Transverse particle acceleration and diffusion in a planetary magnetic field

NASA Technical Reports Server (NTRS)

Barbosa, D. D.

1994-01-01

A general model of particle acceleration by plasma waves coupled with adiabatic radial diffusion in a planetary magnetic field is developed. The model assumes that a spectrum of lower hybird waves is present to resonantly accelerate ions transverse to the magnetic field. The steady state Green's function for the combined radial diffusion and wave acceleration equation is found in terms of a series expansion. The results provide a rigorous demonstration of how a quasi-Maxwellian distribution function is formed in the absence of particle collisons and elucidate the nature of turbulent heating of magnetospheric plasmas. The solution is applied to the magnetosphere of Neptune for which a number of examples are given illustrating how the spectrum of pickup N(+) ions from Triton evolves.

Computations of the three-dimensional flow and heat transfer within a coolant passage of a radial turbine blade

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Roelke, R. J.; Steinthorsson, E.

1991-01-01

A numerical code is developed for computing three-dimensional, turbulent, compressible flow within coolant passages of turbine blades. The code is based on a formulation of the compressible Navier-Stokes equations in a rotating frame of reference in which the velocity dependent variable is specified with respect to the rotating frame instead of the inertial frame. The algorithm employed to obtain solutions to the governing equation is a finite-volume LU algorithm that allows convection, source, as well as diffusion terms to be treated implicitly. In this study, all convection terms are upwind differenced by using flux-vector splitting, and all diffusion terms are centrally differenced. This paper describes the formulation and algorithm employed in the code. Some computed solutions for the flow within a coolant passage of a radial turbine are also presented.

Mathematical Development and Computational Analysis of Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) Based on Bloch Nuclear Magnetic Resonance (NMR) Diffusion Model for Myocardial Motion.

PubMed

Dada, Michael O; Jayeoba, Babatunde; Awojoyogbe, Bamidele O; Uno, Uno E; Awe, Oluseyi E

2017-09-13

Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) is a tagged image analysis method that can measure myocardial motion and strain in near real-time and is considered a potential candidate to make magnetic resonance tagging clinically viable. However, analytical expressions of radially tagged transverse magnetization in polar coordinates (which is required to appropriately describe the shape of the heart) have not been explored because the physics required to directly connect myocardial deformation of tagged Nuclear Magnetic Resonance (NMR) transverse magnetization in polar geometry and the appropriate harmonic phase parameters are not yet available. The analytical solution of Bloch NMR diffusion equation in spherical geometry with appropriate spherical wave tagging function is important for proper analysis and monitoring of heart systolic and diastolic deformation with relevant boundary conditions. In this study, we applied Harmonic Phase MRI method to compute the difference between tagged and untagged NMR transverse magnetization based on the Bloch NMR diffusion equation and obtained radial wave tagging function for analysis of myocardial motion. The analytical solution of the Bloch NMR equations and the computational simulation of myocardial motion as developed in this study are intended to significantly improve healthcare for accurate diagnosis, prognosis and treatment of cardiovascular related deceases at the lowest cost because MRI scan is still one of the most expensive anywhere. The analysis is fundamental and significant because all Magnetic Resonance Imaging techniques are based on the Bloch NMR flow equations.

Drift-wave turbulence and zonal flow generation.

PubMed

Balescu, R

2003-10-01

Drift-wave turbulence in a plasma is analyzed on the basis of the wave Liouville equation, describing the evolution of the distribution function of wave packets (quasiparticles) characterized by position x and wave vector k. A closed kinetic equation is derived for the ensemble-averaged part of this function by the methods of nonequilibrium statistical mechanics. It has the form of a non-Markovian advection-diffusion equation describing coupled diffusion processes in x and k spaces. General forms of the diffusion coefficients are obtained in terms of Lagrangian velocity correlations. The latter are calculated in the decorrelation trajectory approximation, a method recently developed for an accurate measure of the important trapping phenomena of particles in the rugged electrostatic potential. The analysis of individual decorrelation trajectories provides an illustration of the fragmentation of drift-wave structures in the radial direction and the generation of long-wavelength structures in the poloidal direction that are identified as zonal flows.

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.

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.

Dust particle radial confinement in a dc glow discharge.

PubMed

Sukhinin, G I; Fedoseev, A V; Antipov, S N; Petrov, O F; Fortov, V E

2013-01-01

A self-consistent nonlocal model of the positive column of a dc glow discharge with dust particles is presented. Radial distributions of plasma parameters and the dust component in an axially homogeneous glow discharge are considered. The model is based on the solution of a nonlocal Boltzmann equation for the electron energy distribution function, drift-diffusion equations for ions, and the Poisson equation for a self-consistent electric field. The radial distribution of dust particle density in a dust cloud was fixed as a given steplike function or was chosen according to an equilibrium Boltzmann distribution. The balance of electron and ion production in argon ionization by an electron impact and their losses on the dust particle surface and on the discharge tube walls is taken into account. The interrelation of discharge plasma and the dust cloud is studied in a self-consistent way, and the radial distributions of the discharge plasma and dust particle parameters are obtained. It is shown that the influence of the dust cloud on the discharge plasma has a nonlocal behavior, e.g., density and charge distributions in the dust cloud substantially depend on the plasma parameters outside the dust cloud. As a result of a self-consistent evolution of plasma parameters to equilibrium steady-state conditions, ionization and recombination rates become equal to each other, electron and ion radial fluxes become equal to zero, and the radial component of electric field is expelled from the dust cloud.

Dynamic of charged planar geometry in tilted and non-tilted frames

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

Sharif, M., E-mail: msharif.math@pu.edu.pk; Zaeem Ul Haq Bhatti, M., E-mail: mzaeem.math@pu.edu.pk

2015-05-15

We investigate the dynamics of charged planar symmetry with an anisotropic matter field subject to a radially moving observer called a tilted observer. The Einstein-Maxwell field equations are used to obtain a relation between non-tilted and tilted frames and between kinematical and dynamical quantities. Using the Taub mass formalism and conservation laws, two evolution equations are developed to analyze the inhomogeneities in the tilted congruence. It is found that the radial velocity (due to the tilted observer) and the electric charge have a crucial effect on the inhomogeneity factor. Finally, we discuss the stability in the non-tilted frame in themore » pure diffusion case and examine the effects of the electromagnetic field.« less

Engine Systems Ownership Cost Reduction - Aircraft Propulsion Subsystems Integration (APSI)

DTIC Science & Technology

1975-08-01

compreusor fabrication costs. Hybrid Radial Compresscr Diffuser - Combining both the radial and axial sections of a standard diffuser into a single cascade...compressor diffuser by using a single mixed-flow diffuser instead of the separate radial and axial diffuser stator rows. The proposed mixed-flow diffuser...to an axial diffuser. A cost analyses of the hybrid radial diffuser was made and compared to baseline configuration ( radial and axial diffusers). The

Radial mixing in turbomachines

NASA Astrophysics Data System (ADS)

Segaert, P.; Hirsch, Ch.; Deruyck, J.

1991-03-01

A method for computing the effects of radial mixing in a turbomachinery blade row has been developed. The method fits in the framework of a quasi-3D flow computation and hence is applied in a corrective fashion to through flow distributions. The method takes into account both secondary flows and turbulent diffusion as possible sources of mixing. Secondary flow velocities determine the magnitude of the convection terms in the energy redistribution equation while a turbulent diffusion coefficient determines the magnitude of the diffusion terms. Secondary flows are computed by solving a Poisson equation for a secondary streamfunction on a transversal S3-plane, whereby the right-hand side axial vorticity is composed of different contributions, each associated to a particular flow region: inviscid core flow, end-wall boundary layers, profile boundary layers and wakes. The turbulent mixing coefficient is estimated by a semi-empirical correlation. Secondary flow theory is applied to the VUB cascade testcase and comparisons are made between the computational results and the extensive experimental data available for this testcase. This comparison shows that the secondary flow computations yield reliable predictions of the secondary flow pattern, both qualitatively and quantitatively, taking into account the limitations of the model. However, the computations show that use of a uniform mixing coefficient has to be replaced by a more sophisticated approach.

Self-sustained radial oscillating flows between parallel disks

NASA Astrophysics Data System (ADS)

Mochizuki, S.; Yang, W.-J.

1985-05-01

It is pointed out that radial flow between parallel circular disks is of interest in a number of physical systems such as hydrostatic air bearings, radial diffusers, and VTOL aircraft with centrally located downward-positioned jets. The present investigation is concerned with the problem of instability in radial flow between parallel disks. A time-dependent numerical study and experiments are conducted. Both approaches reveal the nucleation, growth, migration, and decay of annular separation bubbles (i.e. vortex or recirculation zones) in the laminar-flow region. A finite-difference technique is utilized to solve the full unsteady vorticity transport equation in the theoretical procedure, while the flow patterns in the experiments are visualized with the aid of dye-injection, hydrogen-bubble, and paraffin-mist methods. It is found that the separation and reattachment of shear layers in the radial flow through parallel disks are unsteady phenomena. The sequence of nucleation, growth, migration, and decay of the vortices is self-sustained.

The Analytical Solution of the Transient Radial Diffusion Equation with a Nonuniform Loss Term.

NASA Astrophysics Data System (ADS)

Loridan, V.; Ripoll, J. F.; De Vuyst, F.

2017-12-01

Many works have been done during the past 40 years to perform the analytical solution of the radial diffusion equation that models the transport and loss of electrons in the magnetosphere, considering a diffusion coefficient proportional to a power law in shell and a constant loss term. Here, we propose an original analytical method to address this challenge with a nonuniform loss term. The strategy is to match any L-dependent electron losses with a piecewise constant function on M subintervals, i.e., dealing with a constant lifetime on each subinterval. Applying an eigenfunction expansion method, the eigenvalue problem becomes presently a Sturm-Liouville problem with M interfaces. Assuming the continuity of both the distribution function and its first spatial derivatives, we are able to deal with a well-posed problem and to find the full analytical solution. We further show an excellent agreement between both the analytical solutions and the solutions obtained directly from numerical simulations for different loss terms of various shapes and with a diffusion coefficient DLL L6. We also give two expressions for the required number of eigenmodes N to get an accurate snapshot of the analytical solution, highlighting that N is proportional to 1/√t0, where t0 is a time of interest, and that N increases with the diffusion power. Finally, the equilibrium time, defined as the time to nearly reach the steady solution, is estimated by a closed-form expression and discussed. Applications to Earth and also Jupiter and Saturn are discussed.

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).

Resonant thickening of self-gravitating discs: imposed or self-induced orbital diffusion in the tightly wound limit

NASA Astrophysics Data System (ADS)

Fouvry, Jean-Baptiste; Pichon, Christophe; Chavanis, Pierre-Henri; Monk, Laura

2017-11-01

The secular thickening of a self-gravitating stellar galactic disc is investigated using the dressed collisionless Fokker-Planck equation and the inhomogeneous multicomponent Balescu-Lenard equation. The thick WKB limits for the diffusion fluxes are found using the epicyclic approximation, while assuming that only radially tightly wound transient spirals are sustained by the disc. This yields simple quadratures for the drift and diffusion coefficients, providing a clear understanding of the positions of maximum vertical orbital diffusion within the disc, induced by fluctuations either external or due to the finite number of particles. These thick limits also offer a consistent derivation of a thick disc Toomre parameter, which is shown to be exponentially boosted by the ratio of the vertical to radial scaleheights. Dressed potential fluctuations within the disc statistically induce a vertical bending of a subset of resonant orbits, triggering the corresponding increase in vertical velocity dispersion. When applied to a tepid stable tapered disc perturbed by shot noise, these two frameworks reproduce qualitatively the formation of ridges of resonant orbits towards larger vertical actions, as found in direct numerical simulations, but overestimates the time-scale involved in their appearance. Swing amplification is likely needed to resolve this discrepancy, as demonstrated in the case of razor-thin discs. Other sources of thickening are also investigated, such as fading sequences of slowing bars, or the joint evolution of a population of giant molecular clouds within the disc.

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)

Plasma Equilibrium in a Magnetic Field with Stochastic Field-Line Trajectories

NASA Astrophysics Data System (ADS)

Krommes, J. A.; Reiman, A. H.

2008-11-01

The nature of plasma equilibrium in a magnetic field with stochastic field lines is examined, expanding upon the ideas first described by Reiman et al. The magnetic partial differential equation (PDE) that determines the equilibrium Pfirsch-Schlüter currents is treated as a passive stochastic PDE for μj/B. Renormalization leads to a stochastic Langevin equation for μ in which the resonances at the rational surfaces are broadened by the stochastic diffusion of the field lines; even weak radial diffusion can significantly affect the equilibrium, which need not be flattened in the stochastic region. Particular attention is paid to satisfying the periodicity constraints in toroidal configurations with sheared magnetic fields. A numerical scheme that couples the renormalized Langevin equation to Ampere's law is described. A. Reiman et al, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes, Phys. Reports 360, 1--351.

Equation of state and some structural and dynamical properties of the confined Lennard-Jones fluid into carbon nanotube: A molecular dynamics study

NASA Astrophysics Data System (ADS)

Abbaspour, Mohsen; Akbarzadeh, Hamed; Salemi, Sirous; Abroodi, Mousarreza

2016-11-01

By considering the anisotropic pressure tensor, two separate equations of state (EoS) as functions of the density, temperature, and carbon nanotube (CNT) diameter have been proposed for the radial and axial directions for the confined Lennard-Jones (LJ) fluid into (11,11), (12,10), and (19,0) CNTs from 120 to 600 K using molecular dynamics (MD) simulations. We have also investigated the effects of the pore size, pore loading, chirality, and temperature on some of the structural and dynamical properties of the confined LJ fluid into (11,11), (12,10), (19,0), and (19,19) CNTs such as the radial density profile and self-diffusion coefficient. We have also determined the EoS for the confined LJ fluid into double and triple walled CNTs.

FORTRAN program for calculating velocities in the meridional plane of a turbomachine 1: Centrifugal compressor

NASA Technical Reports Server (NTRS)

Vanco, M. R.

1972-01-01

The program will determine the velocities in the meridional plane of a backward-swept impeller, a radial impeller, and a vaned diffuser. The velocity gradient equation with the assumption of a hub-to-shroud mean stream surface is solved along arbitrary quasi-orthogonals in the meridional plane. These quasi-orthogonals are fixed straight lines.

An analysis of the flow field near the fuel injection location in a gas core reactor.

NASA Technical Reports Server (NTRS)

Weinstein, H.; Murty, B. G. K.; Porter, R. W.

1971-01-01

An analytical study is presented which shows the effects of large energy release and the concurrent high acceleration of inner stream fluid on the coaxial flow field in a gas core reactor. The governing equations include the assumptions of only radial radiative transport of energy represented as an energy diffusion term in the Euler equations. The method of integral relations is used to obtain the numerical solution. Results show that the rapidly accelerating, heat generating inner stream actually shrinks in radius as it expands axially.

Dependence of radiation belt simulations to assumed radial diffusion rates tested for two empirical models of radial transport

NASA Astrophysics Data System (ADS)

Drozdov, Alexander; Shprits, Yuri; Aseev, Nikita; Kellerman, Adam; Reeves, Geoffrey

2017-04-01

Radial diffusion is one of the dominant physical mechanisms that drives acceleration and loss of the radiation belt electrons, which makes it very important for nowcasting and forecasting space weather models. We investigate the sensitivity of the two parameterizations of the radial diffusion of Brautigam and Albert [2000] and Ozeke et al. [2014] on long-term radiation belt modeling using the Versatile Electron Radiation Belt (VERB). Following Brautigam and Albert [2000] and Ozeke et al. [2014], we first perform 1-D radial diffusion simulations. Comparison of the simulation results with observations shows that the difference between simulations with either radial diffusion parameterization is small. To take into account effects of local acceleration and loss, we perform 3-D simulations, including pitch-angle, energy and mixed diffusion. We found that the results of 3-D simulations are even less sensitive to the choice of parameterization of radial diffusion rates than the results of 1-D simulations at various energies (from 0.59 to 1.80 MeV). This result demonstrates that the inclusion of local acceleration and pitch-angle diffusion can provide a negative feedback effect, such that the result is largely indistinguishable simulations conducted with different radial diffusion parameterizations. We also perform a number of sensitivity tests by multiplying radial diffusion rates by constant factors and show that such an approach leads to unrealistic predictions of radiation belt dynamics. References Brautigam, D. H., and J. M. Albert (2000), Radial diffusion analysis of outer radiation belt electrons during the October 9, 1990, magnetic storm, J. Geophys. Res., 105(A1), 291-309, doi:10.1029/1999ja900344. Ozeke, L. G., I. R. Mann, K. R. Murphy, I. Jonathan Rae, and D. K. Milling (2014), Analytic expressions for ULF wave radiation belt radial diffusion coefficients, J. Geophys. Res. [Space Phys.], 119(3), 1587-1605, doi:10.1002/2013JA019204.

Effects of whistler mode hiss waves on the radiation belts structure during quiet times

NASA Astrophysics Data System (ADS)

Ripoll, J. F.; Santolik, O.; Reeves, G. D.; Kurth, W. S.; Denton, M.; Loridan, V.; Thaller, S. A.; Cunningham, G.; Kletzing, C.; Turner, D. L.; Henderson, M. G.; Ukhorskiy, S.; Drozdov, A.; Cervantes Villa, J. S.; Shprits, Y.

2017-12-01

We present dynamic Fokker-Planck simulations of the electron radiation belts and slot formation during the quiet days that can follow a storm. Simulations are made for all energies and L-shells between 2 and 6 in the view of recovering the observations of two particular events. Pitch angle diffusion is essential to energy structure of the belts and slot region. Pitch angle diffusion is computed from data-driven spatially and temporally-resolved whistler mode hiss wave and ambient plasma observations from the Van Allen Probes satellites. The simulations are performed either with a 3D formulation that uses pitch angle diffusion coefficients or with a simpler 1D Fokker-Planck equation based on losses computed from a lifetime. Validation is carried out globally against Magnetic Electron and Ion Spectrometer observations of the belts at all energy. Results are complemented with a sensitivity study involving different radial diffusion coefficients, electron lifetimes, and pitch angle diffusion coefficients. We discuss which models allow to recover the observed "S-shaped" energy-dependent inner boundary to the outer zone that results from the competition between diffusive radial transport and losses. Periods when the plasmasphere extends beyond L 5 favor long-lasting hiss losses from the outer belt. Through these simulations, we explain the full structure in energy and L-shell of the belts and the slot formation by hiss scattering during quiet storm recovery.

Analytical estimates of radial segregation in Bridgman growth from low-level steady and periodic accelerations

NASA Astrophysics Data System (ADS)

Naumann, Robert J.; Baugher, Charles

1992-08-01

Estimates of the convective flows driven by horizontal temperature gradients in the vertical Bridgman configuration are made for dilute systems subject to the low level accelerations typical of the residual accelerations experienced by a spacecraft in low Earth orbit. The estimates are made by solving the Navier-Stokes momentum equation in one dimension. The mass transport equation is then solved in two dimensions using a first-order perturbation method. This approach is valid provided the convective velocities are small compared to the growth velocity which generally requires a reduced gravity environment. If this condition is satisfied, there will be no circulating cells, and hence no convective transport along the vertical axis. However, the variations in the vertical velocity with radius will give rise to radial segregation. The approximate analytical model developed here can predict the degree of radial segregation for a variety of material and processing parameters to an accuracy well within a factor of two as compared against numerical computations of the full set of Navier-Stokes equations for steady accelerations. It has the advantage of providing more insight into the complex interplay of the processing parameters and how they affect the solute distribution in the grown crystal. This could be extremely valuable in the design of low-gravity experiments in which the intent is to control radial segregation. Also, the analysis can be extended to consider transient and periodic accelerations, which is difficult and costly to do numerically. Surprisingly, it was found that the relative radial segregation falls as the inverse cube of the frequency for periodic accelerations whose periods are short compared with the characteristic diffusion time.

Position-Dependent Diffusion Tensors in Anisotropic Media from Simulation: Oxygen Transport in and through Membranes.

PubMed

Ghysels, An; Venable, Richard M; Pastor, Richard W; Hummer, Gerhard

2017-06-13

A Bayesian-based methodology is developed to estimate diffusion tensors from molecular dynamics simulations of permeants in anisotropic media, and is applied to oxygen in lipid bilayers. By a separation of variables in the Smoluchowski diffusion equation, the multidimensional diffusion is reduced to coupled one-dimensional diffusion problems that are treated by discretization. The resulting diffusivity profiles characterize the membrane transport dynamics as a function of the position across the membrane, discriminating between diffusion normal and parallel to the membrane. The methodology is first validated with neat water, neat hexadecane, and a hexadecane slab surrounded by water, the latter being a simple model for a lipid membrane. Next, a bilayer consisting of pure 1-palmitoyl 2-oleoylphosphatidylcholine (POPC), and a bilayer mimicking the lipid composition of the inner mitochondrial membrane, including cardiolipin, are investigated. We analyze the detailed time evolution of oxygen molecules, in terms of both normal diffusion through and radial diffusion inside the membrane. Diffusion is fast in the more loosely packed interleaflet region, and anisotropic, with oxygen spreading more rapidly in the membrane plane than normal to it. Visualization of the propagator shows that oxygen enters the membrane rapidly, reaching its thermodynamically favored center in about 1 ns, despite the free energy barrier at the headgroup region. Oxygen transport is quantified by computing the oxygen permeability of the membranes and the average radial diffusivity, which confirm the anisotropy of the diffusion. The position-dependent diffusion constants and free energies are used to construct compartmental models and test assumptions used in estimating permeability, including Overton's rule. In particular, a hexadecane slab surrounded by water is found to be a poor model of oxygen transport in membranes because the relevant energy barriers differ substantially.

Analytic expressions for ULF wave radiation belt radial diffusion coefficients

PubMed Central

Ozeke, Louis G; Mann, Ian R; Murphy, Kyle R; Jonathan Rae, I; Milling, David K

2014-01-01

We present analytic expressions for ULF wave-derived radiation belt radial diffusion coefficients, as a function of L and Kp, which can easily be incorporated into global radiation belt transport models. The diffusion coefficients are derived from statistical representations of ULF wave power, electric field power mapped from ground magnetometer data, and compressional magnetic field power from in situ measurements. We show that the overall electric and magnetic diffusion coefficients are to a good approximation both independent of energy. We present example 1-D radial diffusion results from simulations driven by CRRES-observed time-dependent energy spectra at the outer boundary, under the action of radial diffusion driven by the new ULF wave radial diffusion coefficients and with empirical chorus wave loss terms (as a function of energy, Kp and L). There is excellent agreement between the differential flux produced by the 1-D, Kp-driven, radial diffusion model and CRRES observations of differential electron flux at 0.976 MeV—even though the model does not include the effects of local internal acceleration sources. Our results highlight not only the importance of correct specification of radial diffusion coefficients for developing accurate models but also show significant promise for belt specification based on relatively simple models driven by solar wind parameters such as solar wind speed or geomagnetic indices such as Kp. Key Points Analytic expressions for the radial diffusion coefficients are presented The coefficients do not dependent on energy or wave m value The electric field diffusion coefficient dominates over the magnetic PMID:26167440

Dependence of radiation belt simulations to assumed radial diffusion rates

NASA Astrophysics Data System (ADS)

Drozdov, A.; Shprits, Y.; Aseev, N.; Kellerman, A. C.; Reeves, G. D.

2017-12-01

Radial diffusion is one of the dominant physical mechanisms that drives acceleration and loss of the radiation belt electrons due to wave-particle interaction with ultra low frequency (ULF) waves, which makes it very important for radiation belt modeling and forecasting. We investigate the sensitivity of several parameterizations of the radial diffusion including Brautigam and Albert [2000], Ozeke et al. [2014] and Ali et al. [2016] on long-term radiation belt modeling using the Versatile Electron Radiation Belt (VERB). Following previous studies, we first perform 1-D radial diffusion simulations. To take into account effects of local acceleration and loss, we perform additional 3-D simulations, including pitch-angle, energy and mixed diffusion. The obtained result demonstrates that the inclusion of local acceleration and pitch-angle diffusion can provide a negative feedback effect, such that the result is largely indistinguishable between simulations conducted with different radial diffusion parameterizations. We also perform a number of sensitivity tests by multiplying radial diffusion rates by constant factors and show that such an approach leads to unrealistic predictions of radiation belt dynamics.

Symmetry Reductions and Group-Invariant Radial Solutions to the n-Dimensional Wave Equation

NASA Astrophysics Data System (ADS)

Feng, Wei; Zhao, Songlin

2018-01-01

In this paper, we derive explicit group-invariant radial solutions to a class of wave equation via symmetry group method. The optimal systems of one-dimensional subalgebras for the corresponding radial wave equation are presented in terms of the known point symmetries. The reductions of the radial wave equation into second-order ordinary differential equations (ODEs) with respect to each symmetry in the optimal systems are shown. Then we solve the corresponding reduced ODEs explicitly in order to write out the group-invariant radial solutions for the wave equation. Finally, several analytical behaviours and smoothness of the resulting solutions are discussed.

Deduction of the rates of radial diffusion of protons from the structure of the Earth's radiation belts

NASA Astrophysics Data System (ADS)

Kovtyukh, Alexander S.

2016-11-01

From the data on the fluxes and energy spectra of protons with an equatorial pitch angle of α0 ≈ 90° during quiet and slightly disturbed (Kp ≤ 2) periods, I directly calculated the value DLL, which is a measure of the rate of radial transport (diffusion) of trapped particles. This is done by successively solving the systems (chains) of integrodifferential equations which describe the balance of radial transport/acceleration and ionization losses of low-energy protons of the stationary belt. This was done for the first time. For these calculations, I used data of International Sun-Earth Explorer 1 (ISEE-1) for protons with an energy of 24 to 2081 keV at L = 2-10 and data of Explorer-45 for protons with an energy of 78.6 to 872 keV at L = 2-5. Ionization losses of protons (Coulomb losses and charge exchange) were calculated on the basis of modern models of the plasmasphere and the exosphere. It is shown that for protons with μ from ˜ 0.7 to ˜ 7 keV nT-1 at L ≈ 4.5-10, the functions of DLL can be approximated by the following equivalent expressions: DLL ≈ 4.9 × 10-14μ-4.1L8.2 or DLL ≈ 1.3 × 105(EL)-4.1 or DLL ≈ 1.2 × 10-9fd-4.1, where fd is the drift frequency of the protons (in mHz), DLL is measured in s-1, E is measured in kiloelectronvolt and μ is measured in kiloelectronvolt per nanotesla. These results are consistent with the radial diffusion of particles under the action of the electric field fluctuations (pulsations) in the range of Pc6 and contradict the mechanism of the radial diffusion of particles under the action of sudden impulses (SIs) of the magnetic field and also under the action of substorm impulses of the electric field. During magnetic storms DLL increases, and the expressions for DLL obtained here can change completely.

1D Resonance line Broadened Quasilinear (RBQ1D) code for fast ion Alfvenic relaxations and its validations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Podesta, Mario

2017-10-01

The performance of the burning plasma can be limited by the requirements to confine the superalfvenic fusion products which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using the quasi-linear approach [Berk et al., Ph.Plasmas'96] generalized for this problem recently [Duarte et al., Ph.D.'17]. The generalization involves the resonance line broadened interaction regions with the diffusion coefficient prescribed to find the evolution of the velocity distribution function. The baseline eigenmode structures are found using the NOVA-K code perturbatively [Gorelenkov et al., Ph.Plasmas'99]. A RBQ1D code allowing the diffusion in radial direction is presented here. 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 RBQ1D is validated against recent DIIID results [Collins et al., PRL'16]. Supported by the US Department of Energy under DE-AC02-09CH11466.

SYMTRAN - A Time-dependent Symmetric Tandem Mirror Transport Code

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

Hua, D; Fowler, T

2004-06-15

A time-dependent version of the steady-state radial transport model in symmetric tandem mirrors in Ref. [1] has been coded up and first tests performed. Our code, named SYMTRAN, is an adaptation of the earlier SPHERE code for spheromaks, now modified for tandem mirror physics. Motivated by Post's new concept of kinetic stabilization of symmetric mirrors, it is an extension of the earlier TAMRAC rate-equation code omitting radial transport [2], which successfully accounted for experimental results in TMX. The SYMTRAN code differs from the earlier tandem mirror radial transport code TMT in that our code is focused on axisymmetric tandem mirrorsmore » and classical diffusion, whereas TMT emphasized non-ambipolar transport in TMX and MFTF-B due to yin-yang plugs and non-symmetric transitions between the plugs and axisymmetric center cell. Both codes exhibit interesting but different non-linear behavior.« less

An axisymmetric non-hydrostatic model for double-diffusive water systems

NASA Astrophysics Data System (ADS)

Hilgersom, Koen; Zijlema, Marcel; van de Giesen, Nick

2018-02-01

The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In 3-D systems that approach axisymmetry around a central location, computation times can be reduced by applying a 2-D axisymmetric model set-up. This article applies the Reynolds-averaged Navier-Stokes equations described in cylindrical coordinates and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite-volume model can be easily extended to the developed framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature- and salinity-dependent densities, molecular diffusivities, and kinematic viscosity. One quantitative case study, based on an analytical solution derived for the radial expansion of a dense water layer, and two qualitative case studies demonstrate a good behaviour of the model for seepage inflows with contrasting salinities and temperatures. Four case studies with respect to double-diffusive processes in a stratified water body demonstrate that turbulent flows are not yet correctly modelled near the interfaces and that an advanced turbulence model is required.

The Dynamic Mutation Characteristics of Thermonuclear Reaction in Tokamak

PubMed Central

Li, Jing; Quan, Tingting; Zhang, Wei; Deng, Wei

2014-01-01

The stability and bifurcations of multiple limit cycles for the physical model of thermonuclear reaction in Tokamak are investigated in this paper. The one-dimensional Ginzburg-Landau type perturbed diffusion equations for the density of the plasma and the radial electric field near the plasma edge in Tokamak are established. First, the equations are transformed to the average equations with the method of multiple scales and the average equations turn to be a Z 2-symmetric perturbed polynomial Hamiltonian system of degree 5. Then, with the bifurcations theory and method of detection function, the qualitative behavior of the unperturbed system and the number of the limit cycles of the perturbed system for certain groups of parameter are analyzed. At last, the stability of the limit cycles is studied and the physical meaning of Tokamak equations under these parameter groups is given. PMID:24892099

Effect of the radial buoyancy on a circular Couette flow

NASA Astrophysics Data System (ADS)

Meyer, Antoine; Yoshikawa, Harunori N.; Mutabazi, Innocent

2015-11-01

The effect of a radial temperature gradient on the stability of a circular Couette flow is investigated when the gravitational acceleration is neglected. The induced radial stratification of the fluid density coupled with the centrifugal acceleration generates radial buoyancy which is centrifugal for inward heating and centripetal for outward heating. This radial buoyancy modifies the Rayleigh discriminant and induces the asymmetry between inward heating and outward heating in flow behavior. The critical modes are axisymmetric and stationary for inward heating while for outward heating, they can be oscillatory axisymmetric or nonaxisymmetric depending on fluid diffusion properties, i.e., on the Prandtl number Pr. The dependence of the critical modes on Pr is explored for different values of the radius ratio of the annulus. The power input of the radial buoyancy is compared with other power terms. The critical frequency of the oscillatory axisymmetric modes is linked to the Brunt-Väisälä frequency due to the density stratification in the radial gravity field induced by the rotation. These modes are associated with inertial waves. The dispersion relation of the oscillatory axisymmetric modes is derived in the vicinity of the critical conditions. A weakly nonlinear amplitude equation with a forcing term is proposed to explain the domination of these axisymmetric oscillatory modes over the stationary centrifugal mode.

An axisymmetric single-path model for gas transport in the conducting airways.

PubMed

Madasu, Srinath; Borhan, All; Ultman, James S

2006-02-01

In conventional one-dimensional single-path models, radially averaged concentration is calculated as a function of time and longitudinal position in the lungs, and coupled convection and diffusion are accounted for with a dispersion coefficient. The axisymmetric single-path model developed in this paper is a two-dimensional model that incorporates convective-diffusion processes in a more fundamental manner by simultaneously solving the Navier-Stokes and continuity equations with the convection-diffusion equation. A single airway path was represented by a series of straight tube segments interconnected by leaky transition regions that provide for flow loss at the airway bifurcations. As a sample application, the model equations were solved by a finite element method to predict the unsteady state dispersion of an inhaled pulse of inert gas along an airway path having dimensions consistent with Weibel's symmetric airway geometry. Assuming steady, incompressible, and laminar flow, a finite element analysis was used to solve for the axisymmetric pressure, velocity and concentration fields. The dispersion calculated from these numerical solutions exhibited good qualitative agreement with the experimental values, but quantitatively was in error by 20%-30% due to the assumption of axial symmetry and the inability of the model to capture the complex recirculatory flows near bifurcations.

Analysis of a dusty wall jet

NASA Technical Reports Server (NTRS)

Lim, Hock-Bin; Roberts, Leonard

1991-01-01

An analysis is given for the entrainment of dust into a turbulent radial wall jet. Equations are solved based on incompressible flow of a radial wall jet into which dust is entrained from the wall and transported by turbulent diffusion and convection throughout the flow. It is shown that the resulting concentration of dust particles in the flow depends on the difference between the applied shear stress at the surface and the maximum level of shear stress that the surface can withstand (varies as rho(sub d)a(sub g)D) i.e., the pressure due to the weight of a single layer of dust. The analysis is expected to have application to the downflow that results from helicopter and VTOL aircraft.

Radial diffusion in magnetodiscs. [charged particle motion in planetary or stellar magnetosphere

NASA Technical Reports Server (NTRS)

Birmingham, T. J.

1985-01-01

The orbits of charged particles in magnetodiscs are considered. The bounce motion is assumed adiabatic except for transits of a small equatorial region of weak magnetic field strength and high field curvature. Previous theory and modeling have shown that particles scatter randomly in pitch angle with each passage through the equator. A peaked distribution thus diffuses in pitch angle on the time scale of many bounces. It is argued in this paper that spatial diffusion is a further consequence when the magnetodisc has a longitudinal asymmetry. A general expression for DLL, the diffusion of equatorial crossing radii, is derived. DLL is evaluated explicitly for ions in Jupiter's 20-35 radii magnetodisc, assumed to be represented by Connerney et al.'s (1982) Voyager model plus a small image dipole asymmetry. Rates are energy, species, and space dependent but can average as much as a few tenths of a planetary radius per bounce period.

Estimation of the radial diffusion coefficient using REE-associated ground Pc 5 pulsations

NASA Astrophysics Data System (ADS)

Fujimoto, A.; Yumoto, K.

2010-12-01

Pc 5 pulsations with frequencies between 1.67 and 6.67 mHz are believed to contribute to the REE in the outer radiation belt during magnetic storms, by means of the observations [Baker et al., 1998; Rostoker et al., 1998; Mathie and Mann, 2000; O'Brien et al., 2001, 2003] and several theoretical studies. The latter studies are roughly categorized into two themes: in-situ acceleration at L lower than 6.6 by wave-particle interactions [Liu et al., 199 9; Summers et al., 1999; Summers and Ma, 2000] and acceleration by radial diffusion from the outer to the inner magnetosphere [Elkington et al., 1999, 2003; Hudson et al., 2000; Kim et al., 2001]. One possible acceleration mechanism is the resonant interaction with Pc 5 toroidal and poloidal pulsations, referred as the radial diffusion mechanism. One of unsolved problems is where and which Pc 5 pulsation mode (toroidal and/or poloidal) play effective role in the radial diffusion process. In order to verify Pc 5 pulsation as the major roles for REEs, we have to examine the time variation of electron phase space density (cf. Green et al., 2004). Electron phase space density is not directly measured, but we can estimate radial diffusion coefficients which determine the electron transportation efficiency, using ground-based magnetic field data. We estimated the radial diffusion coefficient of ground Pc 5 pulsations associated with the Relativistic Electron Enhancement (REE) in the geosynchronous orbit. In order to estimate the radial diffusion coefficient D_LL, we need the value of in-situ Pc 5 electric field power spectral density. In this paper, however, we estimated the equatorial electric field mapped from Pc 5 pulsations power spectral density on the ground. Reciprocal of radial diffusion coefficient describes the timescale T_LL for an electron to diffuse 1 Re. Applying a superposed epoch analysis about timescales T_LL of the radial diffusion for 12 REE events in 2008, we found that when the relativistic electron enhancements occur, T_LL at higher latitude (L larger than 5) is predominantly diffusional, whereas T_LL at lower latitude (L less than 4) is mainly convectional. We concluded that higher-latitude Pc 5 pulsations play more effective roles than lower latitude Pc 5 pulsations in the radial diffusion process.

Large-scale magnetic field in the accretion discs of young stars: the influence of magnetic diffusion, buoyancy and Hall effect

NASA Astrophysics Data System (ADS)

Khaibrakhmanov, S. A.; Dudorov, A. E.; Parfenov, S. Yu.; Sobolev, A. M.

2017-01-01

We investigate the fossil magnetic field in the accretion and protoplanetary discs using the Shakura and Sunyaev approach. The distinguishing feature of this study is the accurate solution of the ionization balance equations and the induction equation with Ohmic diffusion, magnetic ambipolar diffusion, buoyancy and the Hall effect. We consider the ionization by cosmic rays, X-rays and radionuclides, radiative recombinations, recombinations on dust grains and also thermal ionization. The buoyancy appears as the additional mechanism of magnetic flux escape in the steady-state solution of the induction equation. Calculations show that Ohmic diffusion and magnetic ambipolar diffusion constraint the generation of the magnetic field inside the `dead' zones. The magnetic field in these regions is quasi-vertical. The buoyancy constraints the toroidal magnetic field strength close to the disc inner edge. As a result, the toroidal and vertical magnetic fields become comparable. The Hall effect is important in the regions close to the borders of the `dead' zones because electrons are magnetized there. The magnetic field in these regions is quasi-radial. We calculate the magnetic field strength and geometry for the discs with accretion rates (10^{-8}-10^{-6}) {M}_{⊙} {yr}^{-1}. The fossil magnetic field geometry does not change significantly during the disc evolution while the accretion rate decreases. We construct the synthetic maps of dust emission polarized due to the dust grain alignment by the magnetic field. In the polarization maps, the `dead' zones appear as the regions with the reduced values of polarization degree in comparison to those in the adjacent regions.

Neoclassical Diffusion of Radiation-Belt Electrons Across Very Low L -shells

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

Cunningham, Gregory S.; Loridan, Vivien; Ripoll, Jean-Francois

In the presence of drift-shell splitting intrinsic to the IGRF magnetic field model, pitch-angle scattering from Coulomb collisions experienced by radiation-belt electrons in the upper atmosphere and ionosphere produces extra radial diffusion, a form of neoclassical diffusion. The strength of the neoclassical radial diffusion at L < 1.2 exceeds that expected there from radial-diffusion mechanisms traditionally considered, and decreases with increasing L-shell. In this study we construct a numerical model for this coupled (radial and pitch-angle) collisional diffusion process and apply it to simulate raw count-rate data observed aboard the Gemini spacecraft for several years after the 1962 Starfish nuclearmore » detonation. The data show apparent lifetimes 10-100 times as long as would have been expected from collisional pitch-angle diffusion and Coulomb drag alone. Our model reproduces apparent lifetimes for >0.5-MeV electrons in the region 1.14 < L < 1.26 to within a factor of two (comparable to the uncertainty quoted for the observations). We conclude that neoclassical radial diffusion (resulting from drift-shell splitting intrinsic to IGRF's azimuthal asymmetries) mitigates the decay expected from collisional pitch-angle diffusion and inelastic energy loss alone and thus contributes importantly to the long apparent lifetimes observed at these low L-shells.« less

Neoclassical Diffusion of Radiation-Belt Electrons Across Very Low L -shells

DOE PAGES

Cunningham, Gregory S.; Loridan, Vivien; Ripoll, Jean-Francois; ...

2018-03-30

In the presence of drift-shell splitting intrinsic to the IGRF magnetic field model, pitch-angle scattering from Coulomb collisions experienced by radiation-belt electrons in the upper atmosphere and ionosphere produces extra radial diffusion, a form of neoclassical diffusion. The strength of the neoclassical radial diffusion at L < 1.2 exceeds that expected there from radial-diffusion mechanisms traditionally considered, and decreases with increasing L-shell. In this study we construct a numerical model for this coupled (radial and pitch-angle) collisional diffusion process and apply it to simulate raw count-rate data observed aboard the Gemini spacecraft for several years after the 1962 Starfish nuclearmore » detonation. The data show apparent lifetimes 10-100 times as long as would have been expected from collisional pitch-angle diffusion and Coulomb drag alone. Our model reproduces apparent lifetimes for >0.5-MeV electrons in the region 1.14 < L < 1.26 to within a factor of two (comparable to the uncertainty quoted for the observations). We conclude that neoclassical radial diffusion (resulting from drift-shell splitting intrinsic to IGRF's azimuthal asymmetries) mitigates the decay expected from collisional pitch-angle diffusion and inelastic energy loss alone and thus contributes importantly to the long apparent lifetimes observed at these low L-shells.« less

Neoclassical Diffusion of Radiation-Belt Electrons Across Very Low L-Shells

NASA Astrophysics Data System (ADS)

Cunningham, Gregory S.; Loridan, Vivien; Ripoll, Jean-François; Schulz, Michael

2018-04-01

In the presence of drift-shell splitting intrinsic to the International Geomagnetic Reference Field magnetic field model, pitch angle scattering from Coulomb collisions experienced by radiation-belt electrons in the upper atmosphere and ionosphere produces extra radial diffusion, a form of neoclassical diffusion. The strength of the neoclassical radial diffusion at L < 1.2 exceeds that expected there from radial-diffusion mechanisms traditionally considered and decreases with increasing L-shell. In this work we construct a numerical model for this coupled (radial and pitch angle) collisional diffusion process and apply it to simulate raw count-rate data observed aboard the Gemini spacecraft for several years after the 1962 Starfish nuclear detonation. The data show apparent lifetimes 10-100 times as long as would have been expected from collisional pitch angle diffusion and Coulomb drag alone. Our model reproduces apparent lifetimes for >0.5-MeV electrons in the region 1.14 < L < 1.26 to within a factor of 2 (comparable to the uncertainty quoted for the observations). We conclude that neoclassical radial diffusion (resulting from drift-shell splitting intrinsic to International Geomagnetic Reference Field's azimuthal asymmetries) mitigates the decay expected from collisional pitch angle diffusion and inelastic energy loss alone and thus contributes importantly to the long apparent lifetimes observed at these low L-shells.

Stimulated echo diffusion tensor imaging (STEAM-DTI) with varying diffusion times as a probe of breast tissue.

PubMed

Teruel, Jose R; Cho, Gene Y; Moccaldi Rt, Melanie; Goa, Pål E; Bathen, Tone F; Feiweier, Thorsten; Kim, Sungheon G; Moy, Linda; Sigmund, Eric E

2017-01-01

To explore the application of diffusion tensor imaging (DTI) for breast tissue and breast pathologies using a stimulated-echo acquisition mode (STEAM) with variable diffusion times. In this Health Insurance Portability and Accountability Act-compliant study, approved by the local institutional review board, eight patients and six healthy volunteers underwent an MRI examination at 3 Tesla including STEAM-DTI with several diffusion times ranging from 68.5 to 902.5 ms. A DTI model was fitted to the data for each diffusion time, and parametric maps of mean diffusivity, fractional anisotropy, axial diffusivity, and radial diffusivity were computed for healthy fibroglandular tissue (FGT) and lesions. The median value of radial diffusivity for FGT was fitted to a linear decay to obtain an estimation of the surface-to-volume ratio, from which the radial diameter was calculated. For healthy FGT, radial diffusivity presented a linear decay with the square root of the diffusion time resulting in a range of estimated radial diameters from 202 to 496 µm, while axial diffusivity presented a nearly time-independent diffusion. Residual fat signal was reduced at longer diffusion times due to the shorter T1 of fat. Residual fat signal to the overall signal in the healthy volunteers' FGT was found to range from 2.39% to 2.55% (shortest mixing time), and from 0.40% to 0.51% (longest mixing time) for the b500 images. The use of variable diffusion times may provide an in vivo noninvasive tool to probe diffusion lengths in breast tissue and breast pathology, and might aid by improving fat suppression at longer diffusion times. 2 J. Magn. Reson. Imaging 2017;45:84-93. © 2016 International Society for Magnetic Resonance in Medicine.

Galactic Cosmic-ray Transport in the Global Heliosphere: A Four-Dimensional Stochastic Model

NASA Astrophysics Data System (ADS)

Florinski, V.

2009-04-01

We study galactic cosmic-ray transport in the outer heliosphere and heliosheath using a newly developed transport model based on stochastic integration of the phase-space trajectories of Parker's equation. The model employs backward integration of the diffusion-convection transport equation using Ito calculus and is four-dimensional in space+momentum. We apply the model to the problem of galactic proton transport in the heliosphere during a negative solar minimum. Model results are compared with the Voyager measurements of galactic proton radial gradients and spectra in the heliosheath. We show that the heliosheath is not as efficient in diverting cosmic rays during solar minima as predicted by earlier two-dimensional models.

A Numerical Study of Forbush Decreases with a 3D Cosmic-Ray Modulation Model Based on an SDE Approach

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

Luo, Xi; Feng, Xueshang; Potgieter, Marius S.

Based on the reduced diffusion mechanism for producing Forbush decreases (Fds) in the heliosphere, we constructed a three-dimensional (3D) diffusion barrier, and by incorporating it into a stochastic differential equation (SDE) based time-dependent, cosmic-ray transport model, a 3D numerical model for simulating Fds is built and applied to a period of relatively quiet solar activity. This SDE model generally corroborates previous Fd simulations concerning the effects of the solar magnetic polarity, the tilt angle of the heliospheric current sheet (HCS), and cosmic-ray particle energy. Because the modulation processes in this 3D model are multi-directional, the barrier’s geometrical features affect themore » intensity profiles of Fds differently. We find that both the latitudinal and longitudinal extent of the barrier have relatively fewer effects on these profiles than its radial extent and the level of decreased diffusion inside the disturbance. We find, with the 3D approach, that the HCS rotational motion causes the relative location from the observation point to the HCS to vary, so that a periodic pattern appears in the cosmic-ray intensity at the observing location. Correspondingly, the magnitude and recovery time of an Fd change, and the recovering intensity profile contains oscillation as well. Investigating the Fd magnitude variation with heliocentric radial distance, we find that the magnitude decreases overall and, additionally, that the Fd magnitude exhibits an oscillating pattern as the radial distance increases, which coincides well with the wavy profile of the HCS under quiet solar modulation conditions.« less

A fully-neoclassical finite-orbit-width version of the CQL3D Fokker–Planck code

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

Petrov, Yu V.; Harvey, R. W.

The time-dependent bounce-averaged CQL3D flux-conservative finite-difference Fokker–Planck equation (FPE) solver has been upgraded to include finite-orbit-width (FOW) capabilities which are necessary for an accurate description of neoclassical transport, losses to the walls, and transfer of particles, momentum, and heat to the scrape-off layer. The FOW modifications are implemented in the formulation of the neutral beam source, collision operator, RF quasilinear diffusion operator, and in synthetic particle diagnostics. The collisional neoclassical radial transport appears naturally in the FOW version due to the orbit-averaging of local collision coefficients coupled with transformation coefficients from local (R, Z) coordinates along each guiding-center orbit tomore » the corresponding midplane computational coordinates, where the FPE is solved. In a similar way, the local quasilinear RF diffusion terms give rise to additional radial transport of orbits. We note that the neoclassical results are obtained for ‘full’ orbits, not dependent on a common small orbit-width approximation. Results of validation tests for the FOW version are also presented.« less

A fully-neoclassical finite-orbit-width version of the CQL3D Fokker–Planck code

DOE PAGES

Petrov, Yu V.; Harvey, R. W.

2016-09-08

The time-dependent bounce-averaged CQL3D flux-conservative finite-difference Fokker–Planck equation (FPE) solver has been upgraded to include finite-orbit-width (FOW) capabilities which are necessary for an accurate description of neoclassical transport, losses to the walls, and transfer of particles, momentum, and heat to the scrape-off layer. The FOW modifications are implemented in the formulation of the neutral beam source, collision operator, RF quasilinear diffusion operator, and in synthetic particle diagnostics. The collisional neoclassical radial transport appears naturally in the FOW version due to the orbit-averaging of local collision coefficients coupled with transformation coefficients from local (R, Z) coordinates along each guiding-center orbit tomore » the corresponding midplane computational coordinates, where the FPE is solved. In a similar way, the local quasilinear RF diffusion terms give rise to additional radial transport of orbits. We note that the neoclassical results are obtained for ‘full’ orbits, not dependent on a common small orbit-width approximation. Results of validation tests for the FOW version are also presented.« less

Approximation of a radial diffusion model with a multiple-rate model for hetero-disperse particle mixtures

PubMed Central

Ju, Daeyoung; Young, Thomas M.; Ginn, Timothy R.

2012-01-01

An innovative method is proposed for approximation of the set of radial diffusion equations governing mass exchange between aqueous bulk phase and intra-particle phase for a hetero-disperse mixture of particles such as occur in suspension in surface water, in riverine/estuarine sediment beds, in soils and in aquifer materials. For this purpose the temporal variation of concentration at several uniformly distributed points within a normalized representative particle with spherical, cylindrical or planar shape is fitted with a 2-domain linear reversible mass exchange model. The approximation method is then superposed in order to generalize the model to a hetero-disperse mixture of particles. The method can reduce the computational effort needed in solving the intra-particle mass exchange of a hetero-disperse mixture of particles significantly and also the error due to the approximation is shown to be relatively small. The method is applied to describe desorption batch experiment of 1,2-Dichlorobenzene from four different soils with known particle size distributions and it could produce good agreement with experimental data. PMID:18304692

Confined active Brownian particles: theoretical description of propulsion-induced accumulation

NASA Astrophysics Data System (ADS)

Das, Shibananda; Gompper, Gerhard; Winkler, Roland G.

2018-01-01

The stationary-state distribution function of confined active Brownian particles (ABPs) is analyzed by computer simulations and analytical calculations. We consider a radial harmonic as well as an anharmonic confinement potential. In the simulations, the ABP is propelled with a prescribed velocity along a body-fixed direction, which is changing in a diffusive manner. For the analytical approach, the Cartesian components of the propulsion velocity are assumed to change independently; active Ornstein-Uhlenbeck particle (AOUP). This results in very different velocity distribution functions. The analytical solution of the Fokker-Planck equation for an AOUP in a harmonic potential is presented and a conditional distribution function is provided for the radial particle distribution at a given magnitude of the propulsion velocity. This conditional probability distribution facilitates the description of the coupling of the spatial coordinate and propulsion, which yields activity-induced accumulation of particles. For the anharmonic potential, a probability distribution function is derived within the unified colored noise approximation. The comparison of the simulation results with theoretical predictions yields good agreement for large rotational diffusion coefficients, e.g. due to tumbling, even for large propulsion velocities (Péclet numbers). However, we find significant deviations already for moderate Péclet number, when the rotational diffusion coefficient is on the order of the thermal one.

