal ion and neutral temperature already gives a very good approximation.« less

Symmetry Reductions of Fourth-Order Nonlinear Diffusion Equations: Lubrication Model and Some Generalizations

NASA Astrophysics Data System (ADS)

Gandarias, M. L.; Medina, E.

Fourth-order nonlinear diffusion equations appear frequently in the description of physical processes, among these, the lubrication equation ut = (unuxxxx)x or the corresponding modified version ut = unuxxxx play an important role in the study of the interface movements. In this work we analyze the generalizations of the above equations given by ut = (f(u)uxxxx)x, ut = (f(u)uxxxx, and we find that if f(u) = un or f(u) = e-u the equations admit extra classical symmetries. The corresponding reductions are performed and some solutions are characterized.

Understanding Coupling of Global and Diffuse Solar Radiation with Climatic Variability

NASA Astrophysics Data System (ADS)

Hamdan, Lubna

Global solar radiation data is very important for wide variety of applications and scientific studies. However, this data is not readily available because of the cost of measuring equipment and the tedious maintenance and calibration requirements. Wide variety of models have been introduced by researchers to estimate and/or predict the global solar radiations and its components (direct and diffuse radiation) using other readily obtainable atmospheric parameters. The goal of this research is to understand the coupling of global and diffuse solar radiation with climatic variability, by investigating the relationships between these radiations and atmospheric parameters. For this purpose, we applied multilinear regression analysis on the data of National Solar Radiation Database 1991--2010 Update. The analysis showed that the main atmospheric parameters that affect the amount of global radiation received on earth's surface are cloud cover and relative humidity. Global radiation correlates negatively with both variables. Linear models are excellent approximations for the relationship between atmospheric parameters and global radiation. A linear model with the predictors total cloud cover, relative humidity, and extraterrestrial radiation is able to explain around 98% of the variability in global radiation. For diffuse radiation, the analysis showed that the main atmospheric parameters that affect the amount received on earth's surface are cloud cover and aerosol optical depth. Diffuse radiation correlates positively with both variables. Linear models are very good approximations for the relationship between atmospheric parameters and diffuse radiation. A linear model with the predictors total cloud cover, aerosol optical depth, and extraterrestrial radiation is able to explain around 91% of the variability in diffuse radiation. Prediction analysis showed that the linear models we fitted were able to predict diffuse radiation with efficiency of test adjusted R2 values equal to 0.93, using the data of total cloud cover, aerosol optical depth, relative humidity and extraterrestrial radiation. However, for prediction purposes, using nonlinear terms or nonlinear models might enhance the prediction of diffuse radiation.

Wave and pseudo-diffusion equations from squeezed states

NASA Technical Reports Server (NTRS)

Daboul, Jamil

1993-01-01

We show that the probability distributions P(sub n)(q,p;y) := the absolute value squared of (n(p,q;y), which are obtained from squeezed states, obey an interesting partial differential equation, to which we give two intuitive interpretations: as a wave equation in one space dimension; and as a pseudo-diffusion equation. We also study the corresponding Wehrl entropies S(sub n)(y), and we show that they have minima at zero squeezing, y = 0.

Gravitational instability of filamentary molecular clouds, including ambipolar diffusion; non-isothermal filament

NASA Astrophysics Data System (ADS)

Hosseinirad, Mohammad; Abbassi, Shahram; Roshan, Mahmood; Naficy, Kazem

2018-04-01

Recent observations of the filamentary molecular clouds show that their properties deviate from the isothermal equation of state. Theoretical investigations proposed that the logatropic and the polytropic equations of state with negative indexes can provide a better description for these filamentary structures. Here, we aim to compare the effects of these softer non-isothermal equations of state with their isothermal counterpart on the global gravitational instability of a filamentary molecular cloud. By incorporating the ambipolar diffusion, we use the non-ideal magnetohydrodynamics framework for a filament that is threaded by a uniform axial magnetic field. We perturb the fluid and obtain the dispersion relation both for the logatropic and polytropic equations of state by taking the effects of magnetic field and ambipolar diffusion into account. Our results suggest that, in absence of the magnetic field, a softer equation of state makes the system more prone to gravitational instability. We also observed that a moderate magnetic field is able to enhance the stability of the filament in a way that is sensitive to the equation of state in general. However, when the magnetic field is strong, this effect is suppressed and all the equations of state have almost the same stability properties. Moreover, we find that for all the considered equations of state, the ambipolar diffusion has destabilizing effects on the filament.

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

NASA Technical Reports Server (NTRS)

Wood, William A.

1997-01-01

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

Observation and interpretation of energy efficient, diffuse direct current glow discharge at atmospheric pressure

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

Tang, Jie, E-mail: tangjie1979@opt.ac.cn; Jiang, Weiman; Wang, Yishan

2015-08-24

A diffuse direct-current glow discharge was realized with low energy consumption and high energy utilization efficiency at atmospheric pressure. The formation of diffuse discharge was demonstrated by examining and comparing the electrical properties and optical emissions of plasmas. In combination with theoretical derivation and calculation, we draw guidelines that appearance of nitrogen ions at low electron density is crucial to enhance the ambipolar diffusion for the expansion of discharge channel and the increasing ambipolar diffusion near the cathode plays a key role in the onset of diffuse discharge. An individual-discharge-channel expansion model is proposed to explain the diffuse discharge formation.

Verification of a One-Dimensional Model of CO2 Atmospheric Transport Inside and Above a Forest Canopy Using Observations at the Norunda Research Station

NASA Astrophysics Data System (ADS)

Kovalets, Ivan; Avila, Rodolfo; Mölder, Meelis; Kovalets, Sophia; Lindroth, Anders

2018-02-01

A model of CO2 atmospheric transport in vegetated canopies is tested against measurements of the flow, as well as CO2 concentrations at the Norunda research station located inside a mixed pine-spruce forest. We present the results of simulations of wind-speed profiles and CO2 concentrations inside and above the forest canopy with a one-dimensional model of profiles of the turbulent diffusion coefficient above the canopy accounting for the influence of the roughness sub-layer on turbulent mixing according to Harman and Finnigan (Boundary-Layer Meteorol 129:323-351, 2008; hereafter HF08). Different modelling approaches are used to define the turbulent exchange coefficients for momentum and concentration inside the canopy: (1) the modified HF08 theory—numerical solution of the momentum and concentration equations with a non-constant distribution of leaf area per unit volume; (2) empirical parametrization of the turbulent diffusion coefficient using empirical data concerning the vertical profiles of the Lagrangian time scale and root-mean-square deviation of the vertical velocity component. For neutral, daytime conditions, the second-order turbulence model is also used. The flexibility of the empirical model enables the best fit of the simulated CO2 concentrations inside the canopy to the observations, with the results of simulations for daytime conditions inside the canopy layer only successful provided the respiration fluxes are properly considered. The application of the developed model for radiocarbon atmospheric transport released in the form of ^{14}CO2 is presented and discussed.

Verification of a One-Dimensional Model of CO2 Atmospheric Transport Inside and Above a Forest Canopy Using Observations at the Norunda Research Station

NASA Astrophysics Data System (ADS)

Kovalets, Ivan; Avila, Rodolfo; Mölder, Meelis; Kovalets, Sophia; Lindroth, Anders

2018-07-01

A model of CO2 atmospheric transport in vegetated canopies is tested against measurements of the flow, as well as CO2 concentrations at the Norunda research station located inside a mixed pine-spruce forest. We present the results of simulations of wind-speed profiles and CO2 concentrations inside and above the forest canopy with a one-dimensional model of profiles of the turbulent diffusion coefficient above the canopy accounting for the influence of the roughness sub-layer on turbulent mixing according to Harman and Finnigan (Boundary-Layer Meteorol 129:323-351, 2008; hereafter HF08). Different modelling approaches are used to define the turbulent exchange coefficients for momentum and concentration inside the canopy: (1) the modified HF08 theory—numerical solution of the momentum and concentration equations with a non-constant distribution of leaf area per unit volume; (2) empirical parametrization of the turbulent diffusion coefficient using empirical data concerning the vertical profiles of the Lagrangian time scale and root-mean-square deviation of the vertical velocity component. For neutral, daytime conditions, the second-order turbulence model is also used. The flexibility of the empirical model enables the best fit of the simulated CO2 concentrations inside the canopy to the observations, with the results of simulations for daytime conditions inside the canopy layer only successful provided the respiration fluxes are properly considered. The application of the developed model for radiocarbon atmospheric transport released in the form of ^{14}CO2 is presented and discussed.

Strongly anomalous diffusion in sheared magnetic configurations

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

Vanden Eijnden, E.; Balescu, R.

1996-03-01

The statistical behavior of magnetic lines in a sheared magnetic configuration with reference surface {ital x}=0 is investigated within the framework of the kinetic theory. A Liouville equation is associated with the equations of motion of the stochastic magnetic lines. After averaging over an ensemble of realizations, it yields a convection-diffusion equation within the quasilinear approximation. The diffusion coefficients are space dependent and peaked around the reference surface {ital x}=0. Due to the shear, the diffusion of lines away from the reference surface is slowed down. The behavior of the lines is asymptotically strongly non-Gaussian. The reference surface acts likemore » an attractor around which the magnetic lines spread with an effective subdiffusive behavior. Comparison is also made with more usual treatments based on the study of the first two moments equations. For sheared systems, it is explicitly shown that the Corrsin approximation assumed in the latter approach is no longer valid. It is also concluded that the diffusion coefficients cannot be derived from the mean square displacement of the magnetic lines in an inhomogeneous medium. {copyright} {ital 1996 American Institute of Physics.}« less

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes.

PubMed

Chatterjee, Abhijit; Vlachos, Dionisios G

2007-07-21

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.

Finite Difference Formulation for Prediction of Water Pollution

NASA Astrophysics Data System (ADS)

Johari, Hanani; Rusli, Nursalasawati; Yahya, Zainab

2018-03-01

Water is an important component of the earth. Human being and living organisms are demand for the quality of water. Human activity is one of the causes of the water pollution. The pollution happened give bad effect to the physical and characteristic of water contents. It is not practical to monitor all aspects of water flow and transport distribution. So, in order to help people to access to the polluted area, a prediction of water pollution concentration must be modelled. This study proposed a one-dimensional advection diffusion equation for predicting the water pollution concentration transport. The numerical modelling will be produced in order to predict the transportation of water pollution concentration. In order to approximate the advection diffusion equation, the implicit Crank Nicolson is used. For the purpose of the simulation, the boundary condition and initial condition, the spatial steps and time steps as well as the approximations of the advection diffusion equation have been encoded. The results of one dimensional advection diffusion equation have successfully been used to predict the transportation of water pollution concentration by manipulating the velocity and diffusion parameters.

Mathematical analysis of thermal diffusion shock waves

NASA Astrophysics Data System (ADS)

Gusev, Vitalyi; Craig, Walter; Livoti, Roberto; Danworaphong, Sorasak; Diebold, Gerald J.

2005-10-01

Thermal diffusion, also known as the Ludwig-Soret effect, refers to the separation of mixtures in a temperature gradient. For a binary mixture the time dependence of the change in concentration of each species is governed by a nonlinear partial differential equation in space and time. Here, an exact solution of the Ludwig-Soret equation without mass diffusion for a sinusoidal temperature field is given. The solution shows that counterpropagating shock waves are produced which slow and eventually come to a halt. Expressions are found for the shock time for two limiting values of the starting density fraction. The effects of diffusion on the development of the concentration profile in time and space are found by numerical integration of the nonlinear differential equation.

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

NASA Astrophysics Data System (ADS)

Remizov, I. D.

2012-07-01

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.

Equatorial ground ice on Mars: Steady-state stability

NASA Technical Reports Server (NTRS)

Mellon, Michael T.; Jakosky, Bruce M.; Postawko, Susan E.

1993-01-01

Current Martian equatorial surface temperatures are too warm for water ice to exist at the surface for any appreciable length of time before subliming into the atmosphere. Subsurface temperatures are generally warmer still and, despite the presence of a diffusive barrier of porous regolith material, it has been shown by Smoluchowski, Clifford and Hillel, and Fanale et al. that buried ground ice will also sublime and be lost to the atmosphere in a relatively short time. We investigate the behavior of this subliming subsurface ice and show that it is possible for ice to maintain at a steady-state depth, where sublimation and diffusive loss to the atmosphere is balanced by resupply from beneath by diffusion and recondensation of either a deeper buried ice deposits or ground water. We examine the behavior of equatorial ground ice with a numercial time-marching molecular diffusion model. In our model we allow for diffusion of water vapor through a porous regolith, variations in diffusivity and porosity with ice content, and recondensation of sublimed water vapor. A regolith containing considerable amounts of ice can still be very porous, allowing water vapor to diffuse up from deeper within the ice layer where temperatures are warmer due to the geothermal gradient. This vapor can then recondense nearer to the surface where ice had previously sublimed and been lost to the atmosphere. As a result we find that ice deposits migrate to find a steady-state depth, which represents a balance between diffusive loss to the atmosphere through the overlying porous regolith and diffusive resupply through a porous icy regolith below. This depth depends primarily on the long-term mean surface temperature and the nature of the geothermal gradient, and is independent of the ice-free porosity and the regolith diffusivity. Only the rate of loss of ground ice depends on diffusive properties.

Modeling boundary measurements of scattered light using the corrected diffusion approximation

PubMed Central

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

2012-01-01

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

Optical Oversampled Analog-to-Digital Conversion

DTIC Science & Technology

1992-06-29

hologram weights and interconnects in the digital image halftoning configuration. First, no temporal error diffusion occurs in the digital image... halftoning error diffusion ar- chitecture as demonstrated by Equation (6.1). Equation (6.2) ensures that the hologram weights sum to one so that the exact...optimum halftone image should be faster. Similarly, decreased convergence time suggests that an error diffusion filter with larger spatial dimensions

Modelling the radiotherapy effect in the reaction-diffusion equation.

PubMed

Borasi, Giovanni; Nahum, Alan

2016-09-01

In recent years, the reaction-diffusion (Fisher-Kolmogorov) equation has received much attention from the oncology research community due to its ability to describe the infiltrating nature of glioblastoma multiforme and its extraordinary resistance to any type of therapy. However, in a number of previous papers in the literature on applications of this equation, the term (R) expressing the 'External Radiotherapy effect' was incorrectly derived. In this note we derive an analytical expression for this term in the correct form to be included in the reaction-diffusion equation. The R term has been derived starting from the Linear-Quadratic theory of cell killing by ionizing radiation. The correct definition of R was adopted and the basic principles of differential calculus applied. The compatibility of the R term derived here with the reaction-diffusion equation was demonstrated. Referring to a typical glioblastoma tumour, we have compared the results obtained using our expression for the R term with the 'incorrect' expression proposed by other authors. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Diffusion coefficients of phenylbutazone in supercritical CO2 and in ethanol.

PubMed

Kong, Chang Yi; Watanabe, Kou; Funazukuri, Toshitaka

2013-03-01

The diffusion coefficients D(12) of phenylbutazone at infinite dilution in supercritical CO(2) were measured by the chromatographic impulse response (CIR) method. The measurements were carried out over the temperature range from 308.2 to 343.2 K at pressures up to 40.0 MPa. In addition, the D(12) data of phenylbutazone at infinite dilution in ethanol were also measured by the Taylor dispersion method at 298.2-333.2K and at atmospheric pressure. The D(12) value of phenylbutazone increased from 4.45×10(-10) m(2) s(-1) at 298.2 K and 0.1 MPa in ethanol to about 1.43×10(-8) m(2) s(-1) at 343.2 K and 14.0 MPa in supercritical CO(2). It was found that all diffusion data of phenylbutazone measured in this study in supercritical CO(2) and in ethanol can be satisfactorily represented by the hydrodynamic equation over a wide range of fluid viscosity from supercritical state to liquid state with average absolute relative deviation of 5.4% for 112 data points. Copyright © 2013 Elsevier B.V. All rights reserved.

Effects of Gravity on Soot Formation in a Coflow Laminar Methane/Air Diffusion Flame

NASA Astrophysics Data System (ADS)

Kong, Wenjun; Liu, Fengshan

2010-04-01

Simulations of a laminar coflow methane/air diffusion flame at atmospheric pressure are conducted to gain better understanding of the effects of gravity on soot formation by using detailed gas-phase chemistry, complex thermal and transport properties coupled with a semiempirical two-equation soot model and a nongray radiation model. Soot oxidation by O2, OH and O was considered. Thermal radiation was calculated using the discrete ordinate method coupled with a statistical narrow-band correlated-K model. The spectral absorption coefficient of soot was obtained by Rayleigh's theory for small particles. The results show that the peak temperature decreases with the decrease of the gravity level. The peak soot volume fraction in microgravity is about twice of that in normal gravity under the present conditions. The numerical results agree very well with available experimental results. The predicted results also show that gravity affects the location and intensity for soot nucleation and surface growth.

Epstein-Plesset theory based measurements of concentration of nitrogen gases dissolved in aerated water

NASA Astrophysics Data System (ADS)

Sasaki, Masashi; Yamashita, Tatsuya; Ando, Keita

2016-11-01

Microbubble aeration is used to dissolved gases into water and is an important technique in agriculture and industry. We can measure concentration of dissolved oxygen (DO) in aerated water by commercial DO meters. However, there do not exist commercially available techniques to measure concentration to dissolved nitrogen (DN). In the present study, we propose the method to measure DN in aerated water with the aid of Epstein-Plesset-type analysis. Gas-supersaturated tap water is produced by applying aeration with micro-sized air bubbles and is then stored in a glass container open to the atmosphere. Diffusion-driven growth of bubbles nucleated at the container surface is recorded with a video camera. The bubble growth rate is compare to the extended Epstein-Plesset theory that models mass transfer of both DO and DN into the surface-attached bubbles base on the diffusion equation. Given the DO measurements, we can obtain the DN level by fitting in the comparison.

A Model of Magnetic Braking of Solar Rotation that Satisfies Observational Constraints

NASA Astrophysics Data System (ADS)

Denissenkov, Pavel A.

2010-08-01

The model of magnetic braking of solar rotation considered by Charbonneau & MacGregor has been modified so that it is able to reproduce for the first time the rotational evolution of both the fastest and slowest rotators among solar-type stars in open clusters of different ages, without coming into conflict with other observational constraints, such as the time evolution of the atmospheric Li abundance in solar twins and the thinness of the solar tachocline. This new model assumes that rotation-driven turbulent diffusion, which is thought to amplify the viscosity and magnetic diffusivity in stellar radiative zones, is strongly anisotropic with the horizontal components of the transport coefficients strongly dominating over those in the vertical direction. Also taken into account is the poloidal field decay that helps to confine the width of the tachocline at the solar age. The model's properties are investigated by numerically solving the azimuthal components of the coupled momentum and magnetic induction equations in two dimensions using a finite element method.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

PubMed

Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q

2013-03-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

PubMed Central

Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.

2013-01-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian. PMID:23772179

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

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

2009-07-01

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

Nature of self-diffusion in two-dimensional fluids

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

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; ...

2017-12-18

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

NASA Astrophysics Data System (ADS)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

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

Davis, C.G.

Starting with the initial understanding that pulsation in variable stars is caused by the heat engine of Hydrogen and Helium ionization in their atmospheres (A.S. Eddington in Cox 1980) it was soon realized that non-linear effects were responsible for the detailed features on their light and velocity curves. With the advent of the computer we were able to solve the coupled set of hydrodynamics and radiation diffusion equations to model these non-linear features. This paper describes some recent model results for long period (LP) Cepheids in an attempt to get another handle on Cepheid masses. Section II discusses these resultsmore » and Section III considers the implications of these model results on the problem of the Cepheid mass discrepancy.« less

Diffuse reflectance relations based on diffusion dipole theory for large absorption and reduced scattering

NASA Astrophysics Data System (ADS)

Bremmer, Rolf H.; van Gemert, Martin J. C.; Faber, Dirk J.; van Leeuwen, Ton G.; Aalders, Maurice C. G.

2013-08-01

Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 m at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys. 19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime scenes.

Diffusion in random networks: Asymptotic properties, and numerical and engineering approximations

NASA Astrophysics Data System (ADS)

Padrino, Juan C.; Zhang, Duan Z.

2016-11-01

The ensemble phase averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of a set of pockets connected by tortuous channels. Inside a channel, we assume that fluid transport is governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pores mass density. The so-called dual porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain, whose solution is sought numerically. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt- 1 / 4 rather than xt- 1 / 2 as in the traditional theory. This early time sub-diffusive similarity can be explained by random walk theory through the network. In addition, by applying concepts of fractional calculus, we show that, for small time, the governing equation reduces to a fractional diffusion equation with known solution. We recast this solution in terms of special functions easier to compute. Comparison of the numerical and exact solutions shows excellent agreement.

Diffusive retention of atmospheric gases in chert

NASA Astrophysics Data System (ADS)

Pettitt, E.; Cherniak, D. J.; Watson, E. B.; Schaller, M. F.

2016-12-01

Throughout Earth's history, the volatile contents (N2, CO2, Ar) of both deep and shallow terrestrial reservoirs has been dynamic. Volatiles are important chemical constituents because they play a significant role in regulating Earth's climate, mediating the evolution of complex life, and controlling the properties of minerals and rocks. Estimating levels of atmospheric volatiles in the deep geological past requires interrogation of materials that have acquired and retained a chemical memory from that time. Cherts have the potential to trap atmospheric components during formation and later release those gases for analysis in the laboratory. However, cherts have been underexploited in this regard, partly because their ability to retain a record of volatile components has not been adequately evaluated. Before cherts can be reliably used as indicators of past levels of major atmospheric gases, it is crucial that we understand the diffusive retentiveness of these cryptocrystalline silica phases. As the first step toward quantifying the diffusivity and solubility of carbon dioxide and nitrogen in chert, we have performed 1-atmosphere diffusive-uptake experiments at temperatures up to 450°C. Depth profiles of in-diffusing gases are measured by nuclear reaction analysis (NRA) to help us understand the molecular-scale transport of volatiles and thus the validity of using chert-bound volatiles to record information about Earth history. Data collected to date suggest that at least some cherts are ideal storage containers and can retain volatiles for a geologically long time. In addition to these diffusion experiments, preliminary online-crush fast-scan measurements using a quadrupole mass spectrometer indicate that atmospheric volatiles are released upon crushing various chert samples. By coupling such volatile-release measurements made by mass spectrometry with diffusion experiments, we are uniquely able to address the storage and fidelity of volatiles bound in crustal materials; an important step toward understanding atmospheric evolution over geologic history.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

Is the kinetic equation for turbulent gas-particle flows ill posed?

PubMed

Reeks, M; Swailes, D C; Bragg, A D

2018-02-01

This paper is about the kinetic equation for gas-particle flows, in particular its well-posedness and realizability and its relationship to the generalized Langevin model (GLM) probability density function (PDF) equation. Previous analyses, e.g. [J.-P. Minier and C. Profeta, Phys. Rev. E 92, 053020 (2015)PLEEE81539-375510.1103/PhysRevE.92.053020], have concluded that this kinetic equation is ill posed, that in particular it has the properties of a backward heat equation, and as a consequence, its solution will in the course of time exhibit finite-time singularities. We show that this conclusion is fundamentally flawed because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra positive diffusion that always outweighs the negative diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these positive and negative contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing, we have drawn attention to the limitations of the GLM approach, which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.

Ash fallout scenarios at Vesuvius: Numerical simulations and implications for hazard assessment

NASA Astrophysics Data System (ADS)

Macedonio, G.; Costa, A.; Folch, A.

2008-12-01

Volcanic ash fallout subsequent to a possible renewal of the Vesuvius activity represents a serious threat to the highly urbanized area around the volcano. In order to assess the relative hazard we consider three different possible scenarios such as those following Plinian, Sub-Plinian, and violent Strombolian eruptions. Reference eruptions for each scenario are similar to the 79 AD (Pompeii), the 1631 AD (or 472 AD) and the 1944 AD Vesuvius events, respectively. Fallout deposits for the first two scenarios are modeled using HAZMAP, a model based on a semi-analytical solution of the 2D advection-diffusion-sedimentation equation. In contrast, fallout following a violent Strombolian event is modeled by means of FALL3D, a numerical model based on the solution of the full 3D advection-diffusion-sedimentation equation which is valid also within the atmospheric boundary layer. Inputs for models are total erupted mass, eruption column height, bulk grain-size, bulk component distribution, and a statistical set of wind profiles obtained by the NCEP/NCAR re-analysis. We computed ground load probability maps for different ash loadings. In the case of a Sub-Plinian scenario, the most representative tephra loading maps in 16 cardinal directions were also calculated. The probability maps obtained for the different scenarios are aimed to give support to the risk mitigation strategies.

Advection-diffusion model for the simulation of air pollution distribution from a point source emission

NASA Astrophysics Data System (ADS)

Ulfah, S.; Awalludin, S. A.; Wahidin

2018-01-01

Advection-diffusion model is one of the mathematical models, which can be used to understand the distribution of air pollutant in the atmosphere. It uses the 2D advection-diffusion model with time-dependent to simulate air pollution distribution in order to find out whether the pollutants are more concentrated at ground level or near the source of emission under particular atmospheric conditions such as stable, unstable, and neutral conditions. Wind profile, eddy diffusivity, and temperature are considered in the model as parameters. The model is solved by using explicit finite difference method, which is then visualized by a computer program developed using Lazarus programming software. The results show that the atmospheric conditions alone influencing the level of concentration of pollutants is not conclusive as the parameters in the model have their own effect on each atmospheric condition.

Void Formation during Diffusion - Two-Dimensional Approach

NASA Astrophysics Data System (ADS)

Wierzba, Bartek

2016-06-01

The final set of equations defining the interdiffusion process in solid state is presented. The model is supplemented by vacancy evolution equation. The competition between the Kirkendall shift, backstress effect and vacancy migration is considered. The proper diffusion flux based on the Nernst-Planck formula is proposed. As a result, the comparison of the experimental and calculated evolution of the void formation in the Fe-Pd diffusion couple is shown.

New Solution of Diffusion-Advection Equation for Cosmic-Ray Transport Using Ultradistributions

NASA Astrophysics Data System (ADS)

Rocca, M. C.; Plastino, A. R.; Plastino, A.; Ferri, G. L.; de Paoli, A.

2015-11-01

In this paper we exactly solve the diffusion-advection equation (DAE) for cosmic-ray transport. For such a purpose we use the Theory of Ultradistributions of J. Sebastiao e Silva, to give a general solution for the DAE. From the ensuing solution, we obtain several approximations as limiting cases of various situations of physical and astrophysical interest. One of them involves Solar cosmic-rays' diffusion.

Hypersonic Flight Mechanics. [for atmospheric entry trajectories

NASA Technical Reports Server (NTRS)

Busemann, A.; Vinh, N. X.; Culp, R. D.

1976-01-01

The effects of aerodynamic forces on trajectories at orbital speeds are discussed in terms of atmospheric models. The assumptions for the model are spherical symmetry, nonrotating, and an exponential atmosphere. The equations of flight, and the performance in extra-atmospheric flight are discussed along with the return to the atmosphere, and the entry. Solutions of the exact equations using directly matched asymptotic expansions are presented.

Large eddy simulation modeling of particle-laden flows in complex terrain

NASA Astrophysics Data System (ADS)

Salesky, S.; Giometto, M. G.; Chamecki, M.; Lehning, M.; Parlange, M. B.

2017-12-01

The transport, deposition, and erosion of heavy particles over complex terrain in the atmospheric boundary layer is an important process for hydrology, air quality forecasting, biology, and geomorphology. However, in situ observations can be challenging in complex terrain due to spatial heterogeneity. Furthermore, there is a need to develop numerical tools that can accurately represent the physics of these multiphase flows over complex surfaces. We present a new numerical approach to accurately model the transport and deposition of heavy particles in complex terrain using large eddy simulation (LES). Particle transport is represented through solution of the advection-diffusion equation including terms that represent gravitational settling and inertia. The particle conservation equation is discretized in a cut-cell finite volume framework in order to accurately enforce mass conservation. Simulation results will be validated with experimental data, and numerical considerations required to enforce boundary conditions at the surface will be discussed. Applications will be presented in the context of snow deposition and transport, as well as urban dispersion.