Experiments with a Supersonic Multi-Channel Radial Diffuser.

DTIC Science & Technology

1980-09-01

unlimited. 17 . DISTRIBUTION STATEMENT (o the *bsta~c entered nRItok 20, it dffttt Iton, Report) IS. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue o...Improvements 17 VI SIGNIFICANT TEST RESULTS 20 1. General Considerations 20 2. Typical Radial Diffuser Performance 20 3. Flow Stability Experiments 22 VIII...Adjustments Indicated 39 16 Comparison of the Single Channel Performances for Two Extreme Channel Geometries 40 17 Typical Radial Diffuser Performance

Radial Diffusion Coefficients Using E and B Field Data from the Van Allen Probes: Comparison with the CRRES Study

NASA Astrophysics Data System (ADS)

Ali, A.; Elkington, S. R.; Malaspina, D.

2014-12-01

The Van Allen radiation belts contain highly energetic particles which interact with a variety of plasma and MHD waves. Waves with frequencies in the ULF range are understood to play an important role in loss and acceleration of energetic particles. We are investigating the contributions from perturbations in both the magnetic and the electric fields in driving radial diffusion of charged particles and wish to probe two unanswered questions about ULF wave driven radial transport. First, how important are the fluctuations in the magnetic field compared with the fluctuations in the electric field in driving radial diffusion? Second, how does ULF wave power distribution in azimuth affect radial diffusion? Analytic treatments of the diffusion coefficients generally assume uniform distribution of power in azimuth but in situ measurements suggest otherwise. We present results from a study using the electric and magnetic field measurements from the Van Allen Probes to estimate the radial diffusion coefficients as a function of L and Kp. During the lifetime of the RBSP mission to date, there has been a dearth of solar activity. This compels us to consider Kp as the only time and activity dependent parameter instead of solar wind velocity and pressure.

Radial q-space sampling for DSI.

PubMed

Baete, Steven H; Yutzy, Stephen; Boada, Fernando E

2016-09-01

Diffusion spectrum imaging (DSI) has been shown to be an effective tool for noninvasively depicting the anatomical details of brain microstructure. Existing implementations of DSI sample the diffusion encoding space using a rectangular grid. Here we present a different implementation of DSI whereby a radially symmetric q-space sampling scheme for DSI is used to improve the angular resolution and accuracy of the reconstructed orientation distribution functions. Q-space is sampled by acquiring several q-space samples along a number of radial lines. Each of these radial lines in q-space is analytically connected to a value of the orientation distribution functions at the same angular location by the Fourier slice theorem. Computer simulations and in vivo brain results demonstrate that radial diffusion spectrum imaging correctly estimates the orientation distribution functions when moderately high b-values (4000 s/mm2) and number of q-space samples (236) are used. The nominal angular resolution of radial diffusion spectrum imaging depends on the number of radial lines used in the sampling scheme, and only weakly on the maximum b-value. In addition, the radial analytical reconstruction reduces truncation artifacts which affect Cartesian reconstructions. Hence, a radial acquisition of q-space can be favorable for DSI. Magn Reson Med 76:769-780, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Response of radiation belt simulations to different radial diffusion coefficients for relativistic and ultra-relativistic electrons

NASA Astrophysics Data System (ADS)

Drozdov, Alexander; Mann, Ian; Baker, Daniel N.; Subbotin, Dmitriy; Ozeke, Louis; Shprits, Yuri; Kellerman, Adam

Two parameterizations of the resonant wave-particle interactions of electrons with ULF waves in the magnetosphere by Brautigam and Albert [2000] and Ozeke et al. [2012] are evaluated using the Versatile Electron Radiation Belt (VERB) diffusion code to estimate the effect of changing a diffusion coefficient on the radiation belt simulation. The period of investigation includes geomagnetically quiet and active time. The simulations take into account wave-particle interactions represented by radial diffusion transport, local acceleration, losses due to pitch-angle diffusion, and mixed diffusion. 1. Brautigam, D. H., and J. M. Albert (2000), Radial diffusion analysis of outer radiation belt electrons during the October 9, 1990, magnetic storm, J. Geophys. Res., 105(A1), 291-309, doi:10.1029/1999JA900344 2. Ozeke, L. G., I. R. Mann, K. R. Murphy, I. J. Rae, D. K. Milling, S. R. Elkington, A. A. Chan, and H. J. Singer (2012), ULF wave derived radiation belt radial diffusion coefficients, J. Geophys. Res., 117, A04222, doi:10.1029/2011JA017463.

Pre-Darcy Flow in Porous Media

NASA Astrophysics Data System (ADS)

Dejam, Morteza; Hassanzadeh, Hassan; Chen, Zhangxin

2017-10-01

Fluid flow in porous media is very important in a wide range of science and engineering applications. The entire establishment of fluid flow application in porous media is based on the use of an experimental law proposed by Darcy (1856). There are evidences in the literature that the flow of a fluid in consolidated and unconsolidated porous media does not follow Darcy law at very low fluxes, which is called pre-Darcy flow. In this paper, the unsteady flow regimes of a slightly compressible fluid under the linear and radial pre-Darcy flow conditions are modeled and the corresponding highly nonlinear diffusivity equations are solved analytically by aid of a generalized Boltzmann transformation technique. The influence of pre-Darcy flow on the pressure diffusion for homogeneous porous media is studied in terms of the nonlinear exponent and the threshold pressure gradient. In addition, the pressure gradient, flux, and cumulative production per unit area are compared with the classical solution of the diffusivity equation based on Darcy flow. The presented results advance our understanding of fluid flow in low-permeability media such as shale and tight formations, where pre-Darcy is the dominant flow regime.

Modeling a Single SEP Event from Multiple Vantage Points Using the iPATH Model

NASA Astrophysics Data System (ADS)

Hu, Junxiang; Li, Gang; Fu, Shuai; Zank, Gary; Ao, Xianzhi

2018-02-01

Using the recently extended 2D improved Particle Acceleration and Transport in the Heliosphere (iPATH) model, we model an example gradual solar energetic particle event as observed at multiple locations. Protons and ions that are energized via the diffusive shock acceleration mechanism are followed at a 2D coronal mass ejection-driven shock where the shock geometry varies across the shock front. The subsequent transport of energetic particles, including cross-field diffusion, is modeled by a Monte Carlo code that is based on a stochastic differential equation method. Time intensity profiles and particle spectra at multiple locations and different radial distances, separated in longitudes, are presented. The results shown here are relevant to the upcoming Parker Solar Probe mission.

A numerical study of circulation driven by mixing over a submarine bank

NASA Astrophysics Data System (ADS)

Cummins, Patrick F.; Foreman, Michael G. G.

1998-04-01

A primitive equation model is applied to study the spin-up of a linearly stratified, rotating fluid over an isolated topographic bank. The model has vertical eddy mixing coefficients that decay away from the bottom over a specified e-folding scale. No external flows are imposed, and a circulation develops due solely to diffusion over the sea bed. Vertical mixing, coupled with the condition of zero diffusive flux of heat through the sea floor, leads to a distortion of isothermal surfaces near the bottom. The associated radial pressure gradients drive a radial-overturning circulation with upslope flow just above the bottom and downslope flows at greater height. Coriolis forces on the radial flows accelerate a verticallysheared azimuthal (alongslope) circulation. Near the bottom the azimuthal motion is cyclonic (upwelling favourable), while outside the boundary layer, the motion is anticyclonic. Sensitivity experiments show that this pattern is robust and maintained even with constant mixing coefficients. Attention is given to the driving mechanism for the depth-averaged azimuthal motion. An analysis of the relative angular momentum balance determines that the torque associated with bottom stresses drives the anticyclonic depth-averaged flow. In terms of vorticity, the anticyclonic vortex over the bank arises due to the curl of bottom stress divided by the depth. A parameter sensitivity study indicates that the depth-averaged flow is relatively insensitive to variations in the bottom drag coefficient.

SEAWAT-based simulation of axisymmetric heat transport.

PubMed

Vandenbohede, Alexander; Louwyck, Andy; Vlamynck, Nele

2014-01-01

Simulation of heat transport has its applications in geothermal exploitation of aquifers and the analysis of temperature dependent chemical reactions. Under homogeneous conditions and in the absence of a regional hydraulic gradient, groundwater flow and heat transport from or to a well exhibit radial symmetry, and governing equations are reduced by one dimension (1D) which increases computational efficiency importantly. Solute transport codes can simulate heat transport and input parameters may be modified such that the Cartesian geometry can handle radial flow. In this article, SEAWAT is evaluated as simulator for heat transport under radial flow conditions. The 1971, 1D analytical solution of Gelhar and Collins is used to compare axisymmetric transport with retardation (i.e., as a result of thermal equilibrium between fluid and solid) and a large diffusion (conduction). It is shown that an axisymmetric simulation compares well with a fully three dimensional (3D) simulation of an aquifer thermal energy storage systems. The influence of grid discretization, solver parameters, and advection solution is illustrated. Because of the high diffusion to simulate conduction, convergence criterion for heat transport must be set much smaller (10(-10) ) than for solute transport (10(-6) ). Grid discretization should be considered carefully, in particular the subdivision of the screen interval. On the other hand, different methods to calculate the pumping or injection rate distribution over different nodes of a multilayer well lead to small differences only. © 2013, National Ground Water Association.

Measurement of the eddy diffusion term in chromatographic columns. I. Application to the first generation of 4.6mm I.D. monolithic columns.

PubMed

Gritti, Fabrice; Guiochon, Georges

2011-08-05

The corrected heights equivalent to a theoretical plate (HETP) of three 4.6mm I.D. monolithic Onyx-C(18) columns (Onyx, Phenomenex, Torrance, CA) of different lengths (2.5, 5, and 10 cm) are reported for retained (toluene, naphthalene) and non-retained (uracil, caffeine) small molecules. The moments of the peak profiles were measured according to the accurate numerical integration method. Correction for the extra-column contributions was systematically applied. The peak parking method was used in order to measure the bulk diffusion coefficients of the sample molecules, their longitudinal diffusion terms, and the eddy diffusion term of the three monolithic columns. The experimental results demonstrate that the maximum efficiency was 60,000 plates/m for retained compounds. The column length has a large impact on the plate height of non-retained species. These observations were unambiguously explained by a large trans-column eddy diffusion term in the van Deemter HETP equation. This large trans-rod eddy diffusion term is due to the combination of a large trans-rod velocity bias (≃3%), a small radial dispersion coefficient in silica monolithic columns, and a poorly designed distribution and collection of the sample streamlets at the inlet and outlet of the monolithic rod. Improving the performance of large I.D. monolithic columns will require (1) a detailed knowledge of the actual flow distribution across and along these monolithic rod and (2) the design of appropriate inlet and outlet distributors designed to minimize the nefarious impact of the radial flow heterogeneity on band broadening. Copyright © 2011 Elsevier B.V. All rights reserved.

Quantitative comparison between radial and cylindrically diffusing fibers for photothermal treatment of varicose vein disease (Conference Presentation)

NASA Astrophysics Data System (ADS)

Truong Van, Gia; Kang, Hyun Wook

2017-02-01

For last two decades, endovenous laser therapy (EVLT) is one of the most widely accepted surgical options for treating incompetent great and small saphenous veins. However, due to excessive heating during EVLT, the major complications include pain and burning that often increase the risk of dermatitis disease. The aim of the current study was to quantitatively compare commercially-available radial fibers with newly-developed diffusing applicators for 1470 nm-EVLA in terms of temperature elevation and vein deformation. Rabbit veins were used as an ex vivo model for EVLA. A 5-W 1470 nm laser system in conjunction with the radial and diffusing fibers was employed to thermally coagulate the venous tissue. A goniometric measurement validated uniform and isotropic distribution of laser light in polar and longitudinal directions (i.e., normalized intensity = 0.84±0.08). The diffusing applicator induced a 20 % lower maximum temperature than the radial fiber did (maximum temperature = 79.2 °C for radial vs. 63.3 °C for diffusing). Due to higher irradiance, the radial fiber was associated with a transient temperature change of 5.9 °C/s, which was 1.5-fold faster than the diffusing applicator (i.e., 2.4 °C/s). However, the degree of cross-sectional area reduction in the veins was almost comparable for both the fibers (i.e., 53% for radial vs. 48% for diffusing). Due to longer irradiation length, the diffusing applicator demonstrated wider treatment coverage and less fiber speed-dependent. On account of easy pullback technique and uniform thermal effect, the proposed cylindrically diffusing applicator can be a feasible optical device to effectively treat varicose veins. Further in vivo studies will be performed to identify the complete removal of the vein disease and healing response of the venous tissue.

In-situ observation of impurity diffusion boundary layer in silicon Czochralski growth

NASA Astrophysics Data System (ADS)

Kakimoto, Koichi; Eguchi, Minoru; Watanabe, Hisao; Hibiya, Taketoshi

1990-01-01

In-situ observation of the impurity diffusion boundary layer during single crystal growth of indium-doped silicon was carried out by X-ray radiography. The difference in the transmitted X-ray image compared with molten silicon just beneath the crystal-melt interface was attributed to the concentration of indium impurities having a larger absorption coefficient. The intensity profile of the transmitted X-ray can be reproduced by a transmittance calculation that considers the meniscus shape and impurity distribution. The impurity distribution profile near the crystal-melt interface was estimated using the Burton-Prim-Slichter (BPS) equation. The observed impurity diffusion boundary layer thickness was about 0.5 mm. It was found that the boundary layer thickness was not constant in the radial direction, which cannot be explained by the BPS theory, since it is based on a one-dimensional calculation.

Modeling radiation belt electron dynamics during GEM challenge intervals with the DREAM3D diffusion model

NASA Astrophysics Data System (ADS)

Tu, Weichao; Cunningham, G. S.; Chen, Y.; Henderson, M. G.; Camporeale, E.; Reeves, G. D.

2013-10-01

a response to the Geospace Environment Modeling (GEM) "Global Radiation Belt Modeling Challenge," a 3D diffusion model is used to simulate the radiation belt electron dynamics during two intervals of the Combined Release and Radiation Effects Satellite (CRRES) mission, 15 August to 15 October 1990 and 1 February to 31 July 1991. The 3D diffusion model, developed as part of the Dynamic Radiation Environment Assimilation Model (DREAM) project, includes radial, pitch angle, and momentum diffusion and mixed pitch angle-momentum diffusion, which are driven by dynamic wave databases from the statistical CRRES wave data, including plasmaspheric hiss, lower-band, and upper-band chorus. By comparing the DREAM3D model outputs to the CRRES electron phase space density (PSD) data, we find that, with a data-driven boundary condition at Lmax = 5.5, the electron enhancements can generally be explained by radial diffusion, though additional local heating from chorus waves is required. Because the PSD reductions are included in the boundary condition at Lmax = 5.5, our model captures the fast electron dropouts over a large L range, producing better model performance compared to previous published results. Plasmaspheric hiss produces electron losses inside the plasmasphere, but the model still sometimes overestimates the PSD there. Test simulations using reduced radial diffusion coefficients or increased pitch angle diffusion coefficients inside the plasmasphere suggest that better wave models and more realistic radial diffusion coefficients, both inside and outside the plasmasphere, are needed to improve the model performance. Statistically, the results show that, with the data-driven outer boundary condition, including radial diffusion and plasmaspheric hiss is sufficient to model the electrons during geomagnetically quiet times, but to best capture the radiation belt variations during active times, pitch angle and momentum diffusion from chorus waves are required.

Axial and radial diffusivity in preterm infants who have diffuse white matter changes on magnetic resonance imaging at term-equivalent age.

PubMed

Counsell, Serena J; Shen, Yuji; Boardman, James P; Larkman, David J; Kapellou, Olga; Ward, Philip; Allsop, Joanna M; Cowan, Frances M; Hajnal, Joseph V; Edwards, A David; Rutherford, Mary A

2006-02-01

Diffuse excessive high signal intensity (DEHSI) is observed in the majority of preterm infants at term-equivalent age on conventional MRI, and diffusion-weighted imaging has shown that apparent diffusion coefficient values are elevated in the white matter (WM) in DEHSI. Our aim was to obtain diffusion tensor imaging on preterm infants at term-equivalent age and term control infants to test the hypothesis that radial diffusivity was significantly different in the WM in preterm infants with DEHSI compared with both preterm infants with normal-appearing WM on conventional MRI and term control infants. Diffusion tensor imaging was obtained on 38 preterm infants at term-equivalent age and 8 term control infants. Values for axial (lambda1) and radial [(lambda2 + lambda3)/2] diffusivity were calculated in regions of interest positioned in the central WM at the level of the centrum semiovale, frontal WM, posterior periventricular WM, occipital WM, anterior and posterior portions of the posterior limb of the internal capsule, and the genu and splenium of the corpus callosum. Radial diffusivity was elevated significantly in the posterior portion of the posterior limb of the internal capsule and the splenium of the corpus callosum, and both axial and radial diffusivity were elevated significantly in the WM at the level of the centrum semiovale, the frontal WM, the periventricular WM, and the occipital WM in preterm infants with DEHSI compared with preterm infants with normal-appearing WM and term control infants. There was no significant difference between term control infants and preterm infants with normal-appearing WM in any region studied. These findings suggest that DEHSI represents an oligodendrocyte and/or axonal abnormality that is widespread throughout the cerebral WM.

Multi-specie isothermal flow calculations of widely-spaced co-axial jets in a confined sudden expansion, with the central jet dominant

NASA Astrophysics Data System (ADS)

Sturgess, G. J.; Syed, S. A.

1982-06-01

A numerical simulation is made of the flow in the Wright Aeronautical Propulsion Laboratory diffusion flame research combustor operating with a strong central jet of carbon dioxide in a weak and removed co-axial jet of air. The simulation is based on a finite difference solution of the time-average, steady-state, elliptic form of the Reynolds equations. Closure for these equations is provided by a two-equation turbulence model. Comparisons between measurements and predictions are made for centerline axial velocities and radial profiles of CO2 concentration. Earlier findings for a single specie, constant density, single jet flow that a large expansion ratio confined jet behaves initially as if it were unconfined, are confirmed for the multiple-specie, variable density, multiple-jet system. The lack of universality in the turbulence model constants and the turbulent Schmidt/Prandtl number is discussed.

Design of an efficient space constrained diffuser for supercritical CO2 turbines

NASA Astrophysics Data System (ADS)

Keep, Joshua A.; Head, Adam J.; Jahn, Ingo H.

2017-03-01

Radial inflow turbines are an arguably relevant architecture for energy extraction from ORC and supercritical CO 2 power cycles. At small scale, design constraints can prescribe high exit velocities for such turbines, which lead to high kinetic energy in the turbine exhaust stream. The inclusion of a suitable diffuser in a radial turbine system allows some exhaust kinetic energy to be recovered as static pressure, thereby ensuring efficient operation of the overall turbine system. In supercritical CO 2 Brayton cycles, the high turbine inlet pressure can lead to a sealing challenge if the rotor is supported from the rotor rear side, due to the seal operating at rotor inlet pressure. An alternative to this is a cantilevered layout with the rotor exit facing the bearing system. While such a layout is attractive for the sealing system, it limits the axial space claim of any diffuser. Previous studies into conical diffuser geometries for supercritical CO 2 have shown that in order to achieve optimal static pressure recovery, longer geometries of a shallower cone angle are necessitated when compared to air. A diffuser with a combined annular-radial arrangement is investigated as a means to package the aforementioned geometric characteristics into a limited space claim for a 100kW radial inflow turbine. Simulation results show that a diffuser of this design can attain static pressure rise coefficients greater than 0.88. This confirms that annular-radial diffusers are a viable design solution for supercritical CO2 radial inflow turbines, thus enabling an alternative cantilevered rotor layout.

On the progressive enrichment of the oxygen isotopic composition of water along a leaf.

PubMed

Farquhar, G. D.; Gan, K. S.

2003-06-01

A model has been derived for the enrichment of heavy isotopes of water in leaves, including progressive enrichment along the leaf. In the model, lighter water is preferentially transpired leaving heavier water to diffuse back into the xylem and be carried further along the leaf. For this pattern to be pronounced, the ratio of advection to diffusion (Péclet number) has to be large in the longitudinal direction, and small in the radial direction. The progressive enrichment along the xylem is less than that occurring at the sites of evaporation in the mesophyll, depending on the isolation afforded by the radial Péclet number. There is an upper bound on enrichment, and effects of ground tissue associated with major veins are included. When transpiration rate is spatially nonuniform, averaging of enrichment occurs more naturally with transpiration weighting than with area-based weighting. This gives zero average enrichment of transpired water, the modified Craig-Gordon equation for average enrichment at the sites of evaporation and the Farquhar and Lloyd (In Stable Isotopes and Plant Carbon-Water Relations, pp. 47-70. Academic Press, New York, USA, 1993) prediction for mesophyll water. Earlier results on the isotopic composition of evolved oxygen and of retro-diffused carbon dioxide are preserved if these processes vary in parallel with transpiration rate. Parallel variation should be indicated approximately by uniform carbon isotope discrimination across the leaf.

Response of radiation belt simulations to different radial diffusion coefficients

NASA Astrophysics Data System (ADS)

Drozdov, A.; Shprits, Y.; Subbotin, D.; Kellerman, A. C.

2013-12-01

Resonant interactions between Ultra Low Frequency (ULF) waves and relativistic electrons may violate the third adiabatic invariant of motion, which produces radial diffusion in the electron radiation belts. This process plays an important role in the formation and structure of the outer electron radiation belt and is important for electron acceleration and losses in that region. Two parameterizations of the resonant wave-particle interaction of electrons with ULF waves in the magnetosphere by Brautigam and Albert [2000] and Ozeke et al. [2012] are evaluated using the Versatile Electron Radiation Belt (VERB) diffusion code to estimate their relative effect on the radiation belt simulation. The period of investigation includes quiet time and storm time geomagnetic activity and is compared to data based on satellite observations. Our calculations take into account wave-particle interactions represented by radial diffusion transport, local acceleration, losses due to pitch-angle diffusion, and mixed diffusion. We show that the results of the 3D diffusion simulations depend on the assumed parametrization of waves. The differences between the simulations and potential missing physical mechanisms are discussed. References Brautigam, D. H., and J. M. Albert (2000), Radial diffusion analysis of outer radiation belt electrons during the October 9, 1990, magnetic storm, J. Geophys. Res., 105(A1), 291-309, doi:10.1029/1999JA900344 Ozeke, L. G., I. R. Mann, K. R. Murphy, I. J. Rae, D. K. Milling, S. R. Elkington, A. A. Chan, and H. J. Singer (2012), ULF wave derived radiation belt radial diffusion coefficients, J. Geophys. Res., 117, A04222, doi:10.1029/2011JA017463.

The Dirac equation in Schwarzschild black hole coupled to a stationary electromagnetic field

NASA Astrophysics Data System (ADS)

Al-Badawi, A.; Owaidat, M. Q.

2017-08-01

We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzschild solution to an external, stationary electromagnetic field. The set of equations representing the uncharged Dirac particle in the Newman-Penrose formalism is decoupled into a radial and an angular parts. We obtain exact analytical solutions of the angular equations. We manage to obtain the radial wave equations with effective potentials. Finally, we study the potentials by plotting them as a function of radial distance and examine the effect of the twisting parameter and the frequencies on the potentials.

In vivo quantification of demyelination and recovery using compartment-specific diffusion MRI metrics validated by electron microscopy.

PubMed

Jelescu, Ileana O; Zurek, Magdalena; Winters, Kerryanne V; Veraart, Jelle; Rajaratnam, Anjali; Kim, Nathanael S; Babb, James S; Shepherd, Timothy M; Novikov, Dmitry S; Kim, Sungheon G; Fieremans, Els

2016-05-15

There is a need for accurate quantitative non-invasive biomarkers to monitor myelin pathology in vivo and distinguish myelin changes from other pathological features including inflammation and axonal loss. Conventional MRI metrics such as T2, magnetization transfer ratio and radial diffusivity have proven sensitivity but not specificity. In highly coherent white matter bundles, compartment-specific white matter tract integrity (WMTI) metrics can be directly derived from the diffusion and kurtosis tensors: axonal water fraction, intra-axonal diffusivity, and extra-axonal radial and axial diffusivities. We evaluate the potential of WMTI to quantify demyelination by monitoring the effects of both acute (6weeks) and chronic (12weeks) cuprizone intoxication and subsequent recovery in the mouse corpus callosum, and compare its performance with that of conventional metrics (T2, magnetization transfer, and DTI parameters). The changes observed in vivo correlated with those obtained from quantitative electron microscopy image analysis. A 6-week intoxication produced a significant decrease in axonal water fraction (p<0.001), with only mild changes in extra-axonal radial diffusivity, consistent with patchy demyelination, while a 12-week intoxication caused a more marked decrease in extra-axonal radial diffusivity (p=0.0135), consistent with more severe demyelination and clearance of the extra-axonal space. Results thus revealed increased specificity of the axonal water fraction and extra-axonal radial diffusivity parameters to different degrees and patterns of demyelination. The specificities of these parameters were corroborated by their respective correlations with microstructural features: the axonal water fraction correlated significantly with the electron microscopy derived total axonal water fraction (ρ=0.66; p=0.0014) but not with the g-ratio, while the extra-axonal radial diffusivity correlated with the g-ratio (ρ=0.48; p=0.0342) but not with the electron microscopy derived axonal water fraction. These parameters represent promising candidates as clinically feasible biomarkers of demyelination and remyelination in the white matter. Copyright © 2016 Elsevier Inc. All rights reserved.

Surface Based Analysis of Diffusion Orientation for Identifying Architectonic Domains in the In Vivo Human Cortex

PubMed Central

McNab, Jennifer A.; Polimeni, Jonathan R.; Wang, Ruopeng; Augustinack, Jean C.; Fujimoto, Kyoko; Player, Allison; Janssens, Thomas; Farivar, Reza; Folkerth, Rebecca D.; Vanduffel, Wim; Wald, Lawrence L.

2012-01-01

Diffusion tensor MRI is sensitive to the coherent structure of brain tissue and is commonly used to study large-scale white matter structure. Diffusion in grey matter is more isotropic, however, several groups have observed coherent patterns of diffusion anisotropy within the cerebral cortical grey matter. We extend the study of cortical diffusion anisotropy by relating it to the local coordinate system of the folded cerebral cortex. We use 1mm and sub-millimeter isotropic resolution diffusion imaging to perform a laminar analysis of the principal diffusion orientation, fractional anisotropy, mean diffusivity and partial volume effects. Data from 6 in vivo human subjects, a fixed human brain specimen and an anesthetized macaque were examined. Large regions of cortex show a radial diffusion orientation. In vivo human and macaque data displayed a sharp transition from radial to tangential diffusion orientation at the border between primary motor and somatosensory cortex, and some evidence of tangential diffusion in secondary somatosensory cortex and primary auditory cortex. Ex vivo diffusion imaging in a human tissue sample showed some tangential diffusion orientation in S1 but mostly radial diffusion orientations in both M1 and S1. PMID:23247190

Computation of flow in radial- and mixed-flow cascades by an inviscid-viscous interaction method

NASA Technical Reports Server (NTRS)

Serovy, G. K.; Hansen, E. C.

1980-01-01

The use of inviscid-viscous interaction methods for the case of radial or mixed-flow cascade diffusers is discussed. A literature review of investigations considering cascade flow-field prediction by inviscid-viscous iterative computation is given. Cascade aerodynamics in the third blade row of a multiple-row radial cascade diffuser are specifically investigated.

Recent radial turbine research at the NASA Lewis Research Center

NASA Technical Reports Server (NTRS)

Rohlik, H. E.; Kofskey, M. G.

1971-01-01

The high efficiencies of small radial turbines led to their application in space power systems and numerous APU and shaft power engines. Experimental and analytical work associated with these systems included examination of blade-shroud clearance, blade loading, and exit diffuser design. Results indicate high efficiency over a wide range of specific speed and also insensitivity to clearance and blade loading in the radial part of the rotor. The exit diffuser investigation indicated that a conventional conical outer wall may not provide the velocity variation consistent with minimum overall diffuser loss.

Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-03-01

As is said in [27], the tumor-growth model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models [27]. Simulations of this practical model using numerical methods can be applied for evaluating it. The present paper investigates the solution of the tumor growth model with meshless techniques. Meshless methods are applied based on the collocation technique which employ multiquadrics (MQ) radial basis function (RBFs) and generalized moving least squares (GMLS) procedures. The main advantages of these choices come back to the natural behavior of meshless approaches. As well as, a method based on meshless approach can be applied easily for finding the solution of partial differential equations in high-dimension using any distributions of points on regular and irregular domains. The present paper involves a time-dependent system of partial differential equations that describes four-species tumor growth model. To overcome the time variable, two procedures will be used. One of them is a semi-implicit finite difference method based on Crank-Nicolson scheme and another one is based on explicit Runge-Kutta time integration. The first case gives a linear system of algebraic equations which will be solved at each time-step. The second case will be efficient but conditionally stable. The obtained numerical results are reported to confirm the ability of these techniques for solving the two and three-dimensional tumor-growth equations.

Hydrodynamics of steady state phloem transport with radial leakage of solute

PubMed Central

Cabrita, Paulo; Thorpe, Michael; Huber, Gregor

2013-01-01

Long-distance phloem transport occurs under a pressure gradient generated by the osmotic exchange of water associated with solute exchange in source and sink regions. But these exchanges also occur along the pathway, and yet their physiological role has almost been ignored in mathematical models of phloem transport. Here we present a steady state model for transport phloem which allows solute leakage, based on the Navier-Stokes and convection-diffusion equations which describe fluid motion rigorously. Sieve tube membrane permeability Ps for passive solute exchange (and correspondingly, membrane reflection coefficient) influenced model results strongly, and had to lie in the bottom range of the values reported for plant cells for the results to be realistic. This smaller permeability reflects the efficient specialization of sieve tube elements, minimizing any diffusive solute loss favored by the large concentration difference across the sieve tube membrane. We also found there can be a specific reflection coefficient for which pressure profiles and sap velocities can both be similar to those predicted by the Hagen-Poiseuille equation for a completely impermeable tube. PMID:24409189

Effects of radial diffuser hydraulic design on a double-suction centrifugal pump

NASA Astrophysics Data System (ADS)

Hou, H. C.; Zhang, Y. X.; Xu, C.; Zhang, J. Y.; Li, Z. L.

2016-05-01

In order to study effects of radial diffuser on hydraulic performance of crude oil pump, the steady CFD numerical method is applied and one large double-suction oil pump running in long-distance pipeline is considered. The research focuses on analysing the influence of its diffuser vane profile on hydraulic performance of oil pump. The four different types of cylindrical vane have been designed by in-house codes mainly including double arcs (DA), triple arcs (TA), equiangular spiral line (ES) and linear variable angle spiral line (LVS). During design process diffuser vane angles at inlet and outlet are tentatively given within a certain range and then the wrapping angle of the four types of diffuser vanes can be calculated automatically. Under the given inlet and outlet angles, the linear variable angle spiral line profile has the biggest wrapping angle and profile length which is good to delay channel diffusion but bring more friction hydraulic loss. Finally the vane camber line is thickened at the certain uniform thickness distribution and the 3D diffuser models are generated. The whole flow passage of oil pump with different types of diffusers under various flow rate conditions are numerically simulated based on RNG k-ɛ turbulent model and SIMPLEC algorithm. The numerical results show that different types of diffusers can bring about great difference on the hydraulic performance of oil pump, of which the ES profile diffuser with its proper setting angle shows the best hydraulic performance and its inner flow field is improved obviously. Compared with the head data from model sample, all designed diffusers can make a certain improvement on head characteristic. At the large flow rate conditions the hydraulic efficiency increases obviously and the best efficiency point shift to the large flow rate range. The ES profile diffuser embodies the better advantages on pump performance which can be explained theoretically that the diffuser actually acts as a diffusion device and is good to transform the dynamic energy to pressure energy. Then through the hydraulic loss analysis of each pump component for all diffusers, it shows that the impeller takes up the biggest part of the whole loss about 8.19% averagely, the radial diffuser about 3.70% and the volute about 1.65%. The hydraulic loss of impeller is dominant at the large flow rate while the radial diffuser is at the small flow rate. Among all diffusers, the ES profile diffuser generates the least loss and combined to the distribution of velocity vector and turbulent kinetic energy for two kinds of diffusers it also shows that ES profile is fit to apply in radial diffuser. This research can offer a significant reference for the radial diffuser hydraulic design of such centrifugal pumps.

Simulation of energy-dependent electron diffusion processes in the Earth's outer radiation belt

DOE PAGES

Ma, Q.; Li, W.; Thorne, R. M.; ...

2016-04-28

The radial and local diffusion processes induced by various plasma waves govern the highly energetic electron dynamics in the Earth's radiation belts, causing distinct characteristics in electron distributions at various energies. In this study, we present our simulation results of the energetic electron evolution during a geomagnetic storm using the University of California, Los Angeles 3-D diffusion code. Following the plasma sheet electron injections, the electrons at different energy bands detected by the Magnetic Electron Ion Spectrometer (MagEIS) and Relativistic Electron Proton Telescope (REPT) instruments on board the Van Allen Probes exhibit a rapid enhancement followed by a slow diffusivemore » movement in differential energy fluxes, and the radial extent to which electrons can penetrate into depends on energy with closer penetration toward the Earth at lower energies than higher energies. We incorporate radial diffusion, local acceleration, and loss processes due to whistler mode wave observations to perform a 3-D diffusion simulation. Here, our simulation results demonstrate that chorus waves cause electron flux increase by more than 1 order of magnitude during the first 18 h, and the subsequent radial extents of the energetic electrons during the storm recovery phase are determined by the coupled radial diffusion and the pitch angle scattering by EMIC waves and plasmaspheric hiss. The radial diffusion caused by ULF waves and local plasma wave scattering are energy dependent, which lead to the observed electron flux variations with energy dependences. Lastly, this study suggests that plasma wave distributions in the inner magnetosphere are crucial for the energy-dependent intrusions of several hundred keV to several MeV electrons.« less

Study of toroidal flow generation by ion cyclotron range of frequency minority heating in the Alcator C-Mod plasma

NASA Astrophysics Data System (ADS)

Murakami, S.; Itoh, K.; Zheng, L. J.; Van Dam, J. W.; Bonoli, P.; Rice, J. E.; Fiore, C. L.; Gao, C.; Fukuyama, A.

2016-01-01

The averaged toroidal flow of energetic minority ions during ICRF (ion cyclotron range of frequencies) heating is investigated in the Alcator C-Mod plasma by applying the GNET code, which can solve the drift kinetic equation with complicated orbits of accelerated energetic particles. It is found that a co-directional toroidal flow of the minority ions is generated in the region outside of the resonance location, and that the toroidal velocity reaches more than 40% of the central ion thermal velocity (Vtor ˜ 300 km/s with PICRF ˜ 2 MW). When we shift the resonance location to the outside of |r /a |˜0.5 , the toroidal flow immediately inside of the resonance location is reduced to 0 or changes to the opposite direction, and the toroidal velocity shear is enhanced at r/a ˜ 0.5. A radial diffusion equation for toroidal flow is solved by assuming a torque profile for the minority ion mean flow, and good agreements with experimental radial toroidal flow profiles are obtained. This suggests that the ICRF driven minority ion flow is related to the experimentally observed toroidal rotation during ICRF heating in the Alcator C-Mod plasma.

The stability of the contact interface of cylindrical and spherical shock tubes

NASA Astrophysics Data System (ADS)

Crittenden, Paul E.; Balachandar, S.

2018-06-01

The stability of the contact interface for radial shock tubes is investigated as a model for explosive dispersal. The advection upstream splitting method with velocity and pressure diffusion (AUSM+-up) is used to solve for the radial base flow. To investigate the stability of the resulting contact interface, perturbed governing equations are derived assuming harmonic modes in the transverse directions. The perturbed harmonic flow is solved by assuming an initial disturbance and using a perturbed version of AUSM+-up derived in this paper. The intensity of the perturbation near the contact interface is computed and compared to theoretical results obtained by others. Despite the simplifying assumptions of the theoretical analysis, very good agreement is observed. Not only can the magnitude of the instability be predicted during the initial expansion, but also remarkably the agreement between the numerical and theoretical results can be maintained through the collision between the secondary shock and the contact interface. Since the theoretical results only depend upon the time evolution of the base flow, the stability of various modes could be quickly investigated without explicitly solving a system of partial differential equations for the perturbed flow.

Parallel heat transport in integrable and chaotic magnetic fields

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

Del-Castillo-Negrete, Diego B; Chacon, Luis

2012-01-01

The study of transport in magnetized plasmas is a problem of fundamental interest in controlled fusion, space plasmas, and astrophysics research. Three issues make this problem particularly chal- lenging: (i) The extreme anisotropy between the parallel (i.e., along the magnetic field), , and the perpendicular, , conductivities ( / may exceed 1010 in fusion plasmas); (ii) Magnetic field lines chaos which in general complicates (and may preclude) the construction of magnetic field line coordinates; and (iii) Nonlocal parallel transport in the limit of small collisionality. Motivated by these issues, we present a Lagrangian Green s function method to solve themore » local and non-local parallel transport equation applicable to integrable and chaotic magnetic fields in arbitrary geom- etry. The method avoids by construction the numerical pollution issues of grid-based algorithms. The potential of the approach is demonstrated with nontrivial applications to integrable (magnetic island chain), weakly chaotic (devil s staircase), and fully chaotic magnetic field configurations. For the latter, numerical solutions of the parallel heat transport equation show that the effective radial transport, with local and non-local closures, is non-diffusive, thus casting doubts on the appropriateness of the applicability of quasilinear diffusion descriptions. General conditions for the existence of non-diffusive, multivalued flux-gradient relations in the temperature evolution are derived.« less

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

NASA Astrophysics Data System (ADS)

Thylwe, Karl-Erik; McCabe, Patrick

2012-04-01

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

Pc 5 Spectral Density at ULTIMA stataions and its Radial Diffusion Coefficients for REE

NASA Astrophysics Data System (ADS)

Fujimoto, A.; Tokunaga, T.; Abe, S.; Uozumi, T.; Yoshikawa, A.; Mann, I. R.; Chi, P. J.; Engebretson, M. J.; Yumoto, K.

2009-12-01

Pc 5 magnetic pulsations with frequencies between 1.67 and 6.67 mHz, are believed to contribute to the Relativistic Electron Enhancement (REE) in the outer radiation belt during magnetic storms. Ground-based observations suggested that high-speed solar wind and large-amplitude Pc 5 waves with a long duration during the storm recovery phase are closely associated with the production of relativistic electrons [Baker et al., 1998; Rostoker et al., 1998; Mathie and Mann, 2000; O’Brien et al., 2001, 2003]. On the other hand, many relativistic electron acceleration mechanisms have been proposed theoretically. They are separated roughly into two themes: in situ acceleration at L lower than 6.6 by wave particle interactions (as internal source acceleration mechanisms) [Liu et al., 1999; Summers et al., 1999; Summers and Ma, 2000] and acceleration by radial diffusion to transport and accelerate a source population of electrons from the outer to the inner magnetosphere (as external source acceleration mechanisms) [Elkington et al., 1999, 2003; Hudson et al., 2000; Kim et al., 2001]. One possible external source acceleration mechanism is the resonant interaction with ULF toroidal and poloidal waves. In order to verify which of the two mechanisms is more effective for the REE, we have to examine the time variation of electron phase space density. Electron phase space density is not directly measured, but we can estimate radial diffusion coefficients using observational electric and magnetic data. The goal of this paper is to get more reliable radial diffusion coefficient from ground-based observational magnetic field and to show reasonability of it for radial diffusion model. We use the global magnetometer data obtained from ULTIMA (Ultra Large Terrestrial International Magnetic Array, see http://www.serc.kyushu-u.ac.jp/ultima/ultima.html) stations, to precisely define the radial diffusion timescales. The ULTIMA includes McMAC, CARISAM, 210MM and MAGDAS/CPMN magnetometer arrays. The radial diffusion coefficient can be given from the magnetic field power spectral density as a function of L, frequency (f) and m-number (m) in the Pc 5 frequency range during the REE related magnetic storms [see Brautigam et al., 2005]. We can fit Pc 5 power spectral density (L, f, m) using the ULTIMA data. The m-number of global Pc 5 pulsation on the ground is found to be almost less than 5. This is consistent with m-number required in the radial diffusion theory by Elkington et al. [1999, 2003]. We will compare the observationally estimated diffusion coefficient with theoretical diffusion coefficient [e.g. Elkington et al., 2006], and discuss adequacy of our diffusion coefficient.

Comparison of LFM-test particle simulations and radial diffusion models of radiation belt electron injection into the slot region

NASA Astrophysics Data System (ADS)

Chu, F.; Hudson, M.; Kress, B.

2008-12-01

The physics-based Lyon-Fedder-Mobarry (LFM) code simulates Earth's magnetospheric topology and dynamics by solving the equations of ideal MHD using input solar wind parameters at the upstream boundary. Comparison with electron phase space density evolution during storms using a radial diffusion code, as well as spacecraft measurements where available, will tell us when diffusion is insufficiently accurate for radiation belt simulation, for example, during CME-shock injection events like March 24, 1991, which occurred on MeV electron drift time scales of minutes (Li et al., 1993). The 2004 July and 2004 November storms, comparable in depth of penetration into the slot region to the Halloween 2003 storm, have been modeled with both approaches. The November 8, 2004 storm was preceded by a Storm Sudden Commencement produced by a CME-shock followed by minimum Dst = -373 nT, while the July 23 to July 28 storm interval had milder consecutive drops in Dst, corresponding to multiple CME shocks and southward IMF Bz turnings. We have run the November and July storms with LFM using ACE data as upstream input, running the July storm with lower temporal resolution over a longer time interval. The November storm was different because the SCC shock was unusually intense, therefore the possibility of drift time scale acceleration by the associated magnetosonic impulse produced by the shock exists, as in March 1991 and also Halloween 2003 events (Kress et al., 2007). It can then take a short time (minutes) for electrons to be transported to low L shell while conserving their first invariant, resulting in a peak in energy and phase space density in the slot region. Radial diffusion suffices for some storm periods like the July 2004 sequence of three storms, while the guiding center test particle simulation in MHD fields is necessary to describe prompt injections which occur faster than diffusive time scales, for which November 2004 is a likely candidate. Earlier examples have been studied, including the Kress et al., 2007 study of the Halloween 2003 storm and Li et al., 1993 study of the March 24, 1991 injection event with MHD simulation carried out by Elkington et al. (2002) for this event. Radial diffusion remains the best approach for extended relatively quiet periods like the two month interval following the March 1991 prompt injection. Strong shocks will inject particles into lower L shell within a few minutes violating the third adiabatic invariant, so the diffusion mechanism cannot be adopted for sudden commencements, when Dst increases then decreases drastically; however particle tracing in time-dependent MHD fields will give an accurate estimation, so radial diffusion and particle tracing in MHD fields complement each other in radiation belt studies. Elkington, S. R., M.K. Hudson, M.J. Wiltberger, J.G. Lyon (2002) JASTP, 64, p. 607-615; Kress B. T., M. K. Hudson, M. D. Looper, J. Albert, J. G. Lyon, C. C. Goodrich (2007), J. Geophys. Res., 112, A09215, doi:10.1029/2006JA012218; Li, X., I. Roth, M. Temerin, J. R. Wygant, M. K. Hudson, and J. B. Blake (1993), Geophys. Res. Lett., 20, p. 2423-2426.

Recent radial turbine research at the NASA Lewis Research Center.

NASA Technical Reports Server (NTRS)

Rohlik, H. E.; Kofskey, M. G.

1972-01-01

The major results obtained in several recent experimental programs on small radial inflow turbines for space applications are presented and discussed. Specifically, experimental and analytical work associated with these systems that has included examination of blade-shroud clearance, blade loading, and exit diffuser design, is considered. Results indicate high efficiency over a wide range of specific speed, and also insensitivity to clearance and blade loading in the radial part of the rotor. The exit diffuser investigation indicated that a conventional conical outer wall may not provide the velocity variation consistent with minimum overall diffuser loss.

Improved diffusivity of NaOH solution in autohydrolyzed poplar sapwood chips for chemi-mechanical pulp production.

PubMed

Zhang, Honglei; Hou, Qingxi; Liu, Wei; Yue, Zhen; Jiang, Xiaoya; Ma, Xixi

2018-07-01

This work investigated the changes in the physical structure of autohydrolyzed poplar sapwood chips and the effect on the subsequent alkali liquor diffusion properties for chemi-mechanical pulping (CMP). An alkali impregnation process was conducted by using the autohydrolyzed poplar sapwood with different levels of autohydrolysis intensity. The results showed that the volume porosity, water constraint capacity, and saturated water absorption of the autohydrolyzed poplar sapwood chips increased. Also, the effective capillary cross-sectional area (ECCSA) in the radial direction and the diffusion coefficients of NaOH solution in both the radial and axial directions all increased. Autohydrolysis pretreatment enhanced the alkali liquor diffusion properties in poplar sapwood chips, and the diffusion coefficient was increased more greatly in the radial direction than that in the axial direction. Copyright © 2018 Elsevier Ltd. All rights reserved.

A note on the radial solutions for the supercritical Hénon equation

NASA Astrophysics Data System (ADS)

Barutello, Vivina; Secchi, Simone; Serra, Enrico

2008-05-01

We prove the existence of a positive radial solution for the Hénon equation with arbitrary growth. The solution is found by means of a shooting method and turns out to be an increasing function of the radial variable. Some numerical experiments suggest the existence of many positive oscillating solutions.

Drift-Alfven eigenmodes in inhomogeneous plasma

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

Vranjes, J.; Poedts, S.

2006-03-15

A set of three nonlinear equations describing drift-Alfven waves in a nonuniform magnetized plasma is derived and discussed both in linear and nonlinear limits. In the case of a cylindric radially bounded plasma with a Gaussian density distribution in the radial direction the linearized equations are solved exactly yielding general solutions for modes with quantized frequencies and with radially dependent amplitudes. The full set of nonlinear equations is also solved yielding particular solutions in the form of rotating radially limited structures. The results should be applicable to the description of electromagnetic perturbations in solar magnetic structures and in astrophysical column-likemore » objects including cosmic tornados.« less

Diffusion tensor imaging demonstrates brainstem and cerebellar abnormalities in congenital central hypoventilation syndrome.

PubMed

Kumar, Rajesh; Macey, Paul M; Woo, Mary A; Alger, Jeffry R; Harper, Ronald M

2008-09-01

Congenital central hypoventilation syndrome (CCHS) patients show reduced breathing drive during sleep, decreased hypoxic and hypercapnic ventilatory responses, and autonomic and affective deficits, suggesting both brainstem and forebrain injuries. Forebrain damage was previously described in CCHS, but methodological limitations precluded detection of brainstem injury, a concern because genetic mutations in CCHS target brainstem autonomic nuclei. To assess brainstem and cerebellar areas, we used diffusion tensor imaging-based measures, namely axial diffusivity, reflecting water diffusion parallel to fibers, and sensitive to axonal injury, and radial diffusivity, measuring diffusion perpendicular to fibers, and indicative of myelin injury. Diffusion tensor imaging was performed in 12 CCHS and 26 controls, and axial and radial diffusivity maps were compared between groups using analysis of covariance (covariates; age and gender). Increased axial diffusivity in CCHS appeared within the lateral medulla and clusters with injury extended from the dorsal midbrain through the periaqueductal gray, raphé, and superior cerebellar decussation, ventrally to the basal-pons. Cerebellar cortex and deep nuclei, and the superior and inferior cerebellar peduncles showed increased radial diffusivity. Midbrain, pontine, and lateral medullary structures, and the cerebellum and its fiber systems are injured in CCHS, likely contributing to the characteristics found in the syndrome.

Oscillating solutions for nonlinear Helmholtz equations

NASA Astrophysics Data System (ADS)

Mandel, Rainer; Montefusco, Eugenio; Pellacci, Benedetta

2017-12-01

Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behaviour at infinity is established. Some generalizations to nonautonomous radial equations as well as existence results for nonradial solutions are found. Our theorems prove the existence of standing waves solutions of nonlinear Klein-Gordon or Schrödinger equations with large frequencies.

Diffusive transport of several hundred keV electrons in the Earth's slot region

NASA Astrophysics Data System (ADS)

Ma, Q.; Li, W.; Thorne, R. M.; Bortnik, J.

2017-12-01

We investigate the gradual diffusion of energetic electrons from the inner edge of the outer radiation belt into the slot region. The Van Allen Probes observed slow inward diffusion and decay of 200-600 keV electrons following the intense geomagnetic storm that occurred on 17 March 2013. During the 10-day non-disturbed period following the storm, the peak of electron fluxes gradually moved from L 2.7 to L 2.4, and the flux levels decreased by a factor of 2-4 depending on the electron energy. We simulated the radial intrusion and decay of electrons using a 3-dimentional diffusion code, which reproduced the energy-dependent transport of electrons from 100 keV to 1 MeV in the slot region. At energies of 100-200 keV, the electrons experience fast transport across the slot region due to the dominance of radial diffusion; at energies of 200-600 keV, the electrons gradually diffuse and decay in the slot region due to the comparable radial diffusion rate and pitch angle scattering rate by plasmaspheric hiss; at energies of E > 700 keV, the electrons stopped diffusing near the inner edge of outer radiation belt due to the dominant pitch angle scattering loss. In addition to plasmaspheric hiss, magnetosonic waves and VLF waves can cause the loss of high pitch angle electrons, relaxing the sharp `top-hat' shaped pitch angle distributions created by plasmaspheric hiss. Our simulation indicates the importance of radial diffusion and pitch angle scattering in forming the diffusive intrusion of energetic electrons across the slot region.

Diffusive Transport of Several Hundred keV Electrons in the Earth's Slot Region

NASA Astrophysics Data System (ADS)

Ma, Q.; Li, W.; Thorne, R. M.; Bortnik, J.; Reeves, G. D.; Spence, H. E.; Turner, D. L.; Blake, J. B.; Fennell, J. F.; Claudepierre, S. G.; Kletzing, C. A.; Kurth, W. S.; Hospodarsky, G. B.; Baker, D. N.

2017-10-01

We investigate the gradual diffusion of energetic electrons from the inner edge of the outer radiation belt into the slot region. The Van Allen Probes observed slow inward diffusion and decay of 200-600 keV electrons following the intense geomagnetic storm that occurred on 17 March 2013. During the 10 day nondisturbed period following the storm, the peak of electron fluxes gradually moved from L 2.7 to L 2.4, and the flux levels decreased by a factor of 2-4 depending on the electron energy. We simulated the radial intrusion and decay of electrons using a three-dimensional diffusion code, which reproduced the energy-dependent transport of electrons from 100 keV to 1 MeV in the slot region. At energies of 100-200 keV, the electrons experience fast transport across the slot region due to the dominance of radial diffusion; at energies of 200-600 keV, the electrons gradually diffuse and decay in the slot region due to the comparable rate of radial diffusion and pitch angle scattering by plasmaspheric hiss; at energies of E > 700 keV, the electrons stopped diffusing near the inner edge of outer radiation belt due to the dominant pitch angle scattering loss. In addition to plasmaspheric hiss, magnetosonic waves and VLF transmitters can cause the loss of high pitch angle electrons, relaxing the sharp "top-hat" shaped pitch angle distributions created by plasmaspheric hiss. Our simulation indicates the importance of balance between radial diffusion and loss through pitch angle scattering in forming the diffusive intrusion of energetic electrons across the slot region.

Analytical Solutions of the Gravitational Field Equations in de Sitter and Anti-de Sitter Spacetimes

NASA Astrophysics Data System (ADS)

Da Rocha, R.; Capelas Oliveira, E.

2009-01-01

The generalized Laplace partial differential equation, describing gravitational fields, is investigated in de Sitter spacetime from several metric approaches—such as the Riemann, Beltrami, Börner-Dürr, and Prasad metrics—and analytical solutions of the derived Riccati radial differential equations are explicitly obtained. All angular differential equations trivially have solutions given by the spherical harmonics and all radial differential equations can be written as Riccati ordinary differential equations, which analytical solutions involve hypergeometric and Bessel functions. In particular, the radial differential equations predict the behavior of the gravitational field in de Sitter and anti-de Sitter spacetimes, and can shed new light on the investigations of quasinormal modes of perturbations of electromagnetic and gravitational fields in black hole neighborhood. The discussion concerning the geometry of de Sitter and anti-de Sitter spacetimes is not complete without mentioning how the wave equation behaves on such a background. It will prove convenient to begin with a discussion of the Laplace equation on hyperbolic space, partly since this is of interest in itself and also because the wave equation can be investigated by means of an analytic continuation from the hyperbolic space. We also solve the Laplace equation associated to the Prasad metric. After introducing the so called internal and external spaces—corresponding to the symmetry groups SO(3,2) and SO(4,1) respectively—we show that both radial differential equations can be led to Riccati ordinary differential equations, which solutions are given in terms of associated Legendre functions. For the Prasad metric with the radius of the universe independent of the parametrization, the internal and external metrics are shown to be of AdS-Schwarzschild-like type, and also the radial field equations arising are shown to be equivalent to Riccati equations whose solutions can be written in terms of generalized Laguerre polynomials and hypergeometric confluent functions.

Wave equations in conformal gravity

NASA Astrophysics Data System (ADS)

Du, Juan-Juan; Wang, Xue-Jing; He, You-Biao; Yang, Si-Jiang; Li, Zhong-Heng

2018-05-01

We study the wave equation governing massless fields of all spins (s = 0, 1 2, 1, 3 2 and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes.

Plasma Equilibrium in a Magnetic Field with Stochastic Regions

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

J.A. Krommes and Allan H. Reiman

The nature of plasma equilibrium in a magnetic field with stochastic regions is examined. It is shown that the magnetic differential equation that determines the equilibrium Pfirsch-Schluter currents can be cast in a form similar to various nonlinear equations for a turbulent plasma, allowing application of the mathematical methods of statistical turbulence theory. An analytically tractable model, previously studied in the context of resonance-broadening theory, is applied with particular attention paid to the periodicity constraints required in toroidal configurations. It is shown that even a very weak radial diffusion of the magnetic field lines can have a significant effect onmore » the equilibrium in the neighborhood of the rational surfaces, strongly modifying the near-resonant Pfirsch-Schluter currents. Implications for the numerical calculation of 3D equilibria are discussed« less

Galactic cosmic-ray mediation of a spherical solar wind flow. 1: The steady state cold gas hydrodynamical approximation

NASA Technical Reports Server (NTRS)

Le Roux, J. A.; Ptuskin, V. S.

1995-01-01

Realistic models of the outer heliosphere should consider that the interstellar cosmic-ray pressure becomes comparable to pressures in the solar wind at distances more than 100 AU from the Sun. The cosmic-ray pressure dynamically affects solar wind flow through deceleration. This effect, which occurs over a scale length of the order of the effective diffusion length at large radial distances, has important implications for cosmic-ray modulation and acceleration. As a first step toward solution of this nonlinear problem, a steady state numerical model was developed for a relatively cold spherical solar wind flow which encounters the confining isotropic pressure of the surrounding Galactic medium. This pressure is assumed to be dominated by energetic particles (Galactic cosmic rays). The system of equations, which are solved self-consistently, includes the relevant hydrodynamical equations for the solar wind flow and the spherical cosmic-ray transport equation. To avoid the closure parameter problem of the two-fluid model, the latter equation is solved for the energy-dependent cosmic-ray distribution function.

Determining Enzyme Activity by Radial Diffusion

ERIC Educational Resources Information Center

Davis, Bill D.

1977-01-01

Discusses advantages of radial diffusion assay in determining presence of enzyme and/or rough approximation of amount of enzyme activities. Procedures are included for the preparation of starch-agar plates, and the application and determination of enzyme. Techniques using plant materials (homogenates, tissues, ungerminated embryos, and seedlings)…

A coagulation-fragmentation model for the turbulent growth and destruction of preplanetesimals

NASA Astrophysics Data System (ADS)

Johansen, A.; Brauer, F.; Dullemond, C.; Klahr, H.; Henning, T.

2008-08-01

To treat the problem of growing protoplanetary disc solids across the meter barrier, we consider a very simplified two-component coagulation-fragmentation model that consists of macroscopic boulders and smaller dust grains, the latter being the result of catastrophic collisions between the boulders. Boulders in turn increase their radii by sweeping up the dust fragments. An analytical solution of the dynamical equations predicts that growth by coagulation-fragmentation can be efficient and allow agglomeration of 10-m-sized objects within the time-scale of the radial drift. These results are supported by computer simulations of the motion of boulders and fragments in 3-D time-dependent magnetorotational turbulence. However allowing the fragments to diffuse freely out of the sedimentary layer of boulders drastically reduces the density of both boulders and fragments in the mid-plane, and thus also the growth of the boulder radius. The reason is that the turbulent diffusion time-scale is so much shorter than the collisional time-scale that dust fragments leak out of the mid-plane layer before they can be swept up by the boulders there. Our conclusion that coagulation-fragmentation is not an efficient way to grow across the meter barrier in fully turbulent protoplanetary discs confirms recent results by Brauer, Dullemond, & Henning who solved the coagulation equation in a parameterised turbulence model with collisional fragmentation, cratering, radial drift, and a range of particle sizes. We find that a relatively small population of boulders in a sedimentary mid-plane layer can populate the entire vertical extent of the disc with small grains and that these grains are not first generation dust, but have been through several agglomeration-destruction cycles during the simulations.

Analysis and Comparison with DNS of a Stochastic Model for the Relative Motion of High-Stokes-Number Particles in Isotropic Turbulence

NASA Astrophysics Data System (ADS)

Dhariwal, Rohit; Rani, Sarma; Koch, Donald

2015-11-01

In an earlier work, Rani, Dhariwal, and Koch (JFM, Vol. 756, 2014) developed an analytical closure for the diffusion current in the PDF transport equation describing the relative motion of high-Stokes-number particle pairs in isotropic turbulence. In this study, an improved closure was developed for the diffusion coefficient, such that the motion of the particle-pair center of mass is taken into account. Using the earlier and the new analytical closures, Langevin simulations of pair relative motion were performed for four particle Stokes numbers, Stη = 10 , 20 , 40 , 80 and at two Taylor micro-scale Reynolds numbers Reλ = 76 , 131 . Detailed comparisons of the analytical model predictions with those of DNS were undertaken. It is seen that the pair relative motion statistics obtained from the improved theory show excellent agreement with the DNS statistics. The radial distribution functions (RDFs), and relative velocity PDFs obtained from the improved-closure-based Langevin simulations are found to be in very good agreement with those from DNS. It was found that the RDFs and relative velocity RMS increased with Reλ for all Stη . The collision kernel also increased strongly with Reλ , since it depended on the RDF and the radial relative velocities.

Propagation of Solar Energetic Particles in Three-dimensional Interplanetary Magnetic Fields: Radial Dependence of Peak Intensities

NASA Astrophysics Data System (ADS)

He, H.-Q.; Zhou, G.; Wan, W.

2017-06-01

A functional form {I}\\max (R)={{kR}}-α , where R is the radial distance of a spacecraft, was usually used to model the radial dependence of peak intensities {I}\\max (R) of solar energetic particles (SEPs). In this work, the five-dimensional Fokker-Planck transport equation incorporating perpendicular diffusion is numerically solved to investigate the radial dependence of SEP peak intensities. We consider two different scenarios for the distribution of a spacecraft fleet: (1) along the radial direction line and (2) along the Parker magnetic field line. We find that the index α in the above expression varies in a wide range, primarily depending on the properties (e.g., location and coverage) of SEP sources and on the longitudinal and latitudinal separations between the sources and the magnetic foot points of the observers. Particularly, whether the magnetic foot point of the observer is located inside or outside the SEP source is a crucial factor determining the values of index α. A two-phase phenomenon is found in the radial dependence of peak intensities. The “position” of the break point (transition point/critical point) is determined by the magnetic connection status of the observers. This finding suggests that a very careful examination of the magnetic connection between the SEP source and each spacecraft should be taken in the observational studies. We obtain a lower limit of {R}-1.7+/- 0.1 for empirically modeling the radial dependence of SEP peak intensities. Our findings in this work can be used to explain the majority of the previous multispacecraft survey results, and especially to reconcile the different or conflicting empirical values of the index α in the literature.

Space radiation test model study. Report for 20 May 1985-20 February 1986

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

Nightingale, R.W.; Chiu, Y.T.; Davidson, G.T.

1986-03-14

Dynamic models of the energetic populations in the outer radiation belts are being developed to better understand the extreme variations of particle flux in response to magnetospheric and solar activity. The study utilizes the SCATHA SC3 high-energy electron data, covering energies from 47 keV to 5 MeV with fine pitch-angle measurements (3 deg field of view) over the L-shell range of 5.3 to 8.7. Butter-fly distributions in the dusk sector signify particle losses due to L shell splitting of the particle-drift orbits and the subsequent scattering of the particles from the orbits by the magnetopause. To model the temporal variationsmore » and diffusion procsses of the particle populations, the data were organized into phase-space distributions, binned according to altitude (L shell), energy, pitch angle, and time. These distributions can then be mapped to the equator and plotted for fixed first and second adiabatic invariants of the inherent particle motion. A new and efficient method for calculating the third adiabatic invariant using a line integral of the relevant magnetic potential at the particle mirror points has been developed and is undergoing testing. This method will provide a useful means of displaying the radial diffusion signatures of the outer radiation belts during the more-active periods when the L shell parameter is not a good concept due to severe drift-shell splitting. The first phase of fitting the energetic-electron phase-space distributions with a combined radial and pitch-angle diffusion formulation is well underway. Bessel functions are being fit to the data in an eigenmode expansion method to determine the diffusion coefficients.« less

Analytical and experimental study of mean flow and turbulence characteristics inside the passages of an axial flow inducer

NASA Technical Reports Server (NTRS)

Gorton, C. A.; Lakshminarayana, B.

1980-01-01

The inviscid and viscid effects existing within the passages of a three bladed axial flow inducer operating at a flow coefficient of 0.065 are investigated. The blade static pressure and blade limiting streamline angle distributions were determined and the three components of mean velocity, turbulence intensities, and turbulence stresses were measured at locations inside the inducer blade passage utilizing a rotating three sensor hotwire probe. Applicable equations were derived for the hotwire data reduction analysis and solved numerically to obtain the appropriate flow parameters. The three dimensional inviscid flow in the inducer was predicted by numerically solving the exact equations of motion, and the three dimensional viscid flow was predicted by incorporating the dominant viscous terms into the exact equations. The analytical results are compared with the experimental measurements and design values where appropriate. Radial velocities are found to be of the same order as axial velocities within the inducer passage, confirming the highly three dimensional characteristic of inducer flow. Total relative velocity distribution indicate a substantial velocity deficiency near the tip at mid-passage which expands significantly as the flow proceeds toward the inducer trailing edge. High turbulence intensities and turbulence stresses are concentrated within this core region. Considerable wake diffusion occurs immediately downstream of the inducer trailing edge to decay this loss core. Evidence of boundary layer interactions, blade blockage effects, radially inward flows, annulus wall effects, and backflows are all found to exist within the long, narrow passages of the inducer.

Characterizing Intraorbital Optic Nerve Changes on Diffusion Tensor Imaging in Thyroid Eye Disease Before Dysthyroid Optic Neuropathy.

PubMed

Lee, Hwa; Lee, Young Hen; Suh, Sang-Il; Jeong, Eun-Kee; Baek, Sehyun; Seo, Hyung Suk

The aim of this study was to determine whether the optic nerve is affected by thyroid eye disease (TED) before the development of dysthyroid optic neuropathy with diffusion-tensor imaging (DTI). Twenty TED patients and 20 controls were included. The mean, axial, and radial diffusivities and fractional anisotropy (FA) value were measured at the optic nerves in DTI. Extraocular muscle diameters were measured on computed tomography. The diffusivities and FA of the optic nerves were compared between TED and controls and between active and inactive stages of TED. The correlations between these DTI parameters and the clinical features were determined. The mean, axial, and radial diffusivities were lower in TED compared with the controls (P < 0.05). In contrast, FA was higher in TED (P = 0.001). Radial diffusivity was lower in the active stage of TED than the inactive stage (P = 0.035). The FA was higher in the TED group than in the control group (P = 0.021) and was positively correlated with clinical activity score (r = 0.364, P = 0.021), modified NOSPECS score (r = 0.469, P = 0.002), and extraocular muscle thickness (r = 0.325, P = 0.041) in the TED group. Radial diffusivity was negatively correlated with modified NOSPECS score (r = -0.384, P = 0.014), and axial diffusivity was positively correlated with exophthalmos degree (r = 0.363, P = 0.025). The diffusivities and FA reflected changes in the optic nerve before dysthyroid optic neuropathy in TED. The FA, in particular, reflected TED activity and severity.

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.

Behavior of a spin-1/2 massive charged particle in Schwarzschild immersed in an electromagnetic universe

NASA Astrophysics Data System (ADS)

Al-Badawi, A.

2018-02-01

The Dirac equation is considered in a spacetime that represents a Schwarzschild metric coupled to a uniform external electromagnetic field. Due to the presence of electromagnetic field from the surroundings, the interaction with the spin-1/2 massive charged particle is considered. The equations of the spin-1/2 massive charged particle are separated into radial and angular equations by adopting the Newman-Penrose formalism. The angular equations obtained are similar to the Schwarzschild geometry. For the radial equations we manage to obtain the one dimensional Schrödinger-type wave equations with effective potentials. Finally, we study the behavior of the potentials by plotting them as a function of radial distance and expose the effect of the external parameter, charge and the frequency of the particle on them.

Radial Coherence of Diffusion Tractography in the Cerebral White Matter of the Human Fetus: Neuroanatomic Insights

PubMed Central

Xu, Gang; Takahashi, Emi; Folkerth, Rebecca D.; Haynes, Robin L.; Volpe, Joseph J.; Grant, P. Ellen; Kinney, Hannah C.

2014-01-01

High angular resolution diffusion imaging (HARDI) demonstrates transient radial coherence of telencephalic white matter in the human fetus. Our objective was to define the neuroanatomic basis of this radial coherence through correlative HARDI- and postmortem tissue analyses. Applying immunomarkers to radial glial fibers (RGFs), axons, and blood vessels in 18 cases (19 gestational weeks to 3 postnatal years), we compared their developmental profiles to HARDI tractography in brains of comparable ages (n = 11). At midgestation, radial coherence corresponded with the presence of RGFs. At 30–31 weeks, the transition from HARDI-defined radial coherence to corticocortical coherence began simultaneously with the transformation of RGFs to astrocytes. By term, both radial coherence and RGFs had disappeared. White matter axons were radial, tangential, and oblique over the second half of gestation, whereas penetrating blood vessels were consistently radial. Thus, radial coherence in the fetal white matter likely reflects a composite of RGFs, penetrating blood vessels, and radial axons of which its transient expression most closely matches that of RGFs. This study provides baseline information for interpreting radial coherence in tractography studies of the preterm brain in the assessment of the encephalopathy of prematurity. PMID:23131806

Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

NASA Astrophysics Data System (ADS)

Resita Arum, Sari; A, Suparmi; C, Cari

2016-01-01

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation, then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function. Project supported by the Higher Education Project (Grant No. 698/UN27.11/PN/2015).

Diffusive Transport of Several Hundred keV Electrons in the Earth's Slot Region

DOE PAGES

Ma, Q.; Li, W.; Thorne, R. M.; ...

2017-09-29

Here, we investigate the gradual diffusion of energetic electrons from the inner edge of the outer radiation belt into the slot region. The Van Allen Probes observed slow inward diffusion and decay of ~200–600 keV electrons following the intense geomagnetic storm that occurred on 17 March 2013. During the 10 day nondisturbed period following the storm, the peak of electron fluxes gradually moved from L ~ 2.7 to L ~ 2.4, and the flux levels decreased by a factor of ~2–4 depending on the electron energy. We simulated the radial intrusion and decay of electrons using a three–dimensional diffusion code,more » which reproduced the energy–dependent transport of electrons from ~100 keV to 1 MeV in the slot region. At energies of 100–200 keV, the electrons experience fast transport across the slot region due to the dominance of radial diffusion; at energies of 200–600 keV, the electrons gradually diffuse and decay in the slot region due to the comparable rate of radial diffusion and pitch angle scattering by plasmaspheric hiss; at energies of E > 700 keV, the electrons stopped diffusing near the inner edge of outer radiation belt due to the dominant pitch angle scattering loss. In addition to plasmaspheric hiss, magnetosonic waves and VLF transmitters can cause the loss of high pitch angle electrons, relaxing the sharp “top–hat” shaped pitch angle distributions created by plasmaspheric hiss. Our simulation indicates the importance of balance between radial diffusion and loss through pitch angle scattering in forming the diffusive intrusion of energetic electrons across the slot region.« less

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.

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.

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

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

Du, Qiang, E-mail: jyanghkbu@gmail.com; Yang, Jiang, E-mail: qd2125@columbia.edu

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simplemore » ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.« less

Lognormal-like statistics of a stochastic squeeze process

NASA Astrophysics Data System (ADS)

Shapira, Dekel; Cohen, Doron

2017-10-01

We analyze the full statistics of a stochastic squeeze process. The model's two parameters are the bare stretching rate w and the angular diffusion coefficient D . We carry out an exact analysis to determine the drift and the diffusion coefficient of log(r ) , where r is the radial coordinate. The results go beyond the heuristic lognormal description that is implied by the central limit theorem. Contrary to the common "quantum Zeno" approximation, the radial diffusion is not simply Dr=(1 /8 ) w2/D but has a nonmonotonic dependence on w /D . Furthermore, the calculation of the radial moments is dominated by the far non-Gaussian tails of the log(r ) distribution.

Effects of radial envelope modulations on the collisionless trapped-electron mode in tokamak plasmas

NASA Astrophysics Data System (ADS)

Chen, Hao-Tian; Chen, Liu

2018-05-01

Adopting the ballooning-mode representation and including the effects of radial envelope modulations, we have derived the corresponding linear eigenmode equation for the collisionless trapped-electron mode in tokamak plasmas. Numerical solutions of the eigenmode equation indicate that finite radial envelope modulations can affect the linear stability properties both quantitatively and qualitatively via the significant modifications in the corresponding eigenmode structures.

Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II

NASA Astrophysics Data System (ADS)

Du, Yihong; Guo, Zongming

We study the diffusive logistic equation with a free boundary in higher space dimensions and heterogeneous environment. Such a model may be used to describe the spreading of a new or invasive species, with the free boundary representing the expanding front. For simplicity, we assume that the environment and the solution are radially symmetric. In the special case of one space dimension and homogeneous environment, this free boundary problem was investigated in Du and Lin (2010) [10]. We prove that the spreading-vanishing dichotomy established in Du and Lin (2010) [10] still holds in the more general and ecologically realistic setting considered here. Moreover, when spreading occurs, we obtain best possible upper and lower bounds for the spreading speed of the expanding front. When the environment is asymptotically homogeneous at infinity, these two bounds coincide. Our results indicate that the asymptotic spreading speed determined by this model does not depend on the spatial dimension.

Analysis of Classes of Singular Steady State Reaction Diffusion Equations

NASA Astrophysics Data System (ADS)

Son, Byungjae

We study positive radial solutions to classes of steady state reaction diffusion problems on the exterior of a ball with both Dirichlet and nonlinear boundary conditions. We study both Laplacian as well as p-Laplacian problems with reaction terms that are p-sublinear at infinity. We consider both positone and semipositone reaction terms and establish existence, multiplicity and uniqueness results. Our existence and multiplicity results are achieved by a method of sub-supersolutions and uniqueness results via a combination of maximum principles, comparison principles, energy arguments and a-priori estimates. Our results significantly enhance the literature on p-sublinear positone and semipositone problems. Finally, we provide exact bifurcation curves for several one-dimensional problems. In the autonomous case, we extend and analyze a quadrature method, and in the nonautonomous case, we employ shooting methods. We use numerical solvers in Mathematica to generate the bifurcation curves.

Neoclassical diffusion at low L-shel

NASA Astrophysics Data System (ADS)

Cunningham, G.; Ripoll, J. F.; Loridan, V.; Schulz, M.

2017-12-01

At very low L-shell, the lifetime of MeV electrons is dominated by pitch-angle scattering due to Coulomb collisions with background neutrals and ions. Walt's evaluation of this lifetime explained Van Allen's observations of the decay of the radiation belts in the early 1960's, for L<1.25 but Imhof et al showed that the apparent lifetime of >500 keV electrons for L=[1.15,1.21] was much greater than predicted by Walt's model when the decay was observed over 3 years rather than just a few months. Imhof et al argued that inward radial diffusion from larger L would be a source of electrons at low L, thus increasing the apparent lifetimes that were observed, but did not speculate on the cause of such diffusion across L. Newkirk and Walt estimated the radial diffusion coefficient that would be needed to explain the apparent lifetimes observed by Imhof et al. The radial diffusion coefficients they inferred dropped sharply as L increased, contrasting with the radial diffusion coefficients that had been recently developed by Falthammar [1965], which increase as a power law in L. Newkirk and Walt noted Falthammar's speculation that pitch-angle diffusion caused by Coulomb scattering, when coupled to drift-shell splitting associated with non-dipolar terms in the near-Earth geomagnetic field, might be the physical basis for the radial diffusion, but they did not attempt to quantify this effect. Roederer et al demonstrated that Coulomb scattering plus drift-shell splitting could explain the Newkirk and Walt results but they did not perform an exhaustive study. In the field of magnetically confined fusion, the movement of charged particles to different drift-shells caused by the combination of collisions and drift-shell splitting is labeled `neoclassical' diffusion. By contrast, `anomalous' diffusion results from pitch-angle diffusion caused by wave turbulence combined with drift-shell splitting, an effect recently studied by O'Brien in the outer radiation belt. We have constructed a comprehensive model of neoclassical diffusion at low L as a function of pitch-angle, energy and L-shell, and find that we quantitatively reproduce the results in Newkirk and Walt and Imhof et al, conclusively demonstrating that neoclassical diffusion is an important effect for energetic electrons in the deep inner belt.

Mutual diffusion of binary liquid mixtures containing methanol, ethanol, acetone, benzene, cyclohexane, toluene, and carbon tetrachloride

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

Guevara-Carrion, Gabriela; Janzen, Tatjana; Muñoz-Muñoz, Y. Mauricio

Mutual diffusion coefficients of all 20 binary liquid mixtures that can be formed out of methanol, ethanol, acetone, benzene, cyclohexane, toluene, and carbon tetrachloride without a miscibility gap are studied at ambient conditions of temperature and pressure in the entire composition range. The considered mixtures show a varying mixing behavior from almost ideal to strongly non-ideal. Predictive molecular dynamics simulations employing the Green-Kubo formalism are carried out. Radial distribution functions are analyzed to gain an understanding of the liquid structure influencing the diffusion processes. It is shown that cluster formation in mixtures containing one alcoholic component has a significant impactmore » on the diffusion process. The estimation of the thermodynamic factor from experimental vapor-liquid equilibrium data is investigated, considering three excess Gibbs energy models, i.e., Wilson, NRTL, and UNIQUAC. It is found that the Wilson model yields the thermodynamic factor that best suits the simulation results for the prediction of the Fick diffusion coefficient. Four semi-empirical methods for the prediction of the self-diffusion coefficients and nine predictive equations for the Fick diffusion coefficient are assessed and it is found that methods based on local composition models are more reliable. Finally, the shear viscosity and thermal conductivity are predicted and in most cases favorably compared with experimental literature values.« less

Coupling of Outward Radial Diffusion and Losses at the Magnetopause in the Outer Radiation Belt

NASA Astrophysics Data System (ADS)

Castillo Tibocha, A. M.; Shprits, Y.; Drozdov, A.; Kellerman, A. C.; Aseev, N.

2017-12-01

Sudden dropouts observed in relativistic electron fluxes within the radiation belts are one the most studied and yet poorly understood features of the dynamics of radiation belts. A number of physical processes contributing to these dropout events are triggered by solar wind drivers. Magnetopause losses are one of the most effective mechanisms involved here and usually occur when drifting particles reach the boundary or when inward motion of the magnetopause crosses closed particle drift shells. In both cases, particles are rapidly transported into interplanetary space generating sharp gradients in electron PSD that will promote further outward radial diffusion of particles due to adiabatic transport and the influence of outward ULF waves. Studies suggest that the coupling of these two mechanisms explains nearly all the depletion of MeV electrons observed in the outer region of the radiation belts (L*>5). In this study, we present a simple approach to model electron losses at the magnetopause and outward radial diffusion in the outer radiation belt during geomagnetic storm time. Measured upstream solar wind parameters were used to calculate the radial distance of the subsolar point as proposed by Shue et al. (1997), which was defined as the radial extent of our assumed dipole field configuration. Radial diffusion was modelled using the empirical Kp-dependent DLL [Brautigam and Albert, JGR 2000] diffusion coefficient, which is included in the 3D Versatile Electron Radiation Belt (VERB) code. Simulations of geomagnetic storms were performed in order to evaluate the effects of the integrated mechanisms and the results were compared with Van Allen probe satellite data. Our simulation results reproduce well the observed loss at the magnetopause and electron depletion in the outer radiation belt.

Tidal Forces in Dyonic Reissner-Nördstrom Black Hole

NASA Astrophysics Data System (ADS)

Sharif, M.; Kousar, Lubna

2018-03-01

This paper investigates the tidal as well as magnetic charge effects produced in dyonic Reissner-Nordström black hole. We evaluate Newtonian radial acceleration using radial geodesics for freely falling test particles. We establish system of equations governing radial and angular tidal forces using geodesic deviation equation and discuss their solutions for bodies falling freely towards this black hole. The radial tidal force turns out to be compressing outside the event horizon whereas the angular tidal force changes sign between event and Cauchy horizons unlike Schwarzschild black hole. The radial geodesic component starts decreasing in dyonic Reissner-Nordström black hole unlike Schwarzschild case. We conclude that magnetic charge strongly affects the radial as well as angular components of tidal force.

Regional Microstructural and Volumetric Magnetic Resonance Imaging (MRI) Abnormalities in the Corpus Callosum of Neonates With Congenital Heart Defect Undergoing Cardiac Surgery.

PubMed

Hagmann, Cornelia; Singer, Jitka; Latal, Beatrice; Knirsch, Walter; Makki, Malek

2016-03-01

The purpose of the study is to investigate the structural development of the corpus callosum in term neonates with congenital heart defect before and after surgery using diffusion tensor imaging and 3-dimensional T1-weighted magnetic resonance imaging (MRI). We compared parallel and radial diffusions, apparent diffusion coefficient (ADC), fractional anisotropy, and volume of 5 substructures of the corpus callosum: genu, rostral body, body, isthmus, and splenium. Compared to healthy controls, we found a significantly lower volume of the splenium and total corpus callosum and a higher radial diffusion and lower fractional anisotropy in the splenium of patients presurgery; a lower volume in all substructures in the postsurgery group; higher radial diffusion in the rostral body, body, and splenium; and a higher apparent diffusion coefficient in the splenium of postsurgery patients. Similar fractional anisotropy changes in congenital heart defect patients were reported in preterm infants. Our findings in apparent diffusion coefficient in the splenium of these patients (pre and postsurgery) are comparable to findings in preterm neonates with psychomotor delay. Delayed maturation of the isthmus was also reported in preterm infants. © The Author(s) 2015.

Structure-correlated diffusion anisotropy in nanoporous channel networks by Monte Carlo simulations and percolation theory

NASA Astrophysics Data System (ADS)

Kondrashova, Daria; Valiullin, Rustem; Kärger, Jörg; Bunde, Armin

2017-07-01

Nanoporous silicon consisting of tubular pores imbedded in a silicon matrix has found many technological applications and provides a useful model system for studying phase transitions under confinement. Recently, a model for mass transfer in these materials has been elaborated [Kondrashova et al., Sci. Rep. 7, 40207 (2017)], which assumes that adjacent channels can be connected by "bridges" (with probability pbridge) which allows diffusion perpendicular to the channels. Along the channels, diffusion can be slowed down by "necks" which occur with probability pneck. In this paper we use Monte-Carlo simulations to study diffusion along the channels and perpendicular to them, as a function of pbridge and pneck, and find remarkable correlations between the diffusivities in longitudinal and radial directions. For clarifying the diffusivity in radial direction, which is governed by the concentration of bridges, we applied percolation theory. We determine analytically how the critical concentration of bridges depends on the size of the system and show that it approaches zero in the thermodynamic limit. Our analysis suggests that the critical properties of the model, including the diffusivity in radial direction, are in the universality class of two-dimensional lattice percolation, which is confirmed by our numerical study.

Radial diffusion comparing a THEMIS statistical model with geosynchronous measurements as the outer boundary

NASA Astrophysics Data System (ADS)

Li, Z.; Hudson, M. K.; Chen, Y.

2013-12-01

The outer boundary energetic electron flux is used as a driver in radial diffusion calculations, and its precise determination is critical to the solution. A new model was proposed recently based on THEMIS measurements to express the boundary flux as three fit functions of solar wind parameters in a response window, that depend on energy and which solar parameter is used: speed, density, or both (Shin and Lee, 2013). The Dartmouth radial diffusion model has been run using LANL geosynchronous satellite measurements as the outer boundary for a one-month interval in July to August 2004 and the calculated phase space density (PSD) is compared with GPS measurements at the GPS orbit (L=4.16), at magnetic equatorial plane crossings, as a test of the model. We also used the outer boundary generated from the Shin and Lee model and examined this boundary condition by computing the error relative to the simulation using a LANL geosynchronous spacecraft data-driven outer boundary. The calculation shows that there is overestimation and underestimation at different times, however the new boundary condition can be used to drive the radial diffusion model generally, producing the phase space density increase and dropout during a storm with a relatively small error. Having this new method based on a solar wind parametrized data set, we can run the radial diffusion model for storms when particle measurements are not available at the outer boundary. We chose the Whole Heliosphere Interval (WHI) as an example and compared the result with MHD/test-particle simulations (Hudson et al., 2012), obtaining much better agreement with PSD based on GPS measurements at L=4.16 using the diffusion model, which incorporates atmospheric losses.

Extensive database of liquid phase diffusion coefficients of some frequently used test molecules in reversed-phase liquid chromatography and hydrophilic interaction liquid chromatography.

PubMed

Song, Huiying; Vanderheyden, Yoachim; Adams, Erwin; Desmet, Gert; Cabooter, Deirdre

2016-07-15

Diffusion plays an important role in all aspects of band broadening in chromatography. An accurate knowledge of molecular diffusion coefficients in different mobile phases is therefore crucial in fundamental column performance studies. Correlations available in literature, such as the Wilke-Chang equation, can provide good approximations of molecular diffusion under reversed-phase conditions. However, these correlations have been demonstrated to be less accurate for mobile phases containing a large percentage of acetonitrile, as is the case in hydrophilic interaction liquid chromatography. A database of experimentally measured molecular diffusion coefficients of some 45 polar and apolar compounds that are frequently used as test molecules under hydrophilic interaction liquid chromatography and reversed-phase conditions is therefore presented. Special attention is given to diffusion coefficients of polar compounds obtained in large percentages of acetonitrile (>90%). The effect of the buffer concentration (5-10mM ammonium acetate) on the obtained diffusion coefficients is investigated and is demonstrated to mainly influence the molecular diffusion of charged molecules. Diffusion coefficients are measured using the Taylor-Aris method and hence deduced from the peak broadening of a solute when flowing through a long open tube. The validity of the set-up employed for the measurement of the diffusion coefficients is demonstrated by ruling out the occurrence of longitudinal diffusion, secondary flow interactions and extra-column effects, while it is also shown that radial equilibration in the 15m long capillary is effective. Copyright © 2016 Elsevier B.V. All rights reserved.

Bessel Fourier Orientation Reconstruction (BFOR): An Analytical Diffusion Propagator Reconstruction for Hybrid Diffusion Imaging and Computation of q-Space Indices

PubMed Central

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

2012-01-01

The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier orientation reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA). PMID:22963853

Theory of finite disturbances in a centrifugal compression system with a vaneless radial diffuser

NASA Technical Reports Server (NTRS)

Moore, F. K.

1990-01-01

A previous small perturbation analysis of circumferential waves in circumferential compression systems, assuming inviscid flow, is shown to be consistent with observations that narrow diffusers are more stable than wide ones, when boundary layer displacement effect is included. The Moore-Greitzer analysis for finite strength transients containing both surge and rotating stall in axial machines is adapted for a centrifugal compression system. Under certain assumptions, and except for a new second order swirl, the diffuser velocity field, including resonant singularities, can be carried over from the previous inviscid linear analysis. Nonlinear transient equations are derived and applied in a simple example to show that throttling through a resonant value of flow coefficient must occur in a sudden surge-like drop, accompanied by a transient rotating wave. This inner solution is superseded by an outer surge response on a longer time scale. Surge may occur purely as result of circumferential wave resonance. Numerical results are shown for various parametric choices relating to throttle schedule and the characteristic slope. A number of circumferential modes considered simultaneously is briefly discussed.

Cell growth and differentiation on feeder layers is predicted to be influenced by bioreactor geometry.

PubMed

Peng, C A; Palsson, B Ø

1996-06-05

Tissue function is comprised of a complex interplay between biological and physicochemical rate processes. The design of bioreactors for tissue engineering must account for these processes simultaneously in order to obtain a bioreactor that provides a uniform environment for tissue growth and development. In the present study we consider the effects of fluid flow and mass transfer on the growth of a tissue in a parallel-plate bioreactor configuration. The parenchymal cells grow on a preformed stromal (feeder) layer that secretes a growth factor that stimulates parenchymal stem cell replication and differentiation. The biological dynamics are described by a unilineage model that describes the replication and differentiation of the tissue stem cell. The physicochemical rates are described by the Navier-Stokes and convective-diffusion equations. The model equations are solved by a finite element method. Two dimensionless groups govern the behavior of the solution. One is the Graetz number (Gz) that describes the relative rates of convection and diffusion, and the other a new dimensionless ratio (designated by P) that describes the interplay of the growth factor production, diffusion, and stimulation. Four geometries (slab, gondola, diamond, and radial shapes) for the parallel-plate bioreactor are analyzed. The uniformity of cell growth is measured by a two-dimensional coefficient of variance. The concentration distribution of the stroma-derived growth factor was computed first based on fluid flow and bioreactor geometry. Then the concomitant cell density distribution was obtained by integrating the calculated growth factor concentration with the parenchymal cell growth and unilineage differentiation process. The spatiotemporal cell growth patterns in four different bioreactor configurations were investigated under a variety of combinations of Gz (10(-1), 10(0), and 10(1)) and P(10(-2), 10(-1), 10(0), 10(1), and 10(2)). The results indicate high cell density and uniformity can be achieved for parameter values of P = 0.01, ..., 0.1 and Gz = 0.1, ..., 1.0. Among the four geometries investigated the radial-flow-type bioreactor provides the most uniform environment in which parenchymal cells can grow and differentiate ex vivo due to the absence of walls that are parallel to the flow paths creating slow flowing regions.

A Finite-Orbit-Width Fokker-Planck solver for modeling of energetic particle interactions with waves, with application to Helicons in ITER

NASA Astrophysics Data System (ADS)

Petrov, Yuri V.; Harvey, R. W.

2017-10-01

The bounce-average (BA) finite-difference Fokker-Planck (FP) code CQL3D [1,2] now includes the essential physics to describe the RF heating of Finite-Orbit-Width (FOW) ions in tokamaks. The FP equation is reformulated in terms of Constants-Of-Motion coordinates, which we select to be particle speed, pitch angle, and major radius on the equatorial plane thus obtaining the distribution function directly at this location. Full-orbit, low collisionality neoclassical radial transport emerges from averaging the local friction and diffusion coefficients along guiding center orbits. Similarly, the BA of local quasilinear RF diffusion terms gives rise to additional radial transport. The local RF electric field components needed for the BA operator are usually obtained by a ray-tracing code, such as GENRAY, or in conjunction with full-wave codes. As a new, practical application, the CQL3D-FOW version is used for simulation of alpha-particle heating by high-harmonic waves in ITER. Coupling of high harmonic or helicon fast waves power to electrons is a promising current drive (CD) scenario for high beta plasmas. However, the efficiency of current drive can be diminished by parasitic channeling of RF power into fast ions, such as alphas, through finite Larmor-radius effects. We investigate possibilities to reduce the fast ion heating in CD scenarios.

On the failure of the quasicylindrical approximation and the connection to vortex breakdown in turbulent swirling flow

NASA Astrophysics Data System (ADS)

Gyllenram, W.; Nilsson, H.; Davidson, L.

2007-04-01

This paper analyzes the properties of viscous swirling flow in a pipe. The analysis is based on the time-averaged quasicylindrical Navier-Stokes equations and is applicable to steady, unsteady, and turbulent swirling flow. A method is developed to determine the critical level of swirl (vortex breakdown) for an arbitrary vortex. The method can also be used for an estimation of the radial velocity profile if the other components are given or measured along a single radial line. The quasicylindrical equations are rearranged to yield a single ordinary differential equation for the radial distribution of the radial velocity component. The equation is singular for certain levels of swirl. It is shown that the lowest swirl level at which the equation is singular corresponds exactly to the sufficient condition for axisymmetric vortex breakdown as derived by Wang and Rusak [J. Fluid Mech. 340, 177 (1997)] and Rusak et al. [AIAA J. 36, 1848 (1998)]. In narrow regions around the critical levels of swirl, the solution violates the quasicylindrical assumptions and the flow must undergo a drastic change of structure. The critical swirl level is determined by the sign change of the smallest eigenvalue of the discrete linear operator which relates the radial velocities to effects of viscosity and turbulence. It is shown that neither viscosity nor turbulence directly alters the critical level of swirl.

Diffuser for augmenting a wind turbine

DOEpatents

Foreman, Kenneth M.; Gilbert, Barry L.

1984-01-01

A diffuser for augmenting a wind turbine having means for energizing the boundary layer at several locations along the diffuser walls is improved by the addition of a short collar extending radially outward from the outlet of the diffuser.

Influence of fast alpha diffusion and thermal alpha buildup on tokamak reactor performance

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

Uckan, N.A.; Tolliver, J.S.; Houlberg, W.A.

1987-11-01

The effect of fast alpha diffusion and thermal alpha accumulation on the confinement capability of a candidate Engineering Test Reactor (ETR) plasma (Tokamak Ignition/Burn Experimental Reactor (TIBER-II)) in achieving ignition and steady-state driven operation has been assessed using both global and 1-1/2-D transport models. Estimates are made of the threshold for radial diffusion of fast alphas and thermal alpha buildup. It is shown that a relatively low level of radial transport, when combined with large gradients in the fast alpha density, leads to a significant radial flow with a deleterious effect on plasma performance. Similarly, modest levels of thermal alphamore » concentration significantly influence the ignition and steady-state burn capability. 23 refs., 9 figs., 4 tabs.« less

Performance of an asymmetric short annular diffuser with a nondiverging inner wall using suction. [control of radial profiles of diffuser exit velocity

NASA Technical Reports Server (NTRS)

Juhasz, A.

1974-01-01

The performance of a short highly asymmetric annular diffuser equipped with wall bleed (suction) capability was evaluated at nominal inlet Mach numbers of 0.188, 0.264, and 0.324 with the inlet pressure and temperature at near ambient values. The diffuser had an area ratio of 2.75 and a length- to inlet-height ratio of 1.6. Results show that the radial profiles of diffuser exit velocity could be controlled from a severely hub peaked to a slightly tip biased form by selective use of bleed. At the same time, other performance parameters were also improved. These results indicate the possible application of the diffuser bleed technique to control flow profiles to gas turbine combustors.

Accounting for magnetic diffusion in core flow inversions from geomagnetic secular variation

NASA Astrophysics Data System (ADS)

Amit, Hagay; Christensen, Ulrich R.

2008-12-01

We use numerical dynamos to investigate the possible role of magnetic diffusion at the top of the core. We find that the contribution of radial magnetic diffusion to the secular variation is correlated with that of tangential magnetic diffusion for a wide range of control parameters. The correlation between the two diffusive terms is interpreted in terms of the variation in the strength of poloidal flow along a columnar flow tube. The amplitude ratio of the two diffusive terms is used to estimate the probable contribution of radial magnetic diffusion to the secular variation at Earth-like conditions. We then apply a model where radial magnetic diffusion is proportional to tangential diffusion to core flow inversions of geomagnetic secular variation data. We find that including magnetic diffusion does not change dramatically the global flow but some significant local variations appear. In the non frozen-flux core flow models (termed `diffusive'), the hemispherical dichotomy between the active Atlantic and quiet Pacific is weaker, a cyclonic vortex below North America emerges and the vortex below Asia is stronger. Our results have several important geophysical implications. First, our diffusive flow models contain some flow activity at low latitudes in the Pacific, suggesting a local balance between magnetic field advection and diffusion in that region. Second, the cyclone below North America in our diffusive flows reconciles the difference between mantle-driven thermal wind predictions and frozen-flux core flow models, and is consistent with the prominent intense magnetic flux patch below North America in geomagnetic field models. Finally, we hypothesize that magnetic diffusion near the core surface plays a larger role in the geomagnetic secular variation than usually assumed.

Evaluation of Particle Pinch and Diffusion Coefficients in the Edge Pedestal of DIII-D H-mode Discharges

NASA Astrophysics Data System (ADS)

Stacey, W. M.; Groebner, R. J.

2009-11-01

Momentum balance requires that the radial particle flux satisfy a pinch-diffusion relationship. The pinch can be evaluated in terms of measurable quantities (rotation velocities, Er, etc.) by the use of momentum and particle balance [1,2], the radial particle flux can be determined by momentum balance, and then the diffusion coefficient can be evaluated from the pinch diffusion relation using the measured density gradient. Applications to several DIII-D H-mode plasmas are presented. 6pt [1] W.M. Stacey, Contr. Plasma Phys. 48, 94 (2008). [2] W.M. Stacey and R.J. Groebner, Phys. Plasmas 15, 012503 (2008).

Ratchet effect for nanoparticle transport in hair follicles.

PubMed

Radtke, Matthias; Patzelt, Alexa; Knorr, Fanny; Lademann, Jürgen; Netz, Roland R

2017-07-01

The motion of a single rigid nanoparticle inside a hair follicle is investigated by means of Brownian dynamics simulations. The cuticular hair structure is modeled as a periodic asymmetric ratchet-shaped surface. Induced by oscillating radial hair motion we find directed nanoparticle transport into the hair follicle with maximal velocity at a specific optimal frequency and an optimal particle size. We observe flow reversal when switching from radial to axial oscillatory hair motion. We also study the diffusion behavior and find strongly enhanced diffusion for axial motion with a diffusivity significantly larger than for free diffusion. Copyright © 2016 Elsevier B.V. All rights reserved.

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

Wave Augmented Diffusers for Centrifugal Compressors

NASA Technical Reports Server (NTRS)

Paxson, Daniel E.; Skoch, Gary J.

1998-01-01

A conceptual device is introduced which would utilize unsteady wave motion to slow and turn flows in the diffuser section of a centrifugal compressor. The envisioned device would substantially reduce the size of conventional centrifugal diffusers by eliminating the relatively large ninety degree bend needed to turn the flow from the radial/tangential to the axial direction. The bend would be replaced by a wall and the flow would instead exit through a series of rotating ports located on a disk, adjacent to the diffuser hub, and fixed to the impeller shaft. The ports would generate both expansion and compression waves which would rapidly transition from the hub/shroud (axial) direction to the radial/tangential direction. The waves would in turn induce radial/tangential and axial flow. This paper presents a detailed description of the device. Simplified cycle analysis and performance results are presented which were obtained using a time accurate, quasi-one-dimensional CFD code with models for turning, port flow conditions, and losses due to wall shear stress. The results indicate that a periodic wave system can be established which yields diffuser performance comparable to a conventional diffuser. Discussion concerning feasibility, accuracy, and integration follow.

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.

Numerical Investigation of Vortex Generator Flow Control for External-Compression Supersonic Inlets

NASA Astrophysics Data System (ADS)

Baydar, Ezgihan

Vortex generators (VGs) within external-compression supersonic inlets for Mach 1.6 were investigated to determine their ability to increase total pressure recovery and reduce total pressure distortion. Ramp and vane-type VGs were studied. The geometric factors of interest included height, length, spacing, angle-of-incidence, and positions upstream and downstream of the inlet terminal shock. The flow through the inlet was simulated numerically through the solution of the steady-state, Reynolds-averaged Navier-Stokes equations on multi-block, structured grids using the Wind-US flow solver. The inlet performance was characterized by the inlet total pressure recovery and the radial and circumferential total pressure distortion indices at the engine face. Previous research of downstream VGs in the low-boom supersonic inlet demonstrated improvement in radial distortion up to 24% while my work on external-compression supersonic inlets improved radial distortion up to 86%, which is significant. The design of experiments and statistical analysis methods were applied to quantify the effect of the geometric factors of VGs and search for optimal VG arrays. From the analysis, VG angle-of-incidence and VG height were the most influential factors in increasing total pressure recovery and reducing distortion. The study on the two-dimensional external-compression inlet determined which passive flow control devices, such as counter-rotating vanes or ramps, reduce high distortion levels and improve the health of the boundary layer, relative to the baseline. Downstream vanes demonstrate up to 21% improvement in boundary layer health and 86% improvement in radial distortion. Upstream vanes demonstrated up to 3% improvement in boundary layer health and 9% improvement in radial distortion. Ramps showed no improvement in boundary layer health and radial distortion. Micro-VGs were preferred for their reduced viscous drag and improvement in total pressure recovery at the AIP. Although traditional VGs energize the flow with stronger vortex structures compared to micro-VGs, the AIP is affected with overwhelming amounts of reduced and enhanced flow regions. In summary, vanes are exceptional in reducing radial distortion and improving the health of the boundary layer compared to the ramps. In the study of the STEX inlet, vane-type vortex generators were the preferred devices for boundary layer flow control. In the supersonic diffuser, co-rotating vane arrays and counter-rotating vane arrays did not show improvement. In the subsonic diffuser, co-rotating vane arrays with negative angles-of-incidence and counter-rotating vane arrays were exceptional in reducing radial distortion and improving total pressure recovery. Downstream co-rotating vanes demonstrated up to 41% improvement in radial distortion whereas downstream counter-rotating vanes demonstrated up to 73% improvement. For downstream counter-rotating vanes, a polynomial trend between VG height and radial distortion indicate that increasing VG height improves inlet distortion. In summary, downstream vanes are exceptional in improving total pressure recovery compared to upstream vanes.

White Matter Microstructure in Transsexuals and Controls Investigated by Diffusion Tensor Imaging

PubMed Central

Kranz, Georg S.; Hahn, Andreas; Kaufmann, Ulrike; Küblböck, Martin; Hummer, Allan; Ganger, Sebastian; Seiger, Rene; Winkler, Dietmar; Swaab, Dick F.; Windischberger, Christian; Kasper, Siegfried; Lanzenberger, Rupert

2015-01-01

Biological causes underpinning the well known gender dimorphisms in human behavior, cognition, and emotion have received increased attention in recent years. The advent of diffusion-weighted magnetic resonance imaging has permitted the investigation of the white matter microstructure in unprecedented detail. Here, we aimed to study the potential influences of biological sex, gender identity, sex hormones, and sexual orientation on white matter microstructure by investigating transsexuals and healthy controls using diffusion tensor imaging (DTI). Twenty-three female-to-male (FtM) and 21 male-to-female (MtF) transsexuals, as well as 23 female (FC) and 22 male (MC) controls underwent DTI at 3 tesla. Fractional anisotropy, axial, radial, and mean diffusivity were calculated using tract-based spatial statistics (TBSS) and fiber tractography. Results showed widespread significant differences in mean diffusivity between groups in almost all white matter tracts. FCs had highest mean diffusivities, followed by FtM transsexuals with lower values, MtF transsexuals with further reduced values, and MCs with lowest values. Investigating axial and radial diffusivities showed that a transition in axial diffusivity accounted for mean diffusivity results. No significant differences in fractional anisotropy maps were found between groups. Plasma testosterone levels were strongly correlated with mean, axial, and radial diffusivities. However, controlling for individual estradiol, testosterone, or progesterone plasma levels or for subjects’ sexual orientation did not change group differences. Our data harmonize with the hypothesis that fiber tract development is influenced by the hormonal environment during late prenatal and early postnatal brain development. PMID:25392513

Ex vivo laser lipolysis assisted with radially diffusing optical applicator

NASA Astrophysics Data System (ADS)

Hwang, Jieun; Hau, Nguyen Trung; Park, Sung Yeon; Rhee, Yun-Hee; Ahn, Jin-Chul; Kang, Hyun Wook

2016-05-01

Laser-assisted lipolysis has been implemented to reduce body fat in light of thermal interactions with adipose tissue. However, using a flat fiber with high irradiance often needs rapid cannula movements and even undesirable thermal injury due to direct tissue contact. The aim of the current study was to explore the feasibility of a radially diffusing optical applicator to liquefy the adipose tissue for effective laser lipolysis. The proposed diffuser was evaluated with a flat fiber in terms of temperature elevation and tissue liquefaction after laser lipolysis with a 980-nm wavelength. Given the same power (20 W), the diffusing applicator generated a 30% slower temperature increase with a 25% lower maximum temperature (84±3.2°C in 1 min p<0.001) in the tissue, compared with the flat fiber. Under the equivalent temperature development, the diffuser induced up to fivefold larger area of the adipose liquefaction due to radial light emission than the flat fiber. Ex vivo tissue tests for 5-min irradiation demonstrated that the diffuser (1.24±0.15 g) liquefied 66% more adipose tissue than the flat fiber (0.75±0.05 g). The proposed diffusing applicator can be a feasible therapeutic device for laser lipolysis due to low temperature development and wide coverage of thermal treatment.