A Least-Squares Transport Equation Compatible with Voids

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

Hansen, Jon; Peterson, Jacob; Morel, Jim

Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transportmore » equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S n formulation represents an excellent alternative to existing second-order S n transport formulations« less

Contribution of Atmospheric Diffusion Conditions to the Recent Improvement in Air Quality in China

PubMed Central

Wang, Xiaoyan; Wang, Kaicun; Su, Liangyuan

2016-01-01

This study analyzed hourly mass concentration observations of PM2.5 (particulate matters with diameter less than 2.5 μm) at 512 stations in China from December 2013 to May 2015. We found that the mean concentrations of PM2.5 during the winter and spring of 2015 Dec. 2014 to Feb. 2015 and Mar. 2015 to May 2015) decreased by 20% and 14% compared to the previous year, respectively. Hazardous air-quality days decreased by 11% in 2015 winter, with more frequent good to unhealthy days; and the good and moderate air-quality days in 2015 spring increased by 9% corresponding to the less occurrence of unhealthy conditions. We compared the atmospheric diffusion conditions during these two years and quantified its contribution to the improvement of air quality during the first half of 2015 over China. Our results show that during the 2015 winter and spring, 70% and 57% of the 512 stations experienced more favorable atmospheric diffusion conditions compared to those of previous year. Over central and northern China, approximately 40% of the total decrease in PM2.5 during the 2015 winter can be attributed to the favorable atmospheric diffusion conditions. The atmospheric diffusion conditions during the spring of 2015 were not as favorable as in winter; and the average contributions of the atmospheric conditions were slight. PMID:27805030

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

A new nonlinear diffusion formalism in a magnetized plasma - Application to space physics and astrophysics

NASA Technical Reports Server (NTRS)

Karimbadi, H.; Krauss-Varban, D.

1992-01-01

A novel diffusion formalism that takes into account the finite width of resonances is presented. The resonance diagram technique is shown to reproduce the details of the particle orbits very accurately, and can be used to determine the acceleration/scattering in the presence of a given wave spectrum. Ways in which the nonlinear orbits can be incorporated into the diffusion equation are shown. The resulting diffusion equation is an extension of the Q-L theory to cases where the waves have large amplitudes and/or are coherent. This new equation does not have a gap at 90 deg in cases where the individual orbits can cross the gap. The conditions under which the resonance gap at 90-deg pitch angle exits are also examined.

Finite-volume scheme for anisotropic diffusion

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

Es, Bram van, E-mail: bramiozo@gmail.com; FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands"1; Koren, Barry

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

NASA Astrophysics Data System (ADS)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

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

NASA Astrophysics Data System (ADS)

Luce, C.; Tonina, D.; Gariglio, F. P.; Applebee, R.

2012-12-01

Differences in the diurnal variations of temperature at different depths in streambed sediments are commonly used for estimating vertical fluxes of water in the streambed. We applied spatial and temporal rescaling of the advection-diffusion equation to derive two new relationships that greatly extend the kinds of information that can be derived from streambed temperature measurements. The first equation provides a direct estimate of the Peclet number from the amplitude decay and phase delay information. The analytical equation is explicit (e.g. no numerical root-finding is necessary), and invertable. The thermal front velocity can be estimated from the Peclet number when the thermal diffusivity is known. The second equation allows for an independent estimate of the thermal diffusivity directly from the amplitude decay and phase delay information. Several improvements are available with the new information. The first equation uses a ratio of the amplitude decay and phase delay information; thus Peclet number calculations are independent of depth. The explicit form also makes it somewhat faster and easier to calculate estimates from a large number of sensors or multiple positions along one sensor. Where current practice requires a priori estimation of streambed thermal diffusivity, the new approach allows an independent calculation, improving precision of estimates. Furthermore, when many measurements are made over space and time, expectations of the spatial correlation and temporal invariance of thermal diffusivity are valuable for validation of measurements. Finally, the closed-form explicit solution allows for direct calculation of propagation of uncertainties in error measurements and parameter estimates, providing insight about error expectations for sensors placed at different depths in different environments as a function of surface temperature variation amplitudes. The improvements are expected to increase the utility of temperature measurement methods for studying groundwater-surface water interactions across space and time scales. We discuss the theoretical implications of the new solutions supported by examples with data for illustration and validation.

The dynamics of oceanic fronts. I - The Gulf Stream

NASA Technical Reports Server (NTRS)

Kao, T. W.

1980-01-01

The establishment and maintenance of the mean hydrographic properties of large-scale density fronts in the upper ocean is considered. The dynamics is studied by posing an initial value problem starting with a near-surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density; full time dependent diffusion and Navier-Stokes equations are then used with constant eddy diffusion and viscosity coefficients, together with a constant Coriolis parameter. Scaling analysis reveals three independent scales of the problem including the radius of deformation of the inertial length, buoyancy length, and diffusive length scales. The governing equations are then suitably scaled and the resulting normalized equations are shown to depend on the Ekman number alone for problems of oceanic interest. It is concluded that the mean Gulf Stream dynamics can be interpreted in terms of a solution of the Navier-Stokes and diffusion equations, with the cross-stream circulation responsible for the maintenance of the front; this mechanism is suggested for the maintenance of the Gulf Stream dynamics.

Research and Development of Methods for Estimating Physicochemical Properties of Organic Compounds of Environmental Concern

DTIC Science & Technology

1979-02-01

coefficient (at equilibrium) when hysteresis is apparent. 6. Coefficient n in Freundlich equation for 1/n soil or sediment adsorption isotherms ýX - KC . 7...Biodegradation Chemical structures cal clasaes (e.g., Diffusion Correlations phenols). General Diffusion coefficients Equations terms for organic...OF THE FATE AND TRANSPORT OF ORGANIC CHEMICALS Adsorption coefficients: K, n* from Freundlich equation + Desorption coefficients: K’*, n’* from

Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations.

PubMed

Sánchez-Garduño, Faustino; Pérez-Velázquez, Judith

This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D (0) = 0) and advection-degenerate (at h '(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h ( u ): (1)   h '( u ) is constant k , (2)   h '( u ) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE.

Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations

PubMed Central

Sánchez-Garduño, Faustino

2016-01-01

This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D(0) = 0) and advection-degenerate (at h′(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h(u): (1)  h′(u) is constant k, (2)  h′(u) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE. PMID:27689131

Nonlocal electrical diffusion equation

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

2016-07-01

In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

Isothermal absorption of soluble gases by atmospheric nanoaerosols

NASA Astrophysics Data System (ADS)

Elperin, T.; Fominykh, A.; Krasovitov, B.; Lushnikov, A.

2013-01-01

We investigate mass transfer during the isothermal absorption of atmospheric trace soluble gases by a single droplet whose size is comparable to the molecular mean free path in air at normal conditions. It is assumed that the trace reactant diffuses to the droplet surface and then reacts with the substances inside the droplet according to the first-order rate law. Our analysis applies a flux-matching theory of transport processes in gases and assumes constant thermophysical properties of the gases and liquids. We derive an integral equation of Volterra type for the transient molecular flux density to a liquid droplet and solve it numerically. Numerical calculations are performed for absorption of sulfur dioxide (SO2), dinitrogen trioxide (N2O3), and chlorine (Cl2) by liquid nanoaerosols accompanied by chemical dissociation reaction. It is shown that during gas absorption by nanoaerosols, the kinetic effects play a significant role, and neglecting kinetic effects leads to a significant overestimation of the soluble gas flux into a droplet during the entire period of gas absorption.

Photochemical Control of the Distribution of Venusian Water and Comparison to Venus Express SOIR Observations

NASA Astrophysics Data System (ADS)

Parkinson, Chris; Yung, Yuk; Esposito, Larry; Gao, Peter; Bougher, Steve

2014-11-01

We use the JPL/Caltech 1-D KINETICS photochemical model to solve the continuity diffusion equation for the atmospheric constituent abundances and total number density as a function of radial distance from the planet Venus. The photochemistry of the Venus atmosphere from 58 to 112 km is modeled using an updated and expanded chemical scheme (Zhang et al., 2010; 2012), guided by the results of recent observations. We mainly follow Zhang et al. (2010; 2012) to guide our choice of boundary conditions for 40 species. We fit the SOIR Venus Express results of 1 ppm at 70-90 km (Bertaux et al (2007) by modeling water from between 10 - 35 ppm at our 58 km lower boundary and using an SO2 mixing ratio of 25 ppm as our nominal reference value. We then vary the SO2 mixing ratio at the lower boundary between 5 and 75 ppm and find that it can control the water distribution at higher altitudes.

Isothermal absorption of soluble gases by atmospheric nanoaerosols.

PubMed

Elperin, T; Fominykh, A; Krasovitov, B; Lushnikov, A

2013-01-01

We investigate mass transfer during the isothermal absorption of atmospheric trace soluble gases by a single droplet whose size is comparable to the molecular mean free path in air at normal conditions. It is assumed that the trace reactant diffuses to the droplet surface and then reacts with the substances inside the droplet according to the first-order rate law. Our analysis applies a flux-matching theory of transport processes in gases and assumes constant thermophysical properties of the gases and liquids. We derive an integral equation of Volterra type for the transient molecular flux density to a liquid droplet and solve it numerically. Numerical calculations are performed for absorption of sulfur dioxide (SO(2)), dinitrogen trioxide (N(2)O(3)), and chlorine (Cl(2)) by liquid nanoaerosols accompanied by chemical dissociation reaction. It is shown that during gas absorption by nanoaerosols, the kinetic effects play a significant role, and neglecting kinetic effects leads to a significant overestimation of the soluble gas flux into a droplet during the entire period of gas absorption.

Synchronous flowering of the rubber tree (Hevea brasiliensis) induced by high solar radiation intensity.

PubMed

Yeang, Hoong-Yeet

2007-01-01

How tropical trees flower synchronously near the equator in the absence of significant day length variation or other meteorological cues has long been a puzzle. The rubber tree (Hevea brasiliensis) is used as a model to investigate this phenomenon. The annual cycle of solar radiation intensity is shown to correspond closely with the flowering of the rubber tree planted near the equator and in the subtropics. Unlike in temperate regions, where incoming solar radiation (insolation) is dependent on both day length and radiation intensity, insolation at the equator is due entirely to the latter. Insolation at the upper atmosphere peaks twice a year during the spring and autumn equinoxes, but the actual solar radiation that reaches the ground is attenuated to varying extents in different localities. The rubber tree shows one or two flowering seasons a year (with major and minor seasons in the latter) in accordance with the solar radiation intensity received. High solar radiation intensity, and in particular bright sunshine (as distinct from prolonged diffuse radiation), induces synchronous anthesis and blooming in Hevea around the time of the equinoxes. The same mechanism may be operational in other tropical tree species.

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography.

PubMed

Biswas, Samir Kumar; Kanhirodan, Rajan; Vasu, Ram Mohan; Roy, Debasish

2011-08-01

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.

Modeling short-term concentration fluctuations of semi-volatile pollutants in the soil-plant-atmosphere system.

PubMed

Bao, Zhongwen; Haberer, Christina M; Maier, Uli; Beckingham, Barbara; Amos, Richard T; Grathwohl, Peter

2016-11-01

Temperature changes can drive cycling of semi-volatile pollutants between different environmental compartments (e.g. atmosphere, soil, plants). To evaluate the impact of daily temperature changes on atmospheric concentration fluctuations we employed a physically based model coupling soil, plants and the atmosphere, which accounts for heat transport, effective gas diffusion, sorption and biodegradation in the soil as well as eddy diffusion and photochemical oxidation in the atmospheric boundary layer of varying heights. The model results suggest that temperature-driven re-volatilization and uptake in soils cannot fully explain significant diurnal concentration fluctuations of atmospheric pollutants as for example observed for polychlorinated biphenyls (PCBs). This holds even for relatively low water contents (high gas diffusivity) and high sorption capacity of the topsoil (high organic carbon content and high pollutant concentration in the topsoil). Observed concentration fluctuations, however, can be easily matched if a rapidly-exchanging environmental compartment, such as a plant layer, is introduced. At elevated temperatures, plants release organic pollutants, which are rapidly distributed in the atmosphere by eddy diffusion. For photosensitive compounds, e.g. some polycyclic aromatic hydrocarbons (PAHs), decreasing atmospheric concentrations would be expected during daytime for the bare soil scenario. This decline is buffered by a plant layer, which acts as a ground-level reservoir. The modeling results emphasize the importance of a rapidly-exchanging compartment above ground to explain short-term atmospheric concentration fluctuations. Copyright © 2016 Elsevier B.V. All rights reserved.

On Entropy Production in the Madelung Fluid and the Role of Bohm's Potential in Classical Diffusion

NASA Astrophysics Data System (ADS)

Heifetz, Eyal; Tsekov, Roumen; Cohen, Eliahu; Nussinov, Zohar

2016-07-01

The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow (or decrease) due to an expansion (or compression) of the Madelung fluid. These effects result from the interference between solutions of the Schrödinger equation. Growth of the Shannon entropy due to expansion is common in diffusive processes. However, in the latter the process is irreversible while the processes in the Madelung fluid are always reversible. The relations between interference, compressibility and variation of the Shannon entropy are then examined in several simple examples. Furthermore, we demonstrate that for classical diffusive processes, the "force" accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. Expressing then the diffusion coefficient in terms of the Planck constant reveals the lower bound given by the Heisenberg uncertainty principle in terms of the product between the gas mean free path and the Brownian momentum.

Building 1D resonance broadened quasilinear (RBQ) code for fast ions Alfvénic relaxations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Berk, Herbert

2016-10-01

The performance of the burning plasma is limited by the confinement of superalfvenic fusion products, e.g. alpha particles, which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using a resonance line broadened diffusion coefficient. The interaction of fast ions and AEs is captured for cases where there are either isolated or overlapping modes. A new code RBQ1D is being built which constructs diffusion coefficients based on realistic eigenfunctions that are determined by the ideal MHD code NOVA. The wave particle interaction can be reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. Hence to a good approximation the Quasi-Linear (QL) diffusion equation only contains derivatives in the angular momentum. The diffusion equation is then one dimensional that is efficiently solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The evolution of fast ion constants of motion is governed by the QL diffusion equations which are adapted to find the ion distribution function.

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

NASA Astrophysics Data System (ADS)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

Chemical ageing and transformation of diffusivity in semi-solid multi-component organic aerosol particles

NASA Astrophysics Data System (ADS)

Pfrang, C.; Shiraiwa, M.; Pöschl, U.

2011-04-01

Recent experimental evidence underlines the importance of reduced diffusivity in amorphous semi-solid or glassy atmospheric aerosols. This paper investigates the impact of diffusivity on the ageing of multi-component reactive organic particles representative of atmospheric cooking aerosols. We apply and extend the recently developed KM-SUB model in a study of a 12-component mixture containing oleic and palmitoleic acids. We demonstrate that changes in the diffusivity may explain the evolution of chemical loss rates in ageing semi-solid particles, and we resolve surface and bulk processes under transient reaction conditions considering diffusivities altered by oligomerisation. This new model treatment allows prediction of the ageing of mixed organic multi-component aerosols over atmospherically relevant time scales and conditions. We illustrate the impact of changing diffusivity on the chemical half-life of reactive components in semi-solid particles, and we demonstrate how solidification and crust formation at the particle surface can affect the chemical transformation of organic aerosols.

Chemical ageing and transformation of diffusivity in semi-solid multi-component organic aerosol particles

NASA Astrophysics Data System (ADS)

Pfrang, C.; Shiraiwa, M.; Pöschl, U.

2011-07-01

Recent experimental evidence underlines the importance of reduced diffusivity in amorphous semi-solid or glassy atmospheric aerosols. This paper investigates the impact of diffusivity on the ageing of multi-component reactive organic particles approximating atmospheric cooking aerosols. We apply and extend the recently developed KM-SUB model in a study of a 12-component mixture containing oleic and palmitoleic acids. We demonstrate that changes in the diffusivity may explain the evolution of chemical loss rates in ageing semi-solid particles, and we resolve surface and bulk processes under transient reaction conditions considering diffusivities altered by oligomerisation. This new model treatment allows prediction of the ageing of mixed organic multi-component aerosols over atmospherically relevant timescales and conditions. We illustrate the impact of changing diffusivity on the chemical half-life of reactive components in semi-solid particles, and we demonstrate how solidification and crust formation at the particle surface can affect the chemical transformation of organic aerosols.

Applicability of the Fokker-Planck equation to the description of diffusion effects on nucleation

NASA Astrophysics Data System (ADS)

Sorokin, M. V.; Dubinko, V. I.; Borodin, V. A.

2017-01-01

The nucleation of islands in a supersaturated solution of surface adatoms is considered taking into account the possibility of diffusion profile formation in the island vicinity. It is shown that the treatment of diffusion-controlled cluster growth in terms of the Fokker-Planck equation is justified only provided certain restrictions are satisfied. First of all, the standard requirement that diffusion profiles of adatoms quickly adjust themselves to the actual island sizes (adiabatic principle) can be realized only for sufficiently high island concentration. The adiabatic principle is essential for the probabilities of adatom attachment to and detachment from island edges to be independent of the adatom diffusion profile establishment kinetics, justifying the island nucleation treatment as the Markovian stochastic process. Second, it is shown that the commonly used definition of the "diffusion" coefficient in the Fokker-Planck equation in terms of adatom attachment and detachment rates is justified only provided the attachment and detachment are statistically independent, which is generally not the case for the diffusion-limited growth of islands. We suggest a particular way to define the attachment and detachment rates that allows us to satisfy this requirement as well. When applied to the problem of surface island nucleation, our treatment predicts the steady-state nucleation barrier, which coincides with the conventional thermodynamic expression, even though no thermodynamic equilibrium is assumed and the adatom diffusion is treated explicitly. The effect of adatom diffusional profiles on the nucleation rate preexponential factor is also discussed. Monte Carlo simulation is employed to analyze the applicability domain of the Fokker-Planck equation and the diffusion effect beyond it. It is demonstrated that a diffusional cloud is slowing down the nucleation process for a given monomer interaction with the nucleus edge.

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Diffusion Processes Satisfying a Conservation Law Constraint

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

Bakosi, J.; Ristorcelli, J. R.

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Abundance stratification in the atmospheres of blue horizontal-branch stars

NASA Astrophysics Data System (ADS)

LeBlanc, F.

2013-12-01

Horizontal-branch stars with effective temperatures larger than approximately 11 500 K show abundance anomalies as well as other peculiar observational properties believed to be due to atomic diffusion in their atmosphere. These stars possess low rotational velocities that makes it possible for atomic diffusion to come into play and are therefore of great interest with respect to diffusion theory. Observational anomalies of blue horizontal-branch stars found in globular clusters such as photometric jumps and gaps are reviewed. Recent detections of vertical stratification of elements are also discussed. These results are compared to predictions of atmospheric modeling while including vertical stratification of the elements. The atmospheric structure of these models is calculated self-consistently while taking into account vertical stratification of the elements.

A model for shrinkage strain in photo polymerization of dental composites.

PubMed

Petrovic, Ljubomir M; Atanackovic, Teodor M

2008-04-01

We formulate a new model for the shrinkage strain developed during photo polymerization in dental composites. The model is based on the diffusion type fractional order equation, since it has been proved that polymerization reaction is diffusion controlled (Atai M, Watts DC. A new kinetic model for the photo polymerization shrinkage-strain of dental composites and resin-monomers. Dent Mater 2006;22:785-91). Our model strongly confirms the observation by Atai and Watts (see reference details above) and their experimental results. The shrinkage strain is modeled by a nonlinear differential equation in (see reference details above) and that equation must be solved numerically. In our approach, we use the linear fractional order differential equation to describe the strain rate due to photo polymerization. This equation is solved exactly. As shrinkage is a consequence of the polymerization reaction and polymerization reaction is diffusion controlled, we postulate that shrinkage strain rate is described by a diffusion type equation. We find explicit form of solution to this equation and determine the strain in the resin monomers. Also by using equations of linear viscoelasticity, we determine stresses in the polymer due to the shrinkage. The time evolution of stresses implies that the maximal stresses are developed at the very beginning of the polymerization process. The stress in a dental composite that is light treated has the largest value short time after the treatment starts. The strain settles at the constant value in the time of about 100s (for the cases treated in Atai and Watts). From the model developed here, the shrinkage strain of dental composites and resin monomers is analytically determined. The maximal value of stresses is important, since this value must be smaller than the adhesive bond strength at cavo-restoration interface. The maximum stress determined here depends on the diffusivity coefficient. Since diffusivity coefficient increases as polymerization proceeds, it follows that the periods of light treatments should be shorter at the beginning of the treatment and longer at the end of the treatment, with dark interval between the initial low intensity and following high intensity curing. This is because at the end of polymerization the stress relaxation cannot take place.

REVIEWS OF TOPICAL PROBLEMS: Free convection in geophysical processes

NASA Astrophysics Data System (ADS)

Alekseev, V. V.; Gusev, A. M.

1983-10-01

A highly significant geophysical process, free convection, is examined. Thermal convection often controls the dynamical behavior in several of the earth's envelopes: the atmosphere, ocean, and mantle. Section 2 sets forth the thermohydrodynamic equations that describe convection in a compressible or incompressible fluid, thermochemical convection, and convection in the presence of thermal diffusion. Section 3 reviews the mechanisms for the origin of the global atmospheric and oceanic circulation. Interlatitudinal convection and jet streams are discussed, as well as monsoon circulation and the mean meridional circulation of ocean waters due to the temperature and salinity gradients. Also described are the hypotheses for convective motion in the mantle and the thermal-wave (moving flame) mechanism for inducing global circulation (the atmospheres of Venus and Mars provide illustrations). Eddy formation by convection in a centrifugal force field is considered. Section 4 deals with medium- and small-scale convective processes, including hurricane systems with phase transitions, cellular cloud structure, and convection penetrating into the ocean, with its stepped vertical temperature and salinity microstructure. Self-oscillatory processes involving convection in fresh-water basins are discussed, including effects due to the anomalous (p,T) relation for water.

Technical report series on global modeling and data assimilation. Volume 2: Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere

NASA Technical Reports Server (NTRS)

Li, Yong; Moorthi, S.; Bates, J. Ray; Suarez, Max J.

1994-01-01

High order horizontal diffusion of the form K Delta(exp 2m) is widely used in spectral models as a means of preventing energy accumulation at the shortest resolved scales. In the spectral context, an implicit formation of such diffusion is trivial to implement. The present note describes an efficient method of implementing implicit high order diffusion in global finite difference models. The method expresses the high order diffusion equation as a sequence of equations involving Delta(exp 2). The solution is obtained by combining fast Fourier transforms in longitude with a finite difference solver for the second order ordinary differential equation in latitude. The implicit diffusion routine is suitable for use in any finite difference global model that uses a regular latitude/longitude grid. The absence of a restriction on the timestep makes it particularly suitable for use in semi-Lagrangian models. The scale selectivity of the high order diffusion gives it an advantage over the uncentering method that has been used to control computational noise in two-time-level semi-Lagrangian models.

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

PubMed

Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

2011-03-21

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

Cross-Diffusion Induced Turing Instability and Amplitude Equation for a Toxic-Phytoplankton-Zooplankton Model with Nonmonotonic Functional Response

NASA Astrophysics Data System (ADS)

Han, Renji; Dai, Binxiang

2017-06-01

The spatiotemporal pattern induced by cross-diffusion of a toxic-phytoplankton-zooplankton model with nonmonotonic functional response is investigated in this paper. The linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes in the framework of a weakly nonlinear theory, and the stability analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, we illustrate the theoretical results via numerical simulations. It is shown that the spatiotemporal distribution of the plankton is homogeneous in the absence of cross-diffusion. However, when the cross-diffusivity is greater than the critical value, the spatiotemporal distribution of all the plankton species becomes inhomogeneous in spaces and results in different kinds of patterns: spot, stripe, and the mixture of spot and stripe patterns depending on the cross-diffusivity. Simultaneously, the impact of toxin-producing rate of toxic-phytoplankton (TPP) species and natural death rate of zooplankton species on pattern selection is also explored.

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

PubMed

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

2011-01-01

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

Cusping, transport and variance of solutions to generalized Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Carnaffan, Sean; Kawai, Reiichiro

2017-06-01

We study properties of solutions to generalized Fokker-Planck equations through the lens of the probability density functions of anomalous diffusion processes. In particular, we examine solutions in terms of their cusping, travelling wave behaviours, and variance, within the framework of stochastic representations of generalized Fokker-Planck equations. We give our analysis in the cases of anomalous diffusion driven by the inverses of the stable, tempered stable and gamma subordinators, demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model. We also analyse the cases where the underlying anomalous diffusion contains a Lévy jump component in the parent process, and when a diffusion process is time changed by an uninverted Lévy subordinator. On the whole, we present a combination of four criteria which serve as a theoretical basis for model selection, statistical inference and predictions for physical experiments on anomalously diffusing systems. We discuss possible applications in physical experiments, including, with reference to specific examples, the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue.

Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model

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

Litvinenko, Yuri E.; Fichtner, Horst; Walter, Dominik

2017-05-20

We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatmentmore » of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection–diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.« less

Some Fundamental Issues of Mathematical Simulation in Biology

NASA Astrophysics Data System (ADS)

Razzhevaikin, V. N.

2018-02-01

Some directions of simulation in biology leading to original formulations of mathematical problems are overviewed. Two of them are discussed in detail: the correct solvability of first-order linear equations with unbounded coefficients and the construction of a reaction-diffusion equation with nonlinear diffusion for a model of genetic wave propagation.

Numerical study of centrifugal compressor stage vaneless diffusers

NASA Astrophysics Data System (ADS)

Galerkin, Y.; Soldatova, K.; Solovieva, O.

2015-08-01

The authors analyzed CFD calculations of flow in vaneless diffusers with relative width in range from 0.014 to 0.100 at inlet flow angles in range from 100 to 450 with different inlet velocity coefficients, Reynolds numbers and surface roughness. The aim is to simulate calculated performances by simple algebraic equations. The friction coefficient that represents head losses as friction losses is proposed for simulation. The friction coefficient and loss coefficient are directly connected by simple equation. The advantage is that friction coefficient changes comparatively little in range of studied parameters. Simple equations for this coefficient are proposed by the authors. The simulation accuracy is sufficient for practical calculations. To create the complete algebraic model of the vaneless diffuser the authors plan to widen this method of modeling to diffusers with different relative length and for wider range of Reynolds numbers.

Integral approximations to classical diffusion and smoothed particle hydrodynamics

DOE PAGES

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

2014-12-31

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

Adjoint Sensitivity Analysis of Radiative Transfer Equation: Temperature and Gas Mixing Ratio Weighting Functions for Remote Sensing of Scattering Atmospheres in Thermal IR

NASA Technical Reports Server (NTRS)

Ustinov, E.

1999-01-01

Sensitivity analysis based on using of the adjoint equation of radiative transfer is applied to the case of atmospheric remote sensing in the thermal spectral region with non-negligeable atmospheric scattering.

Spin diffusion and torques in disordered antiferromagnets

NASA Astrophysics Data System (ADS)

Manchon, Aurelien

2017-03-01

We have developed a drift-diffusion equation of spin transport in collinear bipartite metallic antiferromagnets. Starting from a model tight-binding Hamiltonian, we obtain the quantum kinetic equation within Keldysh formalism and expand it to the lowest order in spatial gradient using Wigner expansion method. In the diffusive limit, these equations track the spatio-temporal evolution of the spin accumulations and spin currents on each sublattice of the antiferromagnet. We use these equations to address the nature of the spin transfer torque in (i) a spin-valve composed of a ferromagnet and an antiferromagnet, (ii) a metallic bilayer consisting of an antiferromagnet adjacent to a heavy metal possessing spin Hall effect, and in (iii) a single antiferromagnet possessing spin Hall effect. We show that the latter can experience a self-torque thanks to the non-vanishing spin Hall effect in the antiferromagnet.