Improved diffuser for augmenting a wind turbine

DOEpatents

Foreman, K.M.; Gilbert, B.L.

A diffuser for augmenting a wind turbine having means for energizing the boundary layer at several locations along the diffuser walls is improved by the addition of a short collar extending radially outward from the outlet of the diffuser.

Global Search of a Three-dimensional Low Solidity Circular Cascade Diffuser for Centrifugal Blowers by Meta-model Assisted Optimization

NASA Astrophysics Data System (ADS)

Sakaguchi, Daisaku; Sakue, Daiki; Tun, Min Thaw

2018-04-01

A three-dimensional blade of a low solidity circular cascade diffuser in centrifugal blowers is designed by means of a multi-point optimization technique. The optimization aims at improving static pressure coefficient at a design point and at a small flow rate condition. Moreover, a clear definition of secondary flow expressed by positive radial velocity at hub side is taken into consideration in constraints. The number of design parameters for three-dimensional blade reaches to 10 in this study, such as a radial gap, a radial chord length and mean camber angle distribution of the LSD blade with five control points, control point between hub and shroud with two design freedom. Optimization results show clear Pareto front and selected optimum design shows good improvement of pressure rise in diffuser at small flow rate conditions. It is found that three-dimensional blade has advantage to stabilize the secondary flow effect with improving pressure recovery of the low solidity circular cascade diffuser.

ULF Wave Analysis and Radial Diffusion Calculation Using a Global MHD Model for the 17 March 2015 Storm and Comparison with the 17 March 2013 Storm

NASA Astrophysics Data System (ADS)

Li, Z.; Hudson, M.; Paral, J.; Wiltberger, M. J.; Boyd, A. J.; Turner, D. L.

2016-12-01

The 17 March 2015 `St. Patrick's Day Storm' is the largest geomagnetic storm to date of Solar Cycle 24, with a Dst of -223 nT. The magnetopause moved inside geosynchronous orbit under high solar wind dynamic pressure and strong southward IMF Bz causing loss, however a subsequent drop in pressure allowed for rapid rebuilding of the radiation belts. Local heating has been modeled by other groups for this and the 17 March 2013 storm, only slightly weaker and showing a similar effect on electrons: first a rapid dropout due to inward motion of the magnetopause followed by rapid increase in flux above the pre-storm level and an even greater slow increase likely due to radial diffusion. The latter can be seen in temporal evolution of the electron phase space density measured by the Energetic Particle, Composition, and Thermal Plasma Suite (ECT) instrument on Van Allen Probes. Using the Lyon-Fedder-Mobarry global MHD model driven by upstream solar wind measurements with the Magneotsphere-Ionosphere Coupler (MIX), we have simulated both `St. Patrick's Day'events, analyzing LFM electric and magnetic fields to calculate radial diffusion coefficients. These coefficients have been implemented in a radial diffusion code using the measured electron phase space density profile following the local heating and as the outer boundary condition for subsequent temporally evolution over the next 12 days, beginning 18 March 2015. Agreement with electron phase space density at 1000 MeV/G measured by the MagEIS component of the ECT instrument on Van Allen Probes (30 keV - 4 MeV) was much improved using radial diffusion coefficients from the MHD simulations relative to coefficients parametrized by a global geomagnetic activity index.

Effects of inlet flow field conditions on the performance of centrifugal compressor diffusers: Part 1 -- Discrete-passage diffuser

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

Filipenco, V.G.; Deniz, S.; Johnston, J.M.

2000-01-01

This is Part 1 of a two-part paper considering the performance of radial diffusers for use in a high-performance centrifugal compressor. Part 1 reports on discrete-passage diffusers, while Part 2 describes a test of a straight-channel diffuser designed for equivalent duty. Two builds of discrete-passage diffuser were tested, with 30 and 38 separate passages. Both the 30 and 38 passage diffusers investigated showed comparable range of unstalled operation and similar level of overall diffuser pressure recovery. The paper concentrates on the influence of inlet flow conditions on the pressure recovery and operating range of radial diffusers for centrifugal compressor stages.more » The flow conditions examined include diffuser inlet Mach number, flow angle, blockage, and axial flow nonuniformity. The investigation was carried out in a specially built test facility, designed to provide a controlled inlet flow field to the test diffusers. The facility can provide a wide range of diffuser inlet velocity profile distortion and skew with Mach numbers up to unity and flow angles of 63 to 75 deg from the radical direction. The consequences of different averaging methods for the inlet total pressure distributions, which are needed in the definition of diffuser pressure recovery coefficient for nonuniform diffuser inlet conditions, were also assessed. The overall diffuser pressure recovery coefficient, based on suitably averaged inlet total pressure, was found to correlate well with the momentum-averaged flow angle into the diffuser. It is shown that the generally accepted sensitivity of diffuser pressure recovery performance to inlet flow distortion and boundary layer blockage can be largely attributed to inappropriate quantification of the average dynamic pressure at diffuser inlet. Use of an inlet dynamic pressure based on availability or mass-averaging in combination with definition of inlet flow angle based on mass average of the radial and tangential velocity at diffuser inlet removes this sensitivity.« less

Divergent series and memory of the initial condition in the long-time solution of some anomalous diffusion problems.

PubMed

Yuste, S Bravo; Borrego, R; Abad, E

2010-02-01

We consider various anomalous d -dimensional diffusion problems in the presence of an absorbing boundary with radial symmetry. The motion of particles is described by a fractional diffusion equation. Their mean-square displacement is given by r(2) proportional, variant t(gamma)(00 , the emergence of such series in the long-time domain is a specific feature of subdiffusion problems. We present a method to regularize such series, and, in some cases, validate the procedure by using alternative techniques (Laplace transform method and numerical simulations). In the normal diffusion case, we find that the signature of the initial condition on the approach to the steady state rapidly fades away and the solution approaches a single (the main) decay mode in the long-time regime. In remarkable contrast, long-time memory of the initial condition is present in the subdiffusive case as the spatial part Psi1(r) describing the long-time decay of the solution to the steady state is determined by a weighted superposition of all spatial modes characteristic of the normal diffusion problem, the weight being dependent on the initial condition. Interestingly, Psi1(r) turns out to be independent of the anomalous diffusion exponent gamma .

Two-Dimensional Transport Studies for the Composition and Structure of the Io Plasma Torus

NASA Technical Reports Server (NTRS)

Smyth, William H.

2003-01-01

The overall objective of this project is to investigate the roles of local and spatially extended plasma sources created by Io, plasma torus chemistry, and plasma convective and diffusive transport in producing the long-lived S(+), S(++) and O(+) radial ribbon structures of the plasma torus, their System III longitude and local-time asymmetries, their energy sources and their possible time variability. To accomplish this objective, two-dimensional [radial (L) and System III longitude] plasma transport equations for the flux-tube plasma content and energy content will be solved that include the convective motions for both the east-west electric field and co-rotational velocity-lag profile near Io s orbit, radial diffusion, and the spacetime dependent flux-tube production and loss created by both neutral-plasma and plasma-ion reaction chemistry in the plasma torus. For neutral-plasma chemistry, the project will for the first time undertake the calculation of realistic three-dimensional, spatially-extended, and time-varying contributions to the flux-tube ion-production and loss that are produced by Io's corona and extended neutral clouds. The unknown two-dimensional spatial nature of diffusion in the plasma transport will be isolated and better defined in the investigation by the collective consideration of the foregoing different physical processes. For energy transport, the energy flow from hot pickup ions (and a new electron source) to thermal ions and electrons will be included in investigating the System III longitude and local-time temperature asymmetries in the plasma torus. The research is central to the scope of the NASA Sun-Earth Connection Roadmap in Quest II Campaign 4 "Comparative Planetary Space Environments" by addressing key questions for understanding the magnetosphere of planets with high rotation rates and large internal plasma sources and, in addition, is of considerable importance to the NASA Solar System Exploration Science Theme. In this regard, Jupiter is the most extreme example with its rapid rotation and with its inner Galilean satellite Io providing the dominant plasma source for the magnetosphere.

Self-gravity, Resonances, and Orbital Diffusion in Stellar Disks

NASA Astrophysics Data System (ADS)

Fouvry, Jean-Baptiste; Binney, James; Pichon, Christophe

2015-06-01

Fluctuations in a stellar system's gravitational field cause the orbits of stars to evolve. The resulting evolution of the system can be computed with the orbit-averaged Fokker-Planck equation once the diffusion tensor is known. We present the formalism that enables one to compute the diffusion tensor from a given source of noise in the gravitational field when the system's dynamical response to that noise is included. In the case of a cool stellar disk we are able to reduce the computation of the diffusion tensor to a one-dimensional integral. We implement this formula for a tapered Mestel disk that is exposed to shot noise and find that we are able to explain analytically the principal features of a numerical simulation of such a disk. In particular the formation of narrow ridges of enhanced density in action space is recovered. As the disk's value of Toomre's Q is reduced and the disk becomes more responsive, there is a transition from a regime of heating in the inner regions of the disk through the inner Lindblad resonance to one of radial migration of near-circular orbits via the corotation resonance in the intermediate regions of the disk. The formalism developed here provides the ideal framework in which to study the long-term evolution of all kinds of stellar disks.

Uniform spatial distribution of collagen fibril radii within tendon implies local activation of pC-collagen at individual fibrils

NASA Astrophysics Data System (ADS)

Rutenberg, Andrew D.; Brown, Aidan I.; Kreplak, Laurent

2016-08-01

Collagen fibril cross-sectional radii show no systematic variation between the interior and the periphery of fibril bundles, indicating an effectively constant rate of collagen incorporation into fibrils throughout the bundle. Such spatially homogeneous incorporation constrains the extracellular diffusion of collagen precursors from sources at the bundle boundary to sinks at the growing fibrils. With a coarse-grained diffusion equation we determine stringent bounds, using parameters extracted from published experimental measurements of tendon development. From the lack of new fibril formation after birth, we further require that the concentration of diffusing precursors stays below the critical concentration for fibril nucleation. We find that the combination of the diffusive bound, which requires larger concentrations to ensure homogeneous fibril radii, and lack of nucleation, which requires lower concentrations, is only marginally consistent with fully processed collagen using conservative bounds. More realistic bounds may leave no consistent concentrations. Therefore, we propose that unprocessed pC-collagen diffuses from the bundle periphery followed by local C-proteinase activity and subsequent collagen incorporation at each fibril. We suggest that C-proteinase is localized within bundles, at fibril surfaces, during radial fibrillar growth. The much greater critical concentration of pC-collagen, as compared to fully processed collagen, then provides broad consistency between homogeneous fibril radii and the lack of fibril nucleation during fibril growth.

Simultaneous Modeling of Gradual SEP Events at the Earth and the Mars

NASA Astrophysics Data System (ADS)

Hu, J.; Li, G.

2017-12-01

Solar Energetic Particles (SEP) event is the number one space hazard for spacecraft instruments and astronauts' safety. Recent studies have shown that both longitudinal and radial extent of SEP events can be very significant. In this work, we use the improved Particle Acceleration and Transport in the Heliosphere (iPATH) model to simulate gradual SEP events that have impacts upon both the Earth and the Mars. We follow the propagation of a 2D CME-driven shock. Particles are accelerated at the shock via the diffusive shock acceleration (DSA) mechanism. Transport of the escaped particles to the Earth and the Mars is then followed using a backward stochastic differential equation method. Perpendicular diffusion is considered in both the DSA and the transport process. Model results such as time intensity profile and energetic particle spectrum at the two locations are compared to understand the spatial extent of an SEP event. Observational data at the Earth and the Mars are also studied to validate the model.

White matter microstructure in transsexuals and controls investigated by diffusion tensor imaging.

PubMed

Kranz, Georg S; Hahn, Andreas; Kaufmann, Ulrike; Küblböck, Martin; Hummer, Allan; Ganger, Sebastian; Seiger, Rene; Winkler, Dietmar; Swaab, Dick F; Windischberger, Christian; Kasper, Siegfried; Lanzenberger, Rupert

2014-11-12

Biological causes underpinning the well known gender dimorphisms in human behavior, cognition, and emotion have received increased attention in recent years. The advent of diffusion-weighted magnetic resonance imaging has permitted the investigation of the white matter microstructure in unprecedented detail. Here, we aimed to study the potential influences of biological sex, gender identity, sex hormones, and sexual orientation on white matter microstructure by investigating transsexuals and healthy controls using diffusion tensor imaging (DTI). Twenty-three female-to-male (FtM) and 21 male-to-female (MtF) transsexuals, as well as 23 female (FC) and 22 male (MC) controls underwent DTI at 3 tesla. Fractional anisotropy, axial, radial, and mean diffusivity were calculated using tract-based spatial statistics (TBSS) and fiber tractography. Results showed widespread significant differences in mean diffusivity between groups in almost all white matter tracts. FCs had highest mean diffusivities, followed by FtM transsexuals with lower values, MtF transsexuals with further reduced values, and MCs with lowest values. Investigating axial and radial diffusivities showed that a transition in axial diffusivity accounted for mean diffusivity results. No significant differences in fractional anisotropy maps were found between groups. Plasma testosterone levels were strongly correlated with mean, axial, and radial diffusivities. However, controlling for individual estradiol, testosterone, or progesterone plasma levels or for subjects' sexual orientation did not change group differences. Our data harmonize with the hypothesis that fiber tract development is influenced by the hormonal environment during late prenatal and early postnatal brain development. Copyright © 2014 the authors 0270-6474/14/3415466-10$15.00/0.

A model-based reconstruction for undersampled radial spin echo DTI with variational penalties on the diffusion tensor

PubMed Central

Knoll, Florian; Raya, José G; Halloran, Rafael O; Baete, Steven; Sigmund, Eric; Bammer, Roland; Block, Tobias; Otazo, Ricardo; Sodickson, Daniel K

2015-01-01

Radial spin echo diffusion imaging allows motion-robust imaging of tissues with very low T2 values like articular cartilage with high spatial resolution and signal-to-noise ratio (SNR). However, in vivo measurements are challenging due to the significantly slower data acquisition speed of spin-echo sequences and the less efficient k-space coverage of radial sampling, which raises the demand for accelerated protocols by means of undersampling. This work introduces a new reconstruction approach for undersampled DTI. A model-based reconstruction implicitly exploits redundancies in the diffusion weighted images by reducing the number of unknowns in the optimization problem and compressed sensing is performed directly in the target quantitative domain by imposing a Total Variation (TV) constraint on the elements of the diffusion tensor. Experiments were performed for an anisotropic phantom and the knee and brain of healthy volunteers (3 and 2 volunteers, respectively). Evaluation of the new approach was conducted by comparing the results to reconstructions performed with gridding, combined parallel imaging and compressed sensing, and a recently proposed model-based approach. The experiments demonstrated improvement in terms of reduction of noise and streaking artifacts in the quantitative parameter maps as well as a reduction of angular dispersion of the primary eigenvector when using the proposed method, without introducing systematic errors into the maps. This may enable an essential reduction of the acquisition time in radial spin echo diffusion tensor imaging without degrading parameter quantification and/or SNR. PMID:25594167

A quiescent state of 3 to 8 MeV radiation belt electrons

NASA Astrophysics Data System (ADS)

Selesnick, R. S.; Blake, J. B.; Kolasinski, W. A.; Fritz, T. A.

During a ∼3 month period in mid-1996 outer radiation belt electrons in the energy range from ∼ 3 to 8 MeV were diffusing inward and decaying in intensity with no internal or external source. Measurements from the HIST instrument on POLAR are used to constrain a model for time dependent lossy radial diffusion of these electrons, and to obtain estimates of a parameterized radial diffusion coefficient and lifetime. For lower energy electrons, of ∼ 1 to 3 MeV, a source at L > 6 is apparent throughout most of the same period.

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

Vieira, H.S., E-mail: horacio.santana.vieira@hotmail.com; Bezerra, V.B., E-mail: valdir@fisica.ufpb.br; Muniz, C.R., E-mail: celiomuniz@yahoo.com

This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr–Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the Klein–Gordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles. - Highlights: • The covariant Klein–Gordon equation for a charged massive scalar field in the Kerr–Newman black hole is solved.more » • Both angular and radial parts are transformed to a Heun-type equation. • The resulting Hawking radiation spectrum of scalar particles has a thermal character.« less

The Equivalence of the Radial Return and Mendelson Methods for Integrating the Classical Plasticity Equations

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Aboudi, Jacob; Arnold, Steven M.

2006-01-01

The radial return and Mendelson methods for integrating the equations of classical plasticity, which appear independently in the literature, are shown to be identical. Both methods are presented in detail as are the specifics of their algorithmic implementation. Results illustrate the methods' equivalence across a range of conditions and address the question of when the methods require iteration in order for the plastic state to remain on the yield surface. FORTRAN code implementations of the radial return and Mendelson methods are provided in the appendix.

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.

Radial Distribution Functions of Strongly Coupled Two-Temperature Plasmas

NASA Astrophysics Data System (ADS)

Shaffer, Nathaniel R.; Tiwari, Sanat Kumar; Baalrud, Scott D.

2017-10-01

We present tests of three theoretical models for the radial distribution functions (RDFs) in two-temperature strongly coupled plasmas. RDFs are useful in extending plasma thermodynamics and kinetic theory to strong coupling, but they are usually known only for thermal equilibrium or for approximate one-component model plasmas. Accurate two-component modeling is necessary to understand the impact of strong coupling on inter-species transport, e.g., ambipolar diffusion and electron-ion temperature relaxation. We demonstrate that the Seuferling-Vogel-Toeppfer (SVT) extension of the hypernetted chain equations not only gives accurate RDFs (as compared with classical molecular dynamics simulations), but also has a simple connection with the Yukawa OCP model. This connection gives a practical means to recover the structure of the electron background from knowledge of the ion-ion RDF alone. Using the model RDFs in Effective Potential Theory, we report the first predictions of inter-species transport coefficients of strongly coupled plasmas far from equilibrium. This work is supported by NSF Grant No. PHY-1453736, AFSOR Award No. FA9550-16-1-0221, and used XSEDE computational resources.

Diffuse Cosmic Rays Shining in the Galactic Center: A Novel Interpretation of H.E.S.S. and Fermi-LAT γ-Ray Data.

PubMed

Gaggero, D; Grasso, D; Marinelli, A; Taoso, M; Urbano, A

2017-07-21

We present a novel interpretation of the γ-ray diffuse emission measured by Fermi-LAT and H.E.S.S. in the Galactic center (GC) region and the Galactic ridge (GR). In the first part we perform a data-driven analysis based on PASS8 Fermi-LAT data: We extend down to a few GeV the spectra measured by H.E.S.S. and infer the primary cosmic-ray (CR) radial distribution between 0.1 and 3 TeV. In the second part we adopt a CR transport model based on a position-dependent diffusion coefficient. Such behavior reproduces the radial dependence of the CR spectral index recently inferred from the Fermi-LAT observations. We find that the bulk of the GR emission can be naturally explained by the interaction of the diffuse steady-state Galactic CR sea with the gas present in the central molecular zone. Although we confirm the presence of a residual radial-dependent emission associated with a central source, the relevance of the large-scale diffuse component prevents to claim a solid evidence of GC pevatrons.

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Schulz, Michael; Lyons, Larry R.; Gorney, David J.

1992-01-01

Two refinements to the quasi-linear theory of ion radial diffusion are proposed and examined analytically with simulations of particle trajectories. The resonance-broadening correction by Dungey (1965) is applied to the quasi-linear diffusion theory by Faelthammar (1965) for an individual model storm. Quasi-linear theory is then applied to the mean diffusion coefficients resulting from simulations of particle trajectories in 20 model storms. The correction for drift-resonance broadening results in quasi-linear diffusion coefficients with discrepancies from the corresponding simulated values that are reduced by a factor of about 3. Further reductions in the discrepancies are noted following the averaging of the quasi-linear diffusion coefficients, the simulated coefficients, and the resonance-broadened coefficients for the 20 storms. Quasi-linear theory provides good descriptions of particle transport for a single storm but performs even better in conjunction with the present ensemble-averaging.

Radial q-space sampling for DSI

PubMed Central

Baete, Steven H.; Yutzy, Stephen; Boada, Fernando, E.

2015-01-01

Purpose Diffusion Spectrum Imaging (DSI) has been shown to be an effective tool for non-invasively depicting the anatomical details of brain microstructure. Existing implementations of DSI sample the diffusion encoding space using a rectangular grid. Here we present a different implementation of DSI whereby a radially symmetric q-space sampling scheme for DSI (RDSI) is used to improve the angular resolution and accuracy of the reconstructed Orientation Distribution Functions (ODF). Methods Q-space is sampled by acquiring several q-space samples along a number of radial lines. Each of these radial lines in q-space is analytically connected to a value of the ODF at the same angular location by the Fourier slice theorem. Results Computer simulations and in vivo brain results demonstrate that RDSI correctly estimates the ODF when moderately high b-values (4000 s/mm2) and number of q-space samples (236) are used. Conclusion The nominal angular resolution of RDSI depends on the number of radial lines used in the sampling scheme, and only weakly on the maximum b-value. In addition, the radial analytical reconstruction reduces truncation artifacts which affect Cartesian reconstructions. Hence, a radial acquisition of q-space can be favorable for DSI. PMID:26363002

Radial transport of radiation belt electrons in kinetic field-line resonances

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

Chaston, Christopher C.; Bonnell, J. W.; Wygant, J. R.

A representative case study from the Van Allen Probes during a geomagnetic storm recovery phase reveals enhanced electron fluxes at intermediate pitch angles over energies from ~100 keV to 5 MeV coincident with broadband low-frequency electromagnetic waves. The statistical properties of these waves are used to build a model for radial diffusion via drift-bounce resonances in kinetic Alfvén eigenmodes/kinetic field-line resonances. Estimated diffusion coefficients indicate timescales for radial transport on the order of hours in storm time events at energies from <100 keV to MeVs over equatorial pitch angles from the edge of the loss cone to nearly perpendicular tomore » the geomagnetic field. In conclusion, the correlation of kinetic resonances with electron depletions and enhancements during storm main phase and recovery, and the rapid diffusion these waves drive, suggests that they may modulate the outer radiation belt.« less

Radial transport of radiation belt electrons in kinetic field-line resonances

DOE PAGES

Chaston, Christopher C.; Bonnell, J. W.; Wygant, J. R.; ...

2017-07-25

A representative case study from the Van Allen Probes during a geomagnetic storm recovery phase reveals enhanced electron fluxes at intermediate pitch angles over energies from ~100 keV to 5 MeV coincident with broadband low-frequency electromagnetic waves. The statistical properties of these waves are used to build a model for radial diffusion via drift-bounce resonances in kinetic Alfvén eigenmodes/kinetic field-line resonances. Estimated diffusion coefficients indicate timescales for radial transport on the order of hours in storm time events at energies from <100 keV to MeVs over equatorial pitch angles from the edge of the loss cone to nearly perpendicular tomore » the geomagnetic field. In conclusion, the correlation of kinetic resonances with electron depletions and enhancements during storm main phase and recovery, and the rapid diffusion these waves drive, suggests that they may modulate the outer radiation belt.« less

A velocity-dependent anomalous radial transport model for (2-D, 2-V) kinetic transport codes

NASA Astrophysics Data System (ADS)

Bodi, Kowsik; Krasheninnikov, Sergei; Cohen, Ron; Rognlien, Tom

2008-11-01

Plasma turbulence constitutes a significant part of radial plasma transport in magnetically confined plasmas. This turbulent transport is modeled in the form of anomalous convection and diffusion coefficients in fluid transport codes. There is a need to model the same in continuum kinetic edge codes [such as the (2-D, 2-V) transport version of TEMPEST, NEO, and the code being developed by the Edge Simulation Laboratory] with non-Maxwellian distributions. We present an anomalous transport model with velocity-dependent convection and diffusion coefficients leading to a diagonal transport matrix similar to that used in contemporary fluid transport models (e.g., UEDGE). Also presented are results of simulations corresponding to radial transport due to long-wavelength ExB turbulence using a velocity-independent diffusion coefficient. A BGK collision model is used to enable comparison with fluid transport codes.

Analysis of turbulent free-jet hydrogen-air diffusion flames with finite chemical reaction rates

NASA Technical Reports Server (NTRS)

Sislian, J. P.; Glass, I. I.; Evans, J. S.

1979-01-01

A numerical analysis is presented of the nonequilibrium flow field resulting from the turbulent mixing and combustion of an axisymmetric hydrogen jet in a supersonic parallel ambient air stream. The effective turbulent transport properties are determined by means of a two-equation model of turbulence. The finite-rate chemistry model considers eight elementary reactions among six chemical species: H, O, H2O, OH, O2 and H2. The governing set of nonlinear partial differential equations was solved by using an implicit finite-difference procedure. Radial distributions were obtained at two downstream locations for some important variables affecting the flow development, such as the turbulent kinetic energy and its dissipation rate. The results show that these variables attain their peak values on the axis of symmetry. The computed distribution of velocity, temperature, and mass fractions of the chemical species gives a complete description of the flow field. The numerical predictions were compared with two sets of experimental data. Good qualitative agreement was obtained.

Quantifying white matter tract diffusion parameters in the presence of increased extra-fiber cellularity and vasogenic edema

PubMed Central

Chiang, Chia-Wen; Wang, Yong; Sun, Peng; Lin, Tsen-Hsuan; Trinkaus, Kathryn; Cross, Anne H.; Song, Sheng-Kwei

2014-01-01

The effect of extra-fiber structural and pathological components confounding diffusion tensor imaging (DTI) computation was quantitatively investigated using data generated by both Monte-Carlo simulations and tissue phantoms. Increased extent of vasogenic edema, by addition of various amount of gel to fixed normal mouse trigeminal nerves or by increasing non-restricted isotropic diffusion tensor components in Monte-Carlo simulations, significantly decreased fractional anisotropy (FA), increased radial diffusivity, while less significantly increased axial diffusivity derived by DTI. Increased cellularity, mimicked by graded increase of the restricted isotropic diffusion tensor component in Monte-Carlo simulations, significantly decreased FA and axial diffusivity with limited impact on radial diffusivity derived by DTI. The MC simulation and tissue phantom data were also analyzed by the recently developed diffusion basis spectrum imaging (DBSI) to simultaneously distinguish and quantify the axon/myelin integrity and extra-fiber diffusion components. Results showed that increased cellularity or vasogenic edema did not affect the DBSI-derived fiber FA, axial or radial diffusivity. Importantly, the extent of extra-fiber cellularity and edema estimated by DBSI correlated with experimentally added gel and Monte-Carlo simulations. We also examined the feasibility of applying 25-direction diffusion encoding scheme for DBSI analysis on coherent white matter tracts. Results from both phantom experiments and simulations suggested that the 25-direction diffusion scheme provided comparable DBSI estimation of both fiber diffusion parameters and extra-fiber cellularity/edema extent as those by 99-direction scheme. An in vivo 25-direction DBSI analysis was performed on experimental autoimmune encephalomyelitis (EAE, an animal model of human multiple sclerosis) optic nerve as an example to examine the validity of derived DBSI parameters with post-imaging immunohistochemistry verification. Results support that in vivo DBSI using 25-direction diffusion scheme correctly reflect the underlying axonal injury, demyelination, and inflammation of optic nerves in EAE mice. PMID:25017446

Radial diffusion with outer boundary determined by geosynchronous measurements: Storm and post-storm intervals

NASA Astrophysics Data System (ADS)

Chu, F.; Haines, P.; Hudson, M.; Kress, B.; Freidel, R.; Kanekal, S.

2007-12-01

Work is underway by several groups to quantify diffusive radial transport of radiation belt electrons, including a model for pitch angle scattering losses to the atmosphere. The radial diffusion model conserves the first and second adiabatic invariants and breaks the third invariant. We have developed a radial diffusion code which uses the Crank Nicholson method with a variable outer boundary condition. For the radial diffusion coefficient, DLL, we have several choices, including the Brautigam and Albert (JGR, 2000) diffusion coefficient parameterized by Kp, which provides an ad hoc measure of the power level at ULF wave frequencies in the range of electron drift (mHz), breaking the third invariant. Other diffusion coefficient models are Kp-independent, fixed in time but explicitly dependent on the first invariant, or energy at a fixed L, such as calculated by Elkington et al. (JGR, 2003) and Perry et al. (JGR, 2006) based on ULF wave model fields. We analyzed three periods of electron flux and phase space density (PSD) enhancements inside of geosynchronous orbit: March 31 - May 31, 1991, and July 2004 and Nov 2004 storm intervals. The radial diffusion calculation is initialized with a computed phase space density profile for the 1991 interval using differential flux values from the CRRES High Energy Electron Fluxmeter instrument, covering 0.65 - 7.5 MeV. To calculate the initial phase space density, we convert Roederer L* to McIlwain's L- parameter using the ONERA-DESP program. A time averaged model developed by Vampola1 from the entire 14 month CRRES data set is applied to the July 2004 and Nov 2004 storms. The online CRESS data for specific orbits and the Vampola-model flux are both expressed in McIlwain L-shell, while conversion to L* conserves phase space density in a distorted non-dipolar magnetic field model. A Tsyganenko (T04) magnetic field model is used for conversion between L* and L. The outer boundary PSD is updated using LANL GEO satellite fluxes. After calculating the phase space density time evolution for the two storms and post-injection interval (March 31 - May 31, 1991), we compare results with SAMPEX measurements. A better match with SAMPEX measurements is obtained with a variable outer boundary, also with a Kp-dependent diffusion coefficient, and finally with an energy and L-dependent loss term (Summers et al., JGR, 2004), than with a time-independent diffusion coefficient and a simple Kp-parametrized loss rate and location of the plasmapause. Addition of a varying outer boundary which incorporates measured fluxes at geosynchronous orbit using L* has the biggest effect of the three parametrized variations studied. 1Vampola, A.L., 1996, The ESA Outer Zone Electron Model Update, Environment Modelling for Spaced-based Applications, ESA SP-392, ESTEC, Nordwijk, NL, pp. 151-158, W. Burke and T.-D. Guyenne, eds.

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

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.

Oblique scattering from radially inhomogeneous dielectric cylinders: An exact Volterra integral equation formulation

NASA Astrophysics Data System (ADS)

Tsalamengas, John L.

2018-07-01

We study plane-wave electromagnetic scattering by radially and strongly inhomogeneous dielectric cylinders at oblique incidence. The method of analysis relies on an exact reformulation of the underlying field equations as a first-order 4 × 4 system of differential equations and on the ability to restate the associated initial-value problem in the form of a system of coupled linear Volterra integral equations of the second kind. The integral equations so derived are discretized via a sophisticated variant of the Nyström method. The proposed method yields results accurate up to machine precision without relying on approximations. Numerical results and case studies ably demonstrate the efficiency and high accuracy of the algorithms.

Study on method to simulate light propagation on tissue with characteristics of radial-beam LED based on Monte-Carlo method.

PubMed

Song, Sangha; Elgezua, Inko; Kobayashi, Yo; Fujie, Masakatsu G

2013-01-01

In biomedical, Monte-carlo simulation is commonly used for simulation of light diffusion in tissue. But, most of previous studies did not consider a radial beam LED as light source. Therefore, we considered characteristics of a radial beam LED and applied them on MC simulation as light source. In this paper, we consider 3 characteristics of radial beam LED. The first is an initial launch area of photons. The second is an incident angle of a photon at an initial photon launching area. The third is the refraction effect according to contact area between LED and a turbid medium. For the verification of the MC simulation, we compared simulation and experimental results. The average of the correlation coefficient between simulation and experimental results is 0.9954. Through this study, we show an effective method to simulate light diffusion on tissue with characteristics for radial beam LED based on MC simulation.

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

Grierson, B. A.; Wang, W. X.; Ethier, S.

Intrinsic toroidal rotation of the deuterium main ions in the core of the DIII-D tokamak is observed to transition from flat to hollow, forming an off-axis peak, above a threshold level of direct electron heating. Nonlinear gyrokinetic simulations show that the residual stress associated with electrostatic ion temperature gradient turbulence possesses the correct radial location and stress structure to cause the observed hollow rotation profile. Residual stress momentum flux in the gyrokinetic simulations is balanced by turbulent momentum diffusion, with negligible contributions from turbulent pinch. Finally, the prediction of the velocity profile by integrating the momentum balance equation produces amore » rotation profile that qualitatively and quantitatively agrees with the measured main-ion profile, demonstrating that fluctuation-induced residual stress can drive the observed intrinsic velocity profile.« less

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.

High Efficiency Centrifugal Compressor for Rotorcraft Applications

NASA Technical Reports Server (NTRS)

Medic, Gorazd; Sharma, Om P.; Jongwook, Joo; Hardin, Larry W.; McCormick, Duane C.; Cousins, William T.; Lurie, Elizabeth A.; Shabbir, Aamir; Holley, Brian M.; Van Slooten, Paul R.

2017-01-01

The report "High Efficiency Centrifugal Compressor for Rotorcraft Applications" documents the work conducted at UTRC under the NRA Contract NNC08CB03C, with cost share 2/3 NASA, and 1/3 UTRC, that has been extended to 4.5 years. The purpose of this effort was to identify key technical barriers to advancing the state-of-the-art of small centrifugal compressor stages; to delineate the measurements required to provide insight into the flow physics of the technical barriers; to design, fabricate, install, and test a state-of-the-art research compressor that is representative of the rear stage of an axial-centrifugal aero-engine; and to acquire detailed aerodynamic performance and research quality data to clarify flow physics and to establish detailed data sets for future application. The design activity centered on meeting the goal set outlined in the NASA solicitation-the design target was to increase efficiency at higher work factor, while also reducing the maximum diameter of the stage. To fit within the existing Small Engine Components Test Facility at NASA Glenn Research Center (GRC) and to facilitate component re-use, certain key design parameters were fixed by UTRC, including impeller tip diameter, impeller rotational speed, and impeller inlet hub and shroud radii. This report describes the design effort of the High Efficiency Centrifugal Compressor stage (HECC) and delineation of measurements, fabrication of the compressor, and the initial tests that were performed. A new High-Efficiency Centrifugal Compressor stage with a very challenging reduction in radius ratio was successfully designed, fabricated and installed at GRC. The testing was successful, with no mechanical problems and the running clearances were achieved without impeller rubs. Overall, measured pressure ratio of 4.68, work factor of 0.81, and at design exit corrected flow rate of 3 lbm/s met the target requirements. Polytropic efficiency of 85.5 percent and stall margin of 7.5 percent were measured at design flow rate and speed. The measured efficiency and stall margin were lower than pre-test CFD predictions by 2.4 percentage points (pt) and 4.5 pt, respectively. Initial impressions from the experimental data indicated that the loss in the efficiency and stall margin can be attributed to a design shortfall in the impeller. However, detailed investigation of experimental data and post-test CFD simulations of higher fidelity than pre-test CFD, and in particular the unsteady CFD simulations and the assessment with a wider range of turbulence models, have indicated that the loss in efficiency is most likely due to the impact of unfavorable unsteady impeller/diffuser interactions induced by diffuser vanes, an impeller/diffuser corrected flow-rate mismatch (and associated incidence levels), and, potentially, flow separation in the radial-to-axial bend. An experimental program with a vaneless diffuser is recommended to evaluate this observation. A subsequent redesign of the diffuser (and the radial-to-axial bend) is also recommended. The diffuser needs to be redesigned to eliminate the mismatching of the impeller and the diffuser, targeting a slightly higher flow capacity. Furthermore, diffuser vanes need to be adjusted to align the incidence angles, to optimize the splitter vane location (both radially and circumferentially), and to minimize the unsteady interactions with the impeller. The radial-to-axial bend needs to be redesigned to eliminate, or at least minimize, the flow separation at the inner wall, and its impact on the flow in the diffuser upstream. Lessons were also learned in terms of CFD methodology and the importance of unsteady CFD simulations for centrifugal compressors was highlighted. Inconsistencies in the implementation of a widely used two-equation turbulence model were identified and corrections are recommended. It was also observed that unsteady simulations for centrifugal compressors require significantly longer integration times than what is current practice in industry.

High Efficiency Centrifugal Compressor for Rotorcraft Applications

NASA Technical Reports Server (NTRS)

Medic, Gorazd; Sharma, Om P.; Jongwook, Joo; Hardin, Larry W.; McCormick, Duane C.; Cousins, William T.; Lurie, Elizabeth A.; Shabbir, Aamir; Holley, Brian M.; Van Slooten, Paul R.

2014-01-01

The report "High Efficiency Centrifugal Compressor for Rotorcraft Applications" documents the work conducted at UTRC under the NRA Contract NNC08CB03C, with cost share 2/3 NASA, and 1/3 UTRC, that has been extended to 4.5 years. The purpose of this effort was to identify key technical barriers to advancing the state-of-the-art of small centrifugal compressor stages; to delineate the measurements required to provide insight into the flow physics of the technical barriers; to design, fabricate, install, and test a state-of-the-art research compressor that is representative of the rear stage of an axial-centrifugal aero-engine; and to acquire detailed aerodynamic performance and research quality data to clarify flow physics and to establish detailed data sets for future application. The design activity centered on meeting the goal set outlined in the NASA solicitation-the design target was to increase efficiency at higher work factor, while also reducing the maximum diameter of the stage. To fit within the existing Small Engine Components Test Facility at NASA Glenn Research Center (GRC) and to facilitate component re-use, certain key design parameters were fixed by UTRC, including impeller tip diameter, impeller rotational speed, and impeller inlet hub and shroud radii. This report describes the design effort of the High Efficiency Centrifugal Compressor stage (HECC) and delineation of measurements, fabrication of the compressor, and the initial tests that were performed. A new High-Efficiency Centrifugal Compressor stage with a very challenging reduction in radius ratio was successfully designed, fabricated and installed at GRC. The testing was successful, with no mechanical problems and the running clearances were achieved without impeller rubs. Overall, measured pressure ratio of 4.68, work factor of 0.81, and at design exit corrected flow rate of 3 lbm/s met the target requirements. Polytropic efficiency of 85.5 percent and stall margin of 7.5 percent were measured at design flow rate and speed. The measured efficiency and stall margin were lower than pre-test CFD predictions by 2.4 percentage points (pt) and 4.5 pt, respectively. Initial impressions from the experimental data indicated that the loss in the efficiency and stall margin can be attributed to a design shortfall in the impeller. However, detailed investigation of experimental data and post-test CFD simulations of higher fidelity than pre-test CFD, and in particular the unsteady CFD simulations and the assessment with a wider range of turbulence models, have indicated that the loss in efficiency is most likely due to the impact of unfavorable unsteady impeller/diffuser interactions induced by diffuser vanes, an impeller/diffuser corrected flow-rate mismatch (and associated incidence levels), and, potentially, flow separation in the radial-to-axial bend. An experimental program with a vaneless diffuser is recommended to evaluate this observation. A subsequent redesign of the diffuser (and the radial-to-axial bend) is also recommended. The diffuser needs to be redesigned to eliminate the mismatching of the impeller and the diffuser, targeting a slightly higher flow capacity. Furthermore, diffuser vanes need to be adjusted to align the incidence angles, to optimize the splitter vane location (both radially and circumferentially), and to minimize the unsteady interactions with the impeller. The radial-to-axial bend needs to be redesigned to eliminate, or at least minimize, the flow separation at the inner wall, and its impact on the flow in the diffuser upstream. Lessons were also learned in terms of CFD methodology and the importance of unsteady CFD simulations for centrifugal compressors was highlighted. Inconsistencies in the implementation of a widely used two-equation turbulence model were identified and corrections are recommended. It was also observed that unsteady simulations for centrifugal compressors require significantly longer integration times than what is current practice in industry.

The effects of nonuniform magnetic field strength on density flux and test particle transport in drift wave turbulence

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

Dewhurst, J. M.; Hnat, B.; Dendy, R. O.

2009-07-15

The extended Hasegawa-Wakatani equations generate fully nonlinear self-consistent solutions for coupled density n and vorticity {nabla}{sup 2}{phi}, where {phi} is electrostatic potential, in a plasma with background density inhomogeneity {kappa}=-{partial_derivative} ln n{sub 0}/{partial_derivative}x and magnetic field strength inhomogeneity C=-{partial_derivative} ln B/{partial_derivative}x. Finite C introduces interchange effects and {nabla}B drifts into the framework of drift turbulence through compressibility of the ExB and diamagnetic drifts. This paper addresses the direct computation of the radial ExB density flux {gamma}{sub n}=-n{partial_derivative}{phi}/{partial_derivative}y, tracer particle transport, the statistical properties of the turbulent fluctuations that drive {gamma}{sub n} and tracer motion, and analytical underpinnings. Systematic trends emergemore » in the dependence on C of the skewness of the distribution of pointwise {gamma}{sub n} and in the relative phase of density-velocity and density-potential pairings. It is shown how these effects, together with conservation of potential vorticity {pi}={nabla}{sup 2}{phi}-n+({kappa}-C)x, account for much of the transport phenomenology. Simple analytical arguments yield a Fickian relation {gamma}{sub n}=({kappa}-C)D{sub x} between the radial density flux {gamma}{sub n} and the radial tracer diffusivity D{sub x}, which is shown to explain key trends in the simulations.« less

Dirac and Klein-Gordon-Fock equations in Grumiller’s spacetime

NASA Astrophysics Data System (ADS)

Al-Badawi, A.; Sakalli, I.

We study the Dirac and the chargeless Klein-Gordon-Fock equations in the geometry of Grumiller’s spacetime that describes a model for gravity of a central object at large distances. The Dirac equation is separated into radial and angular equations by adopting the Newman-Penrose formalism. The angular part of the both wave equations are analytically solved. For the radial equations, we managed to reduce them to one dimensional Schrödinger-type wave equations with their corresponding effective potentials. Fermions’s potentials are numerically analyzed by serving their some characteristic plots. We also compute the quasinormal frequencies of the chargeless and massive scalar waves. With the aid of those quasinormal frequencies, Bekenstein’s area conjecture is tested for the Grumiller black hole. Thus, the effects of the Rindler acceleration on the waves of fermions and scalars are thoroughly analyzed.

Gray Matter Atrophy Is Primarily Related to Demyelination of Lesions in Multiple Sclerosis: A Diffusion Tensor Imaging MRI Study.

PubMed

Tóth, Eszter; Szabó, Nikoletta; Csete, Gergõ; Király, András; Faragó, Péter; Spisák, Tamás; Bencsik, Krisztina; Vécsei, László; Kincses, Zsigmond T

2017-01-01

Objective: Cortical pathology, periventricular demyelination, and lesion formation in multiple sclerosis (MS) are related (Hypothesis 1). Factors in the cerebrospinal fluid close to these compartments could possibly drive the parallel processes. Alternatively, the cortical atrophy could be caused by remote axonal transection (Hypothesis 2). Since MRI can differentiate between demyelination and axon loss, we used this imaging modality to investigate the correlation between the pattern of diffusion parameter changes in the periventricular- and deep white matter and the gray matter atrophy. Methods: High-resolution T1-weighted, FLAIR, and diffusion MRI images were acquired in 52 RRMS patients and 50 healthy, age-matched controls. We used EDSS to estimate the clinical disability. We used Tract Based Spatial Statistics to compare diffusion parameters (fractional anisotropy, mean, axial, and radial diffusivity) between groups. We evaluated global brain, white, and gray matter atrophy with SIENAX. Averaged, standard diffusion parameters were calculated in four compartment: periventricular lesioned and normal appearing white matter, non-periventricular lesioned and normal appearing white matter. PLS regression was used to identify which diffusion parameter and in which compartment best predicts the brain atrophy and clinical disability. Results: In our diffusion tensor imaging study compared to controls we found extensive alterations of fractional anisotropy, mean and radial diffusivity and smaller changes of axial diffusivity (maximal p > 0.0002) in patients that suggested demyelination in the lesioned and in the normal appearing white matter. We found significant reduction in total brain, total white, and gray matter (patients: 718.764 ± 14.968, 323.237 ± 7.246, 395.527 ± 8.050 cm 3 , controls: 791.772 ± 22.692, 355.350 ± 10.929, 436.422 ± 12.011 cm 3 ; mean ± SE), ( p < 0.015; p < 0.0001; p < 0.009; respectively) of patients compared to controls. The PLS analysis revealed a combination of demyelination-like diffusion parameters (higher mean and radial diffusivity in patients) in the lesions and in the non-lesioned periventricular white matter, which best predicted the gray matter atrophy ( p < 0.001). Similarly, EDSS was best predicted by the radial diffusivity of the lesions and the non-lesioned periventricular white matter, but axial diffusivity of the periventricular lesions also contributed significantly ( p < 0.0001). Interpretation: Our investigation showed that gray matter atrophy and white matter demyelination are related in MS but white matter axonal loss does not significantly contribute to the gray matter pathology.

One-dimensional time-dependent fluid model of a very high density low-pressure inductively coupled plasma

NASA Astrophysics Data System (ADS)

Chaplin, Vernon H.; Bellan, Paul M.

2015-12-01

A time-dependent two-fluid model has been developed to understand axial variations in the plasma parameters in a very high density (peak ne≳ 5 ×1019 m-3 ) argon inductively coupled discharge in a long 1.1 cm radius tube. The model equations are written in 1D with radial losses to the tube walls accounted for by the inclusion of effective particle and energy sink terms. The ambipolar diffusion equation and electron energy equation are solved to find the electron density ne(z ,t ) and temperature Te(z ,t ) , and the populations of the neutral argon 4s metastable, 4s resonant, and 4p excited state manifolds are calculated to determine the stepwise ionization rate and calculate radiative energy losses. The model has been validated through comparisons with Langmuir probe ion saturation current measurements; close agreement between the simulated and measured axial plasma density profiles and the initial density rise rate at each location was obtained at pA r=30 -60 mTorr . We present detailed results from calculations at 60 mTorr, including the time-dependent electron temperature, excited state populations, and energy budget within and downstream of the radiofrequency antenna.

Design and optimization of a single stage centrifugal compressor for a solar dish-Brayton system

NASA Astrophysics Data System (ADS)

Wang, Yongsheng; Wang, Kai; Tong, Zhiting; Lin, Feng; Nie, Chaoqun; Engeda, Abraham

2013-10-01

According to the requirements of a solar dish-Brayton system, a centrifugal compressor stage with a minimum total pressure ratio of 5, an adiabatic efficiency above 75% and a surge margin more than 12% needs to be designed. A single stage, which consists of impeller, radial vaned diffuser, 90° crossover and two rows of axial stators, was chosen to satisfy this system. To achieve the stage performance, an impeller with a 6:1 total pressure ratio and an adiabatic efficiency of 90% was designed and its preliminary geometry came from an in-house one-dimensional program. Radial vaned diffuser was applied downstream of the impeller. Two rows of axial stators after 90° crossover were added to guide the flow into axial direction. Since jet-wake flow, shockwave and boundary layer separation coexisted in the impeller-diffuser region, optimization on the radius ratio of radial diffuser vane inlet to impeller exit, diffuser vane inlet blade angle and number of diffuser vanes was carried out at design point. Finally, an optimized centrifugal compressor stage fulfilled the high expectations and presented proper performance. Numerical simulation showed that at design point the stage adiabatic efficiency was 79.93% and the total pressure ratio was 5.6. The surge margin was 15%. The performance map including 80%, 90% and 100% design speed was also presented.

Heun Polynomials and Exact Solutions for the Massless Dirac Particle in the C-Metric

NASA Astrophysics Data System (ADS)

Kar, Priyasri; Singh, Ritesh K.; Dasgupta, Ananda; Panigrahi, Prasanta K.

2018-03-01

The equation of motion of a massless Dirac particle in the C-metric leads to the general Heun equation (GHE) for the radial and the polar variables. The GHE, under certain parametric conditions, is cast in terms of a new set of su(1, 1) generators involving differential operators of degrees ±1/2 and 0. Additional Heun polynomials are obtained using this new algebraic structure and are used to construct some exact solutions for the radial and the polar parts of the Dirac equation.

Whole-brain diffusion tensor imaging in correlation to visual-evoked potentials in multiple sclerosis: a tract-based spatial statistics analysis.

PubMed

Lobsien, D; Ettrich, B; Sotiriou, K; Classen, J; Then Bergh, F; Hoffmann, K-T

2014-01-01

Functional correlates of microstructural damage of the brain affected by MS are incompletely understood. The purpose of this study was to evaluate correlations of visual-evoked potentials with microstructural brain changes as determined by DTI in patients with demyelinating central nervous disease. Sixty-one patients with clinically isolated syndrome or MS were prospectively recruited. The mean P100 visual-evoked potential latencies of the right and left eyes of each patient were calculated and used for the analysis. For DTI acquisition, a single-shot echo-planar imaging pulse sequence with 80 diffusion directions was performed at 3T. Fractional anisotropy, radial diffusivity, and axial diffusivity were calculated and correlated with mean P100 visual-evoked potentials by tract-based spatial statistics. Significant negative correlations between mean P100 visual-evoked potentials and fractional anisotropy and significant positive correlations between mean P100 visual-evoked potentials and radial diffusivity were found widespread over the whole brain. The highest significance was found in the optic radiation, frontoparietal white matter, and corpus callosum. Significant positive correlations between mean P100 visual-evoked potentials and axial diffusivity were less widespread, notably sparing the optic radiation. Microstructural changes of the whole brain correlated significantly with mean P100 visual-evoked potentials. The distribution of the correlations showed clear differences among axial diffusivity, fractional anisotropy, and radial diffusivity, notably in the optic radiation. This finding suggests a stronger correlation of mean P100 visual-evoked potentials to demyelination than to axonal damage. © 2014 by American Journal of Neuroradiology.

Changes in the distribution of radiocesium in the wood of Japanese cedar trees from 2011 to 2013.