Quantitative correlations between collision induced dissociation mass spectrometry coupled with electrospray ionization or atmospheric pressure chemical ionization mass spectrometry - Experiment and theory

NASA Astrophysics Data System (ADS)

Ivanova, Bojidarka; Spiteller, Michael

2018-04-01

The problematic that we consider in this paper treats the quantitative correlation model equations between experimental kinetic and thermodynamic parameters of coupled electrospray ionization (ESI) mass spectrometry (MS) or atmospheric pressure chemical ionization (APCI) mass spectrometry with collision induced dissociation mass spectrometry, accounting for the fact that the physical phenomena and mechanisms of ESI- and APCI-ion formation are completely different. There are described forty two fragment reactions of three analytes under independent ESI- and APCI-measurements. The developed new quantitative models allow us to study correlatively the reaction kinetics and thermodynamics using the methods of mass spectrometry, which complementary application with the methods of the quantum chemistry provide 3D structural information of the analytes. Both static and dynamic quantum chemical computations are carried out. The object of analyses are [2,3-dimethyl-4-(4-methyl-benzoyl)-2,3-di-p-tolyl-cyclobutyl]-p-tolyl-methanone (1) and the polycyclic aromatic hydrocarbons derivatives of dibenzoperylen (2) and tetrabenzo [a,c,fg,op]naphthacene (3), respectively. As far as (1) is known to be a product of [2π+2π] cycloaddition reactions of chalcone (1,3-di-p-tolyl-propenone), however producing cyclic derivatives with different stereo selectivity, so that the study provide crucial data about the capability of mass spectrometry to provide determine the stereo selectivity of the analytes. This work also first provides quantitative treatment of the relations '3D molecular/electronic structures'-'quantum chemical diffusion coefficient'-'mass spectrometric diffusion coefficient', thus extending the capability of the mass spectrometry for determination of the exact 3D structure of the analytes using independent measurements and computations of the diffusion coefficients. The determination of the experimental diffusion parameters is carried out within the 'current monitoring method' evaluating the translation diffusion of charged analytes, while the theoretical modelling of MS ions and computations of theoretical diffusion coefficients are based on the Arrhenius type behavior of the charged species under ESI- and APCI-conditions. Although the study provide certain sound considerations for the quantitative relations between the reaction kinetic-thermodynamics and 3D structure of the analytes together with correlations between 3D molecular/electronic structures-quantum chemical diffusion coefficient-mass spectrometric diffusion coefficient, which contribute significantly to the structural analytical chemistry, the results have importance to other areas such as organic synthesis and catalysis as well.

Breakdown of the reaction-diffusion master equation with nonelementary rates

NASA Astrophysics Data System (ADS)

Smith, Stephen; Grima, Ramon

2016-05-01

The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion processes on a spatial lattice, assuming well mixing only on the length scale of the lattice. It is clear that, for the sake of consistency, the solution of the RDME of a chemical system should converge to the solution of the CME of the same system in the limit of fast diffusion: Indeed, this has been tacitly assumed in most literature concerning the RDME. We show that, in the limit of fast diffusion, the RDME indeed converges to a master equation but not necessarily the CME. We introduce a class of propensity functions, such that if the RDME has propensities exclusively of this class, then the RDME converges to the CME of the same system, whereas if the RDME has propensities not in this class, then convergence is not guaranteed. These are revealed to be elementary and nonelementary propensities, respectively. We also show that independent of the type of propensity, the RDME converges to the CME in the simultaneous limit of fast diffusion and large volumes. We illustrate our results with some simple example systems and argue that the RDME cannot generally be an accurate description of systems with nonelementary rates.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

NASA Astrophysics Data System (ADS)

Broche, Rita de Cássia D. S.; de Oliveira, Luiz Augusto F.

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem.

Observations of gamma radiation between 0.4 MeV and 7 MeV at balloon altitudes using a Compton telescope

NASA Technical Reports Server (NTRS)

Lockwood, J. A.; Webber, W. R.; Friling, L. A.; Macri, J.; Hsieh, L.

1981-01-01

Balloon-borne measurements of the atmospheric and diffuse gamma-ray flux in the energy range 0.4-7.0 MeV with a Compton telescope, which included pulse-shape discrimination of the first scattering detector and a time-of-flight system between the first and second detector elements, are reported. Comparison of the diffuse cosmic gamma-ray flux to the atmospheric gamma rays indicates that 0.2-5.0 MeV is the optimum energy range for measurements made at the top of the earth's atmosphere. The measured total atmospheric gamma-ray flux between zero and 40 deg has an energy spectrum that agrees with the calculations of Ling (1975). Observations indicate that the ratio of the diffuse to atmospheric gamma ray fluxes at 3.5 g/sq cm is a maximum, about 1.0, between 0.7 and 3.0 MeV.

Fick's second law transformed: one path to cloaking in mass diffusion.

PubMed

Guenneau, S; Puvirajesinghe, T M

2013-06-06

Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional, time-dependent, anisotropic heterogeneous Fick's equation is considered, which is a parabolic partial differential equation also applicable to heat diffusion, when convection occurs, for example, in fluids. This theory is illustrated with finite-element computations for a liposome particle surrounded by a cylindrical multi-layered cloak in a water-based environment, and for a spherical multi-layered cloak consisting of layers of fluid with an isotropic homogeneous diffusivity, deduced from an effective medium approach. Initial potential applications could be sought in bioengineering.

Stefan-Maxwell Relations and Heat Flux with Anisotropic Transport Coefficients for Ionized Gases in a Magnetic Field with Application to the Problem of Ambipolar Diffusion

NASA Astrophysics Data System (ADS)

Kolesnichenko, A. V.; Marov, M. Ya.

2018-01-01

The defining relations for the thermodynamic diffusion and heat fluxes in a multicomponent, partially ionized gas mixture in an external electromagnetic field have been obtained by the methods of the kinetic theory. Generalized Stefan-Maxwell relations and algebraic equations for anisotropic transport coefficients (the multicomponent diffusion, thermal diffusion, electric and thermoelectric conductivity coefficients as well as the thermal diffusion ratios) associated with diffusion-thermal processes have been derived. The defining second-order equations are derived by the Chapman-Enskog procedure using Sonine polynomial expansions. The modified Stefan-Maxwell relations are used for the description of ambipolar diffusion in the Earth's ionospheric plasma (in the F region) composed of electrons, ions of many species, and neutral particles in a strong electromagnetic field.

From quantum stochastic differential equations to Gisin-Percival state diffusion

NASA Astrophysics Data System (ADS)

Parthasarathy, K. R.; Usha Devi, A. R.

2017-08-01

Starting from the quantum stochastic differential equations of Hudson and Parthasarathy [Commun. Math. Phys. 93, 301 (1984)] and exploiting the Wiener-Itô-Segal isomorphism between the boson Fock reservoir space Γ (L2(R+ ) ⊗(Cn⊕Cn ) ) and the Hilbert space L2(μ ) , where μ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion {B (t ) ,t ≥0 } , we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation [N. Gisin and J. Percival, J. Phys. A 167, 315 (1992)]. This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a randomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

Onset of 2D magnetic reconnection in the solar photosphere, chromosphere, and corona

NASA Astrophysics Data System (ADS)

Snow, B.; Botha, G. J. J.; McLaughlin, J. A.; Hillier, A.

2018-01-01

Aims: We aim to investigate the onset of 2D time-dependent magnetic reconnection that is triggered using an external (non-local) velocity driver located away from, and perpendicular to, an equilibrium Harris current sheet. Previous studies have typically utilised an internal trigger to initiate reconnection, for example initial conditions centred on the current sheet. Here, an external driver allows for a more naturalistic trigger as well as the study of the earlier stages of the reconnection start-up process. Methods: Numerical simulations solving the compressible, resistive magnetohydrodynamic (MHD) equations were performed to investigate the reconnection onset within different atmospheric layers of the Sun, namely the corona, chromosphere and photosphere. Results: A reconnecting state is reached for all atmospheric heights considered, with the dominant physics being highly dependent on atmospheric conditions. The coronal case achieves a sharp rise in electric field (indicative of reconnection) for a range of velocity drivers. For the chromosphere, we find a larger velocity amplitude is required to trigger reconnection (compared to the corona). For the photospheric environment, the electric field is highly dependent on the inflow speed; a sharp increase in electric field is obtained only as the velocity entering the reconnection region approaches the Alfvén speed. Additionally, the role of ambipolar diffusion is investigated for the chromospheric case and we find that the ambipolar diffusion alters the structure of the current density in the inflow region. Conclusions: The rate at which flux enters the reconnection region is controlled by the inflow velocity. This determines all aspects of the reconnection start-up process, that is, the early onset of reconnection is dominated by the advection term in Ohm's law in all atmospheric layers. A lower plasma-β enhances reconnection and creates a large change in the electric field. A high plasma-β hinders the reconnection, yielding a sharp rise in the electric field only when the velocity flowing into the reconnection region approaches the local Alfvén speed.

Tracking Water Diffusion Fronts in a Highly Viscous Aerosol Particle

NASA Astrophysics Data System (ADS)

Bastelberger, Sandra; Krieger, Ulrich; Peter, Thomas

2016-04-01

Field measurements indicate that atmospheric secondary aerosol particles can be present in a highly viscous, glassy state [1]. In contrast to liquid state particles, the gas phase equilibration is kinetically limited and governed by condensed phase diffusion. In recent water diffusion experiments on highly viscous single aerosol particles levitated in an electrodynamic balance (EDB) we observed a characteristic shift behavior of the Mie whispering gallery modes (WGM) indicative of the changing radial structure of the particle, thus providing us with an experimental method to track the diffusion process inside the particle. When a highly viscous, homogeneous particle is exposed to an abrupt increase in relative humidity, the rapid gas phase diffusion and strong concentration dependence of the diffusion coefficient in the condensed phase lead to extremely steep water concentration gradients inside the particle, reminiscent of diffusion fronts. The resulting quasi step-like concentration profile motivates the introduction of a simple core-shell model describing the morphology of the non-equilibrium particle during humidification. The subsequent particle growth and reduction of the shell refractive index can be observed as red and blueshift behavior of the WGM, respectively. The shift pattern can be attributed to a core-shell radius ratio and particle radius derived from model calculations [2]. If supplemented with growth information obtained from the WGM redshift and thermodynamic equilibrium data, we can infer a comprehensive picture of the time evolution of the diffusion fronts in the framework of our core-shell model. The measured time dependent concentration profile is then compared with simulations solving the non-linear diffusion equation [3] [1] Virtanen, A., et al., Nature, 467, 824-827, 2010 [2] Kaiser, T., Schweiger, G., Computers in Physics, Vol. 7, No. 6, 682-686, Nov/Dec 1993 [3] Zobrist, B., Soonsin, V., Luo, B.P., Peter, T. et al., Phys. Chem. Chem. Phys., 13,3514-3526, 2011

Constraining Gas Diffusivity-Soil Water Content Relationships in Forest Soils Using Surface Chamber Fluxes and Depth Profiles of Multiple Trace Gases

NASA Astrophysics Data System (ADS)

Dore, J. E.; Kaiser, K.; Seybold, E. C.; McGlynn, B. L.

2012-12-01

Forest soils are sources of carbon dioxide (CO2) to the atmosphere and can act as either sources or sinks of methane (CH4) and nitrous oxide (N2O), depending on redox conditions and other factors. Soil moisture is an important control on microbial activity, redox conditions and gas diffusivity. Direct chamber measurements of soil-air CO2 fluxes are facilitated by the availability of sensitive, portable infrared sensors; however, corresponding CH4 and N2O fluxes typically require the collection of time-course physical samples from the chamber with subsequent analyses by gas chromatography (GC). Vertical profiles of soil gas concentrations may also be used to derive CH4 and N2O fluxes by the gradient method; this method requires much less time and many fewer GC samples than the direct chamber method, but requires that effective soil gas diffusivities are known. In practice, soil gas diffusivity is often difficult to accurately estimate using a modeling approach. In our study, we apply both the chamber and gradient methods to estimate soil trace gas fluxes across a complex Rocky Mountain forested watershed in central Montana. We combine chamber flux measurements of CO2 (by infrared sensor) and CH4 and N2O (by GC) with co-located soil gas profiles to determine effective diffusivity in soil for each gas simultaneously, over-determining the diffusion equations and providing constraints on both the chamber and gradient methodologies. We then relate these soil gas diffusivities to soil type and volumetric water content in an effort to arrive at empirical parameterizations that may be used to estimate gas diffusivities across the watershed, thereby facilitating more accurate, frequent and widespread gradient-based measurements of trace gas fluxes across our study system. Our empirical approach to constraining soil gas diffusivity is well suited for trace gas flux studies over complex landscapes in general.

Ar Atmosphere: Implications for Structure and Composition of Mercury's Crust

NASA Technical Reports Server (NTRS)

Killen, R. M.; Morgan, T. H.

2001-01-01

We examine the possibilities of sustaining an argon atmosphere by diffusion from the upper 10 km of crust, and alternatively by effusion from a molten or previously molten area at great depth . Ar-40 in the atmospheres of the planets is a measure of potassium abundance in the interiors since Ar-40 is a product of radiogenic decay of K-40 by electron capture with the subsequent emission of a 1.46 eV gamma-ray. Although the Ar-40 in the earth's atmosphere is expected to have accumulated since the late bombardment, Ar-40 in surface-bounded exospheres is eroded quickly by photoionization and electron impact ionization. Thus, the argon content in the exospheres of the Moon, Mercury and probably Europa is representative of current effusion rather than accumulation over the lifetime of the body. Argon content will be a function of K content, temperature, grain size distribution, connected pore volume and possible seismic activity. Although Mercury and the Moon differ in many details, we can train the solutions to diffusion equations to predict the average lunar atmosphere. Then these parameters can be varied for Hermean conditions. Assuming a lunar crustal potassium abundance of 300 ppm, the observed argon atmosphere requires equilibrium between the argon production in the upper 9 Km of the moon (1.135 x 10(exp -3) cm(exp -3) s(exp -1)) and its loss. Hodges et al. conclude that this loss rate and the observed time variability requires argon release through seismic activity, tapping a deep argon source. An important observation is that the extreme surface of the Moon is enhanced in argon rather than depleted, as one would expect from outgassing of radiogenic argon. Manka and Michel concluded that ion implantation explains the surface enhancement of Ar-40. About half of the argon ions produced in the lunar atmosphere would return to the surface, where they would become embedded in the rocks. Similarly, at Mercury we expect the surface rocks to be enhanced in Ar-40 wherever the magnetosphere has been open over time. Thus the measurement of surface composition will reveal the long-term effects of solar wind-magnetosphere interaction. Additional information is contained in the original extended abstract.

Recursion equations in predicting band width under gradient elution.

PubMed

Liang, Heng; Liu, Ying

2004-06-18

The evolution of solute zone under gradient elution is a typical problem of non-linear continuity equation since the local diffusion coefficient and local migration velocity of the mass cells of solute zones are the functions of position and time due to space- and time-variable mobile phase composition. In this paper, based on the mesoscopic approaches (Lagrangian description, the continuity theory and the local equilibrium assumption), the evolution of solute zones in space- and time-dependent fields is described by the iterative addition of local probability density of the mass cells of solute zones. Furthermore, on macroscopic levels, the recursion equations have been proposed to simulate zone migration and spreading in reversed-phase high-performance liquid chromatography (RP-HPLC) through directly relating local retention factor and local diffusion coefficient to local mobile phase concentration. This new approach differs entirely from the traditional theories on plate concept with Eulerian description, since band width recursion equation is actually the accumulation of local diffusion coefficients of solute zones to discrete-time slices. Recursion equations and literature equations were used in dealing with same experimental data in RP-HPLC, and the comparison results show that the recursion equations can accurately predict band width under gradient elution.

Kinetic multi-layer model of aerosol surface and bulk chemistry (KM-SUB): the influence of interfacial transport and bulk diffusion on the oxidation of oleic acid by ozone

NASA Astrophysics Data System (ADS)

Shiraiwa, Manabu; Pfrang, Christian; Pöschl, Ulrich

2010-05-01

Aerosols are ubiquitous in the atmosphere and have strong effects on climate and public health. Gas-particle interactions can significantly change the physical and chemical properties of aerosols such as toxicity, reactivity, hygroscopicity and radiative properties. Chemical reactions and mass transport lead to continuous transformation and changes in the composition of atmospheric aerosols ("chemical aging"). Resistor model formulations are widely used to describe and investigate heterogeneous reactions and multiphase processes in laboratory, field and model studies of atmospheric chemistry. The traditional resistor models, however, are usually based on simplifying assumptions such as steady state conditions, homogeneous mixing, and limited numbers of non-interacting species and processes. In order to overcome these limitations, Pöschl, Rudich and Ammann have developed a kinetic model framework (PRA framework) with a double-layer surface concept and universally applicable rate equations and parameters for mass transport and chemical reactions at the gas-particle interface of aerosols and clouds [1]. Based on the PRA framework, we present a novel kinetic multi-layer model that explicitly resolves mass transport and chemical reaction at the surface and in the bulk of aerosol particles (KM-SUB) [2]. The model includes reversible adsorption, surface reactions and surface-bulk exchange as well as bulk diffusion and reaction. Unlike earlier models, KM-SUB does not require simplifying assumptions about steady-state conditions and radial mixing. The temporal evolution and concentration profiles of volatile and non-volatile species at the gas-particle interface and in the particle bulk can be modeled along with surface concentrations and gas uptake coefficients. In this study we explore and exemplify the effects of bulk diffusion on the rate of reactive gas uptake for a simple reference system, the ozonolysis of oleic acid particles, in comparison to experimental data and earlier model studies. We demonstrate how KM-SUB can be used to interpret and analyze experimental data from laboratory studies, and how the results can be extrapolated to atmospheric conditions. In particular, we show how interfacial transport and bulk transport, i.e., surface accommodation, bulk accommodation and bulk diffusion, influence the kinetics of the chemical reaction. Sensitivity studies suggest that in fine air particulate matter oleic acid and compounds with similar reactivity against ozone (C=C double bonds) can reach chemical life-times of multiple hours only if they are embedded in a (semi-)solid matrix with very low diffusion coefficients (~10-10 cm2 s-1). Depending on the complexity of the investigated system, unlimited numbers of volatile and non-volatile species and chemical reactions can be flexibly added and treated with KM-SUB. We propose and intend to pursue the application of KM-SUB as a basis for the development of a detailed master mechanism of aerosol chemistry as well as for the derivation of simplified but realistic parameterizations for large-scale atmospheric and climate models. References [1] Pöschl et al., Atmos. Chem. and Phys., 7, 5989-6023 (2007). [2] Shiraiwa et al., Atmos. Chem. Phys. Discuss., 10, 281-326 (2010).

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Theory of diffusion of active particles that move at constant speed in two dimensions.

PubMed

Sevilla, Francisco J; Gómez Nava, Luis A

2014-08-01

Starting from a Langevin description of active particles that move with constant speed in infinite two-dimensional space and its corresponding Fokker-Planck equation, we develop a systematic method that allows us to obtain the coarse-grained probability density of finding a particle at a given location and at a given time in arbitrary short-time regimes. By going beyond the diffusive limit, we derive a generalization of the telegrapher equation. Such generalization preserves the hyperbolic structure of the equation and incorporates memory effects in the diffusive term. While no difference is observed for the mean-square displacement computed from the two-dimensional telegrapher equation and from our generalization, the kurtosis results in a sensible parameter that discriminates between both approximations. We carry out a comparative analysis in Fourier space that sheds light on why the standard telegrapher equation is not an appropriate model to describe the propagation of particles with constant speed in dispersive media.

On the Role of Built-in Electric Fields on the Ignition of Oxide Coated NanoAluminum: Ion Mobility versus Fickian Diffusion

DTIC Science & Technology

2010-01-01

on Al ion diffu- sion can be computed using the Nernst –Planck equation . The Nernst –Plank equation is given in Eq. 4,22 J = − D dC dx − zFDC RT d dx...The use of the bulk diffusion equation is reason- able since during the time scales considered the movement of only the atoms initially on the surface

Flow regimes for fluid injection into a confined porous medium

DOE PAGES

Zheng, Zhong; Guo, Bo; Christov, Ivan C.; ...

2015-02-24

We report theoretical and numerical studies of the flow behaviour when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the fluid flow is mainly driven by the injection, and the governingmore » equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the injected fluid is more viscous than the displaced fluid, whereas a rarefaction wave solution is found when the injected fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an injected fluid with a viscosity higher than or equal to that of the displaced fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutions are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions.

PubMed

Péraud, Jean-Philippe; Nonaka, Andrew J; Bell, John B; Donev, Aleksandar; Garcia, Alejandro L

2017-10-10

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson-Nernst-Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation-anion diffusion coefficient. Specifically, we predict a nonzero cation-anion Maxwell-Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced "giant" velocity fluctuations and reduced fluctuations of salt concentration.

Fluctuation-enhanced electric conductivity in electrolyte solutions

PubMed Central

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; Donev, Aleksandar; Garcia, Alejandro L.

2017-01-01

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell–Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration. PMID:28973890

A Variational Assimilation Method for Satellite and Conventional Data: Development of Basic Model for Diagnosis of Cyclone Systems

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Scott, Robert W.; Chen, J.

1991-01-01

A summary is presented of the progress toward the completion of a comprehensive diagnostic objective analysis system based upon the calculus of variations. The approach was to first develop the objective analysis subject to the constraints that the final product satisfies the five basic primitive equations for a dry inviscid atmosphere: the two nonlinear horizontal momentum equations, the continuity equation, the hydrostatic equation, and the thermodynamic equation. Then, having derived the basic model, there would be added to it the equations for moist atmospheric processes and the radiative transfer equation.

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

PubMed

Barrenechea, Gabriel R; Burman, Erik; Karakatsani, Fotini

2017-01-01

For the case of approximation of convection-diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

Fractal Model of Fission Product Release in Nuclear Fuel

NASA Astrophysics Data System (ADS)

Stankunas, Gediminas

2012-09-01

A model of fission gas migration in nuclear fuel pellet is proposed. Diffusion process of fission gas in granular structure of nuclear fuel with presence of inter-granular bubbles in the fuel matrix is simulated by fractional diffusion model. The Grunwald-Letnikov derivative parameter characterizes the influence of porous fuel matrix on the diffusion process of fission gas. A finite-difference method for solving fractional diffusion equations is considered. Numerical solution of diffusion equation shows correlation of fission gas release and Grunwald-Letnikov derivative parameter. Calculated profile of fission gas concentration distribution is similar to that obtained in the experimental studies. Diffusion of fission gas is modeled for real RBMK-1500 fuel operation conditions. A functional dependence of Grunwald-Letnikov derivative parameter with fuel burn-up is established.

Thermodynamics of viscoelastic rate-type fluids with stress diffusion

NASA Astrophysics Data System (ADS)

Málek, Josef; Průša, Vít; Skřivan, Tomáš; Süli, Endre

2018-02-01

We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution equation for the extra stress tensor. It is shown that the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism, while different interpretations of the stress diffusion mechanism lead to different evolution equations for the temperature. The benefits of the knowledge of the thermodynamical background of the derived models are documented in the study of nonlinear stability of equilibrium rest states. The derived models open up the possibility to study fully coupled thermomechanical problems involving viscoelastic rate-type fluids with stress diffusion.

Dusty Pair Plasma—Wave Propagation and Diffusive Transition of Oscillations

NASA Astrophysics Data System (ADS)

Atamaniuk, Barbara; Turski, Andrzej J.

2011-11-01

The crucial point of the paper is the relation between equilibrium distributions of plasma species and the type of propagation or diffusive transition of plasma response to a disturbance. The paper contains a unified treatment of disturbance propagation (transport) in the linearized Vlasov electron-positron and fullerene pair plasmas containing charged dust impurities, based on the space-time convolution integral equations. Electron-positron-dust/ion (e-p-d/i) plasmas are rather widespread in nature. Space-time responses of multi-component linearized Vlasov plasmas on the basis of multiple integral equations are invoked. An initial-value problem for Vlasov-Poisson/Ampère equations is reduced to the one multiple integral equation and the solution is expressed in terms of forcing function and its space-time convolution with the resolvent kernel. The forcing function is responsible for the initial disturbance and the resolvent is responsible for the equilibrium velocity distributions of plasma species. By use of resolvent equations, time-reversibility, space-reflexivity and the other symmetries are revealed. The symmetries carry on physical properties of Vlasov pair plasmas, e.g., conservation laws. Properly choosing equilibrium distributions for dusty pair plasmas, we can reduce the resolvent equation to: (i) the undamped dispersive wave equations, (ii) and diffusive transport equations of oscillations.

A new mechanistic framework to predict OCS fluxes in soils

NASA Astrophysics Data System (ADS)

Sauze, Joana; Ogee, Jérôme; Launois, Thomas; Kesselmeier, Jürgen; Van Diest, Heidi; Wingate, Lisa

2015-04-01

A better description of the amplitude of photosynthetic and respiratory gross CO2 fluxes at large scales is needed to improve our predictions of the current and future global CO2 cycle. Carbonyl sulfide (COS) is the most abundant sulphur gas in the atmosphere and has been proposed as a new tracer of gross photosynthesis, as the uptake of COS from the atmosphere is dominated by the activity of carbonic anhydrase (CA), an enzyme abundant in leaves that also catalyses CO2 hydration during photosynthesis. However, soils also exchange COS with the atmosphere and there is growing evidence that this flux must also be accounted for in atmospheric budgets. In this context a new mechanistic description of soil-atmosphere COS exchange is clearly needed. Soils can take up COS from the atmosphere as the soil biota also contain CA, and COS emissions from soils have also been reported in agricultural fields or anoxic soils. Previous studies have also shown that soil COS fluxes present an optimum soil water content and soil temperature. Here we propose a new mechanistic framework to predict the fluxes of COS between the soils and the atmosphere. We describe the COS soil budget by a first-order reaction-diffusion-production equation, assuming that the hydrolysis of COS by CA is total and irreversible. To describe COS diffusion through the soil matrix, we use different formulations of soil air-filled pore space and temperature, depending on the turbulence level above the soil surface. Using this model we are able to explain the observed presence of an optimum temperature for soil COS uptake and show how this optimum can shift to cooler temperatures in the presence of soil COS emissions. Our model can also explain the observed optimum with soil moisture content previously described in the literature (e.g. Van Diest & Kesselmeier, 2008) as a result of diffusional constraints on COS hydrolysis. These diffusional constraints are also responsible for the response of COS uptake to soil weight and depth observed by Kesselmeier et al. (1999). In order to simulate the exact COS uptake rates and patterns observed on several soils collected from a range of biomes (Van Diest & Kesselmeier, 2008) different CA activities had to be evoked in each soil type, coherent with the expected soil microbial population size and diversity. A better description of the drivers governing soil CA activity and COS emissions from soils is needed before incorporating our new mechanistic model of soil-atmosphere COS uptake in large-scale ecosystem models and COS atmospheric budgets.

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

Liquefaction of Saturated Soil and the Diffusion Equation

NASA Astrophysics Data System (ADS)

Sawicki, Andrzej; Sławińska, Justyna

2015-06-01

The paper deals with the diffusion equation for pore water pressures with the source term, which is widely promoted in the marine engineering literature. It is shown that such an equation cannot be derived in a consistent way from the mass balance and the Darcy law. The shortcomings of the artificial source term are pointed out, including inconsistencies with experimental data. It is concluded that liquefaction and the preceding process of pore pressure generation and the weakening of the soil skeleton should be described by constitutive equations within the well-known framework of applied mechanics. Relevant references are provided

POLUTE. Forest Air Pollutant Uptake Model

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

Murphy, C.E. Jr.; Sinclair, T.R.

1992-02-13

POLUTE is a computer model designed to estimate the uptake of air pollutants by forests. The model utilizes submodels to describe atmospheric diffusion immediately above and within the canopy, and into the sink areas within or on the trees. The program implementing the model is general and can be used, with only minor changes, for any gaseous pollutant. The model provides an estimate describing the response of the vegetarian-atmosphere system to the environment as related to three types of processes: atmospheric diffusion, diffusion near and inside the absorbing plant, and the physical and chemical processes at the sink on ormore » within the plant.« less

Transport mechanisms of contaminants released from fine sediment in rivers

NASA Astrophysics Data System (ADS)

Cheng, Pengda; Zhu, Hongwei; Zhong, Baochang; Wang, Daozeng

2015-12-01

Contaminants released from sediment into rivers are one of the main problems to study in environmental hydrodynamics. For contaminants released into the overlying water under different hydrodynamic conditions, the mechanical mechanisms involved can be roughly divided into convective diffusion, molecular diffusion, and adsorption/desorption. Because of the obvious environmental influence of fine sediment (D_{90}= 0.06 mm), non-cohesive fine sediment, and cohesive fine sediment are researched in this paper, and phosphorus is chosen for a typical adsorption of a contaminant. Through theoretical analysis of the contaminant release process, according to different hydraulic conditions, the contaminant release coupling mathematical model can be established by the N-S equation, the Darcy equation, the solute transport equation, and the adsorption/desorption equation. Then, the experiments are completed in an open water flume. The simulation results and experimental results show that convective diffusion dominates the contaminant release both in non-cohesive and cohesive fine sediment after their suspension, and that they contribute more than 90 % of the total release. Molecular diffusion and desorption have more of a contribution for contaminant release from unsuspended sediment. In unsuspension sediment, convective diffusion is about 10-50 times larger than molecular diffusion during the initial stages under high velocity; it is close to molecular diffusion in the later stages. Convective diffusion is about 6 times larger than molecular diffusion during the initial stages under low velocity, it is about a quarter of molecular diffusion in later stages, and has a similar level with desorption/adsorption. In unsuspended sediment, a seepage boundary layer exists below the water-sediment interface, and various release mechanisms in that layer mostly dominate the contaminant release process. In non-cohesive fine sediment, the depth of that layer increases linearly with shear stress. In cohesive fine sediment, the range seepage boundary is different from that in non-cohesive sediment, and that phenomenon is more obvious under a lower shear stress.

Inhomogeneities in particle composition of single, levitated aerosol particles observed by Mie resonance spectroscopy

NASA Astrophysics Data System (ADS)

Krieger, Ulrich; Lienhard, Daniel; Bastelberger, Sandra; Steimer, Sarah

2014-05-01

Recent observations have indicated that organic aerosol particles in the atmosphere may exist in an amorphous semi-solid or even solid (i.e. glassy) state, e.g. [1]. The influence of highly viscous and glassy states on the timescale of aerosol particle equilibration with respect to water vapor have been investigated for some model systems of atmospheric aerosol, e.g. [2,3]. In particular, it has been shown that the kinetics of the water absorption/desorption process is controlled entirely by liquid-phase diffusion of water molecules for a highly viscous aerosol particle. A liquid phase diffusion model based on numerically solving the non-linear diffusion equation predicts strong internal gradients in water concentration when condensed phase diffusion impedes the water uptake from the gas phase [2]. Here we observe and quantify the internal concentration gradients in single, levitated, micron size aerosol particles of aqueous shikimic acid using elastic Mie resonance spectroscopy. A single, aqueous particle is levitated in an electro-dynamic balance (for details see [2]), dried for several days at room temperature, cooled to the target temperature and exposed to a rapid change in relative humidity. In addition to measuring the elastically backscattered light of a "white light" LED source and recording the full spectrum with a spectrograph as in [2], we use a tunable diode laser (TDL) to scan high resolution TE- and TM spectra. This combination allows observing various Mie resonance mode orders simultaneously. Since we perform the experiment at low temperatures and low humidities the changes in the Mie-spectra due to water uptake are sufficiently slow to resolve the kinetics. Experimental Mie resonance spectra are inverted to concentration profiles of water within the particle by applying the numerical diffusion model [2] in conjunction with Mie calculations of multilayered spheres [4]. [1] A. Virtanen et al. (2010): An amorphous solid state of biogenic secondary organic aerosol particles, Nature 467, 824-827. [2] B. Zobrist et al. (2011): Ultra-slow water diffusion in aqueous sucrose glasses, Phys. Chem. Chem. Phys. 13, 3514-3526. [3] D. L. Bones, J. P. Reid, D. M. Lienhard, and U. K. Krieger (2012): Comparing the mechanism of water condensation and evaporation in glassy aerosol, PNAS 109, 11613-11618. [4] O. Peña and U. Pal (2009): Scattering of electromagnetic radiation by a multilayered sphere, Comput. Phys. Commun. 180, 2348-2354.

Lévy/Anomalous Diffusion as a Mean-Field Theory for 3D Cloud Effects in Shortwave Radiative Transfer: Empirical Support, New Analytical Formulation, and Impact on Atmospheric Absorption

NASA Astrophysics Data System (ADS)

Buldyrev, S.; Davis, A.; Marshak, A.; Stanley, H. E.

2001-12-01

Two-stream radiation transport models, as used in all current GCM parameterization schemes, are mathematically equivalent to ``standard'' diffusion theory where the physical picture is a slow propagation of the diffuse radiation by Gaussian random walks. The space/time spread (technically, the Green function) of this diffusion process is described exactly by a Gaussian distribution; from the statistical physics viewpoint, this follows from the convergence of the sum of many (rescaled) steps between scattering events with a finite variance. This Gaussian picture follows directly from first principles (the radiative transfer equation) under the assumptions of horizontal uniformity and large optical depth, i.e., there is a homogeneous plane-parallel cloud somewhere in the column. The first-order effect of 3D variability of cloudiness, the main source of scattering, is to perturb the distribution of single steps between scatterings which, modulo the ``1-g'' rescaling, can be assumed effectively isotropic. The most natural generalization of the Gaussian distribution is the 1-parameter family of symmetric Lévy-stable distributions because the sum of many zero-mean random variables with infinite variance, but finite moments of order q < α (0 < α < 2), converge to them. It has been shown on heuristic grounds that for these Lévy-based random walks the typical number of scatterings is now (1-g)τ α for transmitted light. The appearance of a non-rational exponent is why this is referred to as ``anomalous'' diffusion. Note that standard/Gaussian diffusion is retrieved in the limit α = 2-. Lévy transport theory has been successfully used in the statistical physics literature to investigate a wide variety of systems with strongly nonlinear dynamics; these applications range from random advection in turbulent fluids to the erratic behavior of financial time-series and, most recently, self-regulating ecological systems. We will briefly survey the state-of-the-art observations that offer compelling empirical support for the Lévy/anomalous diffusion model in atmospheric radiation: (1) high-resolution spectroscopy of differential absorption in the O2 A-band from ground; (2) temporal transient records of lightning strokes transmitted through clouds to a sensitive detector in space; and (3) the Gamma-distributions of optical depths derived from Landsat cloud scenes at 30-m resolution. We will then introduce a rigorous analytical formulation of Lévy/anomalous transport through finite media based on fractional derivatives and Sonin calculus. A remarkable result from this new theoretical development is an extremal property of the α = 1+ case (divergent mean-free-path), as is observed in the cloudy atmosphere. Finally, we will discuss the implications of anomalous transport theory for bulk 3D effects on the current enhanced absorption problem as well as its role as the basis of a next-generation GCM radiation parameterization.

PERFORMANCE OF A NEW DIFFUSIVE SAMPLER FOR HG0 DETERMINATION IN THE TROPOSPHERE

EPA Science Inventory

Mercury behaves uniquely in the atmosphere due to its volatility and long lifetime. The existing methods for measuring atmospheric mercury are either expensive or labour intensive. The present paper presents a new measurement technique, the diffusive sampler, that is portable, in...

Linear response theory and transient fluctuation relations for diffusion processes: a backward point of view

NASA Astrophysics Data System (ADS)

Liu, Fei; Tong, Huan; Ma, Rui; Ou-Yang, Zhong-can

2010-12-01

A formal apparatus is developed to unify derivations of the linear response theory and a variety of transient fluctuation relations for continuous diffusion processes from a backward point of view. The basis is a perturbed Kolmogorov backward equation and the path integral representation of its solution. We find that these exact transient relations could be interpreted as a consequence of a generalized Chapman-Kolmogorov equation, which intrinsically arises from the Markovian characteristic of diffusion processes.

Diffusion of nitrogen oxides and oxygenated volatile organic compounds through snow

NASA Astrophysics Data System (ADS)

Bartels-Rausch, T.; Ammann, M.; Schneebeli, M.; Riche, F.; Wren, S. N.

2013-12-01

Release of trace gases from surface snow on Earth drives atmospheric chemistry, especially in the Polar Regions. The exchange of atmospheric trace gases between snow or firn and atmosphere can also determine how these species are incorporated into glacial ice, which serves as archive. At low wind conditions, such fluxes between the porous surface snow and the overlaying atmosphere are driven by diffusion through the interstitial air. Here we present results from two laboratory studies where we looked at how the structure of the snowpack, the interaction of the trace gases with the snow surface, and the grain boundaries influence the diffusion of NO, NO2, HONO, methanol, and acetone on time scales up to 1 h. The diffusion through a snow sample was the direct observable of the experiments. Results for different snow types are presented, the structures of which were analysed by means of X-ray computed micro-tomography. Grain boundary content was quantified in one sample using a stereological method. The observed diffusion profiles were very well reproduced in simulations based on gas-phase diffusion and the known structure of the snow sample at temperatures above 253 K. At colder temperatures surface interactions start to dominate the diffusion. Parameterizing these in terms of adsorption to the solid ice surface gave much better agreement to the observations than the use of air - liquid partitioning coefficients. This is a central result as field and modelling studies have indicated that the partitioning to liquid water might describe the diffusion through snow much better even at cold temperatures. This will be discussed using our recent results from surface sensitive spectroscopy experiments. No changes in the diffusion was observed by increasing the number of grain boundaries in the snow sample by a factor of 7.

Comparison of Fully-Compressible Equation Sets for Atmospheric Dynamics

NASA Technical Reports Server (NTRS)

Ahmad, Nashat N.

2016-01-01

Traditionally, the equation for the conservation of energy used in atmospheric models is based on potential temperature and is used in place of the total energy conservation. This paper compares the application of the two equations sets for both the Euler and the Navier-Stokes solutions using several benchmark test cases. A high-resolution wave-propagation method which accurately takes into account the source term due to gravity is used for computing the non-hydrostatic atmospheric flows. It is demonstrated that there is little to no difference between the results obtained using the two different equation sets for Euler as well as Navier-Stokes solutions.

Major Pathways to Electron Distribution Function Formation in Regions of Diffuse Aurora

NASA Technical Reports Server (NTRS)

Khazanov, George V.; Sibeck, David G.; Zesta, Eftyhia

2017-01-01

This paper discusses the major pathways of electron distribution function formation in the region of diffuse aurora. The diffuse aurora accounts for about of 75% of the auroral energy precipitating into the upper atmosphere, and its origin has been the subject of much discussion. We show that an earthward stream of precipitating electrons initially injected from the Earth's plasma sheet via wave-particle interactions degrades in the atmosphere toward lower energies and produces secondary electrons via impact ionization of the neutral atmosphere. These electrons of magnetospheric origin are then reflected back into the magnetosphere along closed dipolar magnetic field lines, leading to a series of reflections and consequent magnetospheric interactions that greatly augment the initially precipitating flux at the upper ionospheric boundary (700-800 km). To date this, systematic magnetosphere-ionosphere coupling element has not been included in auroral research models, and, as we demonstrate in this article, has a dramatic effect (200-300%) on the formation of the precipitating fluxes that result in the diffuse aurora. It is shown that wave-particle interaction processes that drive precipitating fluxes in the region of diffuse aurora from the magnetospheric altitudes are only the first step in the formation of electron precipitation at ionospheric altitudes, and they cannot be separated from the atmospheric collisional machine that redistributes and transfers their energy inside the magnetosphere-ionosphere-atmosphere coupling system.

Major pathways to electron distribution function formation in regions of diffuse aurora

NASA Astrophysics Data System (ADS)

Khazanov, George V.; Sibeck, David G.; Zesta, Eftyhia

2017-04-01

This paper discusses the major pathways of electron distribution function formation in the region of diffuse aurora. The diffuse aurora accounts for about of 75% of the auroral energy precipitating into the upper atmosphere, and its origin has been the subject of much discussion. We show that an earthward stream of precipitating electrons initially injected from the Earth's plasma sheet via wave-particle interactions degrades in the atmosphere toward lower energies and produces secondary electrons via impact ionization of the neutral atmosphere. These electrons of magnetospheric origin are then reflected back into the magnetosphere along closed dipolar magnetic field lines, leading to a series of reflections and consequent magnetospheric interactions that greatly augment the initially precipitating flux at the upper ionospheric boundary (700-800 km). To date this, systematic magnetosphere-ionosphere coupling element has not been included in auroral research models, and, as we demonstrate in this article, has a dramatic effect (200-300%) on the formation of the precipitating fluxes that result in the diffuse aurora. It is shown that wave-particle interaction processes that drive precipitating fluxes in the region of diffuse aurora from the magnetospheric altitudes are only the first step in the formation of electron precipitation at ionospheric altitudes, and they cannot be separated from the atmospheric "collisional machine" that redistributes and transfers their energy inside the magnetosphere-ionosphere-atmosphere coupling system.

A Simple Mathematical Model Inspired by the Purkinje Cells: From Delayed Travelling Waves to Fractional Diffusion.

PubMed

Dipierro, Serena; Valdinoci, Enrico

2018-07-01

Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

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

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Birth-jump processes and application to forest fire spotting.

PubMed

Hillen, T; Greese, B; Martin, J; de Vries, G

2015-01-01

Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front.

Reexamination of relaxation of spins due to a magnetic field gradient: Identity of the Redfield and Torrey theories

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

Golub, R.; Rohm, Ryan M.; Swank, C. M.

2011-02-15

There is an extensive literature on magnetic-gradient-induced spin relaxation. Cates, Schaefer, and Happer, in a seminal publication, have solved the problem in the regime where diffusion theory (the Torrey equation) is applicable using an expansion of the density matrix in diffusion equation eigenfunctions and angular momentum tensors. McGregor has solved the problem in the same regime using a slightly more general formulation using the Redfield theory formulated in terms of the autocorrelation function of the fluctuating field seen by the spins and calculating the correlation functions using the diffusion-theory Green's function. The results of both calculations were shown to agreemore » for a special case. In the present work, we show that the eigenfunction expansion of the Torrey equation yields the expansion of the Green's function for the diffusion equation, thus showing the identity of this approach with that of the Redfield theory. The general solution can also be obtained directly from the Torrey equation for the density matrix. Thus, the physical content of the Redfield and Torrey approaches are identical. We then introduce a more general expression for the position autocorrelation function of particles moving in a closed cell, extending the range of applicability of the theory.« less

Lévy/Anomalous Diffusion as a Mean-Field Theory for 3D Cloud Effects in SW-RT: Empirical Support, New Analytical Formulation, and Impact on Atmospheric Absorption

NASA Astrophysics Data System (ADS)

Pfeilsticker, K.; Davis, A.; Marshak, A.; Suszcynsky, D. M.; Buldryrev, S.; Barker, H.

2001-12-01

2-stream RT models, as used in all current GCMs, are mathematically equivalent to standard diffusion theory where the physical picture is a slow propagation of the diffuse radiation by Gaussian random walks. In other words, after the conventional van de Hulst rescaling by 1/(1-g) in R3 and also by (1-g) in t, solar photons follow convoluted fractal trajectories in the atmosphere. For instance, we know that transmitted light is typically scattered about (1-g)τ 2 times while reflected light is scattered on average about τ times, where τ is the optical depth of the column. The space/time spread of this diffusion process is described exactly by a Gaussian distribution; from the statistical physics viewpoint, this follows from the convergence of the sum of many (rescaled) steps between scattering events with a finite variance. This Gaussian picture follows from directly from first principles (the RT equation) under the assumptions of horizontal uniformity and large optical depth, i.e., there is a homogeneous plane-parallel cloud somewhere in the column. The first-order effect of 3D variability of cloudiness, the main source of scattering, is to perturb the distribution of single steps between scatterings which, modulo the '1-g' rescaling, can be assumed effectively isotropic. The most natural generalization of the Gaussian distribution is the 1-parameter family of symmetric Lévy-stable distributions because the sum of many zero-mean random variables with infinite variance, but finite moments of order q < α (0 < α < 2), converge to them. It has been shown on heuristic grounds that for these Lévy-based random walks the typical number of scatterings is now (1-g)τ α for transmitted light. The appearance of a non-rational exponent is why this is referred to as anomalous diffusion. Note that standard/Gaussian diffusion is retrieved in the limit α = 2-. Lévy transport theory has been successfully used in the statistical physics to investigate a wide variety of systems with strongly nonlinear dynamics; these applications range from random advection in turbulent fluids to the erratic behavior of financial time-series and, most recently, self-regulating ecological systems. We will briefly survey the state-of-the-art observations that offer compelling empirical support for the Lévy/anomalous diffusion model in atmospheric radiation: (1) high-resolution spectroscopy of differential absorption in the O2 A-band from ground; (2) temporal transient records of lightning strokes transmitted through clouds to a sensitive detector in space; and (3) the Gamma-distributions of optical depths derived from Landsat cloud scenes at 30-m resolution. We will then introduce a rigorous analytical formulation of anomalous transport through finite media based on fractional derivatives and Sonin calculus. A remarkable result from this new theoretical development is an extremal property of the α = 1+ case (divergent mean-free-path), as is observed in the cloudy atmosphere. Finally, we will discuss the implications of anomalous transport theory for bulk 3D effects on the current enhanced absorption problem as well as its role as the basis of a next-generation GCM RT parameterization.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

NASA Astrophysics Data System (ADS)

Gyrya, V.; Lipnikov, K.

2017-11-01

We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE PAGES

Gyrya, V.; Lipnikov, K.

2017-07-18

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

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

Gyrya, V.; Lipnikov, K.

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

Maximum Path Information and Fokker Planck Equation

NASA Astrophysics Data System (ADS)

Li, Wei; Wang A., Q.; LeMehaute, A.

2008-04-01

We present a rigorous method to derive the nonlinear Fokker-Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang [Chaos, Solitons & Fractals 23 (2005) 1253] for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q (the index of Tsallis entropy [J. Stat. Phys. 52 (1988) 479] and the time t.

Molecular dynamics on diffusive time scales from the phase-field-crystal equation.

PubMed

Chan, Pak Yuen; Goldenfeld, Nigel; Dantzig, Jon

2009-03-01

We extend the phase-field-crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time scales. To illustrate this approach, we calculate the two-point correlation function of a fluid.

Non-Markovian Effects in Turbulent Diffusion in Magnetized Plasmas

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

Zagorodny, Anatoly; Weiland, Jan

2009-10-08

The derivation of the kinetic equations for inhomogeneous plasma in an external magnetic field is presented. The Fokker-Planck-type equations with the non-Markovian kinetic coefficients are proposed. In the time-local limit (small correlation times with respect to the distribution function relaxation time) the relations obtained recover the results known from the appropriate quasilinear theory and the Dupree-Weinstock theory of plasma turbulence. The equations proposed are used to describe zonal flow generation and to estimate the diffusion coefficient for saturated turbulence.

Erosion processes in molassic cliffs: the role of the rock surface temperature and atmospheric conditions

NASA Astrophysics Data System (ADS)

Carrea, Dario; Abellán, Antonio; Guerin, Antoine; Jaboyedoff, Michel; Voumard, Jérémie

2014-05-01

The morphology of the Swiss Plateau is modeled by numerous steep cliffs of Molasse. These cliffs are mainly composed of sub-horizontal alternated layers of sandstone, shale and conglomerates deposed in the Alps foreland basin during the Tertiary period. These Molasse cliffs are affected by erosion processes inducing numerous rockfall events. Thus, it is relevant to understand how different external factors influence Molasse erosion rates. In this study, we focus on analyzing temperature variation during a winter season. As pilot study area we selected a cliff which is formed by a sub-horizontal alternation of outcropping sandstone and shale. The westward facing test site (La Cornalle, Vaud, Switzerland), which is a lateral scarp of a slow moving landslide area, is currently affected by intense erosion. Regarding data acquisition, we monitored both in-situ rock and air temperatures at 15 minutes time-step since October 2013: (1) on the one hand we measured Ground Surface Temperature (GST) at near-surface (0.1 meter depth) using a GST mini-datalogger M-Log5W-Rock model; (2) On the other hand we monitored atmospheric conditions using a weather station (Davis Vantage pro2 plus) collecting numerous parameters (i.e. temperature, irradiation, rain, wind speed, etc.). Furthermore, the area was also seasonally monitored by Ground-Based (GB) LiDAR since 2010 and monthly monitored since September 2013. In order to understand how atmospheric conditions (such as freeze and thaw effect) influence the erosion of the cliff, we modeled the temperature diffusion through the rock mass. To this end, we applied heat diffusion and radiation equation using a 1D temperature profile, obtaining as a result both temperature variations at different depths together with the location of the 0°C isotherm. Our model was calibrated during a given training set using both in-situ rock temperatures and atmospheric conditions. We then carried out a comparison with the rockfall events derived from the 3D GB-LiDAR datasets in order to quantify the erosion rates and to correlate it with atmospheric conditions, aiming to analyze which parameters influence Molasse erosion process.

Lattice Boltzmann scheme for mixture modeling: analysis of the continuum diffusion regimes recovering Maxwell-Stefan model and incompressible Navier-Stokes equations.

PubMed

Asinari, Pietro

2009-11-01

A finite difference lattice Boltzmann scheme for homogeneous mixture modeling, which recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged diffusion approximation, was recently proposed [P. Asinari, Phys. Rev. E 77, 056706 (2008)]. The theoretical basis is the Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. 106, 993 (2002)]. In the present paper, the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed. It comes out that the diffusion speed must be at least one order of magnitude (in terms of Knudsen number) smaller than the barycentric speed, in order to recover the Navier-Stokes equations for mixtures in the incompressible limit. Some further numerical tests are also reported. In particular, (1) the solvent and dilute test cases are considered, because they are limiting cases in which the Maxwell-Stefan model reduces automatically to Fickian cases. Moreover, (2) some tests based on the Stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving Maxwell-Stefan diffusion problems. The proposed scheme agrees well with the expected theoretical results.

FORMATION OF POLYCYCLIC AROMATIC HYDROCARBONS IN AN ATMOSPHERIC PRESSURE ETHYLENE DIFFUSION FLAME. (R825412)

EPA Science Inventory

Abstract

The microstructure of an atmospheric pressure, counterflow, sooting, flat, laminar ethylene diffusion flame has been studied experimentally by withdrawing samples from within the flame using a heated quartz microprobe coupled to an online gas chromatograph/mas...

A cross-diffusion system derived from a Fokker-Planck equation with partial averaging

NASA Astrophysics Data System (ADS)

Jüngel, Ansgar; Zamponi, Nicola

2017-02-01

A cross-diffusion system for two components with a Laplacian structure is analyzed on the multi-dimensional torus. This system, which was recently suggested by P.-L. Lions, is formally derived from a Fokker-Planck equation for the probability density associated with a multi-dimensional Itō process, assuming that the diffusion coefficients depend on partial averages of the probability density with exponential weights. A main feature is that the diffusion matrix of the limiting cross-diffusion system is generally neither symmetric nor positive definite, but its structure allows for the use of entropy methods. The global-in-time existence of positive weak solutions is proved and, under a simplifying assumption, the large-time asymptotics is investigated.

A nonlinear Fokker-Planck equation approach for interacting systems: Anomalous diffusion and Tsallis statistics

NASA Astrophysics Data System (ADS)

Marin, D.; Ribeiro, M. A.; Ribeiro, H. V.; Lenzi, E. K.

2018-07-01

We investigate the solutions for a set of coupled nonlinear Fokker-Planck equations coupled by the diffusion coefficient in presence of external forces. The coupling by the diffusion coefficient implies that the diffusion of each species is influenced by the other and vice versa due to this term, which represents an interaction among them. The solutions for the stationary case are given in terms of the Tsallis distributions, when arbitrary external forces are considered. We also use the Tsallis distributions to obtain a time dependent solution for a linear external force. The results obtained from this analysis show a rich class of behavior related to anomalous diffusion, which can be characterized by compact or long-tailed distributions.

Methods for estimating the optical constants of atmospheric hazes based on complex optical measurements

NASA Technical Reports Server (NTRS)

Zuev, V. E.; Kostin, B. S.; Naats, I. E.

1986-01-01

The methods of multifrequency laser sounding (MLS) are the most effective remote methods for investigating the atmospheric aerosols, since it is possible to obtain complete information on aerosol microstructure and the effective methods for estimating the aerosol optical constants can be developed. The MLS data interpretation consists in the solution of the set of equations containing those of laser sounding and equations for polydispersed optical characteristics. As a rule, the laser sounding equation is written in the approximation of single scattering and the equations for optical characteristics are written assuming that the atmospheric aerosol is formed by spherical and homogeneous particles. To remove the indeterminacy of equations, the method of optical sounding of atmospheric aerosol, consisting in a joint use of a mutifrequency lidar and a spectral photometer in common geometrical scheme of the optical experiment was suggested. The method is used for investigating aerosols in the cases when absorption by particles is small and indicates the minimum necessary for interpretation of a series of measurements.

Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

Asymptotic Analysis of Time-Dependent Neutron Transport Coupled with Isotopic Depletion and Radioactive Decay

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

Brantley, P S

2006-09-27

We describe an asymptotic analysis of the coupled nonlinear system of equations describing time-dependent three-dimensional monoenergetic neutron transport and isotopic depletion and radioactive decay. The classic asymptotic diffusion scaling of Larsen and Keller [1], along with a consistent small scaling of the terms describing the radioactive decay of isotopes, is applied to this coupled nonlinear system of equations in a medium of specified initial isotopic composition. The analysis demonstrates that to leading order the neutron transport equation limits to the standard time-dependent neutron diffusion equation with macroscopic cross sections whose number densities are determined by the standard system of ordinarymore » differential equations, the so-called Bateman equations, describing the temporal evolution of the nuclide number densities.« less

Passive sampling for the isotopic fingerprinting of atmospheric mercury

NASA Astrophysics Data System (ADS)

Bergquist, B. A.; MacLagan, D.; Spoznar, N.; Kaplan, R.; Chandan, P.; Stupple, G.; Zimmerman, L.; Wania, F.; Mitchell, C. P. J.; Steffen, A.; Monaci, F.; Derry, L. A.

2017-12-01

Recent studies show that there are variations in the mercury (Hg) isotopic signature of atmospheric Hg, which demonstrates the potential for source tracing and improved understanding of atmospheric cycling of Hg. However, current methods for both measuring atmospheric Hg and collecting enough atmospheric Hg for isotopic analyses require expensive instruments that need power and expertise. Additionally, methods for collecting enough atmospheric Hg for isotopic analysis require pumping air through traps for long periods (weeks and longer). Combining a new passive atmospheric sampler for mercury (Hg) with novel Hg isotopic analyses will allow for the application of stable Hg isotopes to atmospheric studies of Hg. Our group has been testing a new passive sampler for gaseous Hg that relies on the diffusion of Hg through a diffusive barrier and adsorption onto a sulphur-impregnated activated carbon sorbent. The benefit of this passive sampler is that it is low cost, requires no power, and collects gaseous Hg for up to one year with linear, well-defined uptake, which allows for reproducible and accurate measurements of atmospheric gaseous Hg concentrations ( 8% uncertainty). As little as one month of sampling is often adequate to collect sufficient Hg for isotopic analysis at typical background concentrations. Experiments comparing the isotopic Hg signature in activated carbon samples using different approaches (i.e. by passive diffusion, by passive diffusion through diffusive barriers of different thickness, by active pumping) and at different temperatures confirm that the sampling process itself does not impose mass-independent fractionation (MIF). However, sampling does result in a consistent and thus correctable mass-dependent fractionation (MDF) effect. Therefore, the sampler preserves Hg MIF with very high accuracy and precision, which is necessary for atmospheric source tracing, and reasonable MDF can be estimated with some increase in error. In addition to experimental work, initial field data will be presented including a transect of increasing distance from a known strong source of Hg (Mt. Amiata mine, Italy), downwind of Kilauea volcano in Hawaii, and several other locales including the Arctic station Alert and various sites across Ontario, Canada.

Interface- and discontinuity-aware numerical schemes for plasma 3-T radiation diffusion in two and three dimensions

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

Dai, William W., E-mail: dai@lanl.gov; Scannapieco, Anthony J.

2015-11-01

A set of numerical schemes is developed for two- and three-dimensional time-dependent 3-T radiation diffusion equations in systems involving multi-materials. To resolve sub-cell structure, interface reconstruction is implemented within any cell that has more than one material. Therefore, the system of 3-T radiation diffusion equations is solved on two- and three-dimensional polyhedral meshes. The focus of the development is on the fully coupling between radiation and material, the treatment of nonlinearity in the equations, i.e., in the diffusion terms and source terms, treatment of the discontinuity across cell interfaces in material properties, the formulations for both transient and steady states,more » the property for large time steps, and second order accuracy in both space and time. The discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes and full nonlinearity. The treatment is exact for arbitrarily strong discontinuity. The scheme is fully nonlinear for the full nonlinearity in the 3-T diffusion equations. Three temperatures are fully coupled and are updated simultaneously. The scheme is general in two and three dimensions on general polyhedral meshes. The features of the scheme are demonstrated through numerical examples for transient problems and steady states. The effects of some simplifications of numerical schemes are also shown through numerical examples, such as linearization, simple average of diffusion coefficient, and approximate treatment for the coupling between radiation and material.« less

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

Rossby wave activity in a two-dimensional model - Closure for wave driving and meridional eddy diffusivity

NASA Technical Reports Server (NTRS)

Hitchman, Matthew H.; Brasseur, Guy

1988-01-01

A parameterization of the effects of Rossby waves in the middle atmosphere is proposed for use in two-dimensional models. By adding an equation for conservation of Rossby wave activity, closure is obtained for the meridional eddy fluxes and body force due to Rossby waves. Rossby wave activity is produced in a climatological fashion at the tropopause, is advected by a group velocity which is determined solely by model zonal winds, and is absorbed where it converges. Absorption of Rossby wave activity causes both an easterly torque and an irreversible mixing of potential vorticity, represented by the meridional eddy diffusivity, K(yy). The distribution of Rossby wave driving determines the distribution of K(yy), which is applied to all of the chemical constituents. This provides a self-consistent coupling of the wave activity with the winds, tracer distributions and the radiative field. Typical winter stratospheric values for K(yy) of 2 million sq m/sec are obtained. Poleward tracer advection is enhanced and meridional tracer gradients are reduced where Rossby wave activity is absorbed in the model.