PubMed

Ogawa, Hideki; Hirano, Yurika; Igei, Shigemitsu; Yokota, Kahori; Arai, Shio; Ito, Hirohisa; Kumata, Atsushi; Yoshida, Hirohisa

2016-09-01

The changes in the distribution of (137)Cs in the wood of Japanese cedar (Cryptomeria japonica) trunks within three years after the Fukushima Dai-ichi Nuclear Power Plant (FDNP) accident in 2011 were investigated. Thirteen trees were felled to collect samples at 6 forests in 2 regions of the Fukushima prefecture. The radial distribution of (137)Cs in the wood was measured at different heights. Profiles of (137)Cs distribution in the wood changed considerably from 2011 to 2013, and the process of (137)Cs distribution change in the wood was clarified. From 2011 to 2012, the active transportation from sapwood to heartwood and the radial diffusion in heartwood proceeded quickly, and the radial (137)Cs distribution differed according to the vertical positon of trees. From 2012 to 2013, the vertical diffusion of (137)Cs from the treetop to the ground, probably caused by the gradient of (137)Cs concentration in the trunk, was observed. Eventually, the radial (137)Cs distributions were nearly identical at any vertical positions in 2013. Our results suggested that the active transportation from sapwood to heartwood and the vertical and radial diffusion in heartwood proceeded according to the vertical position of the tree and (137)Cs distribution in the wood approached the equilibrium state within three years after the accident. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

Turbine exhaust diffuser with region of reduced flow area and outer boundary gas flow

DOEpatents

Orosa, John

2014-03-11

An exhaust diffuser system and method for a turbine engine. The outer boundary may include a region in which the outer boundary extends radially inwardly toward the hub structure and may direct at least a portion of an exhaust flow in the diffuser toward the hub structure. At least one gas jet is provided including a jet exit located on the outer boundary. The jet exit may discharge a flow of gas downstream substantially parallel to an inner surface of the outer boundary to direct a portion of the exhaust flow in the diffuser toward the outer boundary to effect a radially outward flow of at least a portion of the exhaust gas flow toward the outer boundary to balance an aerodynamic load between the outer and inner boundaries.

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.

Gestational Age at Birth and Brain White Matter Development in Term-Born Infants and Children.

PubMed

Ou, X; Glasier, C M; Ramakrishnaiah, R H; Kanfi, A; Rowell, A C; Pivik, R T; Andres, A; Cleves, M A; Badger, T M

2017-12-01

Studies on infants and children born preterm have shown that adequate gestational length is critical for brain white matter development. Less is known regarding how variations in gestational age at birth in term infants and children affect white matter development, which was evaluated in this study. Using DTI tract-based spatial statistics methods, we evaluated white matter microstructures in 2 groups of term-born (≥37 weeks of gestation) healthy subjects: 2-week-old infants ( n = 44) and 8-year-old children ( n = 63). DTI parameters including fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity were calculated by voxelwise and ROI methods and were correlated with gestational age at birth, with potential confounding factors such as postnatal age and sex controlled. Fractional anisotropy values, which are markers for white matter microstructural integrity, positively correlated ( P < .05, corrected) with gestational age at birth in most major white matter tracts/regions for the term infants. Mean diffusivity values, which are measures of water diffusivities in the brain, and axial and radial diffusivity values, which are markers for axonal growth and myelination, respectively, negatively correlated ( P < .05, corrected) with gestational age at birth in all major white matter tracts/regions excluding the body and splenium of the corpus callosum for the term infants. No significant correlations with gestational age were observed for any tracts/regions for the term-born 8-year-old children. Our results indicate that longer gestation during the normal term period is associated with significantly greater infant white matter development (as reflected by higher fractional anisotropy and lower mean diffusivity, axial diffusivity, and radial diffusivity values); however, similar associations were not observable in later childhood. © 2017 by American Journal of Neuroradiology.

White matter alterations in the brains of patients with active, remitted, and cured cushing syndrome: a DTI study.

PubMed

Pires, P; Santos, A; Vives-Gilabert, Y; Webb, S M; Sainz-Ruiz, A; Resmini, E; Crespo, I; de Juan-Delago, M; Gómez-Anson, B

2015-06-01

Cushing syndrome appears after chronic exposure to elevated glucocorticoid levels. Cortisol excess may alter white matter microstructure. Our purpose was to study WM changes in patients with Cushing syndrome compared with controls by using DTI and the influence of hypercortisolism. Thirty-five patients with Cushing syndrome and 35 healthy controls, matched for age, education, and sex, were analyzed through DTI (tract-based spatial statistics) for fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity (general linear model, family-wise error, and threshold-free cluster enhancement corrections, P < .05). Furthermore, the influence of hypercortisolism on WM DTI changes was studied by comparing 4 subgroups: 8 patients with Cushing syndrome with active hypercortisolism, 7 with Cushing syndrome with medication-remitted cortisol, 20 surgically cured, and 35 controls. Cardiovascular risk factors were used as covariates. In addition, correlations were analyzed among DTI values, concomitant 24-hour urinary free cortisol levels, and disease duration. There were widespread alterations (reduced fractional anisotropy, and increased mean diffusivity, axial diffusivity, and radial diffusivity values; P < .05) in patients with Cushing syndrome compared with controls, independent of the cardiovascular risk factors present. Both active and cured Cushing syndrome subgroups showed similar changes compared with controls. Patients with medically remitted Cushing syndrome also had reduced fractional anisotropy and increased mean diffusivity and radial diffusivity values, compared with controls. No correlations were found between DTI maps and 24-hour urinary free cortisol levels or with disease duration. Diffuse WM alterations in patients with Cushing syndrome suggest underlying loss of WM integrity and demyelination. Once present, they seem to be independent of concomitant hypercortisolism, persisting after remission/cure. © 2015 by American Journal of Neuroradiology.

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.

The HEUN-SCHRÖDINGER Radial Equation for Dh-Atoms

NASA Astrophysics Data System (ADS)

Tarasov, V. F.

This article deals with the connection between Schrödinger's multidimensional equation for DH-atoms (D≥1) and the confluent Heun equation with two auxiliary parameters ν and τ, where |1-ν| = o(1) and τ∈ℚ+, which influence the spectrum of eigenvalues, the Coulomb potential and the radial function. The case τ = ν = 1 and D = 3 corresponds to the "standard" form of Schrödinger's equation for a 3H-atom. With the help of parameter ν, e.g., some "quantum corrections" may be considered. The cases 0<τ<1 and τ>1, but â = (n-l-1)τ≥0 is an integer, change the "geometry" of the electron cloud in the atom, i.e. the so-called "exotic" 3H-like atoms arise, where Kummer's function 1F1(-â c; z) has â zeros and the discrete spectrum depends only on Z/(νn) but not on l and τ. Diagrams of the radial functions hat Pnl(r;τ ,ν ) as n≤3 are given.

ULF wave analysis and radial diffusion calculation using a global MHD model for the 17 March 2013 and 2015 storms

NASA Astrophysics Data System (ADS)

Li, Zhao; Hudson, Mary; Patel, Maulik; Wiltberger, Michael; Boyd, Alex; Turner, Drew

2017-07-01

The 17 March 2015 St. Patrick's Day Storm is the largest geomagnetic storm to date of Solar Cycle 24, with a Dst of -223 nT. The magnetopause moved inside geosynchronous orbit under high solar wind dynamic pressure and strong southward interplanetary magnetic field Bz causing loss; however, a subsequent drop in pressure allowed for rapid rebuilding of the radiation belts. The 17 March 2013 storm also shows similar effects on outer zone electrons: first, a rapid dropout due to inward motion of the magnetopause followed by rapid increase in flux above the prestorm level early in the recovery phase and a slow increase over the next 12 days. These phases can be seen in temporal evolution of the electron phase space density measured by the Energetic Particle, Composition, and Thermal Plasma Suite (ECT) instruments on Van Allen Probes. Using the Lyon-Fedder-Mobarry global MHD model driven by upstream solar wind measurements, we simulated both St. Patrick's Day 2013 and 2015 events, analyzing Lyon-Fedder-Mobarry electric and magnetic fields to calculate radial diffusion coefficients. These coefficients have been implemented in a radial diffusion code, using the measured electron phase space density following the local heating as the initial radial profile and outer boundary condition for subsequent temporal evolution over the next 12 days, beginning 18 March. Agreement with electron phase space density at 1000 MeV/G measured by the MagEIS component of the ECT instrument suite on Van Allen Probes was much improved using radial diffusion coefficients from the MHD simulations relative to coefficients parameterized by a global geomagnetic activity index.

Innermost Van Allen Radiation Belt for High Energy Protons at Saturn

NASA Technical Reports Server (NTRS)

Cooper, John F.

2008-01-01

The high energy proton radiation belts of Saturn are energetically dominated by the source from cosmic ray albedo neutron decay (CRAND), trapping of protons from beta decay of neutrons emitted from galactic cosmic ray nuclear interactions with the main rings. These belts were originally discovered in wide gaps between the A-ring, Janus/Epimetheus, Mimas, and Enceladus. The narrow F and G rings significant affected the CRAND protons but did not produce total depletion. Voyager 2 measurements subsequently revealed an outermost CRAND proton belt beyond Enceladus. Although the source rate is small, the trapping times limited by radial magnetospheric diffusion are very long, about ten years at peak measured flux inwards of the G ring, so large fluxes can accumulate unless otherwise limited in the trapping region by neutral gas, dust, and ring body interactions. One proposed final extension of the Cassini Orbiter mission would place perikrone in a 3000-km gap between the inner D ring and the upper atmosphere of Saturn. Experience with CRAND in the Earth's inner Van Allen proton belt suggests that a similar innermost belt might be found in this comparably wide region at Saturn. Radial dependence of magnetospheric diffusion, proximity to the ring neutron source, and northward magnetic offset of Saturn's magnetic equator from the ring plane could potentially produce peak fluxes several orders of magnitude higher than previously measured outside the main rings. Even brief passes through such an intense environment of highly penetrating protons would be a significant concern for spacecraft operations and science observations. Actual fluxes are limited by losses in Saturn's exospheric gas and in a dust environment likely comparable to that of the known CRAND proton belts. The first numerical model of this unexplored radiation belt is presented to determine limits on peak magnitude and radial profile of the proton flux distribution.

Nondestructive estimation of wood chemical composition of sections of radial wood strips by diffuse reflectance near infrared spectroscopy

Treesearch

P. David Jones; Laurence R. Schimleck; Gary F. Peter; Richard F. Daniels; Alexander Clark

2006-01-01

The use of calibrated near infrared (NIR) spectroscopy for predicting the chemical composition of Pirus taeda L. (loblolly pine) wood samples is investigated. Seventeen P. taeda radial strips, representing seven different sites were selected and NlR spectra were obtained from the radial longitudinal face of each strip. The spectra...

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

NASA Astrophysics Data System (ADS)

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

2009-03-01

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

CoFlame: A refined and validated numerical algorithm for modeling sooting laminar coflow diffusion flames

NASA Astrophysics Data System (ADS)

Eaves, Nick A.; Zhang, Qingan; Liu, Fengshan; Guo, Hongsheng; Dworkin, Seth B.; Thomson, Murray J.

2016-10-01

Mitigation of soot emissions from combustion devices is a global concern. For example, recent EURO 6 regulations for vehicles have placed stringent limits on soot emissions. In order to allow design engineers to achieve the goal of reduced soot emissions, they must have the tools to so. Due to the complex nature of soot formation, which includes growth and oxidation, detailed numerical models are required to gain fundamental insights into the mechanisms of soot formation. A detailed description of the CoFlame FORTRAN code which models sooting laminar coflow diffusion flames is given. The code solves axial and radial velocity, temperature, species conservation, and soot aggregate and primary particle number density equations. The sectional particle dynamics model includes nucleation, PAH condensation and HACA surface growth, surface oxidation, coagulation, fragmentation, particle diffusion, and thermophoresis. The code utilizes a distributed memory parallelization scheme with strip-domain decomposition. The public release of the CoFlame code, which has been refined in terms of coding structure, to the research community accompanies this paper. CoFlame is validated against experimental data for reattachment length in an axi-symmetric pipe with a sudden expansion, and ethylene-air and methane-air diffusion flames for multiple soot morphological parameters and gas-phase species. Finally, the parallel performance and computational costs of the code is investigated.

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

A determination of the L dependence of the radial diffusion coefficient for protons in Jupiter's inner magnetosphere

NASA Technical Reports Server (NTRS)

Thomsen, M. F.; Goertz, C. K.; Van Allen, J. A.

1977-01-01

In a previous paper (Thomsen et al., 1977), a technique was proposed for estimating the radial diffusion coefficient (n) in the inner magnetosphere of Jupiter from the observations of the sweeping effect of the inner Jovian satellites on the fluxes of the energetic charged particles. The present paper extends this technique to permit the unique identification of the parameters D sub O and n, where the diffusion coefficient is assumed to be of the form D = D sub O L to the nth. The derived value of D sub O depends directly on assumptions regarding the nature and efficiency of the loss mechanism operating on the particles, while the value of n depends only on the assumed width of the loss region. The extended technique is applied to the University of Iowa Pioneer 11 proton data, leading to values of n of about O and D(6) of about 3 x 10 to the -8th (R sub J)-squared/sec, when satellite sweepup losses are assumed to be the only loss operating on the protons. The small value of n is strong evidence that the radial diffusion is driven by ionospheric winds.

Radial diffusion, vertical transport, and refixation of labeled bicarbonate in scots pine stems

NASA Astrophysics Data System (ADS)

Marshall, J. D.; Tarvainen, L.; Wallin, G.

2016-12-01

The CO2 produced by a respiring stem provides an index of metabolic activity in the stem and a quantitative estimate of an important component of the forest carbon budget. Production of CO2 by a given stem volume is lost by three competing processes. First, some diffuses radially outward through the bark. Second, some is dissolved and vertically transported upward out of the control volume by the xylem stream. Third, some is refixed by photosynthesis under the bark. The relative balance among these pathways was quantified in 17-m Scots pine trees by 13C-bicarbonate labeling of the xylem stream and monitoring of the 13CO2 in the xylem water, along with continuous monitoring of the radial diffusive flux at four canopy heights and in transpiration from leaves. Most of the label diffused out radially, as 13CO2, immediately above the labeling site, over about a week. The pulse was weakly and briefly detected 4 m above that height. Further up the stem it was not detected at all. We detected significant refixation of CO2 in the stems at all heights above 4 m, where the bark becomes papery and thin, but the label was so weak at this height that refixation had little influence on the pulse chase. We conclude that the vertical flux is negligible in Scots pine, but that the refixation flux must be accounted for in estimates of whole-stem CO2 efflux.

Cosmic Ray Diffusion Tensor throughout the Heliosphere on the basis of Nearly Incompressible Magnetohydrodynamic Turbulence Model

NASA Astrophysics Data System (ADS)

Zhao, L.; Zank, G. P.; Adhikari, L.

2017-12-01

The radial and rigidity dependence of cosmic ray (CR) diffusion tensor is investigated on the basis of the recently developed 2D and slab turbulence transport model using nearly incompressible (NI) theory (Zank et al. 2017; Adhikari et al. 2017). We use the energy in forward propagating modes from 0.29 to 1 AU and in backward propagating modes from 1 to 75 AU. We employ the quasi-linear theory (QLT) and nonlinear guiding center (NLGC) theory, respectively, to determine the parallel and perpendicular elements of CR diffusion tensor. We also present the effect of both weak and moderately strong turbulence on the drift element of CR diffusion tensor. We find that (1) from 0.29 to 1 AU the radial mean free path (mfp) is dominated by the parallel component, both increase slowly after 0.4 AU; (2) from 1 to 75 AU the radial mfp starts with a rapid increase and then decreases after a peak at about 3.5 AU, mainly caused by pick-up ion sources of turbulence model; (3) after 20 AU the perpendicular mfp is nearly constant and begin to dominate the radial mfp; (4) the rigidity dependence of the parallel mfp is proportional to at 1 AU from 0.1 to 10 GV and the perpendicular mfp is weakly influenced by the rigidity; (5) turbulence does more than suppress the traditional drift element but introduces a new component normal to the magnetic field. This study shows that a proper two-component turbulence model is necessary to produce the complexity of diffusion coefficient for CR modulation throughout the heliosphere.

Separation of Electric Fields Into Potential and Inductive Parts, and Implications for Radial Diffusion

NASA Astrophysics Data System (ADS)

Chan, A. A.; Ilie, R.; Elkington, S. R.; Albert, J.; Huie, W.

2017-12-01

It has been traditional to separate radiation belt radial-diffusion coefficients into two contributions: an "electrostatic" diffusion coefficient, which is assumed to be due to a potential (non-inductive) electric field, and an "electromagnetic" diffusion coefficient , which is assumed to be due to the combined effect of an inductive electric field and the corresponding time-dependent magnetic field. One difficulty in implementing this separation when using magnetospheric fields obtained from measurements, or from MHD simulations, is that only the total electric field is given; the separation of the electric field into potential and inductive parts is not readily available. In this work we separate the electric field using a numerical method based on the Helmholtz decomposition of the total motional electric field calculated by the BATS-R-US MHD code. The inner boundary for the electric potential is based on the Ridley Ionospheric Model solution and we assume floating boundary conditions in the solar wind. Using different idealized solar wind drivers, including a solar wind density that is oscillating at a single frequency or with a broad spectrum of frequencies, we calculate potential and inductive electric fields, electric and magnetic power spectral densities, and corresponding radial diffusion coefficients. Simulations driven by idealized solar wind conditions show a clear separation of the potential and inductive contributions to the power spectral densities and diffusion coefficients. Simulations with more realistic solar wind drivers are underway to better assess the use of electrostatic and electromagnetic diffusion coefficients in understanding ULF wave-particle interactions in Earth's radiation belts.

HARDI DATA DENOISING USING VECTORIAL TOTAL VARIATION AND LOGARITHMIC BARRIER

PubMed Central

Kim, Yunho; Thompson, Paul M.; Vese, Luminita A.

2010-01-01

In this work, we wish to denoise HARDI (High Angular Resolution Diffusion Imaging) data arising in medical brain imaging. Diffusion imaging is a relatively new and powerful method to measure the three-dimensional profile of water diffusion at each point in the brain. These images can be used to reconstruct fiber directions and pathways in the living brain, providing detailed maps of fiber integrity and connectivity. HARDI data is a powerful new extension of diffusion imaging, which goes beyond the diffusion tensor imaging (DTI) model: mathematically, intensity data is given at every voxel and at any direction on the sphere. Unfortunately, HARDI data is usually highly contaminated with noise, depending on the b-value which is a tuning parameter pre-selected to collect the data. Larger b-values help to collect more accurate information in terms of measuring diffusivity, but more noise is generated by many factors as well. So large b-values are preferred, if we can satisfactorily reduce the noise without losing the data structure. Here we propose two variational methods to denoise HARDI data. The first one directly denoises the collected data S, while the second one denoises the so-called sADC (spherical Apparent Diffusion Coefficient), a field of radial functions derived from the data. These two quantities are related by an equation of the form S = SSexp (−b · sADC) (in the noise-free case). By applying these two different models, we will be able to determine which quantity will most accurately preserve data structure after denoising. The theoretical analysis of the proposed models is presented, together with experimental results and comparisons for denoising synthetic and real HARDI data. PMID:20802839

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

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.

Meshless Solution of the Problem on the Static Behavior of Thin and Thick Laminated Composite Beams

NASA Astrophysics Data System (ADS)

Xiang, S.; Kang, G. W.

2018-03-01

For the first time, the static behavior of laminated composite beams is analyzed using the meshless collocation method based on a thin-plate-spline radial basis function. In the approximation of a partial differential equation by using a radial basis function, the shape parameter has an important role in ensuring the numerical accuracy. The choice of a shape parameter in the thin plate spline radial basis function is easier than in other radial basis functions. The governing differential equations are derived based on Reddy's third-order shear deformation theory. Numerical results are obtained for symmetric cross-ply laminated composite beams with simple-simple and cantilever boundary conditions under a uniform load. The results found are compared with available published ones and demonstrate the accuracy of the present method.

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

Vieira, H.S., E-mail: horacio.santana.vieira@hotmail.com; Centro de Ciências, Tecnologia e Saúde, Universidade Estadual da Paraíba, CEP 58233-000, Araruna, PB; Bezerra, V.B., E-mail: valdir@fisica.ufpb.br

Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry. Exact solutions of both angular and radial parts of the covariant Klein–Gordon equation in this background are obtained, and are given in terms of the confluent Heun functions. The role of the presence of the cosmic string in these solutions is showed up. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation spectrum and the energy flux. -- Highlights:more » •A cosmic string is introduced along the axis of symmetry of the dyonic black hole. •The covariant Klein–Gordon equation for a charged massive scalar field in this background is analyzed. •Both angular and radial parts are transformed to a confluent Heun equation. •The resulting Hawking radiation spectrum and the energy flux are obtained.« less

Stress analysis in cylindrical composition-gradient electrodes of lithium-ion battery

NASA Astrophysics Data System (ADS)

Zhong, Yaotian; Liu, Yulan; Wang, B.

2017-07-01

In recent years, the composition-gradient electrode material has been verified to be one of the most promising materials in lithium-ion battery. To investigate diffusion-induced stresses (DIS) generated in a cylindrical composition-gradient electrode, the finite deformation theory and the stress-induced diffusion hypothesis are adopted to establish the constitutive equations. Compared with stress distributions in a homogeneous electrode, the increasing forms of Young's modulus E(R) and partial molar volume Ω(R) from the electrode center to the surface along the radial direction drastically increase the maximal magnitudes of hoop and axial stresses, while both of the decreasing forms are able to make the stress fields smaller and flatter. Also, it is found that the slope of -1 for E(R) with that of -0.5 for Ω(R) is a preferable strategy to prevent the inhomogeneous electrode from cracking, while for the sake of protecting the electrode from compression failure, the optimal slope for inhomogeneous E(R) and the preferential one for Ω(R) are both -0.5. The results provide a theoretical guidance for the design of composition-gradient electrode materials.

Path integral solution for a Klein-Gordon particle in vector and scalar deformed radial Rosen-Morse-type potentials

NASA Astrophysics Data System (ADS)

Khodja, A.; Kadja, A.; Benamira, F.; Guechi, L.

2017-12-01

The problem of a Klein-Gordon particle moving in equal vector and scalar Rosen-Morse-type potentials is solved in the framework of Feynman's path integral approach. Explicit path integration leads to a closed form for the radial Green's function associated with different shapes of the potentials. For q≤-1, and 1/2α ln | q|0, it is shown that the quantization conditions for the bound state energy levels E_{nr} are transcendental equations which can be solved numerically. Three special cases such as the standard radial Manning-Rosen potential (| q| =1), the standard radial Rosen-Morse potential (V2→ -V2,q=1) and the radial Eckart potential (V1→ -V1,q=1) are also briefly discussed.

Diffusing, side-firing, and radial delivery laser balloon catheters for creating subsurface thermal lesions in tissue

NASA Astrophysics Data System (ADS)

Chang, Chun-Hung; Fried, Nathaniel M.

2016-02-01

Infrared lasers have been used in combination with applied cooling methods to preserve superficial skin layers during cosmetic surgery. Similarly, combined laser irradiation and tissue cooling may also allow development of minimally invasive laser therapies beyond dermatology. This study compares diffusing, side-firing, and radial delivery laser balloon catheter designs for creation of subsurface lesions in tissue, ex vivo, using a near-IR laser and applied contact cooling. An Ytterbium fiber laser with 1075 nm wavelength delivered energy through custom built 18 Fr (6-mm-OD) balloon catheters incorporating either 10-mm-long diffusing fiber tip, 90 degree side-firing fiber, or radial delivery cone mirror, through a central lumen. A chilled solution was flowed through a separate lumen into 9-mm-diameter balloon to keep probe cooled at 7°C. Porcine liver tissue samples were used as preliminary tissue model for immediate observation of thermal lesion creation. The diffusing fiber produced subsurface thermal lesions measuring 49.3 +/- 10.0 mm2 and preserved 0.8 +/- 0.1 mm of surface tissue. The side-firing fiber produced subsurface thermal lesions of 2.4 +/- 0.9 mm2 diameter and preserved 0.5 +/- 0.1 mm of surface tissue. The radial delivery probe assembly failed to produce subsurface thermal lesions, presumably due to the small effective spot diameter at the tissue surface, which limited optical penetration depth. Optimal laser power and irradiation time measured 15 W and 100 s for diffusing fiber and 1.4 W and 20 s, for side-firing fiber, respectively. Diffusing and side-firing laser balloon catheter designs provided subsurface thermal lesions in tissue. However, the divergent laser beam in both designs limited the ability to preserve a thicker layer of tissue surface. Further optimization of laser and cooling parameters may be necessary to preserve thicker surface tissue layers.

Modeling the Magnetopause Shadowing Loss during the October 2012 Dropout Event

NASA Astrophysics Data System (ADS)

Tu, Weichao; Cunningham, Gregory

2017-04-01

The relativistic electron flux in Earth's outer radiation belt are observed to drop by orders of magnitude on timescales of a few hours, which is called radiation belt dropouts. Where do the electrons go during the dropouts? This is one of the most important outstanding questions in radiation belt studies. Radiation belt electrons can be lost either by precipitation into the atmosphere or by transport across the magnetopause into interplanetary space. The latter mechanism is called magnetopause shadowing, usually combined with outward radial diffusion of electrons due to the sharp radial gradient it creates. In order to quantify the relative contribution of these two mechanisms to radiation belt dropout, we performed an event study on the October 2012 dropout event observed by Van Allen Probes. First, the precipitating MeV electrons observed by multiple NOAA POES satellites at low altitude did not show evidence of enhanced precipitation during the dropout, which suggested that precipitation was not the dominant loss mechanism for the event. Then, in order to simulate the magnetopause shadowing loss and outward radial diffusion during the dropout, we applied a radial diffusion model with electron lifetimes on the order of electron drift periods outside the last closed drift shell. In addition, realistic and event-specific inputs of radial diffusion coefficients (DLL) and last closed drift shell (LCDS) were implemented in the model. Specifically, we used the new DLL developed by Cunningham [JGR 2016] which were estimated in realistic TS04 [Tsyganenko and Sitnov, JGR 2005] storm time magnetic field model and included physical K (2nd adiabatic invariant) or pitch angle dependence. Event-specific LCDS traced in TS04 model with realistic K dependence was also implemented. Our simulation results showed that these event-specific inputs are critical to explain the electron dropout during the event. The new DLL greatly improved the model performance at low L* regions (L*<3.6) compared to empirical Kp-dependent DLL [Brautigam and Albert, JGR 2000] used in previous radial diffusion models. Combining the event-specific DLL and LCDS, our model well captured the magnetopause shadowing loss and reproduced the electron dropout at L*=4.0-4.5. In addition, we found the K-dependent LCDS is critical to reproduce the pitch angle dependence of the observed electron dropout.

Two-dimensional compressible flow in centrifugal compressors with straight blades

NASA Technical Reports Server (NTRS)

Stanitz, John D; Ellis, Gaylord O

1950-01-01

Six numerical examples are presented for steady, two-dimensional, compressible, nonviscous flow in centrifugal compressors with thin straight blades, the center lines of which generate the surface of a right circular cone when rotated about the axis of the compressor. A seventh example is presented for incompressible flow. The solutions were obtained in a region of the compressors, including the impeller tip, that was considered to be unaffected by the diffuser vanes or by the impeller-inlet configuration. Each solution applies to radial and mixed flow compressors with various cone angles but with the same angle between blades on the conic flow surface. The solution also apply to radial and mixed flow turbines with the rotation and the flow direction reversed. The effects of variations in the following parameters were investigated: (1) flow rate, (2) impeller-tip speed, (3) variation of passage height with radius, and (4) angle between blades on conic flow surface. The numerical results are presented in plots of the streamlines and constant Mach number lines. Correlation equations are developed whereby the flow conditions in any impeller with straight blades can be determined (in the region investigated by this analysis) for all operating conditions.

A Computational and Experimental Study of Coflow Laminar Methane/Air Diffusion Flames: Effects of Fuel Dilution, Inlet Velocity, and Gravity

NASA Technical Reports Server (NTRS)

Cao, S.; Ma, B.; Bennett, B. A. V.; Giassi, D.; Stocker, D. P.; Takahashi, F.; Long, M. B.; Smooke, M. D.

2014-01-01

The influences of fuel dilution, inlet velocity, and gravity on the shape and structure of laminar coflow CH4-air diffusion flames were investigated computationally and experimentally. A series of nitrogen-diluted flames measured in the Structure and Liftoff in Combustion Experiment (SLICE) on board the International Space Station was assessed numerically under microgravity (mu g) and normal gravity (1g) conditions with CH4 mole fraction ranging from 0.4 to 1.0 and average inlet velocity ranging from 23 to 90 cm/s. Computationally, the MC-Smooth vorticity-velocity formulation was employed to describe the reactive gaseous mixture, and soot evolution was modeled by sectional aerosol equations. The governing equations and boundary conditions were discretized 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, flame shape and soot temperature were determined by flame emission images recorded by a digital color camera. Very good agreement between computation and measurement was obtained, and the conclusions were as follows. (1) Buoyant and nonbuoyant luminous flame lengths are proportional to the mass flow rate of the fuel mixture; computed and measured nonbuoyant flames are noticeably longer than their 1g counterparts; the effect of fuel dilution on flame shape (i.e., flame length and flame radius) is negligible when the flame shape is normalized by the methane flow rate. (2) Buoyancy-induced reduction of the flame radius through radially inward convection near the flame front is demonstrated. (3) Buoyant and nonbuoyant flame structure is mainly controlled by the fuel mass flow rate, and the effects from fuel dilution and inlet velocity are secondary.

Particle transport characteristics of the RT-1 magnetospheric plasma using gas-puffing modulation technique

NASA Astrophysics Data System (ADS)

Kenmochi, Naoki; Nishiura, Masaki; Yoshida, Zensho; Sugata, Tetsuya; Nakamura, Kaori; Katsura, Shotaro

2017-10-01

The Ring Trap 1 (RT-1) device creates a laboratory magnetosphere that is realized by a levitated superconducting ring magnet in vacuum. The RT-1 experiment has demonstrated the self-organization of a plasma clump with a steep density gradient; a peaked density distribution is spontaneously created through `inward diffusion'. In order to evaluate particle transport characteristics in the RT-1 magnetospheric plasmas which cause these inward diffusion, density modulation experiments were performed in the RT-1. Density modulation is a powerful method for estimating a diffusion coefficient D and a convection velocity V by puffing a periodic neutral gas. The gas puff modulation causes the change in the electron density measured by two chords of microwave interferometer (the radial positions r = 60 and 70 cm, vertical chord). In the case of 2 Hz gas puff modulation, the phase delay and the modulation-amplitude decay at the chord r = 60 cm are obtained with 15 degree and 0.8, respectively, with respect to the phase and the amplitude at r = 70 cm. The particle balance equations are solved on the assumption of profile shapes for D to evaluate D, V and particle source rate. The result suggests the inward convection in high beta magnetospheric plasmas.

Gas turbine engine with radial diffuser and shortened mid section

DOEpatents

Charron, Richard C.; Montgomery, Matthew D.

2015-09-08

An industrial gas turbine engine (10), including: a can annular combustion assembly (80), having a plurality of discrete flow ducts configured to receive combustion gas from respective combustors (82) and deliver the combustion gas along a straight flow path at a speed and orientation appropriate for delivery directly onto the first row (56) of turbine blades (62); and a compressor diffuser (32) having a redirecting surface (130, 140) configured to receive an axial flow of compressed air and redirect the axial flow of compressed air radially outward.

Air cycle machine for an aircraft environmental control system

NASA Technical Reports Server (NTRS)

Decrisantis, Angelo A. (Inventor); O'Coin, James R. (Inventor); Taddey, Edmund P. (Inventor)

2010-01-01

An ECS system includes an ACM mounted adjacent an air-liquid heat exchanger through a diffuser that contains a diffuser plate. The diffuser plate receives airflow from the ACM which strikes the diffuser plate and flows radially outward and around the diffuser plate and into the air-liquid heat exchanger to provide minimal pressure loss and proper flow distribution into the air-liquid heat exchanger with significantly less packaging space.

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

The Shannon entropy information for mixed Manning Rosen potential in D-dimensional Schrodinger equation

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Nur Pratiwi, Beta; Arya Nugraha, Dewanta

2017-01-01

D dimensional Schrodinger equation for the mixed Manning Rosen potential was investigated using supersymmetric quantum mechanics. We obtained the energy eigenvalues from radial part solution and wavefunctions in radial and angular parts solution. From the lowest radial wavefunctions, we evaluated the Shannon entropy information using Matlab software. Based on the entropy densities demonstrated graphically, we obtained that the wave of position information entropy density moves right when the value of potential parameter q increases, while its wave moves left with the increase of parameter α. The wave of momentum information entropy densities were expressed in graphs. We observe that its amplitude increase with increasing parameter q and α

Development of an explicit multiblock/multigrid flow solver for viscous flows in complex geometries

NASA Technical Reports Server (NTRS)

Steinthorsson, E.; Liou, M. S.; Povinelli, L. A.

1993-01-01

A new computer program is being developed for doing accurate simulations of compressible viscous flows in complex geometries. The code employs the full compressible Navier-Stokes equations. The eddy viscosity model of Baldwin and Lomax is used to model the effects of turbulence on the flow. A cell centered finite volume discretization is used for all terms in the governing equations. The Advection Upwind Splitting Method (AUSM) is used to compute the inviscid fluxes, while central differencing is used for the diffusive fluxes. A four-stage Runge-Kutta time integration scheme is used to march solutions to steady state, while convergence is enhanced by a multigrid scheme, local time-stepping, and implicit residual smoothing. To enable simulations of flows in complex geometries, the code uses composite structured grid systems where all grid lines are continuous at block boundaries (multiblock grids). Example results shown are a flow in a linear cascade, a flow around a circular pin extending between the main walls in a high aspect-ratio channel, and a flow of air in a radial turbine coolant passage.

Development of an explicit multiblock/multigrid flow solver for viscous flows in complex geometries

NASA Technical Reports Server (NTRS)

Steinthorsson, E.; Liou, M.-S.; Povinelli, L. A.

1993-01-01

A new computer program is being developed for doing accurate simulations of compressible viscous flows in complex geometries. The code employs the full compressible Navier-Stokes equations. The eddy viscosity model of Baldwin and Lomax is used to model the effects of turbulence on the flow. A cell centered finite volume discretization is used for all terms in the governing equations. The Advection Upwind Splitting Method (AUSM) is used to compute the inviscid fluxes, while central differencing is used for the diffusive fluxes. A four-stage Runge-Kutta time integration scheme is used to march solutions to steady state, while convergence is enhanced by a multigrid scheme, local time-stepping and implicit residual smoothing. To enable simulations of flows in complex geometries, the code uses composite structured grid systems where all grid lines are continuous at block boundaries (multiblock grids). Example results are shown a flow in a linear cascade, a flow around a circular pin extending between the main walls in a high aspect-ratio channel, and a flow of air in a radial turbine coolant passage.

Characterization of non-diffusive transport in plasma turbulence by means of flux-gradient integro-differential kernels

NASA Astrophysics Data System (ADS)

Alcuson, J. A.; Reynolds-Barredo, J. M.; Mier, J. A.; Sanchez, Raul; Del-Castillo-Negrete, Diego; Newman, David E.; Tribaldos, V.

2015-11-01

A method to determine fractional transport exponents in systems dominated by fluid or plasma turbulence is proposed. The method is based on the estimation of the integro-differential kernel that relates values of the fluxes and gradients of the transported field, and its comparison with the family of analytical kernels of the linear fractional transport equation. Although use of this type of kernels has been explored before in this context, the methodology proposed here is rather unique since the connection with specific fractional equations is exploited from the start. The procedure has been designed to be particularly well-suited for application in experimental setups, taking advantage of the fact that kernel determination only requires temporal data of the transported field measured on an Eulerian grid. The simplicity and robustness of the method is tested first by using fabricated data from continuous-time random walk models built with prescribed transport characteristics. Its strengths are then illustrated on numerical Eulerian data gathered from simulations of a magnetically confined turbulent plasma in a near-critical regime, that is known to exhibit superdiffusive radial transport

Analysis of turbulent free jet hydrogen-air diffusion flames with finite chemical reaction rates

NASA Technical Reports Server (NTRS)

Sislian, J. P.

1978-01-01

The nonequilibrium flow field resulting from the turbulent mixing and combustion of a supersonic axisymmetric hydrogen jet in a supersonic parallel coflowing air stream is analyzed. Effective turbulent transport properties are determined using the (K-epsilon) model. The finite-rate chemistry model considers eight reactions between six chemical species, H, O, H2O, OH, O2, and H2. The governing set of nonlinear partial differential equations is solved by an implicit finite-difference procedure. Radial distributions are obtained at two downstream locations of variables such as turbulent kinetic energy, turbulent dissipation rate, turbulent scale length, and viscosity. The results show that these variables attain peak values at the axis of symmetry. Computed distributions of velocity, temperature, and mass fraction are also given. A direct analytical approach to account for the effect of species concentration fluctuations on the mean production rate of species (the phenomenon of unmixedness) is also presented. However, the use of the method does not seem justified in view of the excessive computer time required to solve the resulting system of equations.

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

Volcanic Plume Heights on Mars: Limits of Validity for Convective Models

NASA Technical Reports Server (NTRS)

Glaze, Lori S.; Baloga, Stephen M.

2002-01-01

Previous studies have overestimated volcanic plume heights on Mars. In this work, we demonstrate that volcanic plume rise models, as currently formulated, have only limited validity in any environment. These limits are easily violated in the current Mars environment and may also be violated for terrestrial and early Mars conditions. We indicate some of the shortcomings of the model with emphasis on the limited applicability to current Mars conditions. Specifically, basic model assumptions are violated when (1) vertical velocities exceed the speed of sound, (2) radial expansion rates exceed the speed of sound, (3) radial expansion rates approach or exceed the vertical velocity, or (4) plume radius grossly exceeds plume height. All of these criteria are violated for the typical Mars example given here. Solutions imply that the convective rise, model is only valid to a height of approximately 10 kilometers. The reason for the model breakdown is hat the current Mars atmosphere is not of sufficient density to satisfy the conservation equations. It is likely that diffusion and other effects governed by higher-order differential equations are important within the first few kilometers of rise. When the same criteria are applied to eruptions into a higher-density early Mars atmosphere, we find that eruption rates higher than 1.4 x 10(exp 9) kilograms per second also violate model assumptions. This implies a maximum extent of approximately 65 kilometers for convective plumes on early Mars. The estimated plume heights for both current and early Mars are significantly lower than those previously predicted in the literature. Therefore, global-scale distribution of ash seems implausible.

A theory of self-organized zonal flow with fine radial structure in tokamak

NASA Astrophysics Data System (ADS)

Zhang, Y. Z.; Liu, Z. Y.; Xie, T.; Mahajan, S. M.; Liu, J.

2017-12-01

The (low frequency) zonal flow-ion temperature gradient (ITG) wave system, constructed on Braginskii's fluid model in tokamak, is shown to be a reaction-diffusion-advection system; it is derived by making use of a multiple spatiotemporal scale technique and two-dimensional (2D) ballooning theory. For real regular group velocities of ITG waves, two distinct temporal processes, sharing a very similar meso-scale radial structure, are identified in the nonlinear self-organized stage. The stationary and quasi-stationary structures reflect a particular feature of the poloidal group velocity. The equation set posed to be an initial value problem is numerically solved for JET low mode parameters; the results are presented in several figures and two movies that show the spatiotemporal evolutions as well as the spectrum analysis—frequency-wave number spectrum, auto power spectrum, and Lissajous diagram. This approach reveals that the zonal flow in tokamak is a local traveling wave. For the quasi-stationary process, the cycle of ITG wave energy is composed of two consecutive phases in distinct spatiotemporal structures: a pair of Cavitons growing and breathing slowly without long range propagation, followed by a sudden decay into many Instantons that carry negative wave energy rapidly into infinity. A spotlight onto the motion of Instantons for a given radial position reproduces a Blob-Hole temporal structure; the occurrence as well as the rapid decay of Caviton into Instantons is triggered by zero-crossing of radial group velocity. A sample of the radial profile of zonal flow contributed from 31 nonlinearly coupled rational surfaces near plasma edge is found to be very similar to that observed in the JET Ohmic phase [J. C. Hillesheim et al., Phys. Rev. Lett. 116, 165002 (2016)]. The theory predicts an interior asymmetric dipole structure associated with the zonal flow that is driven by the gradients of ITG turbulence intensity.

Wind-driving protostellar accretion discs - I. Formulation and parameter constraints

NASA Astrophysics Data System (ADS)

Königl, Arieh; Salmeron, Raquel; Wardle, Mark

2010-01-01

We study a model of weakly ionized, protostellar accretion discs that are threaded by a large-scale, ordered magnetic field and power a centrifugally driven wind. We consider the limiting case where the wind is the main repository of the excess disc angular momentum and generalize the radially localized disc model of Wardle & Königl, which focused on the ambipolar diffusion regime, to other field diffusivity regimes, notably Hall and Ohm. We present a general formulation of the problem for nearly Keplerian, vertically isothermal discs using both the conductivity-tensor and the multifluid approaches and simplify it to a normalized system of ordinary differential equations in the vertical space coordinate. We determine the relevant parameters of the problem and investigate, using the vertical-hydrostatic-equilibrium approximation and other simplifications, the parameter constraints on physically viable solutions for discs in which the neutral particles are dynamically well coupled to the field already at the mid-plane. When the charged particles constitute a two-component ion-electron plasma, one can identify four distinct sub-regimes in the parameter domain where the Hall diffusivity dominates and three sub-regimes in the Ohm-dominated domain. Two of the Hall sub-regimes can be characterized as being ambipolar diffusion-like and two as being Ohm-like: the properties of one member of the first pair of sub-regimes are identical to those of the ambipolar diffusion regime, whereas one member of the second pair has the same characteristics as one of the Ohm sub-regimes. All the Hall sub-regimes have Brb/|Bφb| (ratio of radial-to-azimuthal magnetic field amplitudes at the disc surface) >1, whereas in two Ohm sub-regimes this ratio is <1. When the two-component plasma consists, instead, of positively and negatively charged grains of equal mass, the entire Hall domain and one of the Ohm sub-regimes with Brb/|Bφb| < 1 disappear. All viable solutions require the mid-plane neutral-ion momentum exchange time to be shorter than the local orbital time. We also infer that vertical magnetic squeezing always dominates over gravitational tidal compression in this model. In a follow-up paper we will present exact solutions that test the results of this analysis in the Hall regime.

One-dimensional analysis of plane and radial thin film flows including solid-body rotation

NASA Technical Reports Server (NTRS)

Thomas, S.; Hankey, W.; Faghri, A.; Swanson, T.

1989-01-01

The flow of a thin liquid film with a free surface along a horizontal plate which emanates from a pressurized vessel is examined by integrating the equations of motion across the thin liquid layer and discretizing the integrated equations using finite difference techniques. The effects of 0-g and solid-body rotation will be discussed. The two cases of interest are plane flow and radial flow. In plane flow, the liquid is considered to be flowing along a channel with no change in the width of the channel, whereas in radial flow the liquid spreads out radially over a disk, so that the area changes along the radius. It is desired to determine the height of the liquid film at any location along the plate of disk, so that the heat transfer from the plate or disk can be found. The possibility that the flow could encounter a hydraulic jump is accounted for.

Analytical bound-state solutions of the Schrödinger equation for the Manning-Rosen plus Hulthén potential within SUSY quantum mechanics

NASA Astrophysics Data System (ADS)

Ahmadov, A. I.; Naeem, Maria; Qocayeva, M. V.; Tarverdiyeva, V. A.

2018-01-01

In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any l≠0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

Variability in radial sap flux density patterns and sapwood area among seven co-occurring temperate broad-leaved tree species.

PubMed

Gebauer, Tobias; Horna, Viviana; Leuschner, Christoph

2008-12-01

Forest transpiration estimates are frequently based on xylem sap flux measurements in the outer sections of the hydro-active stem sapwood. We used Granier's constant-heating technique with heating probes at various xylem depths to analyze radial patterns of sap flux density in the sapwood of seven broad-leaved tree species differing in wood density and xylem structure. Study aims were to (1) compare radial sap flux density profiles between diffuse- and ring-porous trees and (2) analyze the relationship between hydro-active sapwood area and stem diameter. In all investigated species except the diffuse-porous beech (Fagus sylvatica L.) and ring-porous ash (Fraxinus excelsior L.), sap flux density peaked at a depth of 1 to 4 cm beneath the cambium, revealing a hump-shaped curve with species-specific slopes. Beech and ash reached maximum sap flux densities immediately beneath the cambium in the youngest annual growth rings. Experiments with dyes showed that the hydro-active sapwood occupied 70 to 90% of the stem cross-sectional area in mature trees of diffuse-porous species, whereas it occupied only about 21% in ring-porous ash. Dendrochronological analyses indicated that vessels in the older sapwood may remain functional for 100 years or more in diffuse-porous species and for up to 27 years in ring-porous ash. We conclude that radial sap flux density patterns are largely dependent on tree species, which may introduce serious bias in sap-flux-derived forest transpiration estimates, if non-specific sap flux profiles are assumed.

Radial orbit error reduction and sea surface topography determination using satellite altimetry

NASA Technical Reports Server (NTRS)

Engelis, Theodossios

1987-01-01

A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface topography with minimum wavelengths of about 500 km and to reduce the radial orbit error caused by geopotential errors. The modeling of the radial orbit error is made using the linearized Lagrangian perturbation theory. Secular and second order effects are also included. After a rather extensive validation of the linearized equations, alternative expressions of the radial orbit error are derived. Numerical estimates for the radial orbit error and geoid undulation error are computed using the differences of two geopotential models as potential coefficient errors, for a SEASAT orbit. To provide statistical estimates of the radial distances and the geoid, a covariance propagation is made based on the full geopotential covariance. Accuracy estimates for the SEASAT orbits are given which agree quite well with already published results. Observation equations are develped using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information provides estimates of parameters representing the sea surface topography and corrections to the gravity field that is used for the orbit generation. The simulation results show that the method can be used to effectively reduce the radial orbit error and recover the sea surface topography.

Comment on "A note on generalized radial mesh generation for plasma electronic structure"

NASA Astrophysics Data System (ADS)

Pain, J.-Ch.

2011-12-01

In a recent note, B.G. Wilson and V. Sonnad [1] proposed a very useful closed form expression for the efficient generation of analytic log-linear radial meshes. The central point of the note is an implicit equation for the parameter h, involving Lambert's function W[x]. The authors mention that they are unaware of any direct proof of this equation (they obtained it by re-summing the Taylor expansion of h[α] using high-order coefficients obtained by analytic differentiation of the implicit definition using symbolic manipulation). In the present comment, we propose a direct proof of that equation.

Ambipolarity in a tokamak with magnetic field ripple

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

Hazeltine, R. D.

In view of the recognized importance of electrostatic fields regarding turbulent transport, the radial electric field in a tokamak with magnetic field ripple is reconsidered. Terms in the ambipolarity condition involving the radial derivative of the field are derived from an extended drift-kinetic equation, including effects of second order in the gyroradius. Such terms are of interest in part because of their known importance in rotational relaxation equations for the axisymmetric case. The electric field is found to satisfy a nonlinear differential equation that is universal in a certain sense, and that implies spatial relaxation of the potential to itsmore » conventionally predicted value.« less

Obstructed metabolite diffusion within skeletal muscle cells in silico.

PubMed

Aliev, Mayis K; Tikhonov, Alexander N

2011-12-01

Using a Monte Carlo simulation technique, we have modeled 3D diffusion of low molecular weight metabolites inside a skeletal muscle cell. The following structural elements are considered: (i) a regular lattice of actin and myosin filaments inside a myofibril, (ii) the membranes of sarcoplasmic reticulum and mitochondria surrounding the myofibrils, (iii) a set of myofibrils inside a skeletal muscle cell encircled by the outer cell membrane, and (iv) an additional set of regular intracellular structures ("macrocompartments") embedded into the cell interior. The macrocompartments are considered to simulate diffusion restrictions because of hypothetical cylindrical structures (16-22 μm in diameter) suggested earlier (de Graaf et al. Biophys J 78: 1657-1664, 2000). This model allowed us to calculate the apparent coefficients of particle diffusion in the radial and axial directions, D(app)(⊥) and D(app)(II), respectively. Particle movements in the axial direction are considered, at first approximation, as unrestricted diffusion (D(app)(II) = const). The apparent coefficient of radial diffusion, D(app)(⊥), decreases with time because of particle collisions with myofilaments and other rigid obstacles. Results of our random walk simulations are in fairly good agreement with experimental data on NMR measurements of restricted radial diffusion of phosphocreatine in white and red skeletal muscles of goldfish (Kinsey et al. NMR Biomed 12:1-7, 1999). Particle reflections from the low-permeable borders of macrocompartments (efficient diameter, D(eff)(MC) ≈ 9.2-10.4 μm) are the prerequisite for agreeing theoretical and experimental data. The low-permeable coverage of hypothetical macrocompartments (99.8% of coverage) provides the main contribution to time-dependent decrease in D(app)(⊥).

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.

One-dimensional time-dependent fluid model of a very high density low-pressure inductively coupled plasma

DOE PAGES

Chaplin, Vernon H.; Bellan, Paul M.

2015-12-28

A time-dependent two-fluid model has been developed to understand axial variations in the plasma parameters in a very high density (peak n e~ > 5x10 19 m –3) argon inductively coupled discharge in a long 1.1 cm radius tube. The model equations are written in 1D, with radial losses to the tube walls accounted for by the inclusion of effective particle and energy sink terms. The ambipolar diffusion equation and electron energy equation are solved to find the electron density n e(z,t) and temperature T e(z,t), and the populations of the neutral argon 4s metastable, 4s resonant, and 4p excitedmore » state manifolds are calculated in order to determine the stepwise ionization rate and calculate radiative energy losses. The model has been validated through comparisons with Langmuir probe ion saturation current measurements; close agreement between the simulated and measured axial plasma density profiles and the initial density rise rate at each location was obtained at p Ar = 30-60 mTorr. Lastly, we present detailed results from calculations at 60 mTorr, including the time-dependent electron temperature, excited state populations, and energy budget within and downstream of the radiofrequency (RF) antenna.« less

Sensitive period for white-matter connectivity of superior temporal cortex in deaf people.

PubMed

Li, Yanyan; Ding, Guosheng; Booth, James R; Huang, Ruiwang; Lv, Yating; Zang, Yufeng; He, Yong; Peng, Danling

2012-02-01

Previous studies have shown that white matter in the deaf brain changes due to hearing loss. However, how white-matter development is influenced by early hearing experience of deaf people is still unknown. Using diffusion tensor imaging and tract-based spatial statistics, we compared white-matter structures among three groups of subjects including 60 congenitally deaf individuals, 36 acquired deaf (AD) individuals, and 38 sex- and age-matched hearing controls (HC). The result showed that the deaf individuals had significantly reduced fractional anisotropy (FA) values in bilateral superior temporal cortex and the splenium of corpus callosum compared to HC. The reduction of FA values in acquired deafness correlated with onset age of deafness, but not the duration of deafness. To explore the underlying mechanism of FA changes in the deaf groups, we further analyzed radial and axial diffusivities and found that (1) the reduced FA values in deaf individuals compared to HC is primarily driven by higher radial diffusivity values and (2) in the AD, higher radial diffusivity was correlated with earlier onset age of deafness, but not the duration of deafness. These findings imply that early sensory experience is critical for the growth of fiber myelination, and anatomical reorganization following auditory deprivation is sensitive to early plasticity in the brain. Copyright © 2010 Wiley Periodicals, Inc.