A MODEL OF MAGNETIC BRAKING OF SOLAR ROTATION THAT SATISFIES OBSERVATIONAL CONSTRAINTS

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

Denissenkov, Pavel A., E-mail: pavel.denisenkov@gmail.co

The model of magnetic braking of solar rotation considered by Charbonneau and MacGregor has been modified so that it is able to reproduce for the first time the rotational evolution of both the fastest and slowest rotators among solar-type stars in open clusters of different ages, without coming into conflict with other observational constraints, such as the time evolution of the atmospheric Li abundance in solar twins and the thinness of the solar tachocline. This new model assumes that rotation-driven turbulent diffusion, which is thought to amplify the viscosity and magnetic diffusivity in stellar radiative zones, is strongly anisotropic withmore » the horizontal components of the transport coefficients strongly dominating over those in the vertical direction. Also taken into account is the poloidal field decay that helps to confine the width of the tachocline at the solar age. The model's properties are investigated by numerically solving the azimuthal components of the coupled momentum and magnetic induction equations in two dimensions using a finite element method.« less

On the Maxwell-Stefan approach to diffusion: a general resolution in the transient regime for one-dimensional systems.

PubMed

Leonardi, Erminia; Angeli, Celestino

2010-01-14

The diffusion process in a multicomponent system can be formulated in a general form by the generalized Maxwell-Stefan equations. This formulation is able to describe the diffusion process in different systems, such as, for instance, bulk diffusion (in the gas, liquid, and solid phase) and diffusion in microporous materials (membranes, zeolites, nanotubes, etc.). The Maxwell-Stefan equations can be solved analytically (only in special cases) or by numerical approaches. Different numerical strategies have been previously presented, but the number of diffusing species is normally restricted, with only few exceptions, to three in bulk diffusion and to two in microporous systems, unless simplifications of the Maxwell-Stefan equations are considered. In the literature, a large effort has been devoted to the derivation of the analytic expression of the elements of the Fick-like diffusion matrix and therefore to the symbolic inversion of a square matrix with dimensions n x n (n being the number of independent components). This step, which can be easily performed for n = 2 and remains reasonable for n = 3, becomes rapidly very complex in problems with a large number of components. This paper addresses the problem of the numerical resolution of the Maxwell-Stefan equations in the transient regime for a one-dimensional system with a generic number of components, avoiding the definition of the analytic expression of the elements of the Fick-like diffusion matrix. To this aim, two approaches have been implemented in a computational code; the first is the simple finite difference second-order accurate in time Crank-Nicolson scheme for which the full mathematical derivation and the relevant final equations are reported. The second is based on the more accurate backward differentiation formulas, BDF, or Gear's method (Shampine, L. F. ; Gear, C. W. SIAM Rev. 1979, 21, 1.), as implemented in the Livermore solver for ordinary differential equations, LSODE (Hindmarsh, A. C. Serial Fortran Solvers for ODE Initial Value Problems, Technical Report; https://computation.llnl.gov/casc/odepack/odepack_ home.html (2006).). Both methods have been applied to a series of specific problems, such as bulk diffusion of acetone and methanol through stagnant air, uptake of two components on a microporous material in a model system, and permeation across a microporous membrane in model systems, both with the aim to validate the method and to add new information to the comprehension of the peculiar behavior of these systems. The approach is validated by comparison with different published results and with analytic expressions for the steady-state concentration profiles or fluxes in particular systems. The possibility to treat a generic number of components (the limitation being essentially the computational power) is also tested, and results are reported on the permeation of a five component mixture through a membrane in a model system. It is worth noticing that the algorithm here reported can be applied also to the Fick formulation of the diffusion problem with concentration-dependent diffusion coefficients.

Predicting Ga and Cu Profiles in Co-Evaporated Cu(In,Ga)Se 2 Using Modified Diffusion Equations and a Spreadsheet

DOE PAGES

Repins, Ingrid L.; Harvey, Steve; Bowers, Karen; ...

2017-05-15

Cu(In,Ga)Se 2(CIGS) photovoltaic absorbers frequently develop Ga gradients during growth. These gradients vary as a function of growth recipe, and are important to device performance. Prediction of Ga profiles using classic diffusion equations is not possible because In and Ga atoms occupy the same lattice sites and thus diffuse interdependently, and there is not yet a detailed experimental knowledge of the chemical potential as a function of composition that describes this interaction. Here, we show how diffusion equations can be modified to account for site sharing between In and Ga atoms. The analysis has been implemented in an Excel spreadsheet,more » and outputs predicted Cu, In, and Ga profiles for entered deposition recipes. A single set of diffusion coefficients and activation energies are chosen, such that simulated elemental profiles track with published data and those from this study. Extent and limits of agreement between elemental profiles predicted from the growth recipes and the spreadsheet tool are demonstrated.« less

Theory and Simulation of Self- and Mutual-Diffusion of Carrier Density and Temperature in Semiconductor Lasers

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Cheung, Samson H.; Ning, C. Z.

2001-01-01

Carrier diffusion and thermal conduction play a fundamental role in the operation of high-power, broad-area semiconductor lasers. Restricted geometry, high pumping level and dynamic instability lead to inhomogeneous spatial distribution of plasma density, temperature, as well as light field, due to strong light-matter interaction. Thus, modeling and simulation of such optoelectronic devices rely on detailed descriptions of carrier dynamics and energy transport in the system. A self-consistent description of lasing and heating in large-aperture, inhomogeneous edge- or surface-emitting lasers (VCSELs) require coupled diffusion equations for carrier density and temperature. In this paper, we derive such equations from the Boltzmann transport equation for the carrier distributions. The derived self- and mutual-diffusion coefficients are in general nonlinear functions of carrier density and temperature including many-body interactions. We study the effects of many-body interactions on these coefficients, as well as the nonlinearity of these coefficients for large-area VCSELs. The effects of mutual diffusions on carrier and temperature distributions in gain-guided VCSELs will be also presented.

Predicting Ga and Cu Profiles in Co-Evaporated Cu(In,Ga)Se 2 Using Modified Diffusion Equations and a Spreadsheet

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

Repins, Ingrid L.; Harvey, Steve; Bowers, Karen

Cu(In,Ga)Se 2(CIGS) photovoltaic absorbers frequently develop Ga gradients during growth. These gradients vary as a function of growth recipe, and are important to device performance. Prediction of Ga profiles using classic diffusion equations is not possible because In and Ga atoms occupy the same lattice sites and thus diffuse interdependently, and there is not yet a detailed experimental knowledge of the chemical potential as a function of composition that describes this interaction. Here, we show how diffusion equations can be modified to account for site sharing between In and Ga atoms. The analysis has been implemented in an Excel spreadsheet,more » and outputs predicted Cu, In, and Ga profiles for entered deposition recipes. A single set of diffusion coefficients and activation energies are chosen, such that simulated elemental profiles track with published data and those from this study. Extent and limits of agreement between elemental profiles predicted from the growth recipes and the spreadsheet tool are demonstrated.« less

Comparing the mechanism of water condensation and evaporation in glassy aerosol.

PubMed

Bones, David L; Reid, Jonathan P; Lienhard, Daniel M; Krieger, Ulrich K

2012-07-17

Atmospheric models generally assume that aerosol particles are in equilibrium with the surrounding gas phase. However, recent observations that secondary organic aerosols can exist in a glassy state have highlighted the need to more fully understand the kinetic limitations that may control water partitioning in ambient particles. Here, we explore the influence of slow water diffusion in the condensed aerosol phase on the rates of both condensation and evaporation, demonstrating that significant inhibition in mass transfer occurs for ultraviscous aerosol, not just for glassy aerosol. Using coarse mode (3-4 um radius) ternary sucrose/sodium chloride/aqueous droplets as a proxy for multicomponent ambient aerosol, we demonstrate that the timescale for particle equilibration correlates with bulk viscosity and can be ≫10(3) s. Extrapolation of these timescales to particle sizes in the accumulation mode (e.g., approximately 100 nm) by applying the Stokes-Einstein equation suggests that the kinetic limitations imposed on mass transfer of water by slow bulk phase diffusion must be more fully investigated for atmospheric aerosol. Measurements have been made on particles covering a range in dynamic viscosity from < 0.1 to > 10(13) Pa s. We also retrieve the radial inhomogeneities apparent in particle composition during condensation and evaporation and contrast the dynamics of slow dissolution of a viscous core into a labile shell during condensation with the slow percolation of water during evaporation through a more homogeneous viscous particle bulk.

Unsteady density-current equations for highly curved terrain

NASA Technical Reports Server (NTRS)

Sivakumaran, N. S.; Dressler, R. F.

1989-01-01

New nonlinear partial differential equations containing terrain curvature and its rate of change are derived that describe the flow of an atmospheric density current. Unlike the classical hydraulic-type equations for density currents, the new equations are valid for two-dimensional, gradually varied flow over highly curved terrain, hence suitable for computing unsteady (or steady) flows over arbitrary mountain/valley profiles. The model assumes the atmosphere above the density current exerts a known arbitrary variable pressure upon the unknown interface. Later this is specialized to the varying hydrostatic pressure of the atmosphere above. The new equations yield the variable velocity distribution, the interface position, and the pressure distribution that contains a centrifugal component, often significantly larger than its hydrostatic component. These partial differential equations are hyperbolic, and the characteristic equations and characteristic directions are derived. Using these to form a characteristic mesh, a hypothetical unsteady curved-flow problem is calculated, not based upon observed data, merely as an example to illustrate the simplicity of their application to unsteady flows over mountains.

POLUTE; forest air pollutant uptake model. [IBM360,370; CSMP

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

Murphy, C.E.

POLUTE is a computer model designed to estimate the uptake of air pollutants by forests. The model utilizes submodels to describe atmospheric diffusion immediately above and within the canopy, and into the sink areas within or on the trees. The program implementing the model is general and can be used, with only minor changes, for any gaseous pollutant. The model provides an estimate describing the response of the vegetarian-atmosphere system to the environment as related to three types of processes: atmospheric diffusion, diffusion near and inside the absorbing plant, and the physical and chemical processes at the sink on ormore » within the plant.IBM360,370; CSMP; OS/370.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions

DOE PAGES

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; ...

2017-09-26

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions

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

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Viscosity and diffusivity in melts: from unary to multicomponent systems

NASA Astrophysics Data System (ADS)

Chen, Weimin; Zhang, Lijun; Du, Yong; Huang, Baiyun

2014-05-01

Viscosity and diffusivity, two important transport coefficients, are systematically investigated from unary melt to binary to multicomponent melts in the present work. By coupling with Kaptay's viscosity equation of pure liquid metals and effective radii of diffusion species, the Sutherland equation is modified by taking the size effect into account, and further derived into an Arrhenius formula for the convenient usage. Its reliability for predicting self-diffusivity and impurity diffusivity in unary liquids is then validated by comparing the calculated self-diffusivities and impurity diffusivities in liquid Al- and Fe-based alloys with the experimental and the assessed data. Moreover, the Kozlov model was chosen among various viscosity models as the most reliable one to reproduce the experimental viscosities in binary and multicomponent melts. Based on the reliable viscosities calculated from the Kozlov model, the modified Sutherland equation is utilized to predict the tracer diffusivities in binary and multicomponent melts, and validated in Al-Cu, Al-Ni and Al-Ce-Ni melts. Comprehensive comparisons between the calculated results and the literature data indicate that the experimental tracer diffusivities and the theoretical ones can be well reproduced by the present calculations. In addition, the vacancy-wind factor in binary liquid Al-Ni alloys with the increasing temperature is also discussed. What's more, the calculated inter-diffusivities in liquid Al-Cu, Al-Ni and Al-Ag-Cu alloys are also in excellent agreement with the measured and theoretical data. Comparisons between the simulated concentration profiles and the measured ones in Al-Cu, Al-Ce-Ni and Al-Ag-Cu melts are further used to validate the present calculation method.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

Hysteresis and Phase Transitions in a Lattice Regularization of an Ill-Posed Forward-Backward Diffusion Equation

NASA Astrophysics Data System (ADS)

Helmers, Michael; Herrmann, Michael

2018-03-01

We consider a lattice regularization for an ill-posed diffusion equation with a trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit. Our main result guarantees for a certain class of single-interface initial data that the lattice solutions satisfy asymptotically a free boundary problem with a hysteretic Stefan condition. The key challenge in the proof is to control the microscopic fluctuations that are inevitably produced by the backward diffusion when a particle passes the spinodal region.

Nonequilibrium diffusive gas dynamics: Poiseuille microflow

NASA Astrophysics Data System (ADS)

Abramov, Rafail V.; Otto, Jasmine T.

2018-05-01

We test the recently developed hierarchy of diffusive moment closures for gas dynamics together with the near-wall viscosity scaling on the Poiseuille flow of argon and nitrogen in a one micrometer wide channel, and compare it against the corresponding Direct Simulation Monte Carlo computations. We find that the diffusive regularized Grad equations with viscosity scaling provide the most accurate approximation to the benchmark DSMC results. At the same time, the conventional Navier-Stokes equations without the near-wall viscosity scaling are found to be the least accurate among the tested closures.

A Comparison of Some Difference Schemes for a Parabolic Problem of Zero-Coupon Bond Pricing

NASA Astrophysics Data System (ADS)

Chernogorova, Tatiana; Vulkov, Lubin

2009-11-01

This paper describes a comparison of some numerical methods for solving a convection-diffusion equation subjected by dynamical boundary conditions which arises in the zero-coupon bond pricing. The one-dimensional convection-diffusion equation is solved by using difference schemes with weights including standard difference schemes as the monotone Samarskii's scheme, FTCS and Crank-Nicolson methods. The schemes are free of spurious oscillations and satisfy the positivity and maximum principle as demanded for the financial and diffusive solution. Numerical results are compared with analytical solutions.

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

The general relativistic thin disc evolution equation

NASA Astrophysics Data System (ADS)

Balbus, Steven A.

2017-11-01

In the classical theory of thin disc accretion discs, the constraints of mass and angular momentum conservation lead to a diffusion-like equation for the turbulent evolution of the surface density. Here, we revisit this problem, extending the Newtonian analysis to the regime of Kerr geometry relevant to black holes. A diffusion-like equation once again emerges, but now with a singularity at the radius at which the effective angular momentum gradient passes through zero. The equation may be analysed using a combination of Wentzel-Kramers-Brillouin techniques, local techniques and matched asymptotic expansions. It is shown that imposing the boundary condition of a vanishing stress tensor (more precisely the radial-azimuthal component thereof) allows smooth stable modes to exist external to the angular momentum singularity, the innermost stable circular orbit, while smoothly vanishing inside this location. The extension of the disc diffusion equation to the domain of general relativity introduces a new tool for numerical and phenomenological studies of accretion discs, and may prove to be a useful technique for understanding black hole X-ray transients.

A 2D multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements

NASA Astrophysics Data System (ADS)

Qin, Shanlin; Liu, Fawang; Turner, Ian W.

2018-03-01

The consideration of diffusion processes in magnetic resonance imaging (MRI) signal attenuation is classically described by the Bloch-Torrey equation. However, many recent works highlight the distinct deviation in MRI signal decay due to anomalous diffusion, which motivates the fractional order generalization of the Bloch-Torrey equation. In this work, we study the two-dimensional multi-term time and space fractional diffusion equation generalized from the time and space fractional Bloch-Torrey equation. By using the Galerkin finite element method with a structured mesh consisting of rectangular elements to discretize in space and the L1 approximation of the Caputo fractional derivative in time, a fully discrete numerical scheme is derived. A rigorous analysis of stability and error estimation is provided. Numerical experiments in the square and L-shaped domains are performed to give an insight into the efficiency and reliability of our method. Then the scheme is applied to solve the multi-term time and space fractional Bloch-Torrey equation, which shows that the extra time derivative terms impact the relaxation process.

Evaluation of the telegrapher's equation and multiple-flux theories for calculating the transmittance and reflectance of a diffuse absorbing slab.

PubMed

Kong, Steven H; Shore, Joel D

2007-03-01

We study the propagation of light through a medium containing isotropic scattering and absorption centers. With a Monte Carlo simulation serving as the benchmark solution to the radiative transfer problem of light propagating through a turbid slab, we compare the transmission and reflection density computed from the telegrapher's equation, the diffusion equation, and multiple-flux theories such as the Kubelka-Munk and four-flux theories. Results are presented for both normally incident light and diffusely incident light. We find that we can always obtain very good results from the telegrapher's equation provided that two parameters that appear in the solution are set appropriately. We also find an interesting connection between certain solutions of the telegrapher's equation and solutions of the Kubelka-Munk and four-flux theories with a small modification to how the phenomenological parameters in those theories are traditionally related to the optical scattering and absorption coefficients of the slab. Finally, we briefly explore how well the theories can be extended to the case of anisotropic scattering by multiplying the scattering coefficient by a simple correction factor.

Equatorial superrotation in a thermally driven zonally symmetric circulation

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Harris, I.

1981-01-01

Near the equator where the Coriolis force vanishes, the momentum balance for the axially symmetric circulation is established between horizontal and vertical diffusion, which, a priori, does not impose constraints on the direction or magnitude of the zonal winds. Solar radiation absorbed at low latitudes is a major force in driving large scale motions with air rising near the equator and falling at higher latitudes. In the upper leg of the meridional cell, angular momentum is redistributed so that the atmosphere tends to subrotate (or corotate) at low latitudes and superrotate at high latitudes. In the lower leg, however, the process is reversed and produces a tendency for the equatorial region to superrotate. The outcome depends on the energy budget which is closely coupled to the momentum budget through the thermal wind equation; a pressure (temperature) maximum is required to sustain equatorial superrotation. Such a condition arises in regions which are convectively unstable and the temperature lapse rate is superadiabatic. It should arise in the tropospheres of Jupiter and Saturn; planetary energy from the interior is carried to higher altitudes where radiation to space becomes important. Upward equatorial motions in the direct and indirect circulations (Ferrel-Thomson type) imposed by insolation can then trap dynamic energy for equatorial heating which can sustain the superrotation of the equatorial region.

A model for calculating the vertical distribution of the atmospheric electric potential in the exchange layer in a maritime clean atmosphere

NASA Astrophysics Data System (ADS)

Kulkarni, M. N.; Kamra, A. K.

2012-11-01

A theoretical model is developed for calculating the vertical distribution of atmospheric electric potential in exchange layer of maritime clean atmosphere. The transport of space charge in electrode layer acts as a convective generator in this model and plays a major role in determining potential distribution in vertical. Eddy diffusion is the main mechanism responsible for the distribution of space charge in vertical. Our results show that potential at a particular level increases with increase in the strength of eddy diffusion under similar conditions. A method is suggested to estimate columnar resistance, the ionospheric potential and the vertical atmospheric electric potential distribution in exchange layer from measurements of total air-earth current density and surface electric field made over oceans. The results are validated and found to be in very good agreement with the previous aircraft measurements. Different parameters involved in the proposed methodology can be determined either theoretically, as in the present work, or experimentally using the near surface atmospheric electrical measurements or using some other surface-based measurement technique such as LIDAR. A graphical relationship between the atmospheric eddy diffusion coefficient and height of exchange layer obtained from atmospheric electrical approach, is reported.

Determination of the ground albedo and the index of absorption of atmospheric particulates by remote sensing. II - Application

NASA Technical Reports Server (NTRS)

King, M. D.

1979-01-01

A hemispherical radiometer has been used to obtain spectrally narrow-band measurements of the downward hemispheric diffuse and total (global) flux densities at varying solar zenith angles on 14 days over Tucson. Data are presented which illustrate the effects of temporally varying atmospheric conditions as well as clear stable conditions on the ratio of the diffuse to direct solar radiation at the earth's surface. The ground albedo and the effective imaginary term of the complex refractive index of atmospheric particulates are derived from the diffuse-direct ratio measurements on seven clear stable days at two wavelengths using the statistical procedure described by King and Herman (1979). Results indicate that the downwelling diffuse radiation field in the midvisible region in Tucson can be adequately described by Mie scattering theory if the ground albedo is 0.279 + or - 0.100 and the index of absorption is 0.0306 + or - 0.0082.

Conformable derivative approach to anomalous diffusion

NASA Astrophysics Data System (ADS)

Zhou, H. W.; Yang, S.; Zhang, S. Q.

2018-02-01

By using a new derivative with fractional order, referred to conformable derivative, an alternative representation of the diffusion equation is proposed to improve the modeling of anomalous diffusion. The analytical solutions of the conformable derivative model in terms of Gauss kernel and Error function are presented. The power law of the mean square displacement for the conformable diffusion model is studied invoking the time-dependent Gauss kernel. The parameters related to the conformable derivative model are determined by Levenberg-Marquardt method on the basis of the experimental data of chloride ions transportation in reinforced concrete. The data fitting results showed that the conformable derivative model agrees better with the experimental data than the normal diffusion equation. Furthermore, the potential application of the proposed conformable derivative model of water flow in low-permeability media is discussed.

Ionic channels: natural nanotubes described by the drift diffusion equations

NASA Astrophysics Data System (ADS)

Eisenberg, Bob

2000-05-01

Ionic channels are a large class of proteins with holes down their middle that control a wide range of cellular functions important in health and disease. Ionic channels can be analysed using a combination of the Poisson and drift diffusion equations familiar from computational electronics because their behavior is dominated by the electrical properties of their simple structure.

Analysis of pulse thermography using similarities between wave and diffusion propagation

NASA Astrophysics Data System (ADS)

Gershenson, M.

2017-05-01

Pulse thermography or thermal wave imaging are commonly used as nondestructive evaluation (NDE) method. While the technical aspect has evolve with time, theoretical interpretation is lagging. Interpretation is still using curved fitting on a log log scale. A new approach based directly on the governing differential equation is introduced. By using relationships between wave propagation and the diffusive propagation of thermal excitation, it is shown that one can transform from solutions in one type of propagation to the other. The method is based on the similarities between the Laplace transforms of the diffusion equation and the wave equation. For diffusive propagation we have the Laplace variable s to the first power, while for the wave propagation similar equations occur with s2. For discrete time the transformation between the domains is performed by multiplying the temperature data vector by a matrix. The transform is local. The performance of the techniques is tested on synthetic data. The application of common back projection techniques used in the processing of wave data is also demonstrated. The combined use of the transform and back projection makes it possible to improve both depth and lateral resolution of transient thermography.

Reaction rates for a generalized reaction-diffusion master equation

DOE PAGES

Hellander, Stefan; Petzold, Linda

2016-01-19

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show inmore » two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules.« less

Reaction rates for a generalized reaction-diffusion master equation

PubMed Central

Hellander, Stefan; Petzold, Linda

2016-01-01

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules. PMID:26871190

[Factors affecting benzene diffusion from contaminated soils to the atmosphere and flux characteristics].

PubMed

Du, Ping; Wang, Shi-Jie; Zhao, Huan-Huan; Wu, Bin; Han, Chun-Mei; Fang, Ji-Dun; Li, Hui-Ying; Hosomi, Masaaki; Li, Fa-Sheng

2013-12-01

The influencing factors of benzene diffusion fluxes from sand and black soil to atmosphere were investigated using a flux chamber (30.0 cm x 17.5 cm x 29.0 cm). In this study, the benzene diffusion fluxes were estimated by measuring the benzene concentrations both in the headspace of the chamber and in the soils of different layers. The results indicated that the soil water content played an important role in benzene diffusion fluxes. The diffusion flux showed positive correlation with the initial benzene concentration and the benzene dissolution concentration for both soil types. The changes of air flow rate from 300 to 900 mL x min(-1) and temperature from 20 degrees C to 40 degrees C resulted in increases of the benzene diffusion flux. Our study of benzene diffusion fluxes from contaminated soils will be beneficial for the predicting model, and emergency management and precautions.

Differential equation of exospheric lateral transport and its application to terrestrial hydrogen

NASA Technical Reports Server (NTRS)

Hodges, R. R., Jr.

1973-01-01

The differential equation description of exospheric lateral transport of Hodges and Johnson is reformulated to extend its utility to light gases. Accuracy of the revised equation is established by applying it to terrestrial hydrogen. The resulting global distributions for several static exobase models are shown to be essentially the same as those that have been computed by Quessette using an integral equation approach. The present theory is subsequently used to elucidate the effects of nonzero lateral flow, exobase rotation, and diurnal tidal winds on the hydrogen distribution. Finally it is shown that the differential equation of exospheric transport is analogous to a diffusion equation. Hence it is practical to consider exospheric transport as a continuation of thermospheric diffusion, a concept that alleviates the need for an artificial exobase dividing thermosphere and exosphere.

Theoretical aspects of tidal and planetary wave propagation at thermospheric heights

NASA Technical Reports Server (NTRS)

Volland, H.; Mayr, H. G.

1977-01-01

A simple semiquantitative model is presented which allows analytic solutions of tidal and planetary wave propagation at thermospheric heights. This model is based on perturbation approximation and mode separation. The effects of viscosity and heat conduction are parameterized by Rayleigh friction and Newtonian cooling. Because of this simplicity, one gains a clear physical insight into basic features of atmospheric wave propagation. In particular, we discuss the meridional structures of pressure and horizontal wind (the solutions of Laplace's equation) and their modification due to dissipative effects at thermospheric heights. Furthermore, we solve the equations governing the height structure of the wave modes and arrive at a very simple asymptotic solution valid in the upper part of the thermosphere. That 'system transfer function' of the thermosphere allows one to estimate immediately the reaction of the thermospheric wave mode parameters such as pressure, temperature, and winds to an external heat source of arbitrary temporal and spatial distribution. Finally, the diffusion effects of the minor constituents due to the global wind circulation are discussed, and some results of numerical calculations are presented.

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

Cheng, He; Liu, Xin; Lu, Xinpei

The atmospheric pressure non-equilibrium plasma has shown a significant potential as a novel food decontamination technology. In this paper, we report a computational study of the intersection of negative streamer produced by air dielectric barrier discharge with bacteria biofilm on an apple surface. The structure, conductivities, and permittivities of bacteria biofilm have been considered in the Poisson's equations and transportation equations of charge and neutral species to realize self-consistent transportation of plasma between electrode and charging surfaces of apple. We find that the ionization near the biofilm facilitates the propagation of negative streamer when the streamer head is 1 mm frommore » the biofilm. The structure of the biofilm results in the non-uniform distribution of ROS and RNS captured by flux and time fluence of these reactive species. The mean free path of charged species in μm scale permitted the plasma penetrate into the cavity of the biofilm, therefore, although the density of ROS and RNS decrease by 6–7 order of magnitude, the diffusion results in the uniform distribution of ROS and RNS inside the cavity during the pulse off period.« less

Atmospheric optical calibration system

DOEpatents

Hulstrom, Roland L.; Cannon, Theodore W.

1988-01-01

An atmospheric optical calibration system is provided to compare actual atmospheric optical conditions to standard atmospheric optical conditions on the basis of aerosol optical depth, relative air mass, and diffuse horizontal skylight to global horizontal photon flux ratio. An indicator can show the extent to which the actual conditions vary from standard conditions. Aerosol scattering and absorption properties, diffuse horizontal skylight to global horizontal photon flux ratio, and precipitable water vapor determined on a real-time basis for optical and pressure measurements are also used to generate a computer spectral model and for correcting actual performance response of a photovoltaic device to standard atmospheric optical condition response on a real-time basis as the device is being tested in actual outdoor conditions.

Extracting surface diffusion coefficients from batch adsorption measurement data: application of the classic Langmuir kinetics model.

PubMed

Chu, Khim Hoong

2017-11-09

Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6  cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.

Turbo fluid machinery and diffusers

NASA Technical Reports Server (NTRS)

Sakurai, T.

1984-01-01

The general theory behind turbo devices and diffusers is explained. Problems and the state of research on basic equations of flow and experimental and measuring methods are discussed. Conventional centrifugation-type compressor and fan diffusers are considered in detail.

Patterns induced by super cross-diffusion in a predator-prey system with Michaelis-Menten type harvesting.