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

Radiation belt electron acceleration during the 17 March 2015 geomagnetic storm: Observations and simulations

DOE PAGES

Li, W.; Ma, Q.; Thorne, R. M.; ...

2016-06-10

Various physical processes are known to cause acceleration, loss, and transport of energetic electrons in the Earth's radiation belts, but their quantitative roles in different time and space need further investigation. During the largest storm over the past decade (17 March 2015), relativistic electrons experienced fairly rapid acceleration up to ~7 MeV within 2 days after an initial substantial dropout, as observed by Van Allen Probes. In the present paper, we evaluate the relative roles of various physical processes during the recovery phase of this large storm using a 3-D diffusion simulation. By quantitatively comparing the observed and simulated electronmore » evolution, we found that chorus plays a critical role in accelerating electrons up to several MeV near the developing peak location and produces characteristic flat-top pitch angle distributions. By only including radial diffusion, the simulation underestimates the observed electron acceleration, while radial diffusion plays an important role in redistributing electrons and potentially accelerates them to even higher energies. Moreover, plasmaspheric hiss is found to provide efficient pitch angle scattering losses for hundreds of keV electrons, while its scattering effect on > 1 MeV electrons is relatively slow. Although an additional loss process is required to fully explain the overestimated electron fluxes at multi-MeV, the combined physical processes of radial diffusion and pitch angle and energy diffusion by chorus and hiss reproduce the observed electron dynamics remarkably well, suggesting that quasi-linear diffusion theory is reasonable to evaluate radiation belt electron dynamics during this big storm.« less

Quantitative MRI in hypomyelinating disorders: Correlation with motor handicap.

PubMed

Steenweg, Marjan E; Wolf, Nicole I; van Wieringen, Wessel N; Barkhof, Frederik; van der Knaap, Marjo S; Pouwels, Petra J W

2016-08-23

To assess the correlation of tissue parameters estimated by quantitative magnetic resonance (MR) techniques and motor handicap in patients with hypomyelination. Twenty-eight patients with different causes of hypomyelination (12 males, 16 females; mean age 10 years) and 61 controls (33 males, 28 females; mean age 8 years) were prospectively investigated. We quantified T2 relaxation time, magnetization transfer ratio, fractional anisotropy, mean, axial, and radial diffusivities, and brain metabolites. We performed measurements in the splenium, parietal deep white matter, and corticospinal tracts in the centrum semiovale. We further analyzed diffusion measures using tract-based spatial statistics. We estimated severity of motor handicap by the gross motor function classification system. We evaluated correlation of handicap with MR measures by linear regression analyses. Fractional anisotropy, magnetization transfer ratio, choline, and N-acetylaspartate/creatine ratio were lower and diffusivities, T2 values, and inositol were higher in patients than in controls. Tract-based spatial statistics showed that these changes were widespread for fractional anisotropy (96% of the white matter skeleton), radial (93%) and mean (84%) diffusivity, and less so for axial diffusivity (20%). Correlation with handicap yielded radial diffusivity and N-acetylaspartate/creatine ratio as strongest independent explanatory variables. Gross motor function classification system grades are in part explained by MR measures. They indicate that mainly lack of myelin and, to a lesser degree, loss of axonal integrity codetermine the degree of motor handicap in patients with hypomyelinating disorders. These MR measures can be used to evaluate strategies that are aimed at promotion of myelination. © 2016 American Academy of Neurology.

Radiation belt electron acceleration during the 17 March 2015 geomagnetic storm: Observations and simulations

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

Li, W.; Ma, Q.; Thorne, R. M.

Various physical processes are known to cause acceleration, loss, and transport of energetic electrons in the Earth's radiation belts, but their quantitative roles in different time and space need further investigation. During the largest storm over the past decade (17 March 2015), relativistic electrons experienced fairly rapid acceleration up to ~7 MeV within 2 days after an initial substantial dropout, as observed by Van Allen Probes. In the present paper, we evaluate the relative roles of various physical processes during the recovery phase of this large storm using a 3-D diffusion simulation. By quantitatively comparing the observed and simulated electronmore » evolution, we found that chorus plays a critical role in accelerating electrons up to several MeV near the developing peak location and produces characteristic flat-top pitch angle distributions. By only including radial diffusion, the simulation underestimates the observed electron acceleration, while radial diffusion plays an important role in redistributing electrons and potentially accelerates them to even higher energies. Moreover, plasmaspheric hiss is found to provide efficient pitch angle scattering losses for hundreds of keV electrons, while its scattering effect on > 1 MeV electrons is relatively slow. Although an additional loss process is required to fully explain the overestimated electron fluxes at multi-MeV, the combined physical processes of radial diffusion and pitch angle and energy diffusion by chorus and hiss reproduce the observed electron dynamics remarkably well, suggesting that quasi-linear diffusion theory is reasonable to evaluate radiation belt electron dynamics during this big storm.« less

Two-dimensional single-shot diffusion-weighted stimulated EPI with reduced FOV for ultrahigh-b radial diffusion-weighted imaging of spinal cord.

PubMed

Sapkota, Nabraj; Shi, Xianfeng; Shah, Lubdha M; Bisson, Erica F; Rose, John W; Jeong, Eun-Kee

2017-06-01

High-resolution diffusion-weighted imaging (DWI) of the spinal cord (SC) is problematic because of the small cross-section of the SC and the large field inhomogeneity. Obtaining the ultrahigh-b DWI poses a further challenge. The purpose of the study was to design and validate two-dimensional (2D) single-shot diffusion-weighted stimulated echo planar imaging with reduced field of view (2D ss-DWSTEPI-rFOV) for ultrahigh-b radial DWI (UHB-rDWI) of the SC. A novel time-efficient 2D ss-DWSTEPI-rFOV sequence was developed based on the stimulated echo sequence. Reduced-phase field of view was obtained by using two slice-selective 90 ° radiofrequency pulses in the presence of the orthogonal slice selection gradients. The sequence was validated on a cylindrical phantom and demonstrated on SC imaging. Ultrahigh-b radial diffusion-weighted ( bmax = 7300 s/mm2) images of the SC with greatly reduced distortion were obtained. The exponential plus constant fitting of the diffusion-decay curve estimated the constant fraction (restricted water fraction) as 0.36 ± 0.05 in the SC white matter. A novel 2D ss-DWSTEPI-rFOV sequence has been designed and demonstrated for high-resolution UHB-rDWI of localized anatomic structures with significantly reduced distortion induced by nonlinear static field inhomogeneity. Magn Reson Med 77:2167-2173, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Direct Determination of the Dependence of the Surface Shear and Dilatational Viscosities on the Thermodynamic State of the Interface: Theoretical Foundations.

PubMed

Lopez; Hirsa

1998-10-01

Recent developments in nonlinear optical techniques for noninvasive probing of a surfactant influenced gas/liquid interface allow for the measurement of the surfactant surface concentration, c, and thus provide new opportunities for the direct determination of its intrinsic viscosities. Here, we present the theoretical foundations, based on the Boussinesq-Scriven surface model without the usual simplification of constant viscosities, for an experimental technique to directly measure the surface shear (µs) and dilatational (kappas) viscosities of a Newtonian interface as functions of the surfactant surface concentration. This ability to directly measure the surfactant concentration permits the use of a simple surface flow for the measurement of the surface viscosities. The requirements are that the interface must be nearly flat, and the flow steady, axisymmetric, and swirling; these flow conditions can be achieved in the deep-channel viscometer driven at relatively fast rates. The tangential stress balance on such an interface leads to two equations; the balance in the azimuthal direction involves only µs and its gradients, and the balance in the radial direction involves both µs and kappas and their gradients. By further exploiting recent developments in laser-based flow measuring techniques, the surface velocities and their gradients which appear in the two equations can be measured directly. The surface tension gradient, which appears in the radial balance equation, is incorporated from the equation of state for the surfactant system and direct measurements of the surfactant surface concentration distribution. The stress balance equations are then ordinary differential equations in the surface viscosities as functions of radial position, which can be readily integrated. Since c is measured as a function of radial position, we then have a direct measurement of µs and kappas as functions of c. Numerical computations of the Navier-Stokes equations are performed to determine the appropriate conditions to achieve the requisite secondary flow. Copyright 1998 Academic Press.

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.

POTHMF: A program for computing potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Gerdt, V. P.; Rostovtsev, V. A.; Vinitsky, S. I.; Abrashkevich, A. G.; Kaschiev, M. S.; Serov, V. V.

2008-02-01

A FORTRAN 77 program is presented which calculates with the relative machine precision potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field. The potential curves are eigenvalues corresponding to the angular oblate spheroidal functions that compose adiabatic basis which depends on the radial variable as a parameter. The matrix elements of radial coupling are integrals in angular variables of the following two types: product of angular functions and the first derivative of angular functions in parameter, and product of the first derivatives of angular functions in parameter, respectively. The program calculates also the angular part of the dipole transition matrix elements (in the length form) expressed as integrals in angular variables involving product of a dipole operator and angular functions. Moreover, the program calculates asymptotic regular and irregular matrix solutions of the coupled adiabatic radial equations at the end of interval in radial variable needed for solving a multi-channel scattering problem by the generalized R-matrix method. Potential curves and radial matrix elements computed by the POTHMF program can be used for solving the bound state and multi-channel scattering problems. As a test desk, the program is applied to the calculation of the energy values, a short-range reaction matrix and corresponding wave functions with the help of the KANTBP program. Benchmark calculations for the known photoionization cross-sections are presented. Program summaryProgram title:POTHMF Catalogue identifier:AEAA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAA_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:8123 No. of bytes in distributed program, including test data, etc.:131 396 Distribution format:tar.gz Programming language:FORTRAN 77 Computer:Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system:OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM:Depends on the number of radial differential equations; the number and order of finite elements; the number of radial points. Test run requires 4 MB Classification:2.5 External routines:POTHMF uses some Lapack routines, copies of which are included in the distribution (see README file for details). Nature of problem:In the multi-channel adiabatic approach the Schrödinger equation for a hydrogen-like atom in a homogeneous magnetic field of strength γ ( γ=B/B, B≅2.35×10 T is a dimensionless parameter which determines the field strength B) is reduced by separating the radial coordinate, r, from the angular variables, (θ,φ), and using a basis of the angular oblate spheroidal functions [3] to a system of second-order ordinary differential equations which contain first-derivative coupling terms [4]. The purpose of this program is to calculate potential curves and matrix elements of radial coupling needed for calculating the low-lying bound and scattering states of hydrogen-like atoms in a homogeneous magnetic field of strength 0<γ⩽1000 within the adiabatic approach [5]. The program evaluates also asymptotic regular and irregular matrix radial solutions of the multi-channel scattering problem needed to extract from the R-matrix a required symmetric shortrange open-channel reaction matrix K [6] independent from matching point [7]. In addition, the program computes the dipole transition matrix elements in the length form between the basis functions that are needed for calculating the dipole transitions between the low-lying bound and scattering states and photoionization cross sections [8]. Solution method:The angular oblate spheroidal eigenvalue problem depending on the radial variable is solved using a series expansion in the Legendre polynomials [3]. The resulting tridiagonal symmetric algebraic eigenvalue problem for the evaluation of selected eigenvalues, i.e. the potential curves, is solved by the LDLT factorization using the DSTEVR program [2]. Derivatives of the eigenfunctions with respect to the radial variable which are contained in matrix elements of the coupled radial equations are obtained by solving the inhomogeneous algebraic equations. The corresponding algebraic problem is solved by using the LDLT factorization with the help of the DPTTRS program [2]. Asymptotics of the matrix elements at large values of radial variable are computed using a series expansion in the associated Laguerre polynomials [9]. The corresponding matching points between the numeric and asymptotic solutions are found automatically. These asymptotics are used for the evaluation of the asymptotic regular and irregular matrix radial solutions of the multi-channel scattering problem [7]. As a test desk, the program is applied to the calculation of the energy values of the ground and excited bound states and reaction matrix of multi-channel scattering problem for a hydrogen atom in a homogeneous magnetic field using the KANTBP program [10]. Restrictions:The computer memory requirements depend on: the number of radial differential equations; the number and order of finite elements; the total number of radial points. Restrictions due to dimension sizes can be changed by resetting a small number of PARAMETER statements before recompiling (see Introduction and listing for details). Running time:The running time depends critically upon: the number of radial differential equations; the number and order of finite elements; the total number of radial points on interval [r,r]. The test run which accompanies this paper took 7 s required for calculating of potential curves, radial matrix elements, and dipole transition matrix elements on a finite-element grid on interval [ r=0, r=100] used for solving discrete and continuous spectrum problems and obtaining asymptotic regular and irregular matrix radial solutions at r=100 for continuous spectrum problem on the Intel Pentium IV 2.4 GHz. The number of radial differential equations was equal to 6. The accompanying test run using the KANTBP program took 2 s for solving discrete and continuous spectrum problems using the above calculated potential curves, matrix elements and asymptotic regular and irregular matrix radial solutions. Note, that in the accompanied benchmark calculations of the photoionization cross-sections from the bound states of a hydrogen atom in a homogeneous magnetic field to continuum we have used interval [ r=0, r=1000] for continuous spectrum problem. The total number of radial differential equations was varied from 10 to 18. References:W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986. http://www.netlib.org/lapack/. M. Abramovits, I.A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965. U. Fano, Colloq. Int. C.N.R.S. 273 (1977) 127; A.F. Starace, G.L. Webster, Phys. Rev. A 19 (1979) 1629-1640; C.V. Clark, K.T. Lu, A.F. Starace, in: H.G. Beyer, H. Kleinpoppen (Eds.), Progress in Atomic Spectroscopy, Part C, Plenum, New York, 1984, pp. 247-320; U. Fano, A.R.P. Rau, Atomic Collisions and Spectra, Academic Press, Florida, 1986. M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352; O. Chuluunbaatar, A.A. Gusev, V.L. Derbov, M.S. Kaschiev, V.V. Serov, T.V. Tupikova, S.I. Vinitsky, Proc. SPIE 6537 (2007) 653706-1-18. M.J. Seaton, Rep. Prog. Phys. 46 (1983) 167-257. M. Gailitis, J. Phys. B 9 (1976) 843-854; J. Macek, Phys. Rev. A 30 (1984) 1277-1278; S.I. Vinitsky, V.P. Gerdt, A.A. Gusev, M.S. Kaschiev, V.A. Rostovtsev, V.N. Samoylov, T.V. Tupikova, O. Chuluunbaatar, Programming and Computer Software 33 (2007) 105-116. H. Friedrich, Theoretical Atomic Physics, Springer, New York, 1991. R.J. Damburg, R.Kh. Propin, J. Phys. B 1 (1968) 681-691; J.D. Power, Phil. Trans. Roy. Soc. London A 274 (1973) 663-702. O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Comm. 177 (2007) 649-675.

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.

Solar wind and the motion of dust grains

NASA Astrophysics Data System (ADS)

Klačka, J.; Petržala, J.; Pástor, P.; Kómar, L.

2012-04-01

In this paper, we investigate the action of solar wind on an arbitrarily shaped interplanetary dust particle. The final relativistically covariant equation of motion of the particle also contains the change of the particle's mass. The non-radial solar wind velocity vector is also included. The covariant equation of motion reduces to the Poynting-Robertson effect in the limiting case when a spherical particle is treated, when the speed of the incident solar wind corpuscles tends to the speed of light and when the corpuscles spread radially from the Sun. The results of quantum mechanics have to be incorporated into the physical considerations, in order to obtain the limiting case. If the solar wind affects the motion of a spherical interplanetary dust particle, then ?. Here, p'in and p'out are the incoming and outgoing radiation momenta (per unit time), respectively, measured in the proper frame of reference of the particle, and ? and ? are the solar wind pressure and the total scattering cross-sections, respectively. An analytical solution of the derived equation of motion yields a qualitative behaviour consistent with numerical calculations. This also holds if we consider a decrease of the particle's mass. Using numerical integration of the derived equation of motion, we confirm our analytical result that the non-radial solar wind (with a constant value of angle between the radial direction and the direction of the solar wind velocity) causes outspiralling of the dust particle from the Sun for large values of the particle's semimajor axis. The non-radial solar wind also increases the time the particle spirals towards the Sun. If we consider the periodical variability of the solar wind with the solar cycle, then there are resonances between the particle's orbital period and the period of the solar cycle.

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.

The ionizing effect of low-energy cosmic rays from a class II object on its protoplanetary disc

NASA Astrophysics Data System (ADS)

Rodgers-Lee, D.; Taylor, A. M.; Ray, T. P.; Downes, T. P.

2017-11-01

We investigate the ionizing effect of low-energy cosmic rays (CRs) from a young star on its protoplanetary disc (PPD). We consider specifically the effect of ∼3 GeV protons injected at the inner edge of the PPD. An increase in the ionization fraction as a result of these CRs could allow the magnetorotational instability to operate in otherwise magnetically dead regions of the disc. For the typical values assumed we find an ionization rate of ζCR ∼ 10-17 s-1 at 1 au. The transport equation is solved by treating the propagation of the CRs as diffusive. We find for increasing diffusion coefficients the CRs penetrate further in the PPD, while varying the mass density profile of the disc is found to have little effect. We investigate the effect of an energy spectrum of CRs. The influence of a disc wind is examined by including an advective term. For advective wind speeds between 1 and 100 km s-1 diffusion dominates at all radii considered here (out to 10 au) for reasonable diffusion coefficients. Overall, we find that low-energy CRs can significantly ionize the mid-plane of PPDs out to ∼1 au. By increasing the luminosity or energy of the CRs, within plausible limits, their radial influence could increase to ∼2 au at the mid-plane but it remains challenging to significantly ionize the mid-plane further out.

Interaction of non-radially symmetric camphor particles

NASA Astrophysics Data System (ADS)

Ei, Shin-Ichiro; Kitahata, Hiroyuki; Koyano, Yuki; Nagayama, Masaharu

2018-03-01

In this study, the interaction between two non-radially symmetric camphor particles is theoretically investigated and the equation describing the motion is derived as an ordinary differential system for the locations and the rotations. In particular, slightly modified non-radially symmetric cases from radial symmetry are extensively investigated and explicit motions are obtained. For example, it is theoretically shown that elliptically deformed camphor particles interact so as to be parallel with major axes. Such predicted motions are also checked by real experiments and numerical simulations.

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.

Asymptotics of a Class of Solutions to the Cylindrical Toda Equations

NASA Astrophysics Data System (ADS)

Tracy, Craig A.; Widom, Harold

The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, , have the representation where Kk$ are integral operators. This class includes the n-periodic cylindrical Toda equations. For n=2 our results reduce to the previously computed asymptotics of the 2D radial sinh-Gordon equation and for n=3 (and with an additional symmetry constraint) they reduce to earlier results for the radial Bullough-Dodd equation. Both of these special cases are examples of Painlevé III and have arisen in various applications. The asymptotics of are derived by computing the small t asymptotics where explicit formulas are given for the quantities ak and bk. The method consists of showing that the resolvent operator of Kk has an approximation in terms of resolvents of certain Wiener-Hopf operators, for which there are explicit integral formulas.

Thermodynamics properties study of diatomic molecules with q-deformed modified Poschl-Teller plus Manning Rosen non-central potential in D dimensions using SUSYQM approach

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Pratiwi, B. N.

2016-04-01

D-dimensional Dirac equation of q-deformed modified Poschl-Teller plus Manning Rosen non-central potential was solved using supersymmetric quantum mechanics (SUSY QM). The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial part of D dimensional Dirac equation and the angular quantum numbers were obtained from angular part of D dimensional Dirac equation. The SUSY operators was used to generate the D dimensional relativistic wave functions both for radial and angular parts. In the non-relativistic limit, the relativistic energy equation was reduced to the non-relativistic energy. In the classical limit, the partition function of vibrational, the specific heat of vibrational, and the mean energy of vibrational of some diatomic molecules were calculated from the equation of non-relativistic energy with the help of error function and Mat-lab 2011.

Analysis of Three-Dimensional, Nonlinear Development of Wave-Like Structure in a Compressible Round Jet

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Mankbadi, Reda R.

2002-01-01

An analysis of the nonlinear development of the large-scale structures or instability waves in compressible round jets was conducted using the integral energy method. The equations of motion were decomposed into two sets of equations; one set governing the mean flow motion and the other set governing the large-scale structure motion. The equations in each set were then combined to derive kinetic energy equations that were integrated in the radial direction across the jet after the boundary-layer approximations were applied. Following the application of further assumptions regarding the radial shape of the mean flow and the large structures, equations were derived that govern the nonlinear, streamwise development of the large structures. Using numerically generated mean flows, calculations show the energy exchanges and the effects of the initial amplitude on the coherent structure development in the jet.

Dynamics of charged bulk viscous collapsing cylindrical source with heat flux

NASA Astrophysics Data System (ADS)

Shah, S. M.; Abbas, G.

2017-04-01

In this paper, we have explored the effects of dissipation on the dynamics of charged bulk viscous collapsing cylindrical source which allows the out-flow of heat flux in the form of radiations. The Misner-Sharp formalism has been implemented to drive the dynamical equation in terms of proper time and radial derivatives. We have investigated the effects of charge and bulk viscosity on the dynamics of collapsing cylinder. To determine the effects of radial heat flux, we have formulated the heat transport equations in the context of Müller-Israel-Stewart theory by assuming that thermodynamics viscous/heat coupling coefficients can be neglected within some approximations. In our discussion, we have introduced the viscosity by the standard (non-causal) thermodynamics approach. The dynamical equations have been coupled with the heat transport equation; the consequences of the resulting coupled heat equation have been analyzed in detail.

Scanning thermal probe microscope method for the determination of thermal diffusivity of nanocomposite thin films

NASA Astrophysics Data System (ADS)

Varandani, Deepak; Agarwal, Khushboo; Brugger, Juergen; Mehta, Bodh Raj

2016-08-01

A commercial scanning thermal microscope has been upgraded to facilitate its use in estimating the radial thermal diffusivity of thin films close to room temperature. The modified setup includes a microcontroller driven microhotplate coupled with a Bluetooth module for wireless control. The microcontroller board (Arduino Leonardo) is used to generate a bias of suitable voltage amplitude and pulse duration which is applied across the microhotplate contact pads. A corresponding heat pulse from the Pt heating element (1 mm2) embedded within the microhotplate is delivered to the lower surface of the thin film (25 mm2) deposited over it. The large difference in the dimensions of the heating source and the thin film surface causes heat to flow radially outwards on the top surface of the latter. The decay of this radial heat wave as it flows outwards is recorded by the scanning thermal microscope in terms of temperature-time (T-t) profiles at varying positions around the central heating zone. A fitting procedure is suggested to extract the thermal diffusivity value from the array of T-t profiles. The efficacy of the above setup has been established by evaluating the thermal diffusivities of Bi2Te3 and Bi2Te3:Si thin film samples. Further, with only minor alterations in design the capabilities of the above setup can be extended to estimate the axial thermal diffusivity and specific heat of thin films, as a function of temperature.

An inverse moisture diffusion algorithm for the determination of diffusion coefficient

Treesearch

Jen Y. Liu; William T. Simpson; Steve P. Verrill

2000-01-01

The finite difference approximation is applied to estimate the moisture-dependent diffusion coefficient by utilizing test data of isothermal moisture desorption in northern red oak (Quercus rubra). The test data contain moisture distributions at discrete locations across the thickness of specimens, which coincides with the radial direction of northern red oak, and at...

An inverse moisture diffusion algorithm for the determination of diffusion coefficient

Treesearch

Jen Y. Liu; William T. Simpson; Steve P. Verrill

2001-01-01

The finite difference approximation is applied to estimate the moisture-dependent diffusion coefficient by utilizing test data of isothermal moisture desorption in northern red oak (Quercus rubra). The test data contain moisture distributions at discrete locations across the thickness of specimens, which coincides with the radial direction of northern red oak, and at...

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.

Operational Real-time Forecast of MeV Electrons at Geosynchronous Orbit Based on ACE and GOES-10 Measurements

NASA Astrophysics Data System (ADS)

Li, X.; Temerin, M. A.; Monk, S.; Baker, D. N.; Reeves, G. D.

2002-05-01

The MeV electrons, also known as `killer electrons', have a deleterious impact on satellites through deep dielectric charging and the bodies of astronauts through radiation damage during extravehicular activity. Using a recently developed model based on the standard radial diffusion equation [Li et al., 2001], we show that the intensity of these MeV electrons at geosynchronous orbit can be quantitatively predicted 1-2 days in advance given knowledge of the solar wind. Our current model is operating in real-time, using real-time data from ACE and GOES-10, to make forecast of >2 MeV eletrons at geosynchronous orbit up to 48 hours in advance, the results are available on the web, currently updated every two hours (http://lasp.colorado.edu/~monk/xlf2.html).

An experimental investigation of two large annular diffusers with swirling and distorted inflow

NASA Technical Reports Server (NTRS)

Eckert, W. T.; Johnston, J. P.; Simons, T. D.; Mort, K. W.; Page, V. R.

1980-01-01

Two annular diffusers downstream of a nacelle-mounted fan were tested for aerodynamic performance, measured in terms of two static pressure recovery parameters (one near the diffuser exit plane and one about three diameters downstream in the settling duct) in the presence of several inflow conditions. The two diffusers each had an inlet diameter of 1.84 m, an area ratio of 2.3, and an equivalent cone angle of 11.5, but were distinguished by centerbodies of different lengths. The dependence of diffuser performance on various combinations of swirling, radially distorted, and/or azimuthally distorted inflow was examined. Swirling flow and distortions in the axial velocity profile in the annulus upstream of the diffuser inlet were caused by the intrinsic flow patterns downstream of a fan in a duct and by artificial intensification of the distortions. Azimuthal distortions or defects were generated by the addition of four artificial devices (screens and fences). Pressure recovery data indicated beneficial effects of both radial distortion (for a limited range of distortion levels) and inflow swirl. Small amounts of azimuthal distortion created by the artificial devices produced only small effects on diffuser performance. A large artificial distortion device was required to produce enough azimuthal flow distortion to significantly degrade the diffuser static pressure recovery.

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.

Time-dependent modulation of galactic cosmic rays by merged interaction regions

NASA Technical Reports Server (NTRS)

Perko, J. S.

1993-01-01

Models that solve the one-dimensional, solar modulation equation have reproduced the 11-year galactic cosmic ray using functional representations of global merged interaction regions (MIRs). This study extends those results to the solution of the modulation equation with explicit time dependence. The magnetometers on Voyagers 1 and 2 provide local magnetic field intensities at regular intervals, from which one calculates the ratio of the field intensity to the average local field. These ratios in turn are inverted to form diffusion coefficients. Strung together in radius and time, these coefficents then fall and rise with the strength of the interplanetary magnetic field, becoming representations of MIRs. These diffusion coefficients, calculated locally, propagate unchanged from approx. 10 AU to the outer boundary (120 AU). Inside 10 AU, all parameters, including the diffusion coefficient are assumed constant in time and space. The model reproduces the time-intensity profiles of Voyager 2 and Pioneer 10. Radial gradient data from 1982-1990 between Pioneer 10 and Voyager 2 are about the same magnitude as those calculated in the model. It is also shows agreement in rough magnitude with the radial gradient between Pioneer 10 and 1 AU. When coupled with enhanced, time-dependent solar wind speed at the probe's high latitude, as measured by independent observers, the model also follows Voyager 1's time-intensity profile reasonably well, providing a natural source the model also follows Voyager 1's time-intensity profile reasonably well, providing a natural source for the observed negative latitudinal gradients. The model exhibits the 11-year cyclical cosmic ray intensity behavior at all radii, including 1 AU, not just at the location of the spacecraft where the magnetic fields are measured. In addition, the model's point of cosmic ray maximum correctly travels at the solar wind speed, illustrating the well-known propagation of modulation. Finally, at least in the inner heliosphere this model accounts for the delay experienced by lower-rigidity protons in reaching their time-intensity peak. The actual delays in this model, however, are somewhat smaller than the data. In the outer heliosphere the models sees no delays, and the data are ambiguous as to their existence. It appears that strong magnetic field compression regions (merged interaction regions) that are 3-4 times the average field strength can, at least in a helioequatorial band, disrupt effects, such as drifts, that could dominate in quieter magnetic fields. The question remains: Is the heliosphere ever quiet enough to allow such effects to be unambiguously measured, at least in the midlatitudes?

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

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.

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.

Controlled Formation of Radial Core-Shell Si/Metal Silicide Crystalline Heterostructures.

PubMed

Kosloff, Alon; Granot, Eran; Barkay, Zahava; Patolsky, Fernando

2018-01-10

The highly controlled formation of "radial" silicon/NiSi  core-shell nanowire heterostructures has been demonstrated for the first time. Here, we investigated the "radial" diffusion of nickel atoms into crystalline nanoscale silicon pillar 11 cores, followed by nickel silicide phase formation and the creation of a well-defined shell structure. The described approach is based on a two-step thermal process, which involves metal diffusion at low temperatures in the range of 200-400 °C, followed by a thermal curing step at a higher temperature of 400 °C. In-depth crystallographic analysis was performed by nanosectioning the resulting silicide-shelled silicon nanopillar heterostructures, giving us the ability to study in detail the newly formed silicide shells. Remarkably, it was observed that the resulting silicide shell thickness has a self-limiting behavior, and can be tightly controlled by the modulation of the initial diffusion-step temperature. In addition, electrical measurements of the core-shell structures revealed that the resulting shells can serve as an embedded conductive layer in future optoelectronic applications. This research provides a broad insight into the Ni silicide "radial" diffusion process at the nanoscale regime, and offers a simple approach to form thickness-controlled metal silicide shells in the range of 5-100 nm around semiconductor nanowire core structures, regardless the diameter of the nanowire cores. These high quality Si/NiSi core-shell nanowire structures will be applied in the near future as building blocks for the creation of utrathin highly conductive optically transparent top electrodes, over vertical nanopillars-based solar cell devices, which may subsequently lead to significant performance improvements of these devices in terms of charge collection and reduced recombination.

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.

Generation and Sustainment of Plasma Rotation by ICRF Heating

NASA Astrophysics Data System (ADS)

Perkins, F. W.

2000-10-01

When tokamak plasmas are heated by the fundamental minority ion-cyclotron process, they are observed to rotate toroidally, even though this heating process introduces negligable angular momentum. This work proposes and evaluates a physics mechanism which resolves this apparent conflict. The argument has two elements. First, it is assumed that angular momentum transport is governed by a diffusion equation with a v_tor = 0 boundary condition at the plasma surface and a torque-density source. When the source consists of separated regions of positive and negative torque density, a finite central rotation velocity results, even though the volume integrated torque density - the angular momentum input - vanishes. Secondly, ions energized by the ICRF process can generate separated regions of positive and negative torque density. Heating increases their banana widths which leads to radial energetic-particle transport that must be balanced by neutralizing radial currents and a j_rB_pR torque density in the bulk plasma. Additional, comparable torque density results from collisional transfer of mechanical angular momentum from energetic particles to the bulk plasma and particle loss through banana particles impacting the wall. Monte-Carlo calculations utilizing the ORBIT code evaluate all sources of torque density and rigorously assure that no net angular momentum is introduced. Two models of ICRF heating, diffusive and instantaneous, give similar results. When the resonance location is on the LFS, the calculated rotation has the magnitude, profile, and co-current sense of Alcator C-Mod observations. For HFS resonance locations, the model predicts counter-current rotation. Scans of rotational profiles vs. resonance location, initial energy, particle loss, pitch, and qm will be presented as will the location of the velocity shear layer its scaling to a reactor.

Effect of magnetic fluctuations on the confinement and dynamics of runaway electrons in the HT-7 tokamak

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

Zhou, R. J.; Hu, L. Q.; Li, E. Z.

2013-03-15

The nature of runaway electrons is such that the confinement and dynamics of the electrons can be strongly affected by magnetic fluctuations in plasma. Experimental results in the HT-7 tokamak indicated significant losses of runaway electrons due to magnetic fluctuations, but the loss processes did not only rely on the fluctuation amplitude. Efficient radial runaway transport required that there were no more than small regions of the plasma volume in which there was very low transport of runaways. A radial runaway diffusion coefficient of D{sub r} Almost-Equal-To 10 m{sup 2}s{sup -1} was derived for the loss processes, and diffusion coefficientmore » near the resonant magnetic surfaces and shielding factor #Greek Upsilon With Hook Symbol#=0.8 were deduced. Test particle equations were used to analyze the effect of magnetic fluctuations on runaway dynamics. It was found that the maximum energy that runaways can gain is very sensitive to the value of {alpha}{sub s} (i.e., the fraction of plasma volume with reduced transport). {alpha}{sub s}=(0.28-0.33) was found for the loss processes in the experiment, and maximum runaway energy could be controlled in the range of E=(4 MeV-6 MeV) in this case. Additionally, to control the maximum runaway energy below 5 MeV, the normalized electric field needed to be under a critical value D{sub {alpha}}=6.8, and the amplitude normalized magnetic fluctuations b(tilde sign) needed to be at least of the order of b(tilde sign) Almost-Equal-To 3 Multiplication-Sign 10{sup -5}.« less

Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions.

PubMed

Bauler, Patricia; Huber, Gary A; McCammon, J Andrew

2012-04-28

Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.

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.

Diffusion coefficients in organic-water solutions and comparison with Stokes-Einstein predictions

NASA Astrophysics Data System (ADS)

Evoy, E.; Kamal, S.; Bertram, A. K.

2017-12-01

Diffusion coefficients of organic species in particles containing secondary organic material (SOM) are necessary for predicting the growth and reactivity of these particles in the atmosphere. Previously, the Stokes-Einstein equation combined with viscosity measurements have been used to predict these diffusion coefficients. However, the accuracy of the Stokes-Einstein equation for predicting diffusion coefficients in SOM-water particles has not been quantified. To test the Stokes-Einstein equation, diffusion coefficients of fluorescent organic probe molecules were measured in citric acid-water and sorbitol-water solutions. These solutions were used as proxies for SOM-water particles found in the atmosphere. Measurements were performed as a function of water activity, ranging from 0.26-0.86, and as a function of viscosity ranging from 10-3 to 103 Pa s. Diffusion coefficients were measured using fluorescence recovery after photobleaching. The measured diffusion coefficients were compared with predictions made using the Stokes-Einstein equation combined with literature viscosity data. Within the uncertainties of the measurements, the measured diffusion coefficients agreed with the predicted diffusion coefficients, in all cases.

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

The electron diffusion coefficient in Jupiter's magnetosphere

NASA Technical Reports Server (NTRS)

Birmingham, T.; Northrop, T.; Baxter, R.; Hess, W.; Lojko, M.

1974-01-01

A steady-state model of Jupiter's electron radiation belt is developed. The model includes injection from the solar wind, radial diffusion, energy degradation by synchrotron radiation, and absorption at Jupiter's surface. A diffusion coefficient of the form D sub RR/R sub J squared = k times R to the m-th power is assumed, and then observed data on synchrotron radiation are used to fit the model. The free parameters determined from this fit are m = 1.95 plus or minus 0.5, k = 1.7 plus or minus 0.5 x 10 to the 9th power per sec, and the magnetic moment of injected particles equals 770 plus or minus 300 MeV/G. The value of m shows quite clearly that the diffusion is not caused by magnetic pumping by a variable solar wind or by a fluctuating convection electric field. The process might be field line exchange driven by atmospheric-ionospheric winds; our diffusion coefficient has roughly the same radial dependence but is considerably smaller in magnitude than the upper bound diffusion coefficients recently suggested for this process by Brice and McDonough (1973) and Jacques and Davis (1972).

Tube wave signatures in cylindrically layered poroelastic media computed with spectral method

NASA Astrophysics Data System (ADS)

Karpfinger, Florian; Gurevich, Boris; Valero, Henri-Pierre; Bakulin, Andrey; Sinha, Bikash

2010-11-01

This paper describes a new algorithm based on the spectral method for the computation of Stoneley wave dispersion and attenuation propagating in cylindrical structures composed of fluid, elastic and poroelastic layers. The spectral method is a numerical method which requires discretization of the structure along the radial axis using Chebyshev points. To approximate the differential operators of the underlying differential equations, we use spectral differentiation matrices. After discretizing equations of motion along the radial direction, we can solve the problem as a generalized algebraic eigenvalue problem. For a given frequency, calculated eigenvalues correspond to the wavenumbers of different modes. The advantage of this approach is that it can very efficiently analyse structures with complicated radial layering composed of different fluid, solid and poroelastic layers. This work summarizes the fundamental equations, followed by an outline of how they are implemented in the numerical spectral schema. The interface boundary conditions are then explained for fluid/porous, elastic/porous and porous interfaces. Finally, we discuss three examples from borehole acoustics. The first model is a fluid-filled borehole surrounded by a poroelastic formation. The second considers an additional elastic layer sandwiched between the borehole and the formation, and finally a model with radially increasing permeability is considered.

Magnetic-flutter-induced pedestal plasma transport

NASA Astrophysics Data System (ADS)

Callen, J. D.; Hegna, C. C.; Cole, A. J.

2013-11-01

Plasma toroidal rotation can limit reconnection of externally applied resonant magnetic perturbation (RMP) fields δB on rational magnetic flux surfaces. Hence it causes the induced radial perturbations δBρ to be small there, thereby inhibiting magnetic island formation and stochasticity at the top of pedestals in high (H-mode) confinement tokamak plasmas. However, the δBρs induced by RMPs increase away from rational surfaces and are shown to induce significant sinusoidal radial motion (flutter) of magnetic field lines with a radial extent that varies linearly with δBρ and inversely with distance from the rational surface because of the magnetic shear. This produces a radial electron thermal diffusivity that is (1/2)(δBρ/B0)2 times a kinetically derived, electron-collision-induced, magnetic-shear-reduced, effective parallel electron thermal diffusivity in the absence of magnetic stochasticity. These low collisionality flutter-induced transport processes and thin magnetic island effects are shown to be highly peaked in the vicinity of rational surfaces at the top of low collisionality pedestals. However, the smaller but finite level of magnetic-flutter-induced electron heat transport midway between rational surfaces is the primary factor that determines the electron temperature difference between rational surfaces at the pedestal top. The magnetic-flutter-induced non-ambipolar electron density transport can be large enough to push the plasma toward an electron density transport root. Requiring ambipolar density transport is shown to determine the radial electric field, the plasma toroidal rotation (via radial force balance), a reduced electron thermal diffusivity and increased ambipolar density transport in the pedestal. At high collisionality the various flutter effects are less strongly peaked at rational surfaces and generally less significant. They are thus less likely to exhibit flutter-induced resonant behaviour and transition toward an electron transport root. Magnetic-flutter-induced plasma transport processes provide a new paradigm for developing an understanding of how RMPs modify the pedestal structure to stabilize peeling-ballooning modes and thereby suppress edge localized modes in low collisionality tokamak H-mode plasmas.

Analytical Solutions of the Schrödinger Equation for the Manning-Rosen plus Hulthén Potential Within SUSY Quantum Mechanics

NASA Astrophysics Data System (ADS)

Ahmadov, A. I.; Naeem, Maria; Qocayeva, M. V.; Tarverdiyeva, V. A.

2018-02-01

In this paper, the bound state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by implementing the novel improved scheme to surmount the centrifugal term. The energy eigenvalues and corresponding radial wave functions are defined for any l ≠ 0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods. By using these two different methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

Evolution of dynamo-generated magnetic fields in accretion disks around compact and young stars

NASA Technical Reports Server (NTRS)

Stepinski, Tomasz F.

1994-01-01

Geometrically thin, optically thick, turbulent accretion disks are believed to surround many stars. Some of them are the compact components of close binaries, while the others are throught to be T Tauri stars. These accretion disks must be magnetized objects because the accreted matter, whether it comes from the companion star (binaries) or from a collapsing molecular cloud core (single young stars), carries an embedded magnetic field. In addition, most accretion disks are hot and turbulent, thus meeting the condition for the MHD turbulent dynamo to maintain and amplify any seed field magnetic field. In fact, for a disk's magnetic field to persist long enough in comparison with the disk viscous time it must be contemporaneously regenerated because the characteristic diffusion time of a magnetic field is typically much shorter than a disk's viscous time. This is true for most thin accretion disks. Consequently, studying magentic fields in thin disks is usually synonymous with studying magnetic dynamos, a fact that is not commonly recognized in the literature. Progress in studying the structure of many accretion disks was achieved mainly because most disks can be regarded as two-dimensional flows in which vertical and radial structures are largely decoupled. By analogy, in a thin disk, one may expect that vertical and radial structures of the magnetic field are decoupled because the magnetic field diffuses more rapidly to the vertical boundary of the disk than along the radius. Thus, an asymptotic method, called an adiabatic approximation, can be applied to accretion disk dynamo. We can represent the solution to the dynamo equation in the form B = Q(r)b(r,z), where Q(r) describes the field distribution along the radius, while the field distribution across the disk is included in the vector function b, which parametrically depends on r and is normalized by the condition max (b(z)) = 1. The field distribution across the disk is established rapidly, while the radial distribution Q(r) evolves on a considerably longer timescale. It is this evolution that is the subject of this paper.

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.

Numerical investigation of a centrifugal compressor with circumferential grooves in vane diffuser

NASA Astrophysics Data System (ADS)

Chen, X. F.; Qin, G. L.; Ai, Z. J.

2015-08-01

Enhancing stall and surge margin has a great importance for the development of turbo compressors. The application of casing treatment is an effective measure to expand the stall margin and stable operation range. Numerical investigations were conducted to predict the performance of a low flow rate centrifugal compressor with circumferential groove casing treatment in vane diffuser. Numerical cases with different radial location, radial width and axial depth of a circumferential single groove and different numbers of circumferential grooves were carried out to compare the results. The CFD analyses results show that the centrifugal compressor with circumferential grooves in diffuser can extend stable range by about 9% while the efficiency over the whole operating range decreases by 0.2 to 1.7%. The evaluation based on stall margin improvement showed the optimal position for the groove to be located was indicated to exist near the leading edge of the diffuser, and a combination of position, width, depth and numbers of circumferential grooves that will maximize both surge margin range and efficiency.

Design of Multishell Sampling Schemes with Uniform Coverage in Diffusion MRI

PubMed Central

Caruyer, Emmanuel; Lenglet, Christophe; Sapiro, Guillermo; Deriche, Rachid

2017-01-01

Purpose In diffusion MRI, a technique known as diffusion spectrum imaging reconstructs the propagator with a discrete Fourier transform, from a Cartesian sampling of the diffusion signal. Alternatively, it is possible to directly reconstruct the orientation distribution function in q-ball imaging, providing so-called high angular resolution diffusion imaging. In between these two techniques, acquisitions on several spheres in q-space offer an interesting trade-off between the angular resolution and the radial information gathered in diffusion MRI. A careful design is central in the success of multishell acquisition and reconstruction techniques. Methods The design of acquisition in multishell is still an open and active field of research, however. In this work, we provide a general method to design multishell acquisition with uniform angular coverage. This method is based on a generalization of electrostatic repulsion to multishell. Results We evaluate the impact of our method using simulations, on the angular resolution in one and two bundles of fiber configurations. Compared to more commonly used radial sampling, we show that our method improves the angular resolution, as well as fiber crossing discrimination. Discussion We propose a novel method to design sampling schemes with optimal angular coverage and show the positive impact on angular resolution in diffusion MRI. PMID:23625329

Influence of mean radial electric field on particle transport induced by RMPs in tokamak plasmas

NASA Astrophysics Data System (ADS)

Chen, Dunqiang; Xu, Yingfeng; Wang, Shaojie

2018-06-01

The quasi-linear theory of the particle diffusion coefficient including the finite Larmor radius effect and the mean radial electric field ( E r without shear) in a stochastic magnetic field is derived. The theory has been verified by comparing with test particle simulations and previous theory. It is found that E r can shift the wave-particle resonance position. The Er-shift effect mainly modifies the ion diffusion coefficients and leads to the modification of ion particle flux. By using the ambipolar condition, we obtained the balanced flux at the edge of a tokamak plasma and found good agreement with recent experimental observations.

Reduction of ion thermal diffusivity associated with the transition of the radial electric field in neutral-beam-heated plasmas in the large helical device.

PubMed

Ida, K; Funaba, H; Kado, S; Narihara, K; Tanaka, K; Takeiri, Y; Nakamura, Y; Ohyabu, N; Yamazaki, K; Yokoyama, M; Murakami, S; Ashikawa, N; deVries, P C; Emoto, M; Goto, M; Idei, H; Ikeda, K; Inagaki, S; Inoue, N; Isobe, M; Itoh, K; Kaneko, O; Kawahata, K; Khlopenkov, K; Komori, A; Kubo, S; Kumazawa, R; Liang, Y; Masuzaki, S; Minami, T; Miyazawa, J; Morisaki, T; Morita, S; Mutoh, T; Muto, S; Nagayama, Y; Nakanishi, H; Nishimura, K; Noda, N; Notake, T; Kobuchi, T; Ohdachi, S; Ohkubo, K; Oka, Y; Osakabe, M; Ozaki, T; Pavlichenko, R O; Peterson, B J; Sagara, A; Saito, K; Sakakibara, S; Sakamoto, R; Sanuki, H; Sasao, H; Sasao, M; Sato, K; Sato, M; Seki, T; Shimozuma, T; Shoji, M; Suzuki, H; Sudo, S; Tamura, N; Toi, K; Tokuzawa, T; Torii, Y; Tsumori, K; Yamamoto, T; Yamada, H; Yamada, I; Yamaguchi, S; Yamamoto, S; Yoshimura, Y; Watanabe, K Y; Watari, T; Hamada, Y; Motojima, O; Fujiwara, M

2001-06-04

Recent large helical device experiments revealed that the transition from ion root to electron root occurred for the first time in neutral-beam-heated discharges, where no nonthermal electrons exist. The measured values of the radial electric field were found to be in qualitative agreement with those estimated by neoclassical theory. A clear reduction of ion thermal diffusivity was observed after the mode transition from ion root to electron root as predicted by neoclassical theory when the neoclassical ion loss is more dominant than the anomalous ion loss.

Modeling the Magnetopause Shadowing and Drift Orbit Bifurcation Loss during the June 2015 Dropout Event

NASA Astrophysics Data System (ADS)

Tu, W.; Cunningham, G.

2017-12-01

The relativistic electron flux in Earth's radiation belt are observed to drop by orders of magnitude on timescale of a few hours. Where do the electrons go during the dropout? This is one of the most important outstanding questions in radiation belt studies. Here we will study the 22 June 2015 dropout event which occurred during one of the largest geomagnetic storms in the last decade. A sudden and nearly complete loss of all the outer zone relativistic and ultra-relativistic electrons were observed after a strong interplanetary shock. The Last Closed Drift Shell (LCDS) calculated using the TS04 model reached as low as L*=3.7 during the shock and stay below L*=4 for 1 hour. The unusually low LCDS values suggest that magnetopause shadowing and the associated outward radial diffusion can contribute significantly to the observed dropout. In addition, Drift Orbit Bifurcation (DOB) has been suggested as an important loss mechanism for radiation belt electrons, especially when the solar wind dynamic pressure is high, but its relative importance has not been quantified. Here, we will model the June 2015 dropout event using a radial diffusion model that includes physical and event-specific inputs. First, we will trace electron drift shells based on TS04 model to identify the LCDS and bifurcation regions as a function of the 2nd adiabatic invariant (K) and time. To model magnetopause shadowing, electron lifetimes in our model will be set to electron drift periods at L*>LCDS. Electron lifetimes inside the bifurcation region have been estimated by Ukhorskiy et al. [JGR 2011, doi:10.1029/2011JA016623] as a function of L* and K, which will also be implemented in the model. This will be the first effort to include the DOB loss in a comprehensive radiation belt model. Furthermore, to realistically simulate outward radial diffusion, the new radial diffusion coefficients that are calculated based on the realistic TS04 model and include physical K dependence [Cunningham, JGR 2016, doi:10.1002/2015JA021981] will be achieved and included here. With these event-specific and physical model inputs, we will test how well the observed fast dropout during the June 2015 event can be reproduced by our model, and quantify the relative contribution of magnetopause shadowing, outward radial diffusion, and DOB to the fast electron depletion.

Quantitative MRI of the spinal cord and brain in adrenomyeloneuropathy: in vivo assessment of structural changes.

PubMed

Castellano, Antonella; Papinutto, Nico; Cadioli, Marcello; Brugnara, Gianluca; Iadanza, Antonella; Scigliuolo, Graziana; Pareyson, Davide; Uziel, Graziella; Köhler, Wolfgang; Aubourg, Patrick; Falini, Andrea; Henry, Roland G; Politi, Letterio S; Salsano, Ettore

2016-06-01

Adrenomyeloneuropathy is the late-onset form of X-linked adrenoleukodystrophy, and is considered the most frequent metabolic hereditary spastic paraplegia. In adrenomyeloneuropathy the spinal cord is the main site of pathology. Differently from quantitative magnetic resonance imaging of the brain, little is known about the feasibility and utility of advanced neuroimaging in quantifying the spinal cord abnormalities in hereditary diseases. Moreover, little is known about the subtle pathological changes that can characterize the brain of adrenomyeloneuropathy subjects in the early stages of the disease. We performed a cross-sectional study on 13 patients with adrenomyeloneuropathy and 12 age-matched healthy control subjects who underwent quantitative magnetic resonance imaging to assess the structural changes of the upper spinal cord and brain. Total cord areas from C2-3 to T2-3 level were measured, and diffusion tensor imaging metrics, i.e. fractional anisotropy, mean, axial and radial diffusivity values were calculated in both grey and white matter of spinal cord. In the brain, grey matter regions were parcellated with Freesurfer and average volume and thickness, and mean diffusivity and fractional anisotropy from co-registered diffusion maps were calculated in each region. Brain white matter diffusion tensor imaging metrics were assessed using whole-brain tract-based spatial statistics, and tractography-based analysis on corticospinal tracts. Correlations among clinical, structural and diffusion tensor imaging measures were calculated. In patients total cord area was reduced by 26.3% to 40.2% at all tested levels (P < 0.0001). A mean 16% reduction of spinal cord white matter fractional anisotropy (P ≤ 0.0003) with a concomitant 9.7% axial diffusivity reduction (P < 0.009) and 34.5% radial diffusivity increase (P < 0.009) was observed, suggesting co-presence of axonal degeneration and demyelination. Brain tract-based spatial statistics showed a marked reduction of fractional anisotropy, increase of radial diffusivity (P < 0.001) and no axial diffusivity changes in several white matter tracts, including corticospinal tracts and optic radiations, indicating predominant demyelination. Tractography-based analysis confirmed the results within corticospinal tracts. No significant cortical volume and thickness reduction or grey matter diffusion tensor imaging values alterations were observed in patients. A correlation between radial diffusivity and disease duration along the corticospinal tracts (r = 0.806, P < 0.01) was found. In conclusion, in adrenomyeloneuropathy patients quantitative magnetic resonance imaging-derived measures identify and quantify structural changes in the upper spinal cord and brain which agree with the expected histopathology, and suggest that the disease could be primarily caused by a demyelination rather than a primitive axonal damage. The results of this study may also encourage the employment of quantitative magnetic resonance imaging in other hereditary diseases with spinal cord involvement. © The Author (2016). Published by Oxford University Press on behalf of the Guarantors of Brain. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

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).