PubMed

Liu, Biao; Wu, Ranchao; Chen, Liping

2018-04-01

Turing instability and pattern formation in a super cross-diffusion predator-prey system with Michaelis-Menten type predator harvesting are investigated. Stability of equilibrium points is first explored with or without super cross-diffusion. It is found that cross-diffusion could induce instability of equilibria. To further derive the conditions of Turing instability, the linear stability analysis is carried out. From theoretical analysis, note that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes by means of weakly nonlinear theory. Dynamical analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, the theoretical results are illustrated via numerical simulations. Copyright © 2018. Published by Elsevier Inc.

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

NASA Technical Reports Server (NTRS)

May, C. E.; Kautz, Harold E.

1978-01-01

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 X 10 to the minus 7th power squared cm per sec + or - 30 percent in 45 percent potassium hydroxide and 1.4 x 10 to the minus 7 squared cm per sec + or - 25 percent in 40 percent sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite size chambers. Details and discussion of the experimental method are also given.

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

NASA Technical Reports Server (NTRS)

May, C. E.; Kautz, H. E.

1978-01-01

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 x 10 to the -7th power sq cm/sec + or - 30% in 45% potassium hydroxide and 1.4 x 10 to the -7th power sq cm/sec + or - 25% in 40% sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half-cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite-size chambers. Details and discussion of the experimental method are also given.

Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory.

PubMed

Contini, D; Martelli, F; Zaccanti, G

1997-07-01

The diffusion approximation of the radiative transfer equation is a model used widely to describe photon migration in highly diffusing media and is an important matter in biological tissue optics. An analysis of the time-dependent diffusion equation together with its solutions for the slab geometry and for a semi-infinite diffusing medium are reported. These solutions, presented for both the time-dependent and the continuous wave source, account for the refractive index mismatch between the turbid medium and the surrounding medium. The results have been compared with those obtained when different boundary conditions were assumed. The comparison has shown that the effect of the refractive index mismatch cannot be disregarded. This effect is particularly important for the transmittance. The discussion of results also provides an analysis of the role of the absorption coefficient in the expression of the diffusion coefficient.

Nonparametric estimates of drift and diffusion profiles via Fokker-Planck algebra.

PubMed

Lund, Steven P; Hubbard, Joseph B; Halter, Michael

2014-11-06

Diffusion processes superimposed upon deterministic motion play a key role in understanding and controlling the transport of matter, energy, momentum, and even information in physics, chemistry, material science, biology, and communications technology. Given functions defining these random and deterministic components, the Fokker-Planck (FP) equation is often used to model these diffusive systems. Many methods exist for estimating the drift and diffusion profiles from one or more identifiable diffusive trajectories; however, when many identical entities diffuse simultaneously, it may not be possible to identify individual trajectories. Here we present a method capable of simultaneously providing nonparametric estimates for both drift and diffusion profiles from evolving density profiles, requiring only the validity of Langevin/FP dynamics. This algebraic FP manipulation provides a flexible and robust framework for estimating stationary drift and diffusion coefficient profiles, is not based on fluctuation theory or solved diffusion equations, and may facilitate predictions for many experimental systems. We illustrate this approach on experimental data obtained from a model lipid bilayer system exhibiting free diffusion and electric field induced drift. The wide range over which this approach provides accurate estimates for drift and diffusion profiles is demonstrated through simulation.

Activation of the marine ecosystem model 3D CEMBS for the Baltic Sea in operational mode

NASA Astrophysics Data System (ADS)

Dzierzbicka-Glowacka, Lidia; Jakacki, Jaromir; Janecki, Maciej; Nowicki, Artur

2013-04-01

The paper presents a new marine ecosystem model 3D CEMBS designed for the Baltic Sea. The ecosystem model is incorporated into the 3D POPCICE ocean-ice model. The Current Baltic Sea model is based on the Community Earth System Model (CESM from the National Center for Atmospheric Research) which was adapted for the Baltic Sea as a coupled sea-ice model. It consists of the Community Ice Code (CICE model, version 4.0) and the Parallel Ocean Program (version 2.1). The ecosystem model is a biological submodel of the 3D CEMBS. It consists of eleven mass conservation equations. There are eleven partial second-order differential equations of the diffusion type with the advective term for phytoplankton, zooplankton, nutrients, dissolved oxygen, and dissolved and particulate organic matter. This model is an effective tool for solving the problem of ecosystem bioproductivity. The model is forced by 48-hour atmospheric forecasts provided by the UM model from the Interdisciplinary Centre for Mathematical and Computational Modelling of Warsaw University (ICM). The study was financially supported by the Polish State Committee of Scientific Research (grants: No N N305 111636, N N306 353239). The partial support for this study was also provided by the project Satellite Monitoring of the Baltic Sea Environment - SatBaltyk founded by European Union through European Regional Development Fund contract no. POIG 01.01.02-22-011/09. Calculations were carried out at the Academy Computer Centre in Gdańsk.

FROM THE HISTORY OF PHYSICS: Mysteries of diffusion and labyrinths of destiny

NASA Astrophysics Data System (ADS)

Bakunin, Oleg G.

2003-03-01

The role of prominent Soviet physicist B I Davydov in the development of our understanding of diffusion is briefly reviewed, with emphasis on the ideas he put forward in the 1930s: introducing additional partial derivatives into diffusion equations and extending diffusion concepts to phase space.

Chemically reacting fluid flow in exoplanet and brown dwarf atmospheres

NASA Astrophysics Data System (ADS)

Bordwell, Baylee; Brown, Benjamin P.; Oishi, Jeffrey S.

2016-11-01

In the past few decades, spectral observations of planets and brown dwarfs have demonstrated significant deviations from predictions in certain chemical abundances. Starting with Jupiter, these deviations were successfully explained to be the effect of fast dynamics on comparatively slow chemical reactions. These dynamical effects are treated using mixing length theory in what is known as the "quench" approximation. In these objects, however, both radiative and convective zones are present, and it is not clear that this approximation applies. To resolve this issue, we solve the fully compressible equations of fluid dynamics in a matched polytropic atmosphere using the state-of-the-art pseudospectral simulation framework Dedalus. Through the inclusion of passive tracers, we explore the transport properties of convective and radiative zones, and verify the classical eddy diffusion parameterization. With the addition of active tracers, we examine the interactions between dynamical and chemical processes using abstract chemical reactions. By locating the quench point (the point at which the dynamical and chemical timescales are the same) in different dynamical regimes, we test the quench approximation, and generate prescriptions for the exoplanet and brown dwarf communities.

Diffuse-Interface Capturing Methods for Compressible Two-Phase Flows

NASA Astrophysics Data System (ADS)

Saurel, Richard; Pantano, Carlos

2018-01-01

Simulation of compressible flows became a routine activity with the appearance of shock-/contact-capturing methods. These methods can determine all waves, particularly discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows due to the abrupt variation of thermodynamic properties across the interfacial region, with discontinuous thermodynamical representations at the interfaces. To overcome this difficulty, researchers have developed augmented systems of governing equations to extend the capturing strategy. These extended systems, reviewed here, are termed diffuse-interface models, because they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they facilitate coupling the dynamics on both sides of the (diffuse) interfaces and tend to the proper pure fluid-governing equations far from the interfaces. This strategy has become efficient for contact interfaces separating fluids that are governed by different equations of state, in the presence or absence of capillary effects, and with phase change. More sophisticated materials than fluids (e.g., elastic-plastic materials) have been considered as well.

A mathematical model of diffusion from a steady source of short duration in a finite mixing layer

NASA Astrophysics Data System (ADS)

Bianconi, Roberto; Tamponi, Matteo

This paper presents an analytical unsteady-state solution to the atmospheric dispersion equation for substances subject to chemical-physical decay in a finite mixing layer for releases of short duration. This solution is suitable for describing critical events relative to accidental release of toxic, flammable or explosive substances. To implement the solution, the Modello per Rilasci a Breve Termine (MRBT) code has been developed, for some characteristics parameters of which the results of the sensitivity analysis are presented. Moreover some examples of application to the calculation of exposure to toxic substances and to the determination of the ignition field of flammable substances are described. Finally, the mathematical model described can be used to interpret the phenomenon of pollutant accumulation.

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

NASA Astrophysics Data System (ADS)

Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

2018-06-01

This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

Numerical simulation of double‐diffusive finger convection

USGS Publications Warehouse

Hughes, Joseph D.; Sanford, Ward E.; Vacher, H. Leonard

2005-01-01

A hybrid finite element, integrated finite difference numerical model is developed for the simulation of double‐diffusive and multicomponent flow in two and three dimensions. The model is based on a multidimensional, density‐dependent, saturated‐unsaturated transport model (SUTRA), which uses one governing equation for fluid flow and another for solute transport. The solute‐transport equation is applied sequentially to each simulated species. Density coupling of the flow and solute‐transport equations is accounted for and handled using a sequential implicit Picard iterative scheme. High‐resolution data from a double‐diffusive Hele‐Shaw experiment, initially in a density‐stable configuration, is used to verify the numerical model. The temporal and spatial evolution of simulated double‐diffusive convection is in good agreement with experimental results. Numerical results are very sensitive to discretization and correspond closest to experimental results when element sizes adequately define the spatial resolution of observed fingering. Numerical results also indicate that differences in the molecular diffusivity of sodium chloride and the dye used to visualize experimental sodium chloride concentrations are significant and cause inaccurate mapping of sodium chloride concentrations by the dye, especially at late times. As a result of reduced diffusion, simulated dye fingers are better defined than simulated sodium chloride fingers and exhibit more vertical mass transfer.

New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis.

PubMed

Ingo, Carson; Magin, Richard L; Parrish, Todd B

2014-11-01

Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag-Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.

Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.

PubMed

Henry, B I; Langlands, T A M; Wearne, S L

2006-09-01

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.

Anomalous diffusion and scaling in coupled stochastic processes

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

Bel, Golan; Nemenman, Ilya

2009-01-01

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin processes with the friction coefficient depending on the state of a similar, unobserved, process. Integrating out the latter, we derive the Pocker-Planck the friction coefficient of the first depends on the state of the second. Integrating out the latter, we derive the Focker-Planck equation for the probability distribution of the former. This has the fonn of diffusion equation with time-dependent diffusion coefficient, resulting in an anomalous diffusion. The diffusion exponent can not be predicted using a simple scaling argument, and anomalous scaling appears as well. Themore » diffusion exponent of the Weiss-Havlin comb model is derived as a special case, and the same exponent holds even for weakly coupled processes. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems with unobserved dynamical degrees of freedom by means of standandard, diffusive Langevin descritpion.« less

WET EFFLUENT PARALLEL PLATE DIFFUSION DENUDER COUPLED CAPILLARY ION CHROMATOGRAPH FOR THE DETERMINATION OF ATMOSPHERIC TRACE GASES. (R825344)

EPA Science Inventory

We describe an inexpensive, compact parallel plate diffusion denuder coupled capillary IC system for the determination of soluble ionogenic atmospheric trace gases. The active sampling area (0.6×10 cm) of the denuder is formed in a novel manner by thermally bonding silica ge...

Nitrogen Chemistry in Titan's Upper Atmosphere

NASA Technical Reports Server (NTRS)

McKay, Christopher P.; Cuzzi, Jeffrey (Technical Monitor)

1996-01-01

In Titan's upper atmosphere N2 is dissociated to N by solar UV and high energy electrons. This flux of N provides for interesting organic chemistry in the lower atmosphere of Titan. Previously the main pathway for the loss of this N was thought to be the formation of HCN, followed by diffusion of this HCN to lower altitudes leading ultimately to condensation. However, recent laboratory simulations of organic chemistry in Titan's atmosphere suggest that formation of the organic haze may be an important sink for atmospheric N. Because estimates of the eddy diffusion profile on Titan have been based on the HCN profile, inclusion of this additional sink for N will affect estimates for all transport processes in Titan's atmosphere. This and other implications of this sink for the N balance on Titan are considered.

A low diffusive Lagrange-remap scheme for the simulation of violent air-water free-surface flows

NASA Astrophysics Data System (ADS)

Bernard-Champmartin, Aude; De Vuyst, Florian

2014-10-01

In 2002, Després and Lagoutière [17] proposed a low-diffusive advection scheme for pure transport equation problems, which is particularly accurate for step-shaped solutions, and thus suited for interface tracking procedure by a color function. This has been extended by Kokh and Lagoutière [28] in the context of compressible multifluid flows using a five-equation model. In this paper, we explore a simplified variant approach for gas-liquid three-equation models. The Eulerian numerical scheme has two ingredients: a robust remapped Lagrange solver for the solution of the volume-averaged equations, and a low diffusive compressive scheme for the advection of the gas mass fraction. Numerical experiments show the performance of the computational approach on various flow reference problems: dam break, sloshing of a tank filled with water, water-water impact and finally a case of Rayleigh-Taylor instability. One of the advantages of the present interface capturing solver is its natural implementation on parallel processors or computers.

A computer program for the simulation of heat and moisture flow in soils

NASA Technical Reports Server (NTRS)

Camillo, P.; Schmugge, T. J.

1981-01-01

A computer program that simulates the flow of heat and moisture in soils is described. The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations. The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time. The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known. These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions. In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator. Simulations of heat and moisture flow under actual field conditions were also performed. Ground truth data were used for the boundary conditions and soil transport properties. The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved.

Extremal equilibria for reaction-diffusion equations in bounded domains and applications

NASA Astrophysics Data System (ADS)

Rodríguez-Bernal, Aníbal; Vidal-López, Alejandro

We show the existence of two special equilibria, the extremal ones, for a wide class of reaction-diffusion equations in bounded domains with several boundary conditions, including non-linear ones. They give bounds for the asymptotic dynamics and so for the attractor. Some results on the existence and/or uniqueness of positive solutions are also obtained. As a consequence, several well-known results on the existence and/or uniqueness of solutions for elliptic equations are revisited in a unified way obtaining, in addition, information on the dynamics of the associated parabolic problem. Finally, we ilustrate the use of the general results by applying them to the case of logistic equations. In fact, we obtain a detailed picture of the positive dynamics depending on the parameters appearing in the equation.

The fundamental equation of eddy covariance and its application in flux measurements

Treesearch

Lianhong Gu; William J. Massman; Ray Leuning; Stephen G. Pallardy; Tilden Meyers; Paul J. Hanson; Jeffery S. Riggs; Kevin P. Hosman; Bai Yang

2012-01-01

A fundamental equation of eddy covariance (FQEC) is derived that allows the net ecosystem exchange (NEE) Ns of a specified atmospheric constituent s to be measured with the constraint of conservation of any other atmospheric constituent (e.g. N2, argon, or dry air). It is shown that if the condition [equation, see PDF] is true, the conservation of mass can be applied...

Reduced equations of motion for quantum systems driven by diffusive Markov processes.

PubMed

Sarovar, Mohan; Grace, Matthew D

2012-09-28

The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Förster resonance transfer in Rydberg atoms with nonperturbative position fluctuations.

Grid adaption based on modified anisotropic diffusion equations formulated in the parametic domain

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

Hagmeijer, R.

1994-11-01

A new grid-adaption algorithm for problems in computational fluid dynamics is presented. The basic equations are derived from a variational problem formulated in the parametric domain of the mapping that defines the existing grid. Modification of the basic equations provides desirable properties in boundary layers. The resulting modified anisotropic diffusion equations are solved for the computational coordinates as functions of the parametric coordinates and these functions are numerically inverted. Numerical examples show that the algorithm is robust, that shocks and boundary layers are well-resolved on the adapted grid, and that the flow solution becomes a globally smooth function of themore » computational coordinates.« less

Diffusivity Measurements of Volatile Organics in Levitated Viscous Aerosol Particles

NASA Astrophysics Data System (ADS)

Bastelberger, Sandra; Krieger, Ulrich; Luo, Beiping; Peter, Thomas

2017-04-01

Field measurements indicating that atmospheric secondary aerosol (SOA) particles can be present in a highly viscous, glassy state have spurred numerous studies addressing low water diffusivities in glassy aerosols, focusing on kinetic limitations to hygroscopic growth and the plasticizing effect of water. Less is known about diffusion limitations of organic molecules and oxidants in viscous matrices and how these might affect atmospheric chemistry and gas-particle phase partitioning of complex mixtures with constituents of different volatility. Often viscosity data has been used to infer diffusivity via the Stokes- Einstein relationship even though strong deviations from this relationship have been observed for matrices of high viscosity. In this study, we provide a quantitative estimate for the diffusivity of a volatile organic in a viscous matrix. Evaporation of single particles generated from an aqueous solution of sucrose and a small quantity of volatile tetraethylene glycol (PEG-4) is investigated in an electrodynamic balance at controlled relative humidity (RH) and temperature conditions, thereby varying the viscosity of the sucrose matrix. The evaporative loss of tetraethylene glycol as determined by Mie resonance spectroscopy is used in conjunction with a diffusion model to retrieve translational diffusion coefficients of tetraethylene glycol. The evaporation of PEG-4 shows a pronounced RH and temperature dependence and is severely depressed for RH 30% corresponding to diffusivities < 10-14 cm2/s at temperatures as high as 15 °C, implying that atmospheric volatile organic compounds (VOC) can be subject to severe diffusion limitations in glassy SOA. Comparison of the experimentally derived diffusivities with viscosity estimates for the ternary system reveals a breakdown of the Stokes-Einstein relationship.

Representative Atmospheric Plume Development for Elevated Releases

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

Eslinger, Paul W.; Lowrey, Justin D.; McIntyre, Justin I.

2014-02-01

An atmospheric explosion of a low-yield nuclear device will produce a large number of radioactive isotopes, some of which can be measured with airborne detection systems. However, properly equipped aircraft may not arrive in the region where an explosion occurred for a number of hours after the event. Atmospheric conditions will have caused the radioactive plume to move and diffuse before the aircraft arrives. The science behind predicting atmospheric plume movement has advanced enough that the location of the maximum concentrations in the plume can be determined reasonably accurately in real time, or near real time. Given the assumption thatmore » an aircraft can follow a plume, this study addresses the amount of atmospheric dilution expected to occur in a representative plume as a function of time past the release event. The approach models atmospheric transport of hypothetical releases from a single location for every day in a year using the publically available HYSPLIT code. The effective dilution factors for the point of maximum concentration in an elevated plume based on a release of a non-decaying, non-depositing tracer can vary by orders of magnitude depending on the day of the release, even for the same number of hours after the release event. However, the median of the dilution factors based on releases for 365 consecutive days at one site follows a power law relationship in time, as shown in Figure S-1. The relationship is good enough to provide a general rule of thumb for estimating typical future dilution factors in a plume starting at the same point. However, the coefficients of the power law function may vary for different release point locations. Radioactive decay causes the effective dilution factors to decrease more quickly with the time past the release event than the dilution factors based on a non-decaying tracer. An analytical expression for the dilution factors of isotopes with different half-lives can be developed given the power law expression for the non-decaying tracer. If the power-law equation for the median dilution factor, Df, based on a non-decaying tracer has the general form Df=a(×t)^(-b) for time t after the release event, then the equation has the form Df=e^(-λt)×a×t^(-b) for a radioactive isotope, where λ is the decay constant for the isotope.« less

A numerical study of the steady scalar convective diffusion equation for small viscosity

NASA Technical Reports Server (NTRS)

Giles, M. B.; Rose, M. E.

1983-01-01

A time-independent convection diffusion equation is studied by means of a compact finite difference scheme and numerical solutions are compared to the analytic inviscid solutions. The correct internal and external boundary layer behavior is observed, due to an inherent feature of the scheme which automatically produces upwind differencing in inviscid regions and the correct viscous behavior in viscous regions.

O the Derivation of the Schroedinger Equation from Stochastic Mechanics.

NASA Astrophysics Data System (ADS)

Wallstrom, Timothy Clarke

The thesis is divided into four largely independent chapters. The first three chapters treat mathematical problems in the theory of stochastic mechanics. The fourth chapter deals with stochastic mechanisms as a physical theory and shows that the Schrodinger equation cannot be derived from existing formulations of stochastic mechanics, as had previously been believed. Since the drift coefficients of stochastic mechanical diffusions are undefined on the nodes, or zeros of the density, an important problem has been to show that the sample paths stay away from the nodes. In Chapter 1, it is shown that for a smooth wavefunction, the closest approach to the nodes can be bounded solely in terms of the time -integrated energy. The ergodic properties of stochastic mechanical diffusions are greatly complicated by the tendency of the particles to avoid the nodes. In Chapter 2, it is shown that a sufficient condition for a stationary process to be ergodic is that there exist positive t and c such that for all x and y, p^{t} (x,y) > cp(y), and this result is applied to show that the set of spin-1over2 diffusions is uniformly ergodic. In stochastic mechanics, the Bopp-Haag-Dankel diffusions on IR^3times SO(3) are used to represent particles with spin. Nelson has conjectured that in the limit as the particle's moment of inertia I goes to zero, the projections of the Bopp -Haag-Dankel diffusions onto IR^3 converge to a Markovian limit process. This conjecture is proved for the spin-1over2 case in Chapter 3, and the limit process identified as the diffusion naturally associated with the solution to the regular Pauli equation. In Chapter 4 it is shown that the general solution of the stochastic Newton equation does not correspond to a solution of the Schrodinger equation, and that there are solutions to the Schrodinger equation which do not satisfy the Guerra-Morato Lagrangian variational principle. These observations are shown to apply equally to other existing formulations of stochastic mechanics, and it is argued that these difficulties represent fundamental inadequacies in the physical foundation of stochastic mechanics.

Nonlinear optical susceptibilities in the diffusion modified AlxGa1-xN/GaN single quantum well

NASA Astrophysics Data System (ADS)

Das, T.; Panda, S.; Panda, B. K.

2018-05-01

Under thermal treatment of the post growth AlGaN/GaN single quantum well, the diffusion of Al and Ga atoms across the interface is expected to form the diffusion modified quantum well with diffusion length as a quantitative parameter for diffusion. The modification of confining potential and position-dependent effective mass in the quantum well due to diffusion is calculated taking the Fick's law. The built-in electric field which arises from spontaneous and piezoelectric polarizations in the wurtzite structure is included in the effective mass equation. The electronic states are calculated from the effective mass equation using the finite difference method for several diffusion lengths. Since the effective well width decreases with increasing diffusion length, the energy levels increase with it. The intersubband energy spacing in the conduction band decreases with diffusion length due to built-in electric field and reduction of effective well width. The linear susceptibility for first-order and the nonlinear second-order and third-order susceptibilities are calculated using the compact density matrix approach taking only two levels. The calculated susceptibilities are red shifted with increase in diffusion lengths due to decrease in intersubband energy spacing.

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2014-01-01

A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

Ordinary differential equation for local accumulation time.

PubMed

Berezhkovskii, Alexander M

2011-08-21

Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics

A non-local structural derivative model for characterization of ultraslow diffusion in dense colloids

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen

2018-03-01

Ultraslow diffusion has been observed in numerous complicated systems. Its mean squared displacement (MSD) is not a power law function of time, but instead a logarithmic function, and in some cases grows even more slowly than the logarithmic rate. The distributed-order fractional diffusion equation model simply does not work for the general ultraslow diffusion. Recent study has used the local structural derivative to describe ultraslow diffusion dynamics by using the inverse Mittag-Leffler function as the structural function, in which the MSD is a function of inverse Mittag-Leffler function. In this study, a new stretched logarithmic diffusion law and its underlying non-local structural derivative diffusion model are proposed to characterize the ultraslow diffusion in aging dense colloidal glass at both the short and long waiting times. It is observed that the aging dynamics of dense colloids is a class of the stretched logarithmic ultraslow diffusion processes. Compared with the power, the logarithmic, and the inverse Mittag-Leffler diffusion laws, the stretched logarithmic diffusion law has better precision in fitting the MSD of the colloidal particles at high densities. The corresponding non-local structural derivative diffusion equation manifests clear physical mechanism, and its structural function is equivalent to the first-order derivative of the MSD.

Influence of heat conducting substrates on explosive crystallization in thin layers

NASA Astrophysics Data System (ADS)

Schneider, Wilhelm

2017-09-01

Crystallization in a thin, initially amorphous layer is considered. The layer is in thermal contact with a substrate of very large dimensions. The energy equation of the layer contains source and sink terms. The source term is due to liberation of latent heat in the crystallization process, while the sink term is due to conduction of heat into the substrate. To determine the latter, the heat diffusion equation for the substrate is solved by applying Duhamel's integral. Thus, the energy equation of the layer becomes a heat diffusion equation with a time integral as an additional term. The latter term indicates that the heat loss due to the substrate depends on the history of the process. To complete the set of equations, the crystallization process is described by a rate equation for the degree of crystallization. The governing equations are then transformed to a moving co-ordinate system in order to analyze crystallization waves that propagate with invariant properties. Dual solutions are found by an asymptotic expansion for large activation energies of molecular diffusion. By introducing suitable variables, the results can be presented in a universal form that comprises the influence of all non-dimensional parameters that govern the process. Of particular interest for applications is the prediction of a critical heat loss parameter for the existence of crystallization waves with invariant properties.

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium.

PubMed

Hibi, Yoshihiko; Kashihara, Ayumi

2018-03-01

A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide-nitrogen gas system and five porous media with permeability coefficients ranging from 10 -13 to 10 -11  m 2 . The results showed that the Knudsen diffusion coefficient of N 2 (D N2 ) (cm 2 /s) was related to the effective permeability coefficient k e (m 2 ) as D N2  = 7.39 × 10 7 k e 0.767 . Thus, the Knudsen diffusion coefficients of N 2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection-diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent gas system. Thus, molecular diffusion considers only the obstruction factor related to tortuosity. Therefore, we introduced a correction factor for a multicomponent gas system into the DGM equation, multiplying the Knudsen diffusion coefficient, which includes the obstruction factor related to tortuosity, by this correction factor. From the present experimental results, the value of this correction factor was 1/27, and it depended only on the structure of the gas system in the porous medium. Copyright © 2018 Elsevier B.V. All rights reserved.

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium

NASA Astrophysics Data System (ADS)

Hibi, Yoshihiko; Kashihara, Ayumi

2018-03-01

A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide-nitrogen gas system and five porous media with permeability coefficients ranging from 10-13 to 10-11 m2. The results showed that the Knudsen diffusion coefficient of N2 (DN2) (cm2/s) was related to the effective permeability coefficient ke (m2) as DN2 = 7.39 × 107ke0.767. Thus, the Knudsen diffusion coefficients of N2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection-diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent gas system. Thus, molecular diffusion considers only the obstruction factor related to tortuosity. Therefore, we introduced a correction factor for a multicomponent gas system into the DGM equation, multiplying the Knudsen diffusion coefficient, which includes the obstruction factor related to tortuosity, by this correction factor. From the present experimental results, the value of this correction factor was 1/27, and it depended only on the structure of the gas system in the porous medium.

Diffusivity measurements of volatile organics in levitated viscous aerosol particles

NASA Astrophysics Data System (ADS)

Bastelberger, Sandra; Krieger, Ulrich K.; Luo, Beiping; Peter, Thomas

2017-07-01

Field measurements indicating that atmospheric secondary organic aerosol (SOA) particles can be present in a highly viscous, glassy state have spurred numerous studies addressing low diffusivities of water in glassy aerosols. The focus of these studies is on kinetic limitations of hygroscopic growth and the plasticizing effect of water. In contrast, much less is known about diffusion limitations of organic molecules and oxidants in viscous matrices. These may affect atmospheric chemistry and gas-particle partitioning of complex mixtures with constituents of different volatility. In this study, we quantify the diffusivity of a volatile organic in a viscous matrix. Evaporation of single particles generated from an aqueous solution of sucrose and small amounts of volatile tetraethylene glycol (PEG-4) is investigated in an electrodynamic balance at controlled relative humidity (RH) and temperature. The evaporative loss of PEG-4 as determined by Mie resonance spectroscopy is used in conjunction with a radially resolved diffusion model to retrieve translational diffusion coefficients of PEG-4. Comparison of the experimentally derived diffusivities with viscosity estimates for the ternary system reveals a breakdown of the Stokes-Einstein relationship, which has often been invoked to infer diffusivity from viscosity. The evaporation of PEG-4 shows pronounced RH and temperature dependencies and is severely depressed for RH ≲ 30 %, corresponding to diffusivities < 10-14 cm2 s-1 at temperatures < 15 °C. The temperature dependence is strong, suggesting a diffusion activation energy of about 300 kJ mol-1. We conclude that atmospheric volatile organic compounds can be subject to severe diffusion limitations in viscous organic aerosol particles. This may enable an important long-range transport mechanism for organic material, including pollutant molecules such as polycyclic aromatic hydrocarbons (PAHs).

Periodic bedforms generated by sublimation on terrestrial and martian ice sheets under the influence of the turbulent atmospheric boundary layer

NASA Astrophysics Data System (ADS)

Bordiec, Maï; Carpy, Sabrina; Perret, Laurent; Bourgeois, Olivier; Massé, Marion

2017-04-01

The redistribution of surface ice induced the wind flow may lead to the development and migration of periodic bedforms, or "ice ripples", at the surface of ice sheets. In certain cold and dry environments, this redistribution need not involve solid particle transport but may be dominated by sublimation and condensation, inducing mass transfers between the ice surface and the overlying steady boundary layer turbulent flow. These mass transfers diffuse the water vapour sublimated from the ice into the atmosphere and become responsible for the amplification and propagation of ripples in a direction perpendicular to their crests. Such ice ripples, 24 cm in wavelength, have been described in the so-called Blue Ice Areas of Antarctica. In order to understand the mechanisms that generate and develop these periodic bedforms on terrestrial glaciers and to evaluate the plausibility that similar bedforms may develop on Mars, we performed a linear stability analysis applied to a turbulent boundary layer flow perturbed by a wavy ice surface. The model is developed as follow. We first solve the flow dynamics using numerical methods analogous to those used in sand wave models assuming that the airflow is similar in both problems. We then add the transport/diffusion equation of water vapour following the same scheme. We use the Reynolds-averaged description of the equation with a Prandtl-like closure. We insert a damping term in the exponential formula of the Van Driest mixing length, depending on the pressure gradient felt by the flow and related to the thickness of the viscous sublayer at the ice-atmosphere interface. This formulation is an efficient way to properly represent the transitional regime under which the ripples grow. Once the mass flux of water vapour is solved, the phase shift between the ripples crests and the maximum of the flux can be deduced for different environments. The temporal evolution of the ice surface can be expressed from these quantities to infer the growth rate, migration direction and velocity of the ripples. The present approach has been first used to model the atmospheric flow developing over wavy terrestrial ice bedforms in the Blue Ice Areas of Antarctica. Both the predicted preferential wavelength and propagation direction of the ice ripple have been found to be in agreement with the observations. The present model has subsequently been applied to the same flow configuration but on Mars. Ice ripples are indeed likely to exist there, given that temperature and pressure conditions in the martian atmosphere favors sublimation/condensation as the dominant mass-transport process. The model has proved able to predict not only the development of ice-ripple on Mars (i.e it showed that some most amplified wavelength also exist under Martian atmospheric conditions) but also both their wavelength and propagation direction. The preferential wavelength of ices-ripples on the Martian polar caps appears to be much larger than on the Earth. Finally, a good match between the most likely ice-ripple wavelength predicted by the model and those deduced from recent available observations of the surface of Martian polar caps is shown.

A stability analysis of the power-law steady state of marine size spectra.

PubMed

Datta, Samik; Delius, Gustav W; Law, Richard; Plank, Michael J

2011-10-01

This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the power-law steady state. It is shown analytically that the steady state of the McKendrick-von Foerster equation without the diffusion term is always unstable. Furthermore, numerical plots show that eigenvalue spectra of the McKendrick-von Foerster equation with diffusion give a good approximation to those of the jump-growth equation. The steady state is more likely to be stable with a low preferred predator:prey mass ratio, a large diet breadth and a high feeding efficiency. The effects of demographic stochasticity are also investigated and it is concluded that these are likely to be small in real systems.

The nature and role of advection in advection-diffusion equations used for modelling bed load transport

NASA Astrophysics Data System (ADS)

Ancey, Christophe; Bohorquez, Patricio; Heyman, Joris

2016-04-01

The advection-diffusion equation arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Stochastic models can also be used to derive this equation, with the significant advantage that they provide information on the statistical properties of particle activity. Stochastic models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. We develop an approach based on birth-death Markov processes, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received little attention. We show that particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

Subdiffusion in Membrane Permeation of Small Molecules.

PubMed

Chipot, Christophe; Comer, Jeffrey

2016-11-02

Within the solubility-diffusion model of passive membrane permeation of small molecules, translocation of the permeant across the biological membrane is traditionally assumed to obey the Smoluchowski diffusion equation, which is germane for classical diffusion on an inhomogeneous free-energy and diffusivity landscape. This equation, however, cannot accommodate subdiffusive regimes, which have long been recognized in lipid bilayer dynamics, notably in the lateral diffusion of individual lipids. Through extensive biased and unbiased molecular dynamics simulations, we show that one-dimensional translocation of methanol across a pure lipid membrane remains subdiffusive on timescales approaching typical permeation times. Analysis of permeant motion within the lipid bilayer reveals that, in the absence of a net force, the mean squared displacement depends on time as t 0.7 , in stark contrast with the conventional model, which assumes a strictly linear dependence. We further show that an alternate model using a fractional-derivative generalization of the Smoluchowski equation provides a rigorous framework for describing the motion of the permeant molecule on the pico- to nanosecond timescale. The observed subdiffusive behavior appears to emerge from a crossover between small-scale rattling of the permeant around its present position in the membrane and larger-scale displacements precipitated by the formation of transient voids.

Diffuse sorption modeling.

PubMed

Pivovarov, Sergey

2009-04-01

This work presents a simple solution for the diffuse double layer model, applicable to calculation of surface speciation as well as to simulation of ionic adsorption within the diffuse layer of solution in arbitrary salt media. Based on Poisson-Boltzmann equation, the Gaines-Thomas selectivity coefficient for uni-bivalent exchange on clay, K(GT)(Me(2+)/M(+))=(Q(Me)(0.5)/Q(M)){M(+)}/{Me(2+)}(0.5), (Q is the equivalent fraction of cation in the exchange capacity, and {M(+)} and {Me(2+)} are the ionic activities in solution) may be calculated as [surface charge, mueq/m(2)]/0.61. The obtained solution of the Poisson-Boltzmann equation was applied to calculation of ionic exchange on clays and to simulation of the surface charge of ferrihydrite in 0.01-6 M NaCl solutions. In addition, a new model of acid-base properties was developed. This model is based on assumption that the net proton charge is not located on the mathematical surface plane but diffusely distributed within the subsurface layer of the lattice. It is shown that the obtained solution of the Poisson-Boltzmann equation makes such calculations possible, and that this approach is more efficient than the original diffuse double layer model.

Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

NASA Astrophysics Data System (ADS)

Elwakil, S. A.; El-Labany, S. K.; Zahran, M. A.; Sabry, R.

2004-04-01

The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D( u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K( u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m>1 is the power of the nonlinear convection term).

Atmospheric optical calibration system

DOEpatents

Hulstrom, R.L.; Cannon, T.W.

1988-10-25

An atmospheric optical calibration system is provided to compare actual atmospheric optical conditions to standard atmospheric optical conditions on the basis of aerosol optical depth, relative air mass, and diffuse horizontal skylight to global horizontal photon flux ratio. An indicator can show the extent to which the actual conditions vary from standard conditions. Aerosol scattering and absorption properties, diffuse horizontal skylight to global horizontal photon flux ratio, and precipitable water vapor determined on a real-time basis for optical and pressure measurements are also used to generate a computer spectral model and for correcting actual performance response of a photovoltaic device to standard atmospheric optical condition response on a real-time basis as the device is being tested in actual outdoor conditions. 7 figs.

Atmospheric optical calibration system

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

Hulstrom, R.L.; Cannon, T.W.

1988-10-25

An atmospheric optical calibration system is provided to compare actual atmospheric optical conditions to standard atmospheric optical conditions on the basis of aerosol optical depth, relative air mass, and diffuse horizontal skylight to global horizontal photon flux ratio. An indicator can show the extent to which the actual conditions vary from standard conditions. Aerosol scattering and absorption properties, diffuse horizontal skylight to global horizontal photon flux ratio, and precipitable water vapor determined on a real-time basis for optical and pressure measurements are also used to generate a computer spectral model and for correcting actual performance response of a photovoltaic devicemore » to standard atmospheric optical condition response on a real-time basis as the device is being tested in actual outdoor conditions. 7 figs.« less

Mathematical modeling of microbially induced crown corrosion in wastewater collection systems and laboratory investigation and modeling of sulfuric acid corrosion of concrete

NASA Astrophysics Data System (ADS)

Jahani, Fereidoun

In the model for microbially induced crown corrosion, the diffusion of sulfide inside the concrete pores, its biological conversion to sulfuric acid, and the corrosion of calcium carbonate aggregates are represented. The corrosion front is modeled as a moving boundary. The location of the interface between the corrosion layer and the concrete is determined as part of the solution to the model equations. This model consisted of a system of one dimensional reaction-diffusion equations coupled to an equation describing the movement of the corrosion front. The equations were solved numerically using finite element Galerkin approximation. The concentration profiles of sulfide in the air and the liquid phases, the pH as a function of concrete depth, and the position of the corrosion front. A new equation for the corrosion rate was also derived. A more specific model for the degradation of a concrete specimen exposed to a sulfuric acid solution was also studied. In this model, diffusion of hydrogen ions and their reaction with alkaline components of concrete were expressed using Fick's Law of diffusion. The model equations described the moving boundary, the dissolution rate of alkaline components in the concrete, volume increase of sulfuric acid solution over the concrete specimen, and the boundary conditions on the surface of the concrete. An apparatus was designed and experiments were performed to measure pH changes on the surface of concrete. The data were used to calculate the dissolution rate of the concrete and, with the model, to determine the diffusion rate of sulfuric acid in the corrosion layer and corrosion layer thickness. Electrochemical Impedance Spectroscopy (EIS) was used to study the corrosion rate of iron pins embedded in the concrete sample. The open circuit potential (OCP) determined the onset of corrosion on the surface of the pins. Visual observation of the corrosion layer thickness was in good agreement with the simulation results.

Dynamics of Solar Energetic Particles in the Presence of a Shock Wave

NASA Astrophysics Data System (ADS)

Timofeev, V. E.; Petukhov, Ivan; Petukhov, Stanislav; Starodubtsev, Sergei

2003-07-01

From the analysis of problem solutions on the solar energetic particle propagation in the presence of a plane shock wave described by the diffusion convective transport equation, the condition and manifestations for the influence of a shock wave on the SEP propagation in the solar wind have been determined. Solar energetic particles (SEP) in gradual events are generated by shock waves (see, for example, [1] and references there). The SEP generation region is limited, on the whole, by the solar corona. Proton fluxes of 470 MeV to 21 GeV energies, a maximum of which occur at a time when the shock in the atmosphere of the Sun reaches heights equal to 5 10 solar radii [2] indicate to it. It is also confirmed by the significant advancing of the occurrence time of maximum in the SEP intensity with kinetic energies more than 10 MeV relative to the shock front arrival moment to Earth's orbit. model calculations for the particles acceleration by the diffusive mechanism in conditions, typical for the solar corona, show that the time taken to pass the solar atmosphere by the shock is quite sufficient to form the particle spectrum corresponding to the SEP characteristics observed [3,4]. Lee and Ryan [5] investigated the problem of SEP gradual event generation, propagation and confirmed the close association between the diffusive acceleration mechanism and SEP events. The absence of depending of particle diffusion coefficients on the energy is a lack of this model. As an extension of preceding investigations, in this work the temporal dynamics of the particle spectrum in the presence of a plane shock for diffusion coefficients depending on the particle energy and also their change in time is studied. The SEP event from a moment of arising of a shock to a moment of it's arrival on the Earth's orbit can be divided on two stages: the first stage (duration is ˜ 1 hour) is a generation of SEP in the solar corona, the second stage (duration is ˜ 1 day) is a propagation in interplanetary space in the presence of a shock. Here we consider the second stage only which as believed to be began with the injection of the particle spectrum formed during the first stage.

Using Methane Absorption to Probe Jupiter's Atmosphere

NASA Technical Reports Server (NTRS)

1997-01-01

Mosaics of a belt-zone boundary near Jupiter's equator in near-infrared light moderately absorbed by atmospheric methane (top panel), and strongly absorbed by atmospheric methane (bottom panel). The four images that make up each of these mosaics were taken within a few minutes of each other. Methane in Jupiter's atmosphere absorbs light at specific wavelengths called absorption bands. By detecting light close and far from these absorption bands, Galileo can probe to different depths in Jupiter's atmosphere. Sunlight near 732 nanometers (top panel) is moderately absorbed by methane. Some of the light reflected from clouds deep in Jupiter's troposphere is absorbed, enhancing the higher features. Sunlight at 886 nanometers (bottom panel) is strongly absorbed by methane. Most of the light reflected from the deeper clouds is absorbed, making these clouds invisible. Features in the diffuse cloud layer higher in Jupiter's atmosphere are greatly enhanced.

North is at the top. The mosaic covers latitudes -13 to +3 degrees and is centered at longitude 282 degrees West. The smallest resolved features are tens of kilometers in size. These images were taken on November 5th, 1996, at a range of 1.2 million kilometers by the Solid State Imaging system aboard NASA's Galileo spacecraft.

The Jet Propulsion Laboratory, Pasadena, CA manages the mission for NASA's Office of Space Science, Washington, DC.

This image and other images and data received from Galileo are posted on the World Wide Web, on the Galileo mission home page at URL http://galileo.jpl.nasa.gov. Background information and educational context for the images can be found at URL http://www.jpl.nasa.gov/galileo/sepo

Similarity considerations and conservation laws for magneto-static atmospheres

NASA Technical Reports Server (NTRS)

Webb, G. M.

1986-01-01

The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, a model magnetostatic atmosphere is constructed in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an 'e-folding' distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J x B force (B, magnetic field induction) and the gas pressure gradient.

The oceanic biological pump modulates the atmospheric transport of persistent organic pollutants to the Arctic.

PubMed

Galbán-Malagón, Cristóbal; Berrojalbiz, Naiara; Ojeda, María-José; Dachs, Jordi

2012-05-29

Semivolatile persistent organic pollutants have the potential to reach remote environments, such as the Arctic Ocean, through atmospheric transport and deposition. Here we show that this transport of polychlorinated biphenyls to the Arctic Ocean is strongly retarded by the oceanic biological pump. A simultaneous sampling of atmospheric, seawater and plankton samples was performed in July 2007 in the Greenland Current and Atlantic sector of the Arctic Ocean. The atmospheric concentrations declined during atmospheric transport over the Greenland Current with estimated half-lives of 1-4 days. These short half-lives can be explained by the high air-to-water net diffusive flux, which is similar in magnitude to the estimated settling fluxes in the water column. Therefore, the decrease of atmospheric concentrations is due to sequestration of atmospheric polychlorinated biphenyls by enhanced air-water diffusive fluxes driven by phytoplankton uptake and organic carbon settling fluxes (biological pump).

Particle Transport through Scattering Regions with Clear Layers and Inclusions

NASA Astrophysics Data System (ADS)

Bal, Guillaume

2002-08-01

This paper introduces generalized diffusion models for the transport of particles in scattering media with nonscattering inclusions. Classical diffusion is known as a good approximation of transport only in scattering media. Based on asymptotic expansions and the coupling of transport and diffusion models, generalized diffusion equations with nonlocal interface conditions are proposed which offer a computationally cheap, yet accurate, alternative to solving the full phase-space transport equations. The paper shows which computational model should be used depending on the size and shape of the nonscattering inclusions in the simplified setting of two space dimensions. An important application is the treatment of clear layers in near-infrared (NIR) spectroscopy, an imaging technique based on the propagation of NIR photons in human tissues.

An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2004-01-01

The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

DIFFUSION IN THE VICINITY OF STANDARD-DESIGN NUCLEAR POWER PLANTS-I. WIND-TUNNEL EVALUATION OF DIFFUSIVE CHARACTERISTICS OF A SIMULATED SUBURBAN NEUTRAL ATMOSPHERIC BOUNDARY LAYER

EPA Science Inventory

A large meteorological wind tunnel was used to simulate a suburban atmospheric boundary layer. The model-prototype scale was 1:300 and the roughness length was approximately 1.0 m full scale. The model boundary layer simulated full scale dispersion from ground-level and elevated ...

Persistent wind-induced enhancement of diffusive CO2 transport in a mountain forest snowpack

Treesearch

D. R. Bowling; W. J. Massman

2011-01-01

Diffusion dominates the transport of trace gases between soil and the atmosphere. Pressure gradients induced by atmospheric flow and wind interacting with topographical features cause a small but persistent bulk flow of air within soil or snow. This forcing, called pressure pumping or wind pumping, leads to a poorly quantified enhancement of gas transport beyond the...

The first boundary-value problem for a fractional diffusion-wave equation in a non-cylindrical domain

NASA Astrophysics Data System (ADS)

Pskhu, A. V.

2017-12-01

We solve the first boundary-value problem in a non-cylindrical domain for a diffusion-wave equation with the Dzhrbashyan- Nersesyan operator of fractional differentiation with respect to the time variable. We prove an existence and uniqueness theorem for this problem, and construct a representation of the solution. We show that a sufficient condition for unique solubility is the condition of Hölder smoothness for the lateral boundary of the domain. The corresponding results for equations with Riemann- Liouville and Caputo derivatives are particular cases of results obtained here.

Solution of the modified Helmholtz equation in a triangular domain and an application to diffusion-limited coalescence.

PubMed

ben-Avraham, D; Fokas, A S

2001-07-01

A new transform method for solving boundary value problems for linear and integrable nonlinear partial differential equations recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation q(xx)(x,y)+q(yy)(x,y)-4 beta(2)q(x,y)=0 in the triangular domain 0< or =x< or =L-y< or =L, with mixed boundary conditions. This solution is applied to the problem of diffusion-limited coalescence, A+A<==>A, in the segment (-L/2,L/2), with traps at the edges.

Singular solution of the Feller diffusion equation via a spectral decomposition.

PubMed

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

An improved model of fission gas atom transport in irradiated uranium dioxide

NASA Astrophysics Data System (ADS)

Shea, J. H.

2018-04-01

The hitherto standard approach to predicting fission gas release has been a pure diffusion gas atom transport model based upon Fick's law. An additional mechanism has subsequently been identified from experimental data at high burnup and has been summarised in an empirical model that is considered to embody a so-called fuel matrix 'saturation' phenomenon whereby the fuel matrix has become saturated with fission gas so that the continued addition of extra fission gas atoms results in their expulsion from the fuel matrix into the fuel rod plenum. The present paper proposes a different approach by constructing an enhanced fission gas transport law consisting of two components: 1) Fick's law and 2) a so-called drift term. The new transport law can be shown to be effectively identical in its predictions to the 'saturation' approach and is more readily physically justifiable. The method introduces a generalisation of the standard diffusion equation which is dubbed the Drift Diffusion Equation. According to the magnitude of a dimensionless Péclet number, P, the new equation can vary from pure diffusion to pure drift, which latter represents a collective motion of the fission gas atoms through the fuel matrix at a translational velocity. Comparison is made between the saturation and enhanced transport approaches. Because of its dependence on P, the Drift Diffusion Equation is shown to be more effective at managing the transition from one type of limiting transport phenomenon to the other. Thus it can adapt appropriately according to the reactor operation.

Singular solution of the Feller diffusion equation via a spectral decomposition

NASA Astrophysics Data System (ADS)

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

THE EFFECT OF DIFFUSION ON THE PARTICLE SPECTRA IN PULSAR WIND NEBULAE

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

Vorster, M. J.; Moraal, H., E-mail: 12792322@nwu.ac.za

2013-03-01

A possible way to calculate particle spectra as a function of position in pulsar wind nebulae is to solve a Fokker-Planck transport equation. This paper presents numerical solutions to the transport equation with the processes of convection, diffusion, adiabatic losses, and synchrotron radiation included. In the first part of the paper, the steady-state version of the transport equation is solved as a function of position and energy. This is done to distinguish the various effects of the aforementioned processes on the solutions to the transport equation. The second part of the paper deals with a time-dependent solution to the transportmore » equation, specifically taking into account the effect of a moving outer boundary. The paper highlights the fact that diffusion can play a significant role in reducing the amount of synchrotron losses, leading to a modification in the expected particle spectra. These modified spectra can explain the change in the photon index of the synchrotron emission as a function of position. The solutions presented in this paper are not limited to pulsar wind nebulae, but can be applied to any similar central source system, e.g., globular clusters.« less

Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Technical Report Series on Global Modeling and Data Assimilation. Volume 22; A Coupled Ocean-Atmosphere Radiative Model for Global Ocean Biogeochemical Models

NASA Technical Reports Server (NTRS)

Gregg, Watson W.; Suarez, Max J. (Editor)

2002-01-01

An ocean-atmosphere radiative model (OARM) evaluates irradiance availability and quality in the water column to support phytoplankton growth and drive ocean thermodynamics. An atmospheric component incorporates spectral and directional effects of clear and cloudy skies as a function of atmospheric optical constituents, and spectral reflectance across the air-sea interface. An oceanic component evaluates the propagation of spectral and directional irradiance through the water column as a function of water, five phytoplankton groups, and chromophoric dissolved organic matter. It tracks the direct and diffuse streams from the atmospheric component, and a third stream, upwelling diffuse irradiance. The atmospheric component of OARM was compared to data sources at the ocean surface with a coefficient of determination (r2) of 0.97 and a root mean square of 12.1%.

Modeling of adsorption dynamics at air-liquid interfaces using statistical rate theory (SRT).

PubMed

Biswas, M E; Chatzis, I; Ioannidis, M A; Chen, P

2005-06-01

A large number of natural and technological processes involve mass transfer at interfaces. Interfacial properties, e.g., adsorption, play a key role in such applications as wetting, foaming, coating, and stabilizing of liquid films. The mechanistic understanding of surface adsorption often assumes molecular diffusion in the bulk liquid and subsequent adsorption at the interface. Diffusion is well described by Fick's law, while adsorption kinetics is less understood and is commonly described using Langmuir-type empirical equations. In this study, a general theoretical model for adsorption kinetics/dynamics at the air-liquid interface is developed; in particular, a new kinetic equation based on the statistical rate theory (SRT) is derived. Similar to many reported kinetic equations, the new kinetic equation also involves a number of parameters, but all these parameters are theoretically obtainable. In the present model, the adsorption dynamics is governed by three dimensionless numbers: psi (ratio of adsorption thickness to diffusion length), lambda (ratio of square of the adsorption thickness to the ratio of adsorption to desorption rate constant), and Nk (ratio of the adsorption rate constant to the product of diffusion coefficient and bulk concentration). Numerical simulations for surface adsorption using the proposed model are carried out and verified. The difference in surface adsorption between the general and the diffusion controlled model is estimated and presented graphically as contours of deviation. Three different regions of adsorption dynamics are identified: diffusion controlled (deviation less than 10%), mixed diffusion and transfer controlled (deviation in the range of 10-90%), and transfer controlled (deviation more than 90%). These three different modes predominantly depend on the value of Nk. The corresponding ranges of Nk for the studied values of psi (10(-2)

Study of atmospheric diffusion using LANDSAT

NASA Technical Reports Server (NTRS)

Torsani, J. A.; Viswanadham, Y.

1982-01-01

The parameters of diffusion patterns of atmospheric pollutants under different conditions were investigated for use in the Gaussian model for calculation of pollution concentration. Value for the divergence pattern of concentration distribution along the Y axis were determined using LANDSAT images. Multispectral scanner images of a point source plume having known characteristics, wind and temperature data, and cloud cover and solar elevation data provided by LANDSAT, were analyzed using the 1-100 system for image analysis. These measured values are compared with pollution transport as predicted by the Pasquill-Gifford, Juelich, and Hoegstroem atmospheric models.

Contraction of high eccentricity satellite orbits using uniformly regular KS canonical elements with oblate diurnally varying atmosphere.

NASA Astrophysics Data System (ADS)

Raj, Xavier James

2016-07-01

Accurate orbit prediction of an artificial satellite under the influence of air drag is one of the most difficult and untraceable problem in orbital dynamics. The orbital decay of these satellites is mainly controlled by the atmospheric drag effects. The effects of the atmosphere are difficult to determine, since the atmospheric density undergoes large fluctuations. The classical Newtonian equations of motion, which is non linear is not suitable for long-term integration. Many transformations have emerged in the literature to stabilize the equations of motion either to reduce the accumulation of local numerical errors or allowing the use of large integration step sizes, or both in the transformed space. One such transformation is known as KS transformation by Kustaanheimo and Stiefel, who regularized the nonlinear Kepler equations of motion and reduced it into linear differential equations of a harmonic oscillator of constant frequency. The method of KS total energy element equations has been found to be a very powerful method for obtaining numerical as well as analytical solution with respect to any type of perturbing forces, as the equations are less sensitive to round off and truncation errors. The uniformly regular KS canonical equations are a particular canonical form of the KS differential equations, where all the ten KS Canonical elements αi and βi are constant for unperturbed motion. These equations permit the uniform formulation of the basic laws of elliptic, parabolic and hyperbolic motion. Using these equations, developed analytical solution for short term orbit predictions with respect to Earth's zonal harmonic terms J2, J3, J4. Further, these equations were utilized to include the canonical forces and analytical theories with air drag were developed for low eccentricity orbits (e < 0.2) with different atmospheric models. Using uniformly regular KS canonical elements developed analytical theory for high eccentricity (e > 0.2) orbits by assuming the atmosphere to be oblate only. In this paper a new non-singular analytical theory is developed for the motion of high eccentricity satellite orbits with oblate diurnally varying atmosphere in terms of the uniformly regular KS canonical elements. The analytical solutions are generated up to fourth-order terms using a new independent variable and c (a small parameter dependent on the flattening of the atmosphere). Due to symmetry, only two of the nine equations need to be solved analytically to compute the state vector and change in energy at the end of each revolution. The theory is developed on the assumption that density is constant on the surfaces of spheroids of fixed ellipticity ɛ (equal to the Earth's ellipticity, 0.00335) whose axes coincide with the Earth's axis. Numerical experimentation with the analytical solution for a wide range of perigee height, eccentricity, and orbital inclination has been carried out up to 100 revolutions. Comparisons are made with numerically integrated values and found that they match quite well. Effectiveness of the present analytical solutions will be demonstrated by comparing the results with other analytical solutions in the literature.

Generalized Fourier analyses of the advection-diffusion equation - Part I: one-dimensional domains

NASA Astrophysics Data System (ADS)

Christon, Mark A.; Martinez, Mario J.; Voth, Thomas E.

2004-07-01

This paper presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speed, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew-symmetric components and characterizing the spectral behaviour of each operator. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. It is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, the streamline upwind control-volume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semi-discrete artifacts observed in the phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behaviour in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behaviour. In Part II of this paper, we consider two-dimensional semi-discretizations of the advection-diffusion equation and also assess the affects of grid-induced anisotropy observed in the non-dimensional phase speed, and the discrete and artificial diffusivities. Although this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common analysis framework. Published in 2004 by John Wiley & Sons, Ltd.

The effect of recombination and attachment on meteor radar diffusion coefficient profiles

NASA Astrophysics Data System (ADS)

Lee, C. S.; Younger, J. P.; Reid, I. M.; Kim, Y. H.; Kim, J.-H.

2013-04-01

Estimates of the ambipolar diffusion coefficient producedusing meteor radar echo decay times display an increasing trend below 80-85 km, which is inconsistent with a diffusion-only theory of the evolution of meteor trails. Data from the 33 MHz meteor radar at King Sejong Station, Antarctica, have been compared with observations from the Aura Earth Observing System Microwave Limb Sounder satellite instrument. It has been found that the height at which the diffusion coefficient gradient reverses follows the height of a constant neutral atmospheric density surface. Numerical simulations of meteor trail diffusion including dissociative recombination with atmospheric ions and three-body attachment of free electrons to neutral molecules indicate that three-body attachment is responsible for the distortion of meteor radar diffusion coefficient profiles at heights below 90 km, including the gradient reversal below 80-85 km. Further investigation has revealed that meteor trails with low initial electron line density produce decay times more consistent with a diffusion-only model of meteor trail evolution.

A study of atmospheric diffusion from the LANDSAT imagery. [pollution transport over the ocean

NASA Technical Reports Server (NTRS)

Dejesusparada, N. (Principal Investigator); Viswanadham, Y.; Torsani, J. A.