Impurity profiles and radial transport in the EXTRAP-T2 reversed field pinch

NASA Astrophysics Data System (ADS)

Sallander, J.

1999-05-01

Radially resolved spectroscopy has been used to measure the radial distribution of impurity ions (O III-O V and C III-CVI) in the EXTRAP-T2 reversed field pinch (RFP). The radial profile of the emission is reconstructed from line emission measured along five lines of sight. The ion density profile is the fitted quantity in the reconstruction of the brightness profile and is thus obtained directly in this process. These measurements are then used to adjust the parameters in transport calculations in order to obtain consistency with the observed ion density profiles. Comparison between model and measurements show that a radial dependence in the diffusion is needed to explain the measured ion densities.

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C072)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C048)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

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.

Vortex Generators in a Streamline-Traced, External-Compression Supersonic Inlet

NASA Technical Reports Server (NTRS)

Baydar, Ezgihan; Lu, Frank K.; Slater, John W.; Trefny, Charles J.

2017-01-01

Vortex generators within a streamline-traced, external-compression supersonic inlet for Mach 1.66 were investigated to determine their ability to increase total pressure recovery and reduce total pressure distortion. The vortex generators studied were rectangular vanes arranged in counter-rotating and co-rotating arrays. The vane geometric factors of interest included height, length, spacing, angle-of-incidence, and positions upstream and downstream of the inlet terminal shock. The flow through the inlet was simulated numerically through the solution of the steady-state, Reynolds-averaged Navier-Stokes equations on multi-block, structured grids using the Wind-US flow solver. The vanes were simulated using a vortex generator model. The inlet performance was characterized by the inlet total pressure recovery and the radial and circumferential total pressure distortion indices at the engine face. Design of experiments and statistical analysis methods were applied to quantify the effect of the geometric factors of the vanes and search for optimal vane arrays. Co-rotating vane arrays with negative angles-of-incidence positioned on the supersonic diffuser were effective in sweeping low-momentum flow from the top toward the sides of the subsonic diffuser. This distributed the low-momentum flow more evenly about the circumference of the subsonic diffuser and reduced distortion. Co-rotating vane arrays with negative angles-of-incidence or counter-rotating vane arrays positioned downstream of the terminal shock were effective in mixing higher-momentum flow with lower-momentum flow to increase recovery and decrease distortion. A strategy of combining a co-rotating vane array on the supersonic diffuser with a counter-rotating vane array on the subsonic diffuser was effective in increasing recovery and reducing distortion.

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.

Radial Photonic Crystal for Detection of Frequency and Position of Radiation Sources

DTIC Science & Technology

2012-08-06

Dehesa, J. Acoustic resonances in two-dimensional radial sonic crystal shells. New J. Phys. 12, 073034 (2010). 15. Kurs, A. et al. Wireless power...microstructured materials, i.e. metamaterials, we present here the first practical realization of a radial wave crystal . This type of device was...parameters, those that define the solution of the wave propagation equations, has opened a very wide range of possibilities going from negative

Diffusion tensor imaging of the brainstem in children with achondroplasia

PubMed Central

BOSEMANI, THANGAMADHAN; ORMAN, GUNES; CARSON, KATHRYN A; MEODED, AVNER; HUISMAN, THIERRY A G M; PORETTI, ANDREA

2014-01-01

Aim The aims of this study were to compare, using diffusion tensor imaging (DTI) of the brainstem, microstructural integrity of the white matter in children with achondroplasia and age-matched participants and to correlate the severity of craniocervical junction (CCJ) narrowing and neurological findings with DTI scalars in children with achondroplasia. This study also aimed to assess the potential role of fibroblast growth factor receptor type 3 on white matter microstructure. Method Diffusion tensor imaging was performed using a 1.5T magnetic resonance scanner and balanced pairs of diffusion gradients along 20 non-collinear directions. Measurements were obtained from regions of interest, sampled in each pontine corticospinal tract (CST), medial lemniscus, and middle cerebellar peduncle, as well as in the lower brainstem and centrum semiovale, for fractional anisotropy and for mean, axial and radial diffusivity. In addition, a severity score for achondroplasia was assessed by measuring CCJ narrowing. Result Eight patients with achondroplasia (seven males, one female; mean age 5y 6mo, range 1y 1mo–15y 1mo) and eight age- and sex-matched comparison participants (mean age 5y 2mo, range 1y 1mo–14y 11mo) were included in this study. Fractional anisotropy was lower and mean diffusivity and radial diffusivity were higher in the lower brainstem of patients with achondroplasia than in age-matched comparison participants. The CST and middle cerebellar peduncle of the participants showed increases in mean, axial, and radial diffusivity. Fractional anisotropy in the lower brainstem was negatively correlated with the degree of CCJ narrowing. No differences in the DTI metrics of the centrum semiovale were observed between the two groups. Interpretation The reduction in fractional anisotropy and increase in diffusivities in the lower brainstem of participants with achondroplasia may reflect secondary encephalomalacic degeneration and cavitation of the affected white matter tracts as shown by histology. In children with achondroplasia, DTI may serve as a potential biomarker for brainstem white matter injury and aid in the care and management of these patients. PMID:24825324

Diffusion tensor imaging of the brainstem in children with achondroplasia.

PubMed

Bosemani, Thangamadhan; Orman, Gunes; Carson, Kathryn A; Meoded, Avner; Huisman, Thierry A G M; Poretti, Andrea

2014-11-01

The aims of this study were to compare, using diffusion tensor imaging (DTI) of the brainstem, microstructural integrity of the white matter in children with achondroplasia and age-matched participants and to correlate the severity of craniocervical junction (CCJ) narrowing and neurological findings with DTI scalars in children with achondroplasia. This study also aimed to assess the potential role of fibroblast growth factor receptor type 3 on white matter microstructure. Diffusion tensor imaging was performed using a 1.5T magnetic resonance scanner and balanced pairs of diffusion gradients along 20 non-collinear directions. Measurements were obtained from regions of interest, sampled in each pontine corticospinal tract (CST), medial lemniscus, and middle cerebellar peduncle, as well as in the lower brainstem and centrum semiovale, for fractional anisotropy and for mean, axial, and radial diffusivity. In addition, a severity score for achondroplasia was assessed by measuring CCJ narrowing. Eight patients with achondroplasia (seven males, one female; mean age 5y 6mo, range 1y 1mo-15y 1mo) and eight age- and sex-matched comparison participants (mean age 5y 2mo, range 1y 1mo-14y 11mo) were included in this study. Fractional anisotropy was lower and mean diffusivity and radial diffusivity were higher in the lower brainstem of patients with achondroplasia than in age-matched comparison participants. The CST and middle cerebellar peduncle of the participants showed increases in mean, axial, and radial diffusivity. Fractional anisotropy in the lower brainstem was negatively correlated with the degree of CCJ narrowing. No differences in the DTI metrics of the centrum semiovale were observed between the two groups. The reduction in fractional anisotropy and increase in diffusivities in the lower brainstem of participants with achondroplasia may reflect secondary encephalomalacic degeneration and cavitation of the affected white matter tracts as shown by histology. In children with achondroplasia, DTI may serve as a potential biomarker for brainstem white matter injury and aid in the care and management of these patients. © 2014 Mac Keith Press.

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 symmetric quartic map for trajectories of magnetic field lines in elongated divertor tokamak plasmas

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

Jones, Morgin; Wadi, Hasina; Ali, Halima

The coordinates of the area-preserving map equations for integration of magnetic field line trajectories in divertor tokamaks can be any coordinates for which a transformation to ({psi}{sub t},{theta},{phi}) coordinates exists [A. Punjabi, H. Ali, T. Evans, and A. Boozer, Phys. Lett. A 364, 140 (2007)]. {psi}{sub t} is toroidal magnetic flux, {theta} is poloidal angle, and {phi} is toroidal angle. This freedom is exploited to construct the symmetric quartic map such that the only parameter that determines magnetic geometry is the elongation of the separatrix surface. The poloidal flux inside the separatrix, the safety factor as a function of normalizedmore » minor radius, and the magnetic perturbation from the symplectic discretization are all held constant, and only the elongation is {kappa} varied. The width of stochastic layer, the area, and the fractal dimension of the magnetic footprint and the average radial diffusion coefficient of magnetic field lines from the stochastic layer; and how these quantities scale with {kappa} is calculated. The symmetric quartic map gives the correct scalings which are consistent with the scalings of coordinates with {kappa}. The effects of m=1, n={+-}1 internal perturbation with the amplitude that is expected to occur in tokamaks are calculated by adding a term [H. Ali, A. Punjabi, A. H. Boozer, and T. Evans, Phys. Plasmas 11, 1908 (2004)] to the symmetric quartic map. In this case, the width of stochastic layer scales as 0.35 power of {kappa}. The area of the footprint is roughly constant. The average radial diffusion coefficient of field lines near the X-point scales linearly with {kappa}. The low mn perturbation changes the quasisymmetric structure of the footprint, and reorganizes it into a single, large scale, asymmetric structure. The symmetric quartic map is combined with the dipole map [A. Punjabi, H. Ali, and A. H. Boozer, Phys. Plasmas 10, 3992 (2003)] to calculate the effects of magnetic perturbation from a current carrying coil. The coil position and coil current coil are constant. The dipole perturbation enhances the magnetic shear. The width of the stochastic layer scales exponentially with {kappa}. The area of the footprint decreases as the {kappa} increases. The radial diffusion coefficient of field lines scales exponentially with {kappa}. The dipole perturbation changes the topology of the footprint. It breaks up the toroidally spiraling footprint into a number of separate asymmetric toroidal strips. Practical applications of the symmetric quartic map to elongated divertor tokamak plasmas are suggested.« less

The symmetric quartic map for trajectories of magnetic field lines in elongated divertor tokamak plasmas

NASA Astrophysics Data System (ADS)

Jones, Morgin; Wadi, Hasina; Ali, Halima; Punjabi, Alkesh

2009-04-01

The coordinates of the area-preserving map equations for integration of magnetic field line trajectories in divertor tokamaks can be any coordinates for which a transformation to (ψt,θ,φ) coordinates exists [A. Punjabi, H. Ali, T. Evans, and A. Boozer, Phys. Lett. A 364, 140 (2007)]. ψt is toroidal magnetic flux, θ is poloidal angle, and φ is toroidal angle. This freedom is exploited to construct the symmetric quartic map such that the only parameter that determines magnetic geometry is the elongation of the separatrix surface. The poloidal flux inside the separatrix, the safety factor as a function of normalized minor radius, and the magnetic perturbation from the symplectic discretization are all held constant, and only the elongation is κ varied. The width of stochastic layer, the area, and the fractal dimension of the magnetic footprint and the average radial diffusion coefficient of magnetic field lines from the stochastic layer; and how these quantities scale with κ is calculated. The symmetric quartic map gives the correct scalings which are consistent with the scalings of coordinates with κ. The effects of m =1, n =±1 internal perturbation with the amplitude that is expected to occur in tokamaks are calculated by adding a term [H. Ali, A. Punjabi, A. H. Boozer, and T. Evans, Phys. Plasmas 11, 1908 (2004)] to the symmetric quartic map. In this case, the width of stochastic layer scales as 0.35 power of κ. The area of the footprint is roughly constant. The average radial diffusion coefficient of field lines near the X-point scales linearly with κ. The low mn perturbation changes the quasisymmetric structure of the footprint, and reorganizes it into a single, large scale, asymmetric structure. The symmetric quartic map is combined with the dipole map [A. Punjabi, H. Ali, and A. H. Boozer, Phys. Plasmas 10, 3992 (2003)] to calculate the effects of magnetic perturbation from a current carrying coil. The coil position and coil current coil are constant. The dipole perturbation enhances the magnetic shear. The width of the stochastic layer scales exponentially with κ. The area of the footprint decreases as the κ increases. The radial diffusion coefficient of field lines scales exponentially with κ. The dipole perturbation changes the topology of the footprint. It breaks up the toroidally spiraling footprint into a number of separate asymmetric toroidal strips. Practical applications of the symmetric quartic map to elongated divertor tokamak plasmas are suggested.

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

A stable computation of log-derivatives from noisy drawdown data

NASA Astrophysics Data System (ADS)

Ramos, Gustavo; Carrera, Jesus; Gómez, Susana; Minutti, Carlos; Camacho, Rodolfo

2017-09-01

Pumping tests interpretation is an art that involves dealing with noise coming from multiple sources and conceptual model uncertainty. Interpretation is greatly helped by diagnostic plots, which include drawdown data and their derivative with respect to log-time, called log-derivative. Log-derivatives are especially useful to complement geological understanding in helping to identify the underlying model of fluid flow because they are sensitive to subtle variations in the response to pumping of aquifers and oil reservoirs. The main problem with their use lies in the calculation of the log-derivatives themselves, which may display fluctuations when data are noisy. To overcome this difficulty, we propose a variational regularization approach based on the minimization of a functional consisting of two terms: one ensuring that the computed log-derivatives honor measurements and one that penalizes fluctuations. The minimization leads to a diffusion-like differential equation in the log-derivatives, and boundary conditions that are appropriate for well hydraulics (i.e., radial flow, wellbore storage, fractal behavior, etc.). We have solved this equation by finite differences. We tested the methodology on two synthetic examples showing that a robust solution is obtained. We also report the resulting log-derivative for a real case.

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.

The effect of sediments on turbulent plume dynamics in a stratified fluid

NASA Astrophysics Data System (ADS)

Stenberg, Erik; Ezhova, Ekaterina; Brandt, Luca

2017-11-01

We report large eddy simulation results of sediment-loaded turbulent plumes in a stratified fluid. The configuration, where the plume is discharged from a round source, provides an idealized model of subglacial discharge from a submarine tidewater glacier and is a starting point for understanding the effect of sediments on the dynamics of the rising plume. The transport of sediments is modeled by means of an advection-diffusion equation where sediment settling velocity is taken into account. We initially follow the experimental setup of Sutherland (Phys. Rev. Fluids, 2016), considering uniformly stratified ambients and further extend the work to pycnocline-type stratifications typical of Greenland fjords. Apart from examining the rise height, radial spread and intrusion of the rising plume, we gain further insights of the plume dynamics by extracting turbulent characteristics and the distribution of the sediments inside the plume.

Main-ion intrinsic toroidal rotation profile driven by residual stress torque from ion temperature gradient turbulence in the DIII-D tokamak

DOE PAGES

Grierson, B. A.; Wang, W. X.; Ethier, S.; ...

2017-01-06

Intrinsic toroidal rotation of the deuterium main ions in the core of the DIII-D tokamak is observed to transition from flat to hollow, forming an off-axis peak, above a threshold level of direct electron heating. Nonlinear gyrokinetic simulations show that the residual stress associated with electrostatic ion temperature gradient turbulence possesses the correct radial location and stress structure to cause the observed hollow rotation profile. Residual stress momentum flux in the gyrokinetic simulations is balanced by turbulent momentum diffusion, with negligible contributions from turbulent pinch. Finally, the prediction of the velocity profile by integrating the momentum balance equation produces amore » rotation profile that qualitatively and quantitatively agrees with the measured main-ion profile, demonstrating that fluctuation-induced residual stress can drive the observed intrinsic velocity profile.« less

Filamentation effect in a gas attenuator for high-repetition-rate X-ray FELs.

PubMed

Feng, Yiping; Krzywinski, Jacek; Schafer, Donald W; Ortiz, Eliazar; Rowen, Michael; Raubenheimer, Tor O

2016-01-01

A sustained filamentation or density depression phenomenon in an argon gas attenuator servicing a high-repetition femtosecond X-ray free-electron laser has been studied using a finite-difference method applied to the thermal diffusion equation for an ideal gas. A steady-state solution was obtained by assuming continuous-wave input of an equivalent time-averaged beam power and that the pressure of the entire gas volume has reached equilibrium. Both radial and axial temperature/density gradients were found and describable as filamentation or density depression previously reported for a femtosecond optical laser of similar attributes. The effect exhibits complex dependence on the input power, the desired attenuation, and the geometries of the beam and the attenuator. Time-dependent simulations were carried out to further elucidate the evolution of the temperature/density gradients in between pulses, from which the actual attenuation received by any given pulse can be properly calculated.

Interplanetary gas. XX - Does the radial solar wind speed increase with latitude

NASA Technical Reports Server (NTRS)

Brandt, J. C.; Harrington, R. S.; Roosen, R. G.

1975-01-01

The astrometric technique used to derive solar wind speeds from ionic comet-tail orientations has been used to test the suggestion that the radial solar wind speed is higher near the solar poles than near the equator. We find no evidence for the suggested latitude variation.

Thermoelastic damping in thin microrings with two-dimensional heat conduction

NASA Astrophysics Data System (ADS)

Fang, Yuming; Li, Pu

2015-05-01

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

Plasma Component of Self-gravitating Disks and Relevant Magnetic Configurations

NASA Astrophysics Data System (ADS)

Bertin, G.; Coppi, B.

2006-04-01

Astrophysical disks in which the disk self-gravity is more important than the gravity force associated with the central object can have significant plasma components where appreciable toroidal current densities are produced. When the vertical confinement of the plasma rotating structures that can form is kept by the Lorentz force rather than by the vertical component of the gravity force, the disk self-gravity remains important only in the radial equilibrium condition, modifying the rotation curve from the commonly considered Keplerian rotation. The equilibrium equations that are solved involve the vertical and the horizontal components of the total momentum conservation equations, coupled with the lowest order form of the gravitational Poisson's equation. The resulting poloidal field configuration can be visualized as a sequence [1] of Field Reverse Configurations, in the radial direction, consisting of pairs of oppositely directed current channels. The plasma density thus acquires a significant radial modulation that may grow to the point where plasma rings can form [2]. [1] B. Coppi, Phys. Plasmas, 12, 057302 (2005) [2] B. Coppi and F. Rousseau, to be published in Astrophys. J. (April 2006)

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.

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

Longitudinal brain white matter alterations in minimal hepatic encephalopathy before and after liver transplantation.

PubMed

Lin, Wei-Che; Chou, Kun-Hsien; Chen, Chao-Long; Chen, Hsiu-Ling; Lu, Cheng-Hsien; Li, Shau-Hsuan; Huang, Chu-Chung; Lin, Ching-Po; Cheng, Yu-Fan

2014-01-01

Cerebral edema is the common pathogenic mechanism for cognitive impairment in minimal hepatic encephalopathy. Whether complete reversibility of brain edema, cognitive deficits, and their associated imaging can be achieved after liver transplantation remains an open question. To characterize white matter integrity before and after liver transplantation in patients with minimal hepatic encephalopathy, multiple diffusivity indices acquired via diffusion tensor imaging was applied. Twenty-eight patients and thirty age- and sex-matched healthy volunteers were included. Multiple diffusivity indices were obtained from diffusion tensor images, including mean diffusivity, fractional anisotropy, axial diffusivity and radial diffusivity. The assessment was repeated 6-12 month after transplantation. Differences in white matter integrity between groups, as well as longitudinal changes, were evaluated using tract-based spatial statistical analysis. Correlation analyses were performed to identify first scan before transplantation and interval changes among the neuropsychiatric tests, clinical laboratory tests, and diffusion tensor imaging indices. After transplantation, decreased water diffusivity without fractional anisotropy change indicating reversible cerebral edema was found in the left anterior cingulate, claustrum, postcentral gyrus, and right corpus callosum. However, a progressive decrease in fractional anisotropy and an increase in radial diffusivity suggesting demyelination were noted in temporal lobe. Improved pre-transplantation albumin levels and interval changes were associated with better recoveries of diffusion tensor imaging indices. Improvements in interval diffusion tensor imaging indices in the right postcentral gyrus were correlated with visuospatial function score correction. In conclusion, longitudinal voxel-wise analysis of multiple diffusion tensor imaging indices demonstrated different white matter changes in minimal hepatic encephalopathy patients. Transplantation improved extracellular cerebral edema and the results of associated cognition tests. However, white matter demyelination may advance in temporal lobe.

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.

Predictive models for radial sap flux variation in coniferous, diffuse-porous and ring-porous temperate trees

Treesearch

Aaron B. Berdanier; Chelcy F. Miniat; James S. Clark

2016-01-01

Accurately scaling sap flux observations to tree or stand levels requires accounting for variation in sap flux between wood types and by depth into the tree. However, existing models for radial variation in axial sap flux are rarely used because they are difficult to implement, there is uncertainty about their predictive ability and calibration measurements...

On the Voyager 1 Zero Radial Velocity Measurements in the Inner Heliosheath

NASA Astrophysics Data System (ADS)

Pogorelov, N. V.; Borovikov, S. N.; Kryukov, I.; Zank, G. P.

2011-12-01

Theoretical analysis of the Voyager 1 data revealed a very small, or even negative, value of the solar wind (SW) radial velocity component. This should not be surprising if we take into account time-dependent processes that take place in the inner heliosheath (IHS). We analyze solar cycle modeling of the SW interaction with the local interstellar medium (LISM) and demonstrate the existence of small and negative values of the SW radial velocity. It shown that, in reality, a similar picture can be observed in the outer heliosheath (OHS), where on the contrary, extended regions of the positive radial velocity are observed. Another scenario discussed in this talk is related to effects of transients, such as global merged interaction regions and corotating interacting regions. Numerical results are obtained with the SW-LISM interaction model developed in the UAHuntsville and implemented in the Multi-Scale Fluid-Kinetic Simulation Suite. This model treats ions magnetohydrodynamically while the transport of neutral atoms is performed kinetically by solving the Boltzmann equation with a Monte Carlo approach or using a multi-fluid approach developed in mid-90's by G. P. Zank. Pickup ions (PUIs) can be treated as a separate fluid. The evolution of the PUI-generated turbulence is addressed on the differential level by adding three additional equations, which are solved self-consistently with the MHD-kinetic system of equations.

Modeling electrochemical deposition inside nanotubes to obtain metal-semiconductor multiscale nanocables or conical nanopores.

PubMed

Lebedev, Konstantin; Mafé, Salvador; Stroeve, Pieter

2005-08-04

Nanocables with a radial metal-semiconductor heterostructure have recently been prepared by electrochemical deposition inside metal nanotubes. First, a bare nanoporous polycarbonate track-etched membrane is coated uniformly with a metal film by electroless deposition. The film forms a working electrode for further deposition of a semiconductor layer that grows radially inside the nanopore when the deposition rate is slow. We propose a new physical model for the nanocable synthesis and study the effects of the deposited species concentration, potential-dependent reaction rate, and nanopore dimensions on the electrochemical deposition. The problem involves both axial diffusion through the nanopore and radial transport to the nanopore surface, with a surface reaction rate that depends on the axial position and the time. This is so because the radial potential drop across the deposited semiconductor layer changes with the layer thickness through the nanopore. Since axially uniform nanocables are needed for most applications, we consider the relative role of reaction and axial diffusion rates on the deposition process. However, in those cases where partial, empty-core deposition should be desirable (e.g., for producing conical nanopores to be used in single nanoparticle detection), we give conditions where asymmetric geometries can be experimentally realized.

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.

Sparse and optimal acquisition design for diffusion MRI and beyond

PubMed Central

Koay, Cheng Guan; Özarslan, Evren; Johnson, Kevin M.; Meyerand, M. Elizabeth

2012-01-01

Purpose: Diffusion magnetic resonance imaging (MRI) in combination with functional MRI promises a whole new vista for scientists to investigate noninvasively the structural and functional connectivity of the human brain—the human connectome, which had heretofore been out of reach. As with other imaging modalities, diffusion MRI data are inherently noisy and its acquisition time-consuming. Further, a faithful representation of the human connectome that can serve as a predictive model requires a robust and accurate data-analytic pipeline. The focus of this paper is on one of the key segments of this pipeline—in particular, the development of a sparse and optimal acquisition (SOA) design for diffusion MRI multiple-shell acquisition and beyond. Methods: The authors propose a novel optimality criterion for sparse multiple-shell acquisition and quasimultiple-shell designs in diffusion MRI and a novel and effective semistochastic and moderately greedy combinatorial search strategy with simulated annealing to locate the optimum design or configuration. The goal of the optimality criteria is threefold: first, to maximize uniformity of the diffusion measurements in each shell, which is equivalent to maximal incoherence in angular measurements; second, to maximize coverage of the diffusion measurements around each radial line to achieve maximal incoherence in radial measurements for multiple-shell acquisition; and finally, to ensure maximum uniformity of diffusion measurement directions in the limiting case when all the shells are coincidental as in the case of a single-shell acquisition. The approach taken in evaluating the stability of various acquisition designs is based on the condition number and the A-optimal measure of the design matrix. Results: Even though the number of distinct configurations for a given set of diffusion gradient directions is very large in general—e.g., in the order of 10232 for a set of 144 diffusion gradient directions, the proposed search strategy was found to be effective in finding the optimum configuration. It was found that the square design is the most robust (i.e., with stable condition numbers and A-optimal measures under varying experimental conditions) among many other possible designs of the same sample size. Under the same performance evaluation, the square design was found to be more robust than the widely used sampling schemes similar to that of 3D radial MRI and of diffusion spectrum imaging (DSI). Conclusions: A novel optimality criterion for sparse multiple-shell acquisition and quasimultiple-shell designs in diffusion MRI and an effective search strategy for finding the best configuration have been developed. The results are very promising, interesting, and practical for diffusion MRI acquisitions. PMID:22559620

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.

Multimodal Imaging Evidence for Axonal and Myelin Deterioration in Amnestic Mild Cognitive Impairment

PubMed Central

Gold, Brian T.; Jiang, Yang; Powell, David K.; Smith, Charles D.

2012-01-01

White matter (WM) microstructural declines have been demonstrated in Alzheimer’s disease and amnestic mild cognitive impairment (aMCI). However, the pattern of WM microstructural changes in aMCI after controlling for WM atrophy is unknown. Here, we address this issue through joint consideration of aMCI alterations in fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity, as well as macrostructural volume in WM and gray matter compartments. Participants were 18 individuals with aMCI and 24 healthy seniors. Voxelwise analyses of diffusion tensor imaging data was carried out using tract-based spatial statistics (TBSS) and voxelwise analyses of high-resolution structural data was conducted using voxel based morphometry. After controlling for WM atrophy, the main pattern of TBSS findings indicated reduced fractional anisotropy with only small alterations in mean diffusivity/radial diffusivity/axial diffusivity. These WM microstructural declines bordered and/or were connected to gray matter structures showing volumetric declines. However, none of the potential relationships between WM integrity and volume in connected gray matter structures was significant, and adding fractional anisotropy information improved the classificatory accuracy of aMCI compared to the use of hippocampal atrophy alone. These results suggest that WM microstructural declines provide unique information not captured by atrophy measures that may aid the magnetic resonance imaging contribution to aMCI detection. PMID:22460327

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

Effects of low-level sarin and cyclosarin exposure on white matter integrity in Gulf War Veterans.

PubMed

Chao, Linda L; Zhang, Yu; Buckley, Shannon

2015-05-01

We previously found evidence of reduced gray and white matter volume in Gulf War (GW) veterans with predicted low-level exposure to sarin (GB) and cyclosarin (GF). Because loss of white matter tissue integrity has been linked to both gray and white matter atrophy, the current study sought to test the hypothesis that GW veterans with predicted GB/GF exposure have evidence of disrupted white matter microstructural integrity. Measures of fractional anisotropy and directional (i.e., axial and radial) diffusivity were assessed from the 4T diffusion tensor images (DTI) of 59 GW veterans with predicted GB/GF exposure and 59 "matched" unexposed GW veterans (mean age: 48 ± 7 years). The DTI data were analyzed using regions of interest (ROI) analyses that accounted for age, sex, total brain gray and white matter volume, trauma exposure, posttraumatic stress disorder, current major depression, and chronic multisymptom illness status. There were no significant group differences in fractional anisotropy or radial diffusivity. However, there was increased axial diffusivity in GW veterans with predicted GB/GF exposure compared to matched, unexposed veterans throughout the brain, including the temporal stem, corona radiata, superior and inferior (hippocampal) cingulum, inferior and superior fronto-occipital fasciculus, internal and external capsule, and superficial cortical white matter blades. Post hoc analysis revealed significant correlations between higher fractional anisotropy and lower radial diffusivity with better neurobehavioral performance in unexposed GW veterans. In contrast, only increased axial diffusivity in posterior limb of the internal capsule was associated with better psychomotor function in GW veterans with predicted GB/GF exposure. The finding that increased axial diffusivity in a region of the brain that contains descending corticospinal fibers was associated with better psychomotor function and the lack of significant neurobehavioral deficits in veterans with predicted GB/GF exposure hint at the possibility that the widespread increases in axial diffusivity that we observed in GW veterans with predicted GB/GF exposure relative to unexposed controls may reflect white matter reorganization after brain injury (i.e., exposure to GB/GF). Published by Elsevier B.V.

White Matter Damage Relates to Oxygen Saturation in Children With Sickle Cell Anemia Without Silent Cerebral Infarcts.

PubMed

Kawadler, Jamie M; Kirkham, Fenella J; Clayden, Jonathan D; Hollocks, Matthew J; Seymour, Emma L; Edey, Rosanna; Telfer, Paul; Robins, Andrew; Wilkey, Olu; Barker, Simon; Cox, Tim C S; Clark, Chris A

2015-07-01

Sickle cell anemia is associated with compromised oxygen-carrying capability of hemoglobin and a high incidence of overt and silent stroke. However, in children with no evidence of cerebral infarction, there are changes in brain morphometry relative to healthy controls, which may be related to chronic anemia and oxygen desaturation. A whole-brain tract-based spatial statistics analysis was carried out in 25 children with sickle cell anemia with no evidence of abnormality on T2-weighted magnetic resonance imaging (13 male, age range: 8-18 years) and 14 age- and race-matched controls (7 male, age range: 10-19 years) to determine the extent of white matter injury. The hypotheses that white matter damage is related to daytime peripheral oxygen saturation and steady-state hemoglobin were tested. Fractional anisotropy was found to be significantly lower in patients in the subcortical white matter (corticospinal tract and cerebellum), whereas mean diffusivity and radial diffusivity were higher in patients in widespread areas. There was a significant negative relationship between radial diffusivity and oxygen saturation (P<0.05) in the anterior corpus callosum and a trend-level negative relationship between radial diffusivity and hemoglobin (P<0.1) in the midbody of the corpus callosum. These data show widespread white matter abnormalities in a sample of asymptomatic children with sickle cell anemia, and provides for the first time direct evidence of a relationship between brain microstructure and markers of disease severity (eg, peripheral oxygen saturation and steady-state hemoglobin). This study suggests that diffusion tensor imaging metrics may serve as a biomarker for future trials of reducing hypoxic exposure. © 2015 American Heart Association, Inc.

Association between left ventricular mechanics and diffuse myocardial fibrosis in patients with repaired Tetralogy of Fallot: a cross-sectional study.

PubMed

Haggerty, Christopher M; Suever, Jonathan D; Pulenthiran, Arichanah; Mejia-Spiegeler, Abba; Wehner, Gregory J; Jing, Linyuan; Charnigo, Richard J; Fornwalt, Brandon K; Fogel, Mark A

2017-12-11

Patients with repaired tetralogy of Fallot (TOF) have progressive, adverse biventricular remodeling, leading to abnormal contractile mechanics. Defining the mechanisms underlying this dysfunction, such as diffuse myocardial fibrosis, may provide insights into poor long-term outcomes. We hypothesized that left ventricular (LV) diffuse fibrosis is related to impaired LV mechanics. Patients with TOF were evaluated with cardiac magnetic resonance in which modified Look-Locker (MOLLI) T1-mapping and spiral cine Displacement encoding (DENSE) sequences were acquired at three LV short-axis positions. Linear mixed modeling was used to define the association between regional LV mechanics from DENSE based on regional T1-derived diffuse fibrosis measures, such as extracellular volume fraction (ECV). Forty patients (26 ± 11 years) were included. LV ECV was generally within normal range (0.24 ± 0.05). For LV mechanics, peak circumferential strains (-15 ± 3%) and dyssynchrony indices (16 ± 8 ms) were moderately impaired, while peak radial strains (29 ± 8%) were generally normal. After adjusting for patient age, sex, and regional LV differences, ECV was associated with log-adjusted LV dyssynchrony index (β = 0.67) and peak LV radial strain (β = -0.36), but not LV circumferential strain. Moreover, post-contrast T1 was associated with log-adjusted LV diastolic circumferential strain rate (β = 0.37). We observed several moderate associations between measures of fibrosis and impaired mechanics, particularly the LV dyssynchrony index and peak radial strain. Diffuse fibrosis may therefore be a causal factor in some ventricular dysfunction in TOF.

Experimental investigation on pressurization performance of cryogenic tank during high-temperature helium pressurization process

NASA Astrophysics Data System (ADS)

Lei, Wang; Yanzhong, Li; Yonghua, Jin; Yuan, Ma

2015-03-01

Sufficient knowledge of thermal performance and pressurization behaviors in cryogenic tanks during rocket launching period is of importance to the design and optimization of a pressurization system. In this paper, ground experiments with liquid oxygen (LO2) as the cryogenic propellant, high-temperature helium exceeding 600 K as the pressurant gas, and radial diffuser and anti-cone diffuser respectively at the tank inlet were performed. The pressurant gas requirements, axial and radial temperature distributions, and energy distributions inside the propellant tank were obtained and analyzed to evaluate the comprehensive performance of the pressurization system. It was found that the pressurization system with high-temperature helium as the pressurant gas could work well that the tank pressure was controlled within a specified range and a stable discharging liquid rate was achieved. For the radial diffuser case, the injected gas had a direct impact on the tank inner wall. The severe gas-wall heat transfer resulted in about 59% of the total input energy absorbed by the tank wall. For the pressurization case with anti-cone diffuser, the direct impact of high-temperature gas flowing toward the liquid surface resulted in a greater deal of energy transferred to the liquid propellant, and the percentage even reached up to 38%. Moreover, both of the two cases showed that the proportion of energy left in ullage to the total input energy was quite small, and the percentage was only about 22-24%. This may indicate that a more efficient diffuser should be developed to improve the pressurization effect. Generally, the present experimental results are beneficial to the design and optimization of the pressurization system with high-temperature gas supplying the pressurization effect.

Characterization of spinal cord white matter by suppressing signal from hindered space. A Monte Carlo simulation and an ex vivo ultrahigh-b diffusion-weighted imaging study.

PubMed

Sapkota, Nabraj; Yoon, Sook; Thapa, Bijaya; Lee, YouJung; Bisson, Erica F; Bowman, Beth M; Miller, Scott C; Shah, Lubdha M; Rose, John W; Jeong, Eun-Kee

2016-11-01

Signal measured from white matter in diffusion-weighted imaging is difficult to interpret because of the heterogeneous structure of white matter. Characterization of the white matter will be straightforward if the signal contributed from the hindered space is suppressed and purely restricted signal is analyzed. In this study, a Monte Carlo simulation (MCS) of water diffusion in white matter was performed to understand the behavior of the diffusion-weighted signal in white matter. The signal originating from the hindered space of an excised pig cervical spinal cord white matter was suppressed using the ultrahigh-b radial diffusion-weighted imaging. A light microscopy image of a section of white matter was obtained from the excised pig cervical spinal cord for the MCS. The radial diffusion-weighted signals originating from each of the intra-axonal, extra-axonal, and total spaces were studied using the MCS. The MCS predicted that the radial diffusion-weighted signal remains almost constant in the intra-axonal space and decreases gradually to about 2% of its initial value in the extra-axonal space when the b-value is increased to 30,000s/mm 2 . The MCS also revealed that the diffusion-weighted signal for a b-value greater than 20,000s/mm 2 is mostly from the intra-axonal space. The decaying behavior of the signal-b curve obtained from ultrahigh-b diffusion-weighted imaging (b max ∼30,000s/mm 2 ) of the excised pig cord was very similar to the decaying behavior of the total signal-b curve synthesized in the MCS. A mono-exponential plus constant fitting of the signal-b curve obtained from a white matter pixel estimated the values of constant fraction and apparent diffusion coefficient of decaying fraction as 0.32±0.05 and (0.16±0.01)×10 -3 mm 2 /s, respectively, which agreed well with the results of the MCS. The signal measured in the ultrahigh-b region (b>20,000s/mm 2 ) is mostly from the restricted (intra-axonal) space. Integrity and intactness of the axons can be evaluated by assessing the remaining signal in the ultrahigh-b region. Published by Elsevier Inc.

Measurements and modeling of transport and impurity radial profiles in the EXTRAP T2R reversed field pinch

NASA Astrophysics Data System (ADS)

Kuldkepp, M.; Brunsell, P. R.; Cecconello, M.; Dux, R.; Menmuir, S.; Rachlew, E.

2006-09-01

Radial impurity profiles of oxygen in the rebuilt reversed field pinch EXTRAP T2R [P. R. Brunsell et al., Plasma Phys. Control. Fusion 43, 1457 (2001)] have been measured with a multichannel spectrometer. Absolute ion densities for oxygen peak between 1-4×1010cm-3 for a central electron density of 1×1013cm-3. Transport simulations with the one-dimensional transport code STRAHL with a diffusion coefficient of 20m2 s-1 yield density profiles similar to those measured. Direct measurement of the ion profile evolution during pulsed poloidal current drive suggests that the diffusion coefficient is reduced by a factor ˜2 in the core but remains unaffected toward the edge. Core transport is not significantly affected by the radial magnetic field growth seen at the edge in discharges without feedback control. This indicates that the mode core amplitude remains the same while the mode eigenfunction increases at the edge.

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.

Brain aging in humans, chimpanzees (Pan troglodytes), and rhesus macaques (Macaca mulatta): magnetic resonance imaging studies of macro- and microstructural changes

PubMed Central

Chen, Xu; Errangi, Bhargav; Li, Longchuan; Glasser, Matthew F.; Westlye, Lars T.; Fjell, Anders M.; Walhovd, Kristine B.; Hu, Xiaoping; Herndon, James G.; Preuss, Todd M.; Rilling, James K.

2013-01-01

Among primates, humans are uniquely vulnerable to many age-related neurodegenerative disorders. We used structural and diffusion magnetic resonance imaging (MRI) to examine the brains of chimpanzees and rhesus monkeys across each species' adult lifespan, and compared these results with published findings in humans. As in humans, gray matter volume decreased with age in chimpanzees and rhesus monkeys. Also like humans, chimpanzees showed a trend for decreased white matter volume with age, but this decrease occurred proportionally later in the chimpanzee lifespan than in humans. Diffusion MRI revealed widespread age-related decreases in fractional anisotropy and increases in radial diffusivity in chimpanzees and macaques. However, both the fractional anisotropy decline and the radial diffusivity increase started at a proportionally earlier age in humans than in chimpanzees. Thus, even though overall patterns of gray and white matter aging are similar in humans and chimpanzees, the longer lifespan of humans provides more time for white matter to deteriorate before death, with the result that some neurological effects of aging may be exacerbated in our species. PMID:23623601

SNOW LINES AS PROBES OF TURBULENT DIFFUSION IN PROTOPLANETARY DISKS

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

Owen, James E.

2014-07-20

Sharp chemical discontinuities can occur in protoplanetary disks, particularly at ''snow lines'' where a gas-phase species freezes out to form ice grains. Such sharp discontinuities will diffuse out due to the turbulence suspected to drive angular momentum transport in accretion disks. We demonstrate that the concentration gradient—in the vicinity of the snow line—of a species present outside a snow line but destroyed inside is strongly sensitive to the level of turbulent diffusion (provided the chemical and transport timescales are decoupled) and provides a direct measurement of the radial ''Schmidt number'' (the ratio of the angular momentum transport to radial turbulentmore » diffusion). Taking as an example the tracer species N{sub 2}H{sup +}, which is expected to be destroyed inside the CO snow line (as recently observed in TW Hya) we show that ALMA observations possess significant angular resolution to constrain the Schmidt number. Since different turbulent driving mechanisms predict different Schmidt numbers, a direct measurement of the Schmidt number in accretion disks would allow inferences to be made about the nature of the turbulence.« less

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.

Anatomical explanations for acute depressions in radial pattern of axial sap flow in two diffuse-porous mangrove species: implications for water use.

PubMed

Zhao, Hewei; Yang, Shengchang; Guo, Xudong; Peng, Congjiao; Gu, Xiaoxuan; Deng, Chuanyuan; Chen, Luzhen

2018-02-01

Mangrove species have developed uniquely efficient water-use strategies in order to survive in highly saline and anaerobic environments. Herein, we estimated the stand water use of two diffuse-porous mangrove species of the same age, Sonneratia apetala Buch. Ham and Sonneratia caseolaris (L.) Engl., growing in a similar intertidal environment. Specifically, to investigate the radial patterns of axial sap flow density (Js) and understand the anatomical traits associated with them, we measured axial sap flow density in situ together with micromorphological observations. A significant decrease of Js was observed for both species. This result was accompanied by the corresponding observations of wood structure and blockages in xylem sapwood, which appeared to influence and, hence, explained the acute radial reductions of axial sap flow in the stems of both species. However, higher radial resistance in sapwood of S. caseolaris caused a steeper decline of Js radially when compared with S. apetala, thus explaining the latter's more efficient use of water. Without first considering acute reductions in Js into the sapwood from the outer bark, a total of ~55% and 51% of water use would have been overestimated, corresponding to average discrepancies in stand water use of 5.6 mm day-1 for S. apetala trees and 2.5 mm day-1 for S. caseolaris trees. This suggests that measuring radial pattern of Js is a critical factor in determining whole-tree or stand water use. © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

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...

The radial electric field dynamics in the neoclassical plasmas

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

Novakovskii, S.V.; Liu, C.S.; Sagdeev, R.Z.

1997-12-01

A numerical simulation and analytical theory of the radial electric field dynamics in low collisional tokamak plasmas are presented. An initial value code {open_quotes}ELECTRIC{close_quotes} has been developed to solve the ion drift kinetic equation with a full collisional operator in the Hirshman{endash}Sigmar{endash}Clarke form together with the Maxwell equations. Different scenarios of relaxation of the radial electric field toward the steady-state in response to sudden and adiabatic changes of the equilibrium temperature gradient are presented. It is shown, that while the relaxation is usually accompanied by the geodesic acoustic oscillations, during the adiabatic change these oscillations are suppressed and only themore » magnetic pumping remains. Both the collisional damping and the Landau resonance interaction are shown to be important relaxation mechanisms. Scalings of the relaxation rates versus basic plasma parameters are presented. {copyright} {ital 1997 American Institute of Physics.}« less

Scrape-off layer tokamak plasma turbulence

NASA Astrophysics Data System (ADS)

Bisai, N.; Singh, R.; Kaw, P. K.

2012-05-01

Two-dimensional (2D) interchange turbulence in the scrape-off layer of tokamak plasmas and their subsequent contribution to anomalous plasma transport has been studied in recent years using electron continuity, current balance, and electron energy equations. In this paper, numerically it is demonstrated that the inclusion of ion energy equation in the simulation changes the nature of plasma turbulence. Finite ion temperature reduces floating potential by about 15% compared with the cold ion temperature approximation and also reduces the radial electric field. Rotation of plasma blobs at an angular velocity about 1.5×105 rad/s has been observed. It is found that blob rotation keeps plasma blob charge separation at an angular position with respect to the vertical direction that gives a generation of radial electric field. Plasma blobs with high electron temperature gradients can align the charge separation almost in the radial direction. Influence of high ion temperature and its gradient has been presented.

MRI assessment of the thigh musculature in dermatomyositis and healthy subjects using diffusion tensor imaging, intravoxel incoherent motion and dynamic DTI.

PubMed

Sigmund, E E; Baete, S H; Luo, T; Patel, K; Wang, D; Rossi, I; Duarte, A; Bruno, M; Mossa, D; Femia, A; Ramachandran, S; Stoffel, D; Babb, J S; Franks, A; Bencardino, J

2018-06-04

Dermatomyositis (DM) is an idiopathic inflammatory myopathy involving severe debilitation in need of diagnostics. We evaluated the proximal lower extremity musculature with diffusion tensor imaging (DTI), intravoxel incoherent motion (IVIM) and dynamic DTI in DM patients and controls and compared with standard clinical workup.  METHODS: In this IRB-approved, HIPAA-compliant study with written informed consent, anatomical, Dixon fat/water and diffusion imaging were collected in bilateral thigh MRI of 22 controls and 27 DM patients in a 3T scanner. Compartments were scored on T1/T2 scales. Single voxel dynamic DTI metrics in quadriceps before and after 3-min leg exercise were measured. Spearman rank correlation and mixed model analysis of variance/covariance (ANOVA/ANCOVA) were used to correlate with T1 and T2 scores and to compare patients with controls. DM patients showed significantly lower pseudo-diffusion and volume in quadriceps than controls. All subjects showed significant correlation between T1 score and signal-weighted fat fraction; tissue diffusion and pseudo-diffusion varied significantly with T1 and T2 score in patients. Radial and mean diffusion exercise response in patients was significantly higher than controls. Static and dynamic diffusion imaging metrics show correlation with conventional imaging scores, reveal spatial heterogeneity, and provide means to differentiate dermatomyositis patients from controls. • Diffusion imaging shows regional differences between thigh muscles of dermatomyositis patients and controls. • Signal-weighted fat fraction and diffusion metrics correlate with T1/T2 scores of disease severity. • Dermatomyositis patients show significantly higher radial diffusion exercise response than controls.

An update of Leighton's solar dynamo model

NASA Astrophysics Data System (ADS)

Cameron, R. H.; Schüssler, M.

2017-03-01

In 1969, Leighton developed a quasi-1D mathematical model of the solar dynamo, building upon the phenomenological scenario of Babcock published in 1961. Here we present a modification and extension of Leighton's model. Using the axisymmetric component (longitudinal average) of the magnetic field, we consider the radial field component at the solar surface and the radially integrated toroidal magnetic flux in the convection zone, both as functions of latitude. No assumptions are made with regard to the radial location of the toroidal flux. The model includes the effects of (I) turbulent diffusion at the surface and in the convection zone; (II) poleward meridional flow at the surface and an equatorward return flow affecting the toroidal flux; (III) latitudinal differential rotation and the near-surface layer of radial rotational shear; (iv) downward convective pumping of magnetic flux in the shear layer; and (v) flux emergence in the form of tilted bipolar magnetic regions treated as a source term for the radial surface field. While the parameters relevant for the transport of the surface field are taken from observations, the model condenses the unknown properties of magnetic field and flow in the convection zone into a few free parameters (turbulent diffusivity, effective return flow, amplitude of the source term, and a parameter describing the effective radial shear). Comparison with the results of 2D flux transport dynamo codes shows that the model captures the essential features of these simulations. We make use of the computational efficiency of the model to carry out an extended parameter study. We cover an extended domain of the 4D parameter space and identify the parameter ranges that provide solar-like solutions. Dipole parity is always preferred and solutions with periods around 22 yr and a correct phase difference between flux emergence in low latitudes and the strength of the polar fields are found for a return flow speed around 2 m s-1, turbulent diffusivity below about 80 km2s-1, and dynamo excitation not too far above the threshold (linear growth rate less than 0.1 yr-1).

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.

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.

Determination of the diffusivity, dispersion, skewness and kurtosis in heterogeneous porous flow. Part I: Analytical solutions with the extended method of moments.

NASA Astrophysics Data System (ADS)

Ginzburg, Irina; Vikhansky, Alexander

2018-05-01

The extended method of moments (EMM) is elaborated in recursive algorithmic form for the prediction of the effective diffusivity, the Taylor dispersion dyadic and the associated longitudinal high-order coefficients in mean-concentration profiles and residence-time distributions. The method applies in any streamwise-periodic stationary d-dimensional velocity field resolved in the piecewise continuous heterogeneous porosity field. It is demonstrated that EMM reduces to the method of moments and the volume-averaging formulation in microscopic velocity field and homogeneous soil, respectively. The EMM simultaneously constructs two systems of moments, the spatial and the temporal, without resorting to solving of the high-order upscaled PDE. At the same time, the EMM is supported with the reconstruction of distribution from its moments, allowing to visualize the deviation from the classical ADE solution. The EMM can be handled by any linear advection-diffusion solver with explicit mass-source and diffusive-flux jump condition on the solid boundary and permeable interface. The prediction of the first four moments is decisive in the optimization of the dispersion, asymmetry, peakedness and heavy-tails of the solute distributions, through an adequate design of the composite materials, wetlands, chemical devices or oil recovery. The symbolic solutions for dispersion, skewness and kurtosis are constructed in basic configurations: diffusion process and Darcy flow through two porous blocks in "series", straight and radial Poiseuille flow, porous flow governed by the Stokes-Brinkman-Darcy channel equation and a fracture surrounded by penetrable diffusive matrix or embedded in porous flow. We examine the moments dependency upon porosity contrast, aspect ratio, Péclet and Darcy numbers, but also for their response on the effective Brinkman viscosity applied in flow modeling. Two numerical Lattice Boltzmann algorithms, a direct solver of the microscopic ADE in heterogeneous structure and a novel scheme for EMM numerical formulation, are called for validation of the constructed analytical predictions.

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.

High Aspect Ratio Semiconductor Heterojunction Solar Cells

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

Redwing, Joan; Mallouk, Tom; Mayer, Theresa

2013-05-17

The project focused on the development of high aspect ratio silicon heterojunction (HARSH) solar cells. The solar cells developed in this study consisted of high density vertical arrays of radial junction silicon microwires/pillars formed on Si substrates. Prior studies have demonstrated that vertical Si wire/pillar arrays enable reduced reflectivity and improved light trapping characteristics compared to planar solar cells. In addition, the radial junction structure offers the possibility of increased carrier collection in solar cells fabricated using material with short carrier diffusion lengths. However, the high junction and surface area of radial junction Si wire/pillar array devices can be problematicmore » and lead to increased diode leakage and enhanced surface recombination. This study investigated the use of amorphous hydrogenated Si in the form of a heterojunction-intrinsic-thin layer (HIT) structure as a junction formation method for these devices. The HIT layer structure has widely been employed to reduce surface recombination in planar crystalline Si solar cells. Consequently, it was anticipated that it would also provide significant benefits to the performance of radial junction Si wire/pillar array devices. The overall goals of the project were to demonstrate a HARSH cell with a HIT-type structure in the radial junction Si wire/pillar array configuration and to develop potentially low cost pathways to fabricate these devices. Our studies demonstrated that the HIT structure lead to significant improvements in the open circuit voltage (V oc>0.5) of radial junction Si pillar array devices compared to devices fabricated using junctions formed by thermal diffusion or low pressure chemical vapor deposition (LPCVD). In addition, our work experimentally demonstrated that the radial junction structure lead to improvements in efficiency compared to comparable planar devices for devices fabricated using heavily doped Si that had reduced carrier diffusion lengths. Furthermore, we made significant advances in employing the bottom-up vapor-liquid-solid (VLS) growth technique for the fabrication of the Si wire arrays. Our work elucidated the effects of growth conditions and substrate pattern geometry on the growth of large area Si microwire arrays grown with SiCl4. In addition, we also developed a process to grow p-type Si nanowire arrays using aluminum as the catalyst metal instead of gold. Finally, our work demonstrated the feasibility of growing vertical arrays of Si wires on non-crystalline glass substrates using polycrystalline Si template layers. The accomplishments demonstrated in this project will pave the way for future advances in radial junction wire array solar cells.« less

Fast Diffusion to Self-Similarity: Complete Spectrum, Long-Time Asymptotics, and Numerology

NASA Astrophysics Data System (ADS)

Denzler, Jochen; McCann, Robert J.

2005-03-01

The complete spectrum is determined for the operator on the Sobolev space W1,2ρ(Rn) formed by closing the smooth functions of compact support with respect to the norm Here the Barenblatt profile ρ is the stationary attractor of the rescaled diffusion equation in the fast, supercritical regime m the same diffusion dynamics represent the steepest descent down an entropy E(u) on probability measures with respect to the Wasserstein distance d2. Formally, the operator H=HessρE is the Hessian of this entropy at its minimum ρ, so the spectral gap H≧α:=2-n(1-m) found below suggests the sharp rate of asymptotic convergence: from any centered initial data 0≦u(0,x) ∈ L1(Rn) with second moments. This bound improves various results in the literature, and suggests the conjecture that the self-similar solution u(t,x)=R(t)-nρ(x/R(t)) is always slowest to converge. The higher eigenfunctions which are polynomials with hypergeometric radial parts and the presence of continuous spectrum yield additional insight into the relations between symmetries of Rn and the flow. Thus the rate of convergence can be improved if we are willing to replace the distance to ρ with the distance to its nearest mass-preserving dilation (or still better, affine image). The strange numerology of the spectrum is explained in terms of the number of moments of ρ.

A Search for Plasma "Fingers" in the Io Torus

NASA Astrophysics Data System (ADS)

Jaggar, S.; Schneider, N. M.; Bagenal, F.; Trauger, J. T.

1996-09-01

We have compared model and data images of the Io plasma torus to test the radial diffusion model of Yang et al. (J. Geophys. Res., Vol 99, p. 8755, 1994). They predict that radial diffusion takes the form of `fingers' of dense plasma flowing outward due to the centrifugal force. Furthermore, they show that the spatial scale of these significant longitudinal variations is approximately 15(o) . The observations used in this study were obtained using a 2.4m telescope at Las Campanas Observatory using a narrowband filter to isolate emissions from S(++) at 9531 Angstroms. S(++) images are dominated by emission from the warm torus where outward radial transport is expected. Although S(+) images are brighter, they are contaminated by emission from the cold torus where fingers are not expected. We used the Colorado Io Torus Emission Package (CITEP)(Taylor et al., J. Geophys. Res., Vol. 100, p. 19541, 1995) to simulate images of the torus with fingers. CITEP is a comprehensive program which incorporates accurate atomic physics, plasma physics and magnetic field models to simulate the brightness and morphology or torus emissions. We used a Voyager empirical model (Bagenal, J. Geophys. Res., Vol. 99, p. 11043, 1994) modulated by a sinusoidal longitudinal density variation with a 15(o) period and an amplitude proportional to the density at that L-shell. We compared simulated images with data to determine the minimum density contrast necessary to make fingers detectable. We place an upper limit on the density contrast of +/- 20% on a 15(o) spatial scale. We conclude that either the density contrast of this mode of transport is small, or other processes are more important for radial transport. This constraint can also be used in other radial diffusion models which predict density variations on this spatial scale. This work has been supported by NASA's Planetary Astronomy and Planetary Atmospheres programs.

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.

Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation.

PubMed

Santos, Andrés; de Haro, Mariano López

2016-06-01

Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1≤d≤3) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.097801], a good agreement being observed.

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

NASA Astrophysics Data System (ADS)

Zabihi, F.; Saffarian, M.

2016-07-01

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

Study of low Reynolds number nozzle flows, including radial pressure gradients

NASA Technical Reports Server (NTRS)

Rae, W. J.

1972-01-01

An analysis is presented of the laminar, axisymmetric flow in a nozzle, including both axial and radial variations of the pressure. The system of equations derived is believed to contain all of the terms necessary for describing the flow through a relatively sharp throat (i.e., one for which the longitudinal radius of curvature of the throat is comparable to, or less than, the transverse radius). A finite difference approximation of these equations is described, together with a computer program for finding numerical solutions. An instability was found in the starting solution; a series of attempts to eliminate this instability is described.

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.

Radially localized helicon modes in nonuniform plasma

PubMed

Breizman; Arefiev

2000-04-24

A radial density gradient in an axisymmetric cylindrical plasma column forms a potential well for nonaxisymmetric helicon modes ( m not equal0). This paper presents an analytic description of such modes in the limit of small longitudinal wave numbers. The corresponding mode equation indicates the possibility of efficient resonant absorption of rf power in helicon discharges at unusually low frequencies.

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.

Gravity influence on the clustering of charged particles in turbulence

NASA Astrophysics Data System (ADS)

Lu, Jiang; Nordsiek, Hansen; Shaw, Raymond

2010-11-01

We report results aimed at studying the interactions of bidisperse charged inertial particles in homogeneous, isotropic turbulence, under the influence of gravitational settling. We theoretically and experimentally investigate the impact of gravititational settling on particle clustering, which is quantified by the radial distribution function (RDF). The theory is based on a drift-diffusion (Fokker-Planck) model with gravitational settling appearing as a diffusive term depending on a dimensionless settling parameter. The experiments are carried out in a laboratory chamber with nearly homogeneous, isotropic turbulence in which the flow is seeded with charged particles and digital holography used to obtain 3D particle positions and velocities. The derived radial distribution function for bidisperse settling charged particles is compared to the experimental RDFs.

Mass spectrum and decay constants of radially excited vector mesons

NASA Astrophysics Data System (ADS)

Mojica, Fredy F.; Vera, Carlos E.; Rojas, Eduardo; El-Bennich, Bruno

2017-07-01

We calculate the masses and weak decay constants of flavorless and flavored ground and radially excited JP=1- mesons within a Poincaré covariant continuum framework based on the Bethe-Salpeter equation. We use in both the quark's gap equation and the meson bound-state equation an infrared massive and finite interaction in the leading symmetry-preserving truncation. While our numerical results are in rather good agreement with experimental values where they are available, no single parametrization of the QCD inspired interaction reproduces simultaneously the ground and excited mass spectrum, which confirms earlier work on pseudoscalar mesons. This feature being a consequence of the lowest truncation, we pin down the range and strength of the interaction in both cases to identify common qualitative features that may help to tune future interaction models beyond the rainbow-ladder approximation.

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

A study of the viscous and nonadiabatic flow in radial turbines

NASA Technical Reports Server (NTRS)

Khalil, I.; Tabakoff, W.

1981-01-01

A method for analyzing the viscous nonadiabatic flow within turbomachine rotors is presented. The field analysis is based upon the numerical integration of the incompressible Navier-Stokes equations together with the energy equation over the rotors blade-to-blade stream channels. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system that suits the most complicated blade geometries. Effects of turbulence are modeled with two equations; one expressing the development of the turbulence kinetic energy and the other its dissipation rate. The method of analysis is applied to a radial inflow turbine. The solution obtained indicates the severity of the complex interaction mechanism that occurs between different flow regimes (i.e., boundary layers, recirculating eddies, separation zones, etc.). Comparison with nonviscous flow solutions tend to justify strongly the inadequacy of using the latter with standard boundary layer techniques to obtain viscous flow details within turbomachine rotors. Capabilities and limitations of the present method of analysis are discussed.

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.

Axial diffusivity of the corona radiata correlated with ventricular size in adult hydrocephalus.

PubMed

Cauley, Keith A; Cataltepe, Oguz

2014-07-01

Hydrocephalus causes changes in the diffusion-tensor properties of periventricular white matter. Understanding the nature of these changes may aid in the diagnosis and treatment planning of this relatively common neurologic condition. Because ventricular size is a common measure of the severity of hydrocephalus, we hypothesized that a quantitative correlation could be made between the ventricular size and diffusion-tensor changes in the periventricular corona radiata. In this article, we investigated this relationship in adult patients with hydrocephalus and in healthy adult subjects. Diffusion-tensor imaging metrics of the corona radiata were correlated with ventricular size in 14 adult patients with acute hydrocephalus, 16 patients with long-standing hydrocephalus, and 48 consecutive healthy adult subjects. Regression analysis was performed to investigate the relationship between ventricular size and the diffusion-tensor metrics of the corona radiata. Subject age was analyzed as a covariable. There is a linear correlation between fractional anisotropy of the corona radiata and ventricular size in acute hydrocephalus (r = 0.784, p < 0.001), with positive correlation with axial diffusivity (r = 0.636, p = 0.014) and negative correlation with radial diffusivity (r = 0.668, p = 0.009). In healthy subjects, axial diffusion in the periventricular corona radiata is more strongly correlated with ventricular size than with patient age (r = 0.466, p < 0.001, compared with r = 0.058, p = 0.269). Axial diffusivity of the corona radiata is linearly correlated with ventricular size in healthy adults and in patients with hydrocephalus. Radial diffusivity of the corona radiata decreases linearly with ventricular size in acute hydrocephalus but is not significantly correlated with ventricular size in healthy subjects or in patients with long-standing hydrocephalus.

Multi-Component Diffusion with Application To Computational Aerothermodynamics

NASA Technical Reports Server (NTRS)

Sutton, Kenneth; Gnoffo, Peter A.

1998-01-01

The accuracy and complexity of solving multicomponent gaseous diffusion using the detailed multicomponent equations, the Stefan-Maxwell equations, and two commonly used approximate equations have been examined in a two part study. Part I examined the equations in a basic study with specified inputs in which the results are applicable for many applications. Part II addressed the application of the equations in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) computational code for high-speed entries in Earth's atmosphere. The results showed that the presented iterative scheme for solving the Stefan-Maxwell equations is an accurate and effective method as compared with solutions of the detailed equations. In general, good accuracy with the approximate equations cannot be guaranteed for a species or all species in a multi-component mixture. 'Corrected' forms of the approximate equations that ensured the diffusion mass fluxes sum to zero, as required, were more accurate than the uncorrected forms. Good accuracy, as compared with the Stefan- Maxwell results, were obtained with the 'corrected' approximate equations in defining the heating rates for the three Earth entries considered in Part II.

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.

Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth.

PubMed

Ambrosi, D; Pezzuto, S; Riccobelli, D; Stylianopoulos, T; Ciarletta, P

2017-12-01

The experimental evidence that a feedback exists between growth and stress in tumors poses challenging questions. First, the rheological properties (the "constitutive equations") of aggregates of malignant cells are still a matter of debate. Secondly, the feedback law (the "growth law") that relates stress and mitotic-apoptotic rate is far to be identified. We address these questions on the basis of a theoretical analysis of in vitro and in vivo experiments that involve the growth of tumor spheroids. We show that solid tumors exhibit several mechanical features of a poroelastic material, where the cellular component behaves like an elastic solid. When the solid component of the spheroid is loaded at the boundary, the cellular aggregate grows up to an asymptotic volume that depends on the exerted compression. Residual stress shows up when solid tumors are radially cut, highlighting a peculiar tensional pattern. By a novel numerical approach we correlate the measured opening angle and the underlying residual stress in a sphere. The features of the mechanobiological system can be explained in terms of a feedback of mechanics on the cell proliferation rate as modulated by the availability of nutrient, that is radially damped by the balance between diffusion and consumption. The volumetric growth profiles and the pattern of residual stress can be theoretically reproduced assuming a dependence of the target stress on the concentration of nutrient which is specific of the malignant tissue.

Measurements and modeling of the impact of weak magnetic fields on the plasma properties of a planar slot antenna driven plasma source

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

Yoshikawa, Jun, E-mail: jun.yoshikawa@tel.com; Susa, Yoshio; Ventzek, Peter L. G.

The radial line slot antenna plasma source is a type of surface wave plasma source driven by a planar slot antenna. Microwave power is transmitted through a slot antenna structure and dielectric window to a plasma characterized by a generation zone adjacent to the window and a diffusion zone that contacts a substrate. The diffusion zone is characterized by a very low electron temperature. This renders the source useful for soft etch applications and thin film deposition processes requiring low ion energy. Another property of the diffusion zone is that the plasma density tends to decrease from the axis tomore » the walls under the action of ambipolar diffusion at distances far from where the plasma is generated. A previous simulation study [Yoshikawa and. Ventzek, J. Vac. Sci. Technol. A 31, 031306 (2013)] predicted that the anisotropy in transport parameters due to weak static magnetic fields less than 50 G could be leveraged to manipulate the plasma profile in the radial direction. These simulations motivated experimental tests in which weak magnetic fields were applied to a radial line slot antenna source. Plasma absorption probe measurements of electron density and etch rate showed that the magnetic fields remote from the wafer were able to manipulate both parameters. A summary of these results is presented in this paper. Argon plasma simulation trends are compared with experimental plasma and etch rate measurements. A test of the impact of magnetic fields on charge up damage showed no perceptible negative effect.« less

Study on the radial vibration and acoustic field of an isotropic circular ring radiator.

PubMed

Lin, Shuyu; Xu, Long

2012-01-01

Based on the exact analytical theory, the radial vibration of an isotropic circular ring is studied and its electro-mechanical equivalent circuit is obtained. By means of the equivalent circuit model, the resonance frequency equation is derived; the relationship between the radial resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions, the material property is analyzed. For comparison, numerical method is used to simulate the radial vibration of isotropic circular rings. The resonance frequency and the radial vibrational displacement distribution are obtained, and the radial radiation acoustic field of the circular ring in radial vibration is simulated. It is illustrated that the radial resonance frequencies from the analytical method and the numerical method are in good agreement when the height is much less than the radius. When the height becomes large relative to the radius, the frequency deviation from the two methods becomes large. The reason is that the exact analytical theory is limited to thin circular ring whose height must be much less than its radius. Copyright © 2011 Elsevier B.V. All rights reserved.

Radial vibration and ultrasonic field of a long tubular ultrasonic radiator.

PubMed

Shuyu, Lin; Zhiqiang, Fu; Xiaoli, Zhang; Yong, Wang; Jing, Hu

2013-09-01

The radial vibration of a metal long circular tube is studied analytically and its electro-mechanical equivalent circuit is obtained. Based on the equivalent circuit, the radial resonance frequency equation is derived. The theoretical relationship between the radial resonance frequency and the geometrical dimensions is studied. Finite element method is used to simulate the radial vibration and the radiated ultrasonic field and the results are compared with those from the analytical method. It is concluded that the radial resonance frequency for a solid metal rod is larger than that for a metal tube with the same outer radius. The radial resonance frequencies from the analytical method are in good agreement with those from the numerical method. Based on the acoustic field analysis, it is concluded that the long metal tube with small wall thickness is superior to that with large wall thickness in producing radial vibration and ultrasonic radiation. Therefore, it is expected to be used as an effective radial ultrasonic radiator in ultrasonic sewage treatment, ultrasonic antiscale and descaling and other ultrasonic liquid handling applications. Copyright © 2013 Elsevier B.V. All rights reserved.

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.

Aerodynamically induced radial forces in a centrifugal gas compressor: Part 2 -- Computational investigation

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

Flathers, M.B.; Bache, G.E.

1999-10-01

Radial loads and direction of a centrifugal gas compressor containing a high specific speed mixed flow impeller and a single tongue volute were determined both experimentally and computationally at both design and off-design conditions. The experimental methodology was developed in conjunction with a traditional ASME PTC-10 closed-loop test to determine radial load and direction. The experimental study is detailed in Part 1 of this paper (Moore and Flathers, 1998). The computational method employs a commercially available, fully three-dimensional viscous code to analyze the impeller and the volute interaction. An uncoupled scheme was initially used where the impeller and volute weremore » analyzed as separate models using a common vaneless diffuser geometry. The two calculations were then repeated until the boundary conditions at a chosen location in the common vaneless diffuser were nearly the same. Subsequently, a coupled scheme was used where the entire stage geometry was analyzed in one calculation, thus eliminating the need for manual iteration of the two independent calculations. In addition to radial load and direction information, this computational procedure also provided aerodynamic stage performance. The effect of impeller front face and rear face cavities was also quantified. The paper will discuss computational procedures, including grid generation and boundary conditions, as well as comparisons of the various computational schemes to experiment. The results of this study will show the limitations and benefits of Computational Fluid Dynamics (CFD) for determination of radial load, direction, and aerodynamic stage performance.« less

Vectorized and multitasked solution of the few-group neutron diffusion equations

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

Zee, S.K.; Turinsky, P.J.; Shayer, Z.

1989-03-01

A numerical algorithm with parallelism was used to solve the two-group, multidimensional neutron diffusion equations on computers characterized by shared memory, vector pipeline, and multi-CPU architecture features. Specifically, solutions were obtained on the Cray X/MP-48, the IBM-3090 with vector facilities, and the FPS-164. The material-centered mesh finite difference method approximation and outer-inner iteration method were employed. Parallelism was introduced in the inner iterations using the cyclic line successive overrelaxation iterative method and solving in parallel across lines. The outer iterations were completed using the Chebyshev semi-iterative method that allows parallelism to be introduced in both space and energy groups. Formore » the three-dimensional model, power, soluble boron, and transient fission product feedbacks were included. Concentrating on the pressurized water reactor (PWR), the thermal-hydraulic calculation of moderator density assumed single-phase flow and a closed flow channel, allowing parallelism to be introduced in the solution across the radial plane. Using a pinwise detail, quarter-core model of a typical PWR in cycle 1, for the two-dimensional model without feedback the measured million floating point operations per second (MFLOPS)/vector speedups were 83/11.7. 18/2.2, and 2.4/5.6 on the Cray, IBM, and FPS without multitasking, respectively. Lower performance was observed with a coarser mesh, i.e., shorter vector length, due to vector pipeline start-up. For an 18 x 18 x 30 (x-y-z) three-dimensional model with feedback of the same core, MFLOPS/vector speedups of --61/6.7 and an execution time of 0.8 CPU seconds on the Cray without multitasking were measured. Finally, using two CPUs and the vector pipelines of the Cray, a multitasking efficiency of 81% was noted for the three-dimensional model.« less

Description of sorbing tracers transport in fractured media using the lattice model approach

NASA Astrophysics Data System (ADS)

Jiménez-Hornero, Francisco J.; Giráldez, Juan V.; Laguna, Ana

2005-12-01

The transport of contaminants in fractured media is a complex phenomenon with a great environmental impact. It has been described with several models, most of them based on complex partial differential equations, that are difficult to apply when equilibrium and nonequilibrium dynamics are considered in complex boundaries. With the aim of overcoming this limitation, a combination of two lattice Bathnagar, Gross and Krook (BGK) models, derived from the lattice Boltzmann model, is proposed in this paper. The fractured medium is assumed to be a single fissure in a porous rock matrix. The proposed approach permits us to deal with two processes with different length scales: advection-dispersion in the fissure and diffusion within the rock matrix. In addition to the mentioned phenomena, sorption reactions are also considered. The combined model has been tested using the experimental breakthrough curves obtained by Garnier et al. (Garnier, J.M., Crampon, N., Préaux, C., Porel, G., Vreulx, M., 1985. Traçage par 13C, 2H, I - et uranine dans la nappe de la craie sénonienne en écoulement radial convergent (Béthune, France). J. Hidrol. 78, 379-392.) giving acceptable results. A study on the influence of the lattice BGK models parameters controlling sorption and matrix diffusion on the breakthrough curves shape is included.

Dielectric model and theoretical analysis of cationic reverse micellar solutions in CTAB/isooctane/n-hexanol/water systems.

PubMed

Yang, Likun; Zhao, Kongshuang

2007-08-14

Dielectric relaxation spectra of CTAB reverse micellar solutions, CTAB/isooctane/n-hexanol/water systems with different concentrations of CTAB and different water contents, were investigated in the frequency range from 40 Hz to 110 MHz. Two striking dielectric relaxations were observed at about 10(4) Hz and 10(5) Hz, respectively. Dielectric parameters were obtained by fitting the data using the Cole-Cole equation with two Cole-Cole dispersion terms and the electrode polarization term. These parameters show different variation with the increase of the concentration of CTAB or the water content. In order to explain the two relaxations systematically and obtain detailed information on the systems and the inner surface of the reverse micelles, an electrical model has been constituted. On the basis of this model, the low-frequency dielectric relaxation was interpreted by the radial diffusion of free counterions in the diffuse layer with Grosse model. For the high-frequency dielectric relaxation, Hanai theory and the corresponding analysis method were used to calculate the phase parameters of the constituent phases in these systems. The reasonable analysis results suggest that the high-frequency relaxation probably originated from the interfacial polarization. The structural and electrical information of the present systems were obtained from the phase parameters simultaneously.

Diffusion of dissolved CO2 in water propagating from a cylindrical bubble in a horizontal Hele-Shaw cell

NASA Astrophysics Data System (ADS)

Peñas-López, Pablo; van Elburg, Benjamin; Parrales, Miguel A.; Rodríguez-Rodríguez, Javier

2017-06-01

The dissolution of a gas bubble in a confined geometry is a problem of interest in technological applications such as microfluidics or carbon sequestration, as well as in many natural flows of interest in geophysics. While the dissolution of spherical or sessile bubbles has received considerable attention in the literature, the case of a two-dimensional bubble in a Hele-Shaw cell, which constitutes perhaps the simplest possible confined configuration, has been comparatively less studied. Here, we use planar laser-induced fluorescence to experimentally investigate the diffusion-driven transport of dissolved CO2 that propagates from a cylindrical mm-sized bubble in air-saturated water confined in a horizontal Hele-Shaw cell. We observe that the radial trajectory of an isoconcentration front, rf(t ) , evolves in time as approximately rf-R0∝√{t } , where R0 denotes the initial bubble radius. We then characterize the unsteady CO2 concentration field via two simple analytical models, which are then validated against a numerical simulation. The first model treats the bubble as an instantaneous line source of CO2, whereas the second assumes a constant interfacial concentration. Finally, we provide an analogous Epstein-Plesset equation with the intent of predicting the dissolution rate of a cylindrical bubble.

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.

A reaction-diffusion model of CO2 influx into an oocyte

PubMed Central

Somersalo, Erkki; Occhipinti, Rossana; Boron, Walter F.; Calvetti, Daniela

2012-01-01

We have developed and implemented a novel mathematical model for simulating transients in surface pH (pHS) and intracellular pH (pHi) caused by the influx of carbon dioxide (CO2) into a Xenopus oocyte. These transients are important tools for studying gas channels. We assume that the oocyte is a sphere surrounded by a thin layer of unstirred fluid, the extracellular unconvected fluid (EUF), which is in turn surrounded by the well-stirred bulk extracellular fluid (BECF) that represents an infinite reservoir for all solutes. Here, we assume that the oocyte plasma membrane is permeable only to CO2. In both the EUF and intracellular space, solute concentrations can change because of diffusion and reactions. The reactions are the slow equilibration of the CO2 hydration-dehydration reactions and competing equilibria among carbonic acid (H2CO3)/bicarbonate ( HCO3-) and a multitude of non-CO2/HCO3- buffers. Mathematically, the model is described by a coupled system of reaction-diffusion equations that—assuming spherical radial symmetry—we solved using the method of lines with appropriate stiff solvers. In agreement with experimental data (Musa-Aziz et al, PNAS 2009, 106:5406–5411), the model predicts that exposing the cell to extracellular 1.5% CO2/10 mM HCO3- (pH 7.50) causes pHi to fall and pHS to rise rapidly to a peak and then decay. Moreover, the model provides insights into the competition between diffusion and reaction processes when we change the width of the EUF, membrane permeability to CO2, native extra-and intracellular carbonic anhydrase-like activities, the non-CO2/HCO3- (intrinsic) intracellular buffering power, or mobility of intrinsic intracellular buffers. PMID:22728674

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

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.

Ultra-low-frequency wave-driven diffusion of radiation belt relativistic electrons

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

Su, Zhenpeng; Zhu, Hui; Xiao, Fuliang

The Van Allen radiation belts are typically two zones of energetic particles encircling the Earth separated by the slot region. How the outer radiation belt electrons are accelerated to relativistic energies remains an unanswered question. Recent studies have presented compelling evidence for the local acceleration by very-low-frequency (VLF) chorus waves. However, there has been a competing theory to the local acceleration, radial diffusion by ultra-low-frequency (ULF) waves, whose importance has not yet been determined definitively. Here we report a unique radiation belt event with intense ULF waves but no detectable VLF chorus waves. So, our results demonstrate that the ULFmore » waves moved the inner edge of the outer radiation belt earthward 0.3 Earth radii and enhanced the relativistic electron fluxes by up to one order of magnitude near the slot region within about 10 h, providing strong evidence for the radial diffusion of radiation belt relativistic electrons.« less

Ultra-low-frequency wave-driven diffusion of radiation belt relativistic electrons

DOE PAGES

Su, Zhenpeng; Zhu, Hui; Xiao, Fuliang; ...

2015-12-22

The Van Allen radiation belts are typically two zones of energetic particles encircling the Earth separated by the slot region. How the outer radiation belt electrons are accelerated to relativistic energies remains an unanswered question. Recent studies have presented compelling evidence for the local acceleration by very-low-frequency (VLF) chorus waves. However, there has been a competing theory to the local acceleration, radial diffusion by ultra-low-frequency (ULF) waves, whose importance has not yet been determined definitively. Here we report a unique radiation belt event with intense ULF waves but no detectable VLF chorus waves. So, our results demonstrate that the ULFmore » waves moved the inner edge of the outer radiation belt earthward 0.3 Earth radii and enhanced the relativistic electron fluxes by up to one order of magnitude near the slot region within about 10 h, providing strong evidence for the radial diffusion of radiation belt relativistic electrons.« less

Ion transport and loss in the earth's quiet ring current. I - Data and standard model

NASA Technical Reports Server (NTRS)

Sheldon, R. B.; Hamilton, D. C.

1993-01-01

A study of the transport and loss of ions in the earth's quiet time ring current, in which the standard radial diffusion model developed for the high-energy radiation belt particles is compared with the measurements of the lower-energy ring current ions, is presented. The data set provides ionic composition information in an energy range that includes the bulk of the ring current energy density, 1-300 keV/e. Protons are found to dominate the quiet time energy density at all altitudes, peaking near L of about 4 at 60 keV/cu cm, with much smaller contributions from O(+) (1-10 percent), He(+) (1-5 percent), and He(2+) (less than 1 percent). A minimization procedure is used to fit the amplitudes of the standard electric radial diffusion coefficient, yielding 5.8 x 10 exp -11 R(E-squared)/s. Fluctuation ionospheric electric fields are suggested as the source of the additional diffusion detected.

Gradual Diffusion and Punctuated Phase Space Density Enhancements of Highly Relativistic Electrons: Van Allen Probes Observations

NASA Technical Reports Server (NTRS)

Baker, D. N.; Jaynes, A. N.; Li, X.; Henderson, M. G.; Kanekal, S. G.; Reeves, G. D.; Spence, H. E.; Claudepierre, S. G.; Fennell, J. F.; Hudson, M. K.

2014-01-01

The dual-spacecraft Van Allen Probes mission has provided a new window into mega electron volt (MeV) particle dynamics in the Earth's radiation belts. Observations (up to E (is) approximately 10MeV) show clearly the behavior of the outer electron radiation belt at different timescales: months-long periods of gradual inward radial diffusive transport and weak loss being punctuated by dramatic flux changes driven by strong solar wind transient events. We present analysis of multi-MeV electron flux and phase space density (PSD) changes during March 2013 in the context of the first year of Van Allen Probes operation. This March period demonstrates the classic signatures both of inward radial diffusive energization and abrupt localized acceleration deep within the outer Van Allen zone (L (is) approximately 4.0 +/- 0.5). This reveals graphically that both 'competing' mechanisms of multi-MeV electron energization are at play in the radiation belts, often acting almost concurrently or at least in rapid succession.

A comprehensive model of ion diffusion and charge exchange in the cold Io torus

NASA Technical Reports Server (NTRS)

Barbosa, D. D.; Moreno, M. A.

1988-01-01

A comprehensive analytic model of radial diffusion in the cold Io torus is developed. The model involves a generalized molecular cloud theory of SO2 and its dissociation fragments SO, O2, S, and O, which are formed at a relatively large rate by solar UV photodissociation of SO2. The key component of the new theory is SO, which can react with S(+) through a near-resonant charge exchange process that is exothermic. This provides a mechanism for the rapid depletion of singly ionized sulfur in the cold torus and can account for the large decrease in the total flux tube content inward of Io's orbit. The model is used to demonstrate quantitatively the effects of radial diffusion in a charge exchange environment that acts as a combined source and sink for ions in various charge states. A detailed quantitative explanation for the O(2+) component of the cold torus is given, and insight is derived into the workings of the so-called plasma 'ribbon'.

Transport, charge exchange and loss of energetic heavy ions in the earth's radiation belts - Applicability and limitations of theory

NASA Technical Reports Server (NTRS)

Spjeldvik, W. N.

1981-01-01

Computer simulations of processes which control the relative abundances of ions in the trapping regions of geospace are compared with observations from discriminating ion detectors. Energy losses due to Coulomb collisions between ions and exospheric neutrals are considered, along with charge exchange losses and internal charge exchanges. The time evolution of energetic ion fluxes of equatorially mirroring ions under radial diffusion is modelled to include geomagnetic and geoelectric fluctutations. Limits to the validity of diffusion transport theory are discussed, and the simulation is noted to contain provisions for six ionic charge states and the source effect on the radiation belt oxygen ion distributions. Comparisons are made with ion flux data gathered on Explorer 45 and ISEE-1 spacecraft and results indicate that internal charge exchanges cause the radiation belt ion charge state to be independent of source charge rate characteristics, and relative charge state distribution is independent of the radially diffusive transport rate below the charge state redistribution zone.

Long-term white matter tract reorganization following prolonged febrile seizures.

PubMed

Pujar, Suresh S; Seunarine, Kiran K; Martinos, Marina M; Neville, Brian G R; Scott, Rod C; Chin, Richard F M; Clark, Chris A

2017-05-01

Diffusion magnetic resonance imaging (MRI) studies have demonstrated acute white matter changes following prolonged febrile seizures (PFS), but their longer-term evolution is unknown. We investigated a population-based cohort to determine white matter diffusion properties 8 years after PFS. We used diffusion tensor imaging (DTI) and applied Tract-Based Spatial Statistics for voxel-wise comparison of white matter microstructure between 26 children with PFS and 27 age-matched healthy controls. Age, gender, handedness, and hippocampal volumes were entered as covariates for voxel-wise analysis. Mean duration between the episode of PFS and follow-up was 8.2 years (range 6.7-9.6). All children were neurologically normal, and had normal conventional neuroimaging. On voxel-wise analysis, compared to controls, the PFS group had (1) increased fractional anisotropy in early maturing central white matter tracts, (2) increased mean and axial diffusivity in several peripheral white matter tracts and late-maturing central white matter tracts, and (3) increased radial diffusivity in peripheral white matter tracts. None of the tracts had reduced fractional anisotropy or diffusivity indices in the PFS group. In this homogeneous, population-based sample, we found increased fractional anisotropy in early maturing central white matter tracts and increased mean and axial diffusivity with/without increased radial diffusivity in several late-maturing peripheral white matter tracts 8 years post-PFS. We propose disruption in white matter maturation secondary to seizure-induced axonal injury, with subsequent neuroplasticity and microstructural reorganization as a plausible explanation. © 2017 The Authors. Epilepsia published by Wiley Periodicals, Inc. on behalf of International League Against Epilepsy.

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

Green's function of radial inhomogeneous spheres excited by internal sources.

PubMed

Zouros, Grigorios P; Kokkorakis, Gerassimos C

2011-01-01

Green's function in the interior of penetrable bodies with inhomogeneous compressibility by sources placed inside them is evaluated through a Schwinger-Lippmann volume integral equation. In the case of a radial inhomogeneous sphere, the radial part of the unknown Green's function can be expanded in a double Dini's series, which allows analytical evaluation of the involved cumbersome integrals. The simple case treated here can be extended to more difficult situations involving inhomogeneous density as well as to the corresponding electromagnetic or elastic problem. Finally, numerical results are given for various inhomogeneous compressibility distributions.

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

The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

NASA Astrophysics Data System (ADS)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

A well-balanced meshless tsunami propagation and inundation model

NASA Astrophysics Data System (ADS)

Brecht, Rüdiger; Bihlo, Alexander; MacLachlan, Scott; Behrens, Jörn

2018-05-01

We present a novel meshless tsunami propagation and inundation model. We discretize the nonlinear shallow-water equations using a well-balanced scheme relying on radial basis function based finite differences. For the inundation model, radial basis functions are used to extrapolate the dry region from nearby wet points. Numerical results against standard one- and two-dimensional benchmarks are presented.

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

Kawahara, Hajime, E-mail: divrot@gmail.com

We consider the effect of planetary spin on the planetary radial velocity (PRV) in dayside spectra of exoplanets. To understand the spin effect qualitatively, we derive an analytic formula of the intensity-weighted radial velocity from the planetary surface on the following assumptions: (1) constant and solid rotation without precession, (2) stable and uniform distribution of molecules/atoms, (3) emission models from the dayside hemisphere, and (4) a circular orbit. On these assumptions, we find that the curve of the PRV is distorted by the planetary spin and this anomaly is characterized by the spin radial velocity at the equator and amore » projected angle on a celestial plane between the spin axis and the axis of orbital motion {lambda}{sub p} in a manner analogous to the Rossiter-McLaughlin effect. The latter can constrain the planetary obliquity. Creating mock PRV data with 3 km s{sup -1} accuracy, we demonstrate how {lambda}{sub p} and the spin radial velocity at the equator are estimated. We find that the stringent constraint of eccentricity is crucial to detect the spin effect. Though our formula is still qualitative, we conclude that the PRV in the dayside spectra will be a powerful means for constraining the planetary spin.« less

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.

Interactions Between Energetic Electrons and Realistic Whistler Mode Waves in the Jovian Magnetosphere

NASA Astrophysics Data System (ADS)

de Soria-Santacruz Pich, M.; Drozdov, A.; Menietti, J. D.; Garrett, H. B.; Kellerman, A. C.; Shprits, Y. Y.

2016-12-01

The radiation belts of Jupiter are the most intense of all the planets in the solar system. Their source is not well understood but they are believed to be the result of inward radial transport beyond the orbit of Io. In the case of Earth, the radiation belts are the result of local acceleration and radial diffusion from whistler waves, and it has been suggested that this type of acceleration may also be significant in the magnetosphere of Jupiter. Multiple diffusion codes have been developed to study the dynamics of the Earth's magnetosphere and characterize the interaction between relativistic electrons and whistler waves; in the present paper we adapt one of these codes, the two-dimensional version of the Versatile Electron Radiation Belt (VERB) computer code, to the case of the Jovian magnetosphere. We use realistic parameters to determine the importance of whistler emissions in the acceleration and loss of electrons in the Jovian magnetosphere. More specifically, we use an extensive wave survey from the Galileo spacecraft and initial conditions derived from the Galileo Interim Radiation Electron Model version 2 (GIRE2) to estimate the pitch angle and energy diffusion of the electron population due to lower and upper band whistlers as a function of latitude and radial distance from the planet, and we calculate the decay rates that result from this interaction.

Transport of ion beam in an annular magnetically expanding helicon double layer thruster

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

Zhang, Yunchao, E-mail: yunchao.zhang@anu.edu.au; Charles, Christine; Boswell, Rod

2014-06-15

An ion beam generated by an annular double layer has been measured in a helicon thruster, which sustains a magnetised low-pressure (5.0 × 10{sup −4} Torr) argon plasma at a constant radio-frequency (13.56 MHz) power of 300 W. After the ion beam exits the annular structure, it merges into a solid centrally peaked structure in the diffusion chamber. As the annular ion beam moves towards the inner region in the diffusion chamber, a reversed-cone plasma wake (with a half opening angle of about 30°) is formed. This process is verified by measuring both the radial and axial distributions of the beam potential and beammore » current. The beam potential changes from a two-peak radial profile (maximum value ∼ 30 V, minimum value ∼ 22.5 V) to a flat (∼28 V) along the axial direction; similarly, the beam current changes from a two-peak to one-peak radial profile and the maximum value decreases by half. The inward cross-magnetic-field motion of the beam ions is caused by a divergent electric field in the source. Cross-field diffusion of electrons is also observed in the inner plume and is determined as being of non-ambipolar origin.« less

BDNF Val66Met polymorphism modulates the effect of loneliness on white matter microstructure in young adults.

PubMed

Meng, Jie; Hao, Lei; Wei, Dongtao; Sun, Jiangzhou; Li, Yu; Qiu, Jiang

2017-12-01

Loneliness is a common experience. Susceptibility to loneliness is a stable trait and is heritable. Previous studies have suggested that loneliness may impact regional gray matter density and brain activation to social stimuli, but its relation to white matter structure and how it may interact with genetic factors remains unclear. In this study, we investigated whether and how a common polymorphism (Val66Met) in the brain-derived neurotrophic factor gene modulated the association between loneliness and white matter microstructure in 162 young adults. The tract-based spatial statistics analyses revealed that the relationships between loneliness and white matter microstructures were significantly different between Val/Met heterozygotes and Val/Val homozygotes. Specifically, loneliness was significantly correlated with reduced fractional anisotropy and increased radial diffusivity in widespread white matter fibers within Val/Met heterozygotes. It was also significantly correlated with increased radial diffusivity in Met/Met genotypes but showed no significant association with white matter measures in Val/Val genotypes. Furthermore, the associations between loneliness and fractional anisotropy (or radial diffusivity) in Val/Met heterozygotes turned out to be global effects. These results provide evidence that loneliness may interact with the BDNF Val66Met polymorphism to shape the microstructures of white matter, and the Val/Met heterozygotes may be more susceptible to social environment. Copyright © 2017 Elsevier B.V. All rights reserved.

Generalized radially self-accelerating helicon beams.

PubMed

Vetter, Christian; Eichelkraut, Toni; Ornigotti, Marco; Szameit, Alexander

2014-10-31

We report, in theory and experiment, on a new class of optical beams that are radially self-accelerating and nondiffracting. These beams continuously evolve on spiraling trajectories while maintaining their amplitude and phase distribution in their rotating rest frame. We provide a detailed insight into the theoretical origin and characteristics of radial self-acceleration and prove our findings experimentally. As radially self-accelerating beams are nonparaxial and a solution to the full scalar Helmholtz equation, they can be implemented in many linear wave systems beyond optics, from acoustic and elastic waves to surface waves in fluids and soft matter. Our work generalized the study of classical helicon beams to a complete set of solutions for rotating complex fields.

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.

Mathematical modeling and fluorescence imaging to study the Ca2+ turnover in skinned muscle fibers.

PubMed Central

Uttenweiler, D; Weber, C; Fink, R H

1998-01-01

A mathematical model was developed for the simulation of the spatial and temporal time course of Ca2+ ion movement in caffeine-induced calcium transients of chemically skinned muscle fiber preparations. Our model assumes cylindrical symmetry and quantifies the radial profile of Ca2+ ion concentration by solving the diffusion equations for Ca2+ ions and various mobile buffers, and the rate equations for Ca2+ buffering (mobile and immobile buffers) and for the release and reuptake of Ca2+ ions by the sarcoplasmic reticulum (SR), with a finite-difference algorithm. The results of the model are compared with caffeine-induced spatial Ca2+ transients obtained from saponin skinned murine fast-twitch fibers by fluorescence photometry and imaging measurements using the ratiometric dye Fura-2. The combination of mathematical modeling and digital image analysis provides a tool for the quantitative description of the total Ca2+ turnover and the different contributions of all interacting processes to the overall Ca2+ transient in skinned muscle fibers. It should thereby strongly improve the usage of skinned fibers as quantitative assay systems for many parameters of the SR and the contractile apparatus helping also to bridge the gap to the intact muscle fiber. PMID:9545029

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

Brain aging in humans, chimpanzees (Pan troglodytes), and rhesus macaques (Macaca mulatta): magnetic resonance imaging studies of macro- and microstructural changes.

PubMed

Chen, Xu; Errangi, Bhargav; Li, Longchuan; Glasser, Matthew F; Westlye, Lars T; Fjell, Anders M; Walhovd, Kristine B; Hu, Xiaoping; Herndon, James G; Preuss, Todd M; Rilling, James K

2013-10-01

Among primates, humans are uniquely vulnerable to many age-related neurodegenerative disorders. We used structural and diffusion magnetic resonance imaging (MRI) to examine the brains of chimpanzees and rhesus monkeys across each species' adult lifespan, and compared these results with published findings in humans. As in humans, gray matter volume decreased with age in chimpanzees and rhesus monkeys. Also like humans, chimpanzees showed a trend for decreased white matter volume with age, but this decrease occurred proportionally later in the chimpanzee lifespan than in humans. Diffusion MRI revealed widespread age-related decreases in fractional anisotropy and increases in radial diffusivity in chimpanzees and macaques. However, both the fractional anisotropy decline and the radial diffusivity increase started at a proportionally earlier age in humans than in chimpanzees. Thus, even though overall patterns of gray and white matter aging are similar in humans and chimpanzees, the longer lifespan of humans provides more time for white matter to deteriorate before death, with the result that some neurological effects of aging may be exacerbated in our species. Copyright © 2013 Elsevier Inc. All rights reserved.

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Schulz, Michael; Lyons, Larry R.; Gorney, David J.

1992-01-01

Guiding-center simulations of stormtime transport of ring-current and radiation-belt ions having first adiabatic invariants mu is approximately greater than 15 MeV/G (E is approximately greater than 165 keV at L is approximately 3) are surprisingly well described (typically within a factor of approximately less than 4) by the quasilinear theory of radial diffusion. This holds even for the case of an individual model storm characterized by substorm-associated impulses in the convection electric field, provided that the actual spectrum of the electric field is incorporated in the quasilinear theory. Correction of the quasilinear diffusion coefficient D(sub LL)(sup ql) for drift-resonance broadening (so as to define D(sub LL)(sup ql)) reduced the typical discrepancy with the diffusion coefficients D(sub LL)(sup sim) deduced from guiding-center simulations of representative-particle trajectories to a factor of approximately 3. The typical discrepancy was reduced to a factor of approximately 1.4 by averaging D(sub LL)(sup sim), D(sub LL)(sup ql), and D(sub LL)(sup rb) over an ensemble of model storms characterized by different (but statistically equivalent) sets of substorm-onset times.

Effect of lost charged particles on the breakdown characteristics of the gaseous electrical discharge in non-uniform axial electric field

NASA Astrophysics Data System (ADS)

Noori, H.; Ranjbar, A. H.

2017-10-01

The secondary emission coefficient is a valuable parameter for numerical modeling of the discharge process in gaseous insulation. A theoretical model has been developed to consider the effects of the radial electric field, non-uniformity of the axial electric field, and radial diffusion of charged particles on the secondary emission coefficient. In the model, a modified breakdown criterion is employed to determine the effective secondary electron emission, γeff. Using the geometry factor gi which is introduced based on the effect of radial diffusion of charged particles on the fraction of ions which arrive at the cathode, the geometry-independent term of γeff (Δi) was obtained as a function of the energy of the incident ions on the cathode. The results show that Δi is approximately a unique function of the ion energy for the ratios of d/R = 39, 50, 77, 115, and 200. It means that the considered mechanisms in the model are responsible for the deviation from Paschen's law.

Macrosegregation of GeSi Alloys Grown in a Static Magnetic Field

NASA Technical Reports Server (NTRS)

Ritter, T. M.; Volz, M. P.; Cobb, S. D.; Szofran, F. R.

1999-01-01

Axial and radial macrosegregation profiles have been determined for GeSi alloy crystals grown by the vertical Bridgman technique. An axial 5 Tesla magnetic field was applied to several samples during growth to decrease the melt velocities by means of the Lorentz force. Compositions were measured with either energy dispersive X-ray spectroscopy (EDS) on a scanning electron microscope (SEM) or by wavelength dispersive X-ray spectroscopy (WDS) on a microprobe. The crystals were processed in graphite, hot-pressed boron nitride (BN), and pyrolytic boron nitride (PBN) ampoules, which produced various solid-liquid interface shapes during solidification. Those samples grown in a graphite ampoule exhibited radial profiles consistent with a highly concave interface and axial profiles indicative of complete mixing in the melt. The samples grown in BN and PBN ampoules had less radial variation. Axial macrosegregation profiles of these samples fell between the predictions for a completely mixed melt and one where solute transport is dominated by diffusion. Possible explanations for the apparent insufficiency of the magnetic field to achieve diffusion controlled growth conditions are discussed.

Characteristic Length Scales in Fracture Networks: Hydraulic Connectivity through Periodic Hydraulic Tests

NASA Astrophysics Data System (ADS)

Becker, M.; Bour, O.; Le Borgne, T.; Longuevergne, L.; Lavenant, N.; Cole, M. C.; Guiheneuf, N.

2017-12-01

Determining hydraulic and transport connectivity in fractured bedrock has long been an important objective in contaminant hydrogeology, petroleum engineering, and geothermal operations. A persistent obstacle to making this determination is that the characteristic length scale is nearly impossible to determine in sparsely fractured networks. Both flow and transport occur through an unknown structure of interconnected fracture and/or fracture zones making the actual length that water or solutes travel undetermined. This poses difficulties for flow and transport models. For, example, hydraulic equations require a separation distance between pumping and observation well to determine hydraulic parameters. When wells pairs are close, the structure of the network can influence the interpretation of well separation and the flow dimension of the tested system. This issue is explored using hydraulic tests conducted in a shallow fractured crystalline rock. Periodic (oscillatory) slug tests were performed at the Ploemeur fractured rock test site located in Brittany, France. Hydraulic connectivity was examined between three zones in one well and four zones in another, located 6 m apart in map view. The wells are sufficiently close, however, that the tangential distance between the tested zones ranges between 6 and 30 m. Using standard periodic formulations of radial flow, estimates of storativity scale inversely with the square of the separation distance and hydraulic diffusivity directly with the square of the separation distance. Uncertainty in the connection paths between the two wells leads to an order of magnitude uncertainty in estimates of storativity and hydraulic diffusivity, although estimates of transmissivity are unaffected. The assumed flow dimension results in alternative estimates of hydraulic parameters. In general, one is faced with the prospect of assuming the hydraulic parameter and inverting the separation distance, or vice versa. Similar uncertainties exist, for instance, when trying to invert transport parameters from tracer mean residence time. This field test illustrates that when dealing with fracture networks, there is a need for analytic methods of complexity that lie between simple radial solutions and discrete fracture network models.

Evaluating the Role and Effects of Precipitation on Relativistic Electron Losses during Storms

NASA Astrophysics Data System (ADS)

Chen, Y.; Fu, X.

2016-12-01

Theoretic studies have suggested that during storm times various waves (e.g., whistler-mode chorus and electromagnetic ion cyclotron waves) can cause significant precipitation of relativistic ( MeV) electrons that are originally trapped inside the outer radiation belt. However, the role of precipitation and its quantitative contribution to the losses of outer-belt electrons remain open questions. In this study, we tackle these questions by systemically examining the latest wave and electron in-situ, simultaneous observations made at different altitudes by Van Allen Probes from near equator, NOAA POES at low Earth orbits near/across electron loss cone, and BARREL under the mesosphere. After calibrating with DEMTER observations, we first confirm and quantify the response of POES MEPED proton channels to MeV electrons. Next, we identify a list of precipitation events from BARREL and POES measurements, examine the temporal adn spatial relation between the two data sets, and estimate the intensities of electron precipitation with ascertained uncertainties. Then, from Van Allen Probes data, we select another list of dropout events during storms. By cross checking the above two lists, we are able to determine the causal relation between precipitation and dropouts through individual case as well as statistical studies so as to quantify the contributions from precipitation. This study mainly focuses on the relatively small L-shells with positive phase space density radial gradient in order to alleviate the impacts from outward radial diffusion and adiabatic effects. Based upon the recent discovery of cross-energy cross-pitch angle coherence, we pay particular attention to the cross-term diffusions which may account for the extra "loss" needed by observed MeV electron dropouts. Results from this observational study will advance our knowledge on the loss mechanism of outer-belt electrons, and thus lay down another stepping stone towards high-fidelity physics-based models for radiation belts.

Disturbance severity and canopy position control the radial growth response of maple trees (Acer spp.) in forests of northwest Ohio impacted by emerald ash borer (Agrilus planipennis)

Treesearch

K.C. Costilow; Kathleen Knight; Charles Flower

2017-01-01

Key message. Radial growth of silver and red maples was investigated across three forests in northwest Ohio following the outbreak of the invasive emerald ash borer. The growth response of maples was driven by an advancement in canopy class and disturbance severity. Context. Forest disturbances resulting in species-specific diffuse mortality cause shifts in aboveground...

Theoretical predictions of latitude dependencies in the solar wind

NASA Technical Reports Server (NTRS)

Winge, C. R., Jr.; Coleman, P. J., Jr.

1974-01-01

Results are presented which were obtained with the Winge-Coleman model for theoretical predictions of latitudinal dependencies in the solar wind. A first-order expansion is described which allows analysis of first-order latitudinal variations in the coronal boundary conditions and results in a second-order partial differential equation for the perturbation stream function. Latitudinal dependencies are analytically separated out in the form of Legendre polynomials and their derivative, and are reduced to the solution of radial differential equations. This analysis is shown to supply an estimate of how large the coronal variation in latitude must be to produce an 11 km/sec/deg gradient in the radial velocity of the solar wind, assuming steady-state processes.

A Novel Approach to Solve Linearized Stellar Pulsation Equations

NASA Astrophysics Data System (ADS)

Bard, Christopher; Teitler, S.

2011-01-01

We present a new approach to modeling linearized, non-radial pulsations in differentially rotating, massive stars. As a first step in this direction, we consider adiabatic pulsations and adopt the Cowling approximation that perturbations of the gravitational potential and its radial derivative are negligible. The angular dependence of the pulsation modes is expressed as a series expansion of associated Legendre polynomials; the resulting coupled system of differential equations is then solved by finding the eigenfrequencies at which the determinant of a characteristic matrix vanishes. Our method improves on previous treatments by removing the requirement that an arbitrary normalization be applied to the eigenfunctions; this brings the benefit of improved numerical robustness.

Corrigendum to "Scattering above energy norm of solutions of a loglog energy-supercritical Schrödinger equation with radial data"

NASA Astrophysics Data System (ADS)

Roy, Tristan

2018-05-01

The purpose of this corrigendum is to point out some errors that appear in [1]. Our main result remains valid, i.e scattering of H˜k : =H˙k (Rn) ∩H˙1 (Rn) solutions of the loglog energy-supercritical