1981-01-01

LANDSAT multispectral scanner data of the smoke plumes which originated in eastern Cabo Frio, Brazil and crossed over into the Atlantic Ocean, are analyzed to illustrate how high resolution LANDSAT imagery can aid meteorologists in evaluating specific air pollution events. The eleven LANDSAT images selected are for different months and years. The results show that diffusion is governed primarily by water and air temperature differences. With colder water, low level air is very stable and the vertical diffusion is minimal; but water warmer than the air induces vigorous diffusion. The applicability of three empirical methods for determining the horizontal eddy diffusivity coefficient in the Gaussian plume formula was evaluated with the estimated standard deviation of the crosswind distribution of material in the plume from the LANDSAT imagery. The vertical diffusion coefficient in stable conditions is estimated using Weinstock's formulation. These results form a data base for use in the development and validation of meso scale atmospheric diffusion models.

Oxygen-induced high diffusion rate of magnesium dopants in GaN/AlGaN based UV LED heterostructures.

PubMed

Michałowski, Paweł Piotr; Złotnik, Sebastian; Sitek, Jakub; Rosiński, Krzysztof; Rudziński, Mariusz

2018-05-23

Further development of GaN/AlGaN based optoelectronic devices requires optimization of the p-type material growth process. In particular, uncontrolled diffusion of Mg dopants may decrease the performance of a device. Thus it is meaningful to study the behavior of Mg and the origins of its diffusion in detail. In this work we have employed secondary ion mass spectrometry to study the diffusion of magnesium in GaN/AlGaN structures. We show that magnesium has a strong tendency to form Mg-H complexes which immobilize Mg atoms and restrain their diffusion. However, these complexes are not present in samples post-growth annealed in an oxygen atmosphere or Al-rich AlGaN structures which naturally have a high oxygen concentration. In these samples, more Mg atoms are free to diffuse and thus the average diffusion length is considerably larger than for a sample annealed in an inert atmosphere.

Venus' superrotation, mixing length theory and eddy diffusion - A parametric study

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Harris, I.; Schatten, K. H.; Stevens-Rayburn, D. R.; Chan, K. L.

1988-01-01

The concept of the Hadley mechanism is adopted to describe the axisymmetric circulation of the Venus atmosphere. It is shown that, for the atmosphere of a slowly rotating planet such as Venus, a form of the nonliner 'closure' (self-consistent solution) of the fluid dynamics system which constrains the magnitude of the eddy diffusion coefficients can be postulated. A nonlinear one-layer spectral model of the zonally symmetric circulation was then used to establish the relationship between the heat source, the meridional circulation, and the eddy diffusion coefficients, yielding large zonal velocities. Computer experiments indicated that proportional changes in the heat source and eddy diffusion coefficients do not significantly change the zonal velocities. It was also found that, for large eddy diffusion coefficients, the meridional velocity is virtually constant; below a threshold in the diffusion rate, the meridional velocity decreases; and, for large eddy diffusion and small heating rates, the zonal velocities decrease with decreasing planetary rotation rates.

Solution of the comoving-frame equation of transfer in spherically symmetric flows. V - Multilevel atoms. [in early star atmospheres

NASA Technical Reports Server (NTRS)

Mihalas, D.; Kunasz, P. B.

1978-01-01

The coupled radiative transfer and statistical equilibrium equations for multilevel ionic structures in the atmospheres of early-type stars are solved. Both lines and continua are treated consistently; the treatment is applicable throughout a transonic wind, and allows for the presence of background continuum sources and sinks in the transfer. An equivalent-two-level-atoms approach provides the solution for the equations. Calculations for simplified He (+)-like model atoms in parameterized isothermal wind models indicate that subordinate line profiles are sensitive to the assumed mass-loss rate, and to the assumed structure of the velocity law in the atmospheres.

Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES

NASA Astrophysics Data System (ADS)

Marras, Simone; Nazarov, Murtazo; Giraldo, Francis X.

2015-11-01

The high order spectral element approximation of the Euler equations is stabilized via a dynamic sub-grid scale model (Dyn-SGS). This model was originally designed for linear finite elements to solve compressible flows at large Mach numbers. We extend its application to high-order spectral elements to solve the Euler equations of low Mach number stratified flows. The major justification of this work is twofold: stabilization and large eddy simulation are achieved via one scheme only. Because the diffusion coefficients of the regularization stresses obtained via Dyn-SGS are residual-based, the effect of the artificial diffusion is minimal in the regions where the solution is smooth. The direct consequence is that the nominal convergence rate of the high-order solution of smooth problems is not degraded. To our knowledge, this is the first application in atmospheric modeling of a spectral element model stabilized by an eddy viscosity scheme that, by construction, may fulfill stabilization requirements, can model turbulence via LES, and is completely free of a user-tunable parameter. From its derivation, it will be immediately clear that Dyn-SGS is independent of the numerical method; it could be implemented in a discontinuous Galerkin, finite volume, or other environments alike. Preliminary discontinuous Galerkin results are reported as well. The straightforward extension to non-linear scalar problems is also described. A suite of 1D, 2D, and 3D test cases is used to assess the method, with some comparison against the results obtained with the most known Lilly-Smagorinsky SGS model.

Radial inhomogeneities in particle composition of single, levitated aerosol particles observed by Mie resonance spectroscopy (Invited)

NASA Astrophysics Data System (ADS)

Krieger, U. K.; Steimer, S.; Lienhard, D.; Bastelberger, S.

2013-12-01

Recent observations have indicated that organic aerosol particles in the atmosphere may exist in an amorphous semi-solid or even solid (i.e. glassy) state, e.g. [1]. The influence of highly viscous and glassy states on the timescale of aerosol particle equilibration with respect to water vapor have been investigated for some model systems of atmospheric aerosol, e.g. [2,3]. In particular, it has been shown that the kinetics of the water absorption/desorption process is controlled entirely by liquid-phase diffusion of water molecules for a highly viscous aerosol particle. A liquid phase diffusion model based on numerically solving the non-linear diffusion equation predicts strong internal gradients in water concentration when condensed phase diffusion impedes the water uptake from the gas phase [2]. Here we observe and quantify the internal concentration gradients in single, levitated, micron size aerosol particles of aqueous MBTCA (3-methyl-1,2,3-Butanetricarboxylic acid) and shikimic acid using elastic Mie resonance spectroscopy. A single, aqueous particle is levitated in an electro-dynamic balance (for details see [2]), dried for several days at room temperature, cooled to the target temperature and exposed to a rapid change in relative humidity. In addition to measuring the elastically backscattered light of a 'white light ' LED source and recording the full spectrum with a spectrograph as in [2], we use a tunable diode laser (TDL) to scan high resolution TE- and TM spectra. This combination allows observing various Mie resonance mode orders simultaneously. Since we perform the experiment at low temperatures and low humidities the changes in the Mie-spectra due to water uptake are sufficiently slow to resolve the kinetics. Experimental Mie resonance spectra are inverted to concentration profiles of water within the particle by applying the numerical diffusion model [2] in conjunction with Mie calculations of multilayered spheres [4]. Potential implications for gas to particle partitioning and heterogeneous chemistry are discussed. [1] A. Virtanen et al. (2010): An amorphous solid state of biogenic secondary organic aerosol particles, Nature 467, 824-827. [2] B. Zobrist et al. (2011): Ultra-slow water diffusion in aqueous sucrose glasses, Phys. Chem. Chem. Phys. 13, 3514-3526. [3] D. L. Bones, J. P. Reid, D. M. Lienhard, and U. K. Krieger (2012): Comparing the mechanism of water condensation and evaporation in glassy aerosol, PNAS 109, 11613-11618. [4] O. Peña and U. Pal (2009): Scattering of electromagnetic radiation by a multilayered sphere, Comput. Phys. Commun. 180, 2348-2354.

Analysis and experimental study on formation conditions of large-scale barrier-free diffuse atmospheric pressure air plasmas in repetitive pulse mode

NASA Astrophysics Data System (ADS)

Li, Lee; Liu, Lun; Liu, Yun-Long; Bin, Yu; Ge, Ya-Feng; Lin, Fo-Chang

2014-01-01

Atmospheric air diffuse plasmas have enormous application potential in various fields of science and technology. Without dielectric barrier, generating large-scale air diffuse plasmas is always a challenging issue. This paper discusses and analyses the formation mechanism of cold homogenous plasma. It is proposed that generating stable diffuse atmospheric plasmas in open air should meet the three conditions: high transient power with low average power, excitation in low average E-field with locally high E-field region, and multiple overlapping electron avalanches. Accordingly, an experimental configuration of generating large-scale barrier-free diffuse air plasmas is designed. Based on runaway electron theory, a low duty-ratio, high voltage repetitive nanosecond pulse generator is chosen as a discharge excitation source. Using the wire-electrodes with small curvature radius, the gaps with highly non-uniform E-field are structured. Experimental results show that the volume-scaleable, barrier-free, homogeneous air non-thermal plasmas have been obtained between the gap spacing with the copper-wire electrodes. The area of air cold plasmas has been up to hundreds of square centimeters. The proposed formation conditions of large-scale barrier-free diffuse air plasmas are proved to be reasonable and feasible.

A diffuse-interface method for two-phase flows with soluble surfactants

PubMed Central

Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel

2010-01-01

A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier–Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed. PMID:21218125

A strictly Markovian expansion for plasma turbulence theory

NASA Technical Reports Server (NTRS)

Jones, F. C.

1976-01-01

The collision operator that appears in the equation of motion for a particle distribution function that was averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. An expansion is derived for the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest nontrivial order. The validity of this expansion is seen to be the same as that of the standard quasilinear expansion.

On linearization and preconditioning for radiation diffusion coupled to material thermal conduction equations

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

Feng, Tao, E-mail: fengtao2@mail.ustc.edu.cn; Graduate School of China Academy Engineering Physics, Beijing 100083; An, Hengbin, E-mail: an_hengbin@iapcm.ac.cn

2013-03-01

Jacobian-free Newton–Krylov (JFNK) method is an effective algorithm for solving large scale nonlinear equations. One of the most important advantages of JFNK method is that there is no necessity to form and store the Jacobian matrix of the nonlinear system when JFNK method is employed. However, an approximation of the Jacobian is needed for the purpose of preconditioning. In this paper, JFNK method is employed to solve a class of non-equilibrium radiation diffusion coupled to material thermal conduction equations, and two preconditioners are designed by linearizing the equations in two methods. Numerical results show that the two preconditioning methods canmore » improve the convergence behavior and efficiency of JFNK method.« less

A statistical mechanics approach to computing rare transitions in multi-stable turbulent geophysical flows

NASA Astrophysics Data System (ADS)

Laurie, J.; Bouchet, F.

2012-04-01

Many turbulent flows undergo sporadic random transitions, after long periods of apparent statistical stationarity. For instance, paths of the Kuroshio [1], the Earth's magnetic field reversal, atmospheric flows [2], MHD experiments [3], 2D turbulence experiments [4,5], 3D flows [6] show this kind of behavior. The understanding of this phenomena is extremely difficult due to the complexity, the large number of degrees of freedom, and the non-equilibrium nature of these turbulent flows. It is however a key issue for many geophysical problems. A straightforward study of these transitions, through a direct numerical simulation of the governing equations, is nearly always impracticable. This is mainly a complexity problem, due to the large number of degrees of freedom involved for genuine turbulent flows, and the extremely long time between two transitions. In this talk, we consider two-dimensional and geostrophic turbulent models, with stochastic forces. We consider regimes where two or more attractors coexist. As an alternative to direct numerical simulation, we propose a non-equilibrium statistical mechanics approach to the computation of this phenomenon. Our strategy is based on large deviation theory [7], derived from a path integral representation of the stochastic process. Among the trajectories connecting two non-equilibrium attractors, we determine the most probable one. Moreover, we also determine the transition rates, and in which cases this most probable trajectory is a typical one. Interestingly, we prove that in the class of models we consider, a mechanism exists for diffusion over sets of connected attractors. For the type of stochastic forces that allows this diffusion, the transition between attractors is not a rare event. It is then very difficult to characterize the flow as bistable. However for another class of stochastic forces, this diffusion mechanism is prevented, and genuine bistability or multi-stability is observed. We discuss how these results are probably connected to the long debated existence of multi-stability in the atmosphere and oceans.

Diffusion coefficients of water in biobased hydrogel polymer matrices by nuclear magnetic resonance imaging

USDA-ARS?s Scientific Manuscript database

The diffusion coefficient of water in biobased hydrogels were measured utilizing a simple NMR method. This method tracks the migration of deuterium oxide through imaging data that is fit to a diffusion equation. The results show that a 5 wt% soybean oil based hydrogel gives aqueous diffusion of 1.37...

A combined kick-out and dissociative diffusion mechanism of grown-in Be in InGaAs and InGaAsP. A new finite difference-Bairstow method for solution of the diffusion equations

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

Koumetz, Serge D., E-mail: Serge.Koumetz@univ-rouen.fr; Martin, Patrick; Murray, Hugues

Experimental results on the diffusion of grown-in beryllium (Be) in indium gallium arsenide (In{sub 0.53}Ga{sub 0.47}As) and indium gallium arsenide phosphide (In{sub 0.73}Ga{sub 0.27}As{sub 0.58}P{sub 0.42}) gas source molecular beam epitaxy alloys lattice-matched to indium phosphide (InP) can be successfully explained in terms of a combined kick-out and dissociative diffusion mechanism, involving neutral Be interstitials (Be{sub i}{sup 0}), singly positively charged gallium (Ga), indium (In) self-interstitials (I{sub III}{sup +}) and singly positively charged Ga, In vacancies (V{sub III}{sup +}). A new numerical method of solution to the system of diffusion equations, based on the finite difference approximations and Bairstow's method,more » is proposed.« less

Spatial pattern dynamics due to the fitness gradient flux in evolutionary games.

PubMed

deForest, Russ; Belmonte, Andrew

2013-06-01

We introduce a nondiffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent alternative to diffusive coupling. We study numerically the development of patterns in one dimension (1D) for two-strategy games including the coordination game and the prisoner's dilemma, and in two dimensions (2D) for the rock-paper-scissors game. In 1D we observe modified traveling wave solutions in the presence of diffusion, and asymptotic attracting states under a frozen-strategy assumption without diffusion. In 2D we observe spiral formation and breakup in the frozen-strategy rock-paper-scissors game without diffusion. A change of variables appropriate to replicator dynamics is shown to correctly capture the 1D asymptotic steady state via a nonlinear diffusion equation.

Nonlinear diffusion and viral spread through the leaf of a plant

NASA Astrophysics Data System (ADS)

Edwards, Maureen P.; Waterhouse, Peter M.; Munoz-Lopez, María Jesús; Anderssen, Robert S.

2016-10-01

The spread of a virus through the leaf of a plant is both spatially and temporally causal in that the present status depends on the past and the spatial spread is compactly supported and progresses outwards. Such spatial spread is known to occur for certain nonlinear diffusion processes. The first compactly supported solution for nonlinear diffusion equations appears to be that of Pattle published in 1959. In that paper, no explanation is given as to how the solution was derived. Here, we show how the solution can be derived using Lie symmetry analysis. This lays a foundation for exploring the behavior of other choices for nonlinear diffusion and exploring the addition of reaction terms which do not eliminate the compactly supported structure. The implications associated with using the reaction-diffusion equation to model the spatial-temporal spread of a virus through the leaf of a plant are discussed.

The effects of the Asselin time filter on numerical solutions to the linearized shallow-water wave equations

NASA Technical Reports Server (NTRS)

Schlesinger, R. E.; Johnson, D. R.; Uccellini, L. W.

1983-01-01

In the present investigation, a one-dimensional linearized analysis is used to determine the effect of Asselin's (1972) time filter on both the computational stability and phase error of numerical solutions for the shallow water wave equations, in cases with diffusion but without rotation. An attempt has been made to establish the approximate optimal values of the filtering parameter nu for each of the 'lagged', Dufort-Frankel, and Crank-Nicholson diffusion schemes, suppressing the computational wave mode without materially altering the physical wave mode. It is determined that in the presence of diffusion, the optimum filter length depends on whether waves are undergoing significant propagation. When moderate propagation is present, with or without diffusion, the Asselin filter has little effect on the spatial phase lag of the physical mode for the leapfrog advection scheme of the three diffusion schemes considered.

Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

NASA Astrophysics Data System (ADS)

Barletti, Luigi; Negulescu, Claudia

2018-05-01

We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a strip of vanishing width on a macroscopic scale, such strip is viewed as a quantum interface that couples the classical regions at its left and right sides. In the two classical regions, where the potential is assumed to be smooth, electron and hole transport is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of a Hilbert expansion and a boundary layer analysis, and consists of drift-diffusion equations in the classical regions, coupled by quantum diffusive transmission conditions through the interface. The boundary layer analysis leads to the discussion of a four-fold Milne (half-space, half-range) transport problem.

Spatial pattern dynamics due to the fitness gradient flux in evolutionary games

NASA Astrophysics Data System (ADS)

deForest, Russ; Belmonte, Andrew

2013-06-01

We introduce a nondiffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent alternative to diffusive coupling. We study numerically the development of patterns in one dimension (1D) for two-strategy games including the coordination game and the prisoner's dilemma, and in two dimensions (2D) for the rock-paper-scissors game. In 1D we observe modified traveling wave solutions in the presence of diffusion, and asymptotic attracting states under a frozen-strategy assumption without diffusion. In 2D we observe spiral formation and breakup in the frozen-strategy rock-paper-scissors game without diffusion. A change of variables appropriate to replicator dynamics is shown to correctly capture the 1D asymptotic steady state via a nonlinear diffusion equation.

Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas

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

Lee, Jungpyo; Wright, John; Bertelli, Nicola

In this study, a reduced model of quasilinear velocity diffusion by a small Larmor radius approximation is derived to couple the Maxwell’s equations and the Fokker Planck equation self-consistently for the ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change (Wdot ) is used to derive the reduced model diffusion coefficients for the fundamental damping (n = 1) and the second harmonic damping (n = 2) to the lowest order of the finite Larmormore » radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of the dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results.« less

Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion.

PubMed

Bodrova, Anna S; Chechkin, Aleksei V; Cherstvy, Andrey G; Safdari, Hadiseh; Sokolov, Igor M; Metzler, Ralf

2016-07-27

It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.

Using Global Invariant Manifolds to Understand Metastability in the Burgers Equation With Small Viscosity

NASA Astrophysics Data System (ADS)

Beck, Margaret; Wayne, C. Eugene

2009-01-01

The large-time behavior of solutions to the Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusion wave. More precisely, it is shown that in terms of similarity, or scaling, variables in an algebraically weighted L^2 space, the self-similar diffusion waves correspond to a one-dimensional global center manifold of stationary solutions. Through each of these fixed points there exists a one-dimensional, global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus, metastability corresponds to a fast transient in which solutions approach this metastable manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally, convergence to the self-similar diffusion wave.

Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas

DOE PAGES

Lee, Jungpyo; Wright, John; Bertelli, Nicola; ...

2017-04-24

In this study, a reduced model of quasilinear velocity diffusion by a small Larmor radius approximation is derived to couple the Maxwell’s equations and the Fokker Planck equation self-consistently for the ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change (Wdot ) is used to derive the reduced model diffusion coefficients for the fundamental damping (n = 1) and the second harmonic damping (n = 2) to the lowest order of the finite Larmormore » radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of the dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results.« less

Evaluation of the impact of atmospheric ozone and aerosols on the horizontal global/diffuse UV Index at Livorno (Italy)

NASA Astrophysics Data System (ADS)

Scaglione, Daniele; Giulietti, Danilo; Morelli, Marco

2016-08-01

A study was conducted at Livorno (Italy) to evaluate the impact of atmospheric aerosols and ozone on the solar UV radiation and its diffuse component at ground in clear sky conditions. Solar UV radiation has been quantified in terms of UV Index (UVI), following the ISO 17166:1999/CIE S007/E-1998 international standard. UVI has been calculated by exploiting the libRadtran radiative transfer modelling software as a function of both the Aerosols Optical Depth (AOD) and the Total Ozone Column (TOC). In particular AOD and TOC values have been remotely sensed by the Ozone Monitoring Instrument (OMI) on board the NASA's EOS (Earth Observing System) satellites constellation. An experimental confirmation was also obtained by exploiting global UVI ground-based measurements from the 26/9/14 to 12/8/15 and diffuse UVI ground-based measurements from the 17/5/15 to 12/8/15. For every considered value of Solar Zenith Angle (SZA) and atmospheric condition, estimates and measurements confirm that the diffuse component contributes for more than 50% on the global UV radiation. Therefore an exposure of human skin also to diffuse solar UV radiation can be potentially harmful for health and need to be accurately monitored, e.g. by exploiting innovative applications such as a mobile app with a satellite-based UV dosimeter that has been developed. Global and diffuse UVI variations due to the atmosphere are primarily caused by the TOC variations (typically cyclic): the maximum TOC variation detected by OMI in the area under study leads to a corresponding variation in global and diffuse UVI of about 50%. Aerosols in the area concerned, mainly of maritime nature, have instead weaker effects causing a maximum variation of the global and diffuse UVI respectively of 9% and 35% with an SZA of 20° and respectively of 13% and 10% with an SZA of 60°.

Continuous time anomalous diffusion in a composite medium.

PubMed

Stickler, B A; Schachinger, E

2011-08-01

The one-dimensional continuous time anomalous diffusion in composite media consisting of a finite number of layers in immediate contact is investigated. The diffusion process itself is described with the help of two probability density functions (PDFs), one of which is an arbitrary jump-length PDF, and the other is a long-tailed waiting-time PDF characterized by the waiting-time index β∈(0,1). The former is assumed to be a function of the space coordinate x and the time coordinate t while the latter is a function of x and the time interval. For such an environment a very general form of the diffusion equation is derived which describes the continuous time anomalous diffusion in a composite medium. This result is then specialized to two particular forms of the jump-length PDF, namely the continuous time Lévy flight PDF and the continuous time truncated Lévy flight PDF. In both cases the PDFs are characterized by the Lévy index α∈(0,2) which is regarded to be a function of x and t. It is possible to demonstrate that for particular choices of the indices α and β other equations for anomalous diffusion, well known from the literature, follow immediately. This demonstrates the very general applicability of the derivation and of the resulting fractional differential equation discussed here.

An Investigation of Flow over High Roughness. Task I: Study of Airflow in Simulated Temperature and Tropical Forest Canopies, Fort Huachuca.

DTIC Science & Technology

ATMOSPHERIC MOTION, TREES), (*AEROSOLS, DIFFUSION ), TROPICAL REGIONS, SIMULATION, ATMOSPHERIC TEMPERATURE, TURBULENT BOUNDARY LAYER, ROUGHNESS, FORESTRY, ATMOSPHERE MODELS, WIND TUNNELS, COLORADO, MILITARY FACILITIES

Study of the effect of wind speed on evaporation from soil through integrated modeling of the atmospheric boundary layer and shallow subsurface.

PubMed

Davarzani, Hossein; Smits, Kathleen; Tolene, Ryan M; Illangasekare, Tissa

2014-01-01

In an effort to develop methods based on integrating the subsurface to the atmospheric boundary layer to estimate evaporation, we developed a model based on the coupling of Navier-Stokes free flow and Darcy flow in porous medium. The model was tested using experimental data to study the effect of wind speed on evaporation. The model consists of the coupled equations of mass conservation for two-phase flow in porous medium with single-phase flow in the free-flow domain under nonisothermal, nonequilibrium phase change conditions. In this model, the evaporation rate and soil surface temperature and relative humidity at the interface come directly from the integrated model output. To experimentally validate numerical results, we developed a unique test system consisting of a wind tunnel interfaced with a soil tank instrumented with a network of sensors to measure soil-water variables. Results demonstrated that, by using this coupling approach, it is possible to predict the different stages of the drying process with good accuracy. Increasing the wind speed increases the first stage evaporation rate and decreases the transition time between two evaporative stages (soil water flow to vapor diffusion controlled) at low velocity values; then, at high wind speeds the evaporation rate becomes less dependent on the wind speed. On the contrary, the impact of wind speed on second stage evaporation (diffusion-dominant stage) is not significant. We found that the thermal and solute dispersion in free-flow systems has a significant influence on drying processes from porous media and should be taken into account.

Subsurface Xenon Migration by Atmospheric Pumping Using an Implicit Non-Iterative Algorithm for a Locally 1D Dual-Porosity Model

NASA Astrophysics Data System (ADS)

Annewandter, R.; Kalinowksi, M. B.

2009-04-01

An underground nuclear explosion injects radionuclids in the surrounding host rock creating an initial radionuclid distribution. In the case of fractured permeable media, cyclical changes in atmospheric pressure can draw gaseous species upwards to the surface, establishing a ratcheting pump effect. The resulting advective transport is orders of magnitude more significant than transport by molecular diffusion. In the 1990s the US Department of Energy funded the socalled Non-Proliferation Experiment conducted by the Lawrence Livermore National Laboratory to investigate this barometric pumping effect for verifying compliance with respect to the Comprehensive Nuclear Test Ban Treaty. A chemical explosive of approximately 1 kt TNT-equivalent has been detonated in a cavity located 390 m deep in the Rainier Mesa (Nevada Test Site) in which two tracer gases were emplaced. Within this experiment SF6 was first detected in soil gas samples taken near fault zones after 50 days and 3He after 325 days. For this paper a locally one-dimensional dual-porosity model for flow along the fracture and within the permeable matrix was used after Nilson and Lie (1990). Seepage of gases and diffusion of tracers between fracture and matrix are accounted. The advective flow along the fracture and within the matrix block is based on the FRAM filtering remedy and methodology of Chapman. The resulting system of equations is solved by an implicit non-iterative algorithm. Results on time of arrival and subsurface concentration levels for the CTBT-relevant xenons will be presented.

Study of the effect of wind speed on evaporation from soil through integrated modeling of the atmospheric boundary layer and shallow subsurface

PubMed Central

Davarzani, Hossein; Smits, Kathleen; Tolene, Ryan M; Illangasekare, Tissa

2014-01-01

In an effort to develop methods based on integrating the subsurface to the atmospheric boundary layer to estimate evaporation, we developed a model based on the coupling of Navier-Stokes free flow and Darcy flow in porous medium. The model was tested using experimental data to study the effect of wind speed on evaporation. The model consists of the coupled equations of mass conservation for two-phase flow in porous medium with single-phase flow in the free-flow domain under nonisothermal, nonequilibrium phase change conditions. In this model, the evaporation rate and soil surface temperature and relative humidity at the interface come directly from the integrated model output. To experimentally validate numerical results, we developed a unique test system consisting of a wind tunnel interfaced with a soil tank instrumented with a network of sensors to measure soil-water variables. Results demonstrated that, by using this coupling approach, it is possible to predict the different stages of the drying process with good accuracy. Increasing the wind speed increases the first stage evaporation rate and decreases the transition time between two evaporative stages (soil water flow to vapor diffusion controlled) at low velocity values; then, at high wind speeds the evaporation rate becomes less dependent on the wind speed. On the contrary, the impact of wind speed on second stage evaporation (diffusion-dominant stage) is not significant. We found that the thermal and solute dispersion in free-flow systems has a significant influence on drying processes from porous media and should be taken into account. PMID:25309005

Slip and barodiffusion phenomena in slow flows of a gas mixture

NASA Astrophysics Data System (ADS)

Zhdanov, V. M.

2017-03-01

The slip and barodiffusion problems for the slow flows of a gas mixture are investigated on the basis of the linearized moment equations following from the Boltzmann equation. We restrict ourselves to the set of the third-order moment equations and state two general relations (resembling conservation equations) for the moments of the distribution function similar to the conditions used by Loyalka [S. K. Loyalka, Phys. Fluids 14, 2291 (1971), 10.1063/1.1693331] in his approximation method (the modified Maxwell method). The expressions for the macroscopic velocities of the gas mixture species, the partial viscous stress tensors, and the reduced heat fluxes for the stationary slow flow of a gas mixture in the semi-infinite space over a plane wall are obtained as a result of the exact solution of the linearized moment equations in the 10- and 13-moment approximations. The general expression for the slip velocity and the simple and accurate expressions for the viscous, thermal, diffusion slip, and baroslip coefficients, which are given in terms of the basic transport coefficients, are derived by using the modified Maxwell method. The solutions of moment equations are also used for investigation of the flow and diffusion of a gas mixture in a channel formed by two infinite parallel plates. A fundamental result is that the barodiffusion factor in the cross-section-averaged expression for the diffusion flux contains contributions associated with the viscous transfer of momentum in the gas mixture and the effect of the Knudsen layer. Our study revealed that the barodiffusion factor is equal to the diffusion slip coefficient (correct to the opposite sign). This result is consistent with the Onsager's reciprocity relations for kinetic coefficients following from nonequilibrium thermodynamics of the discontinuous systems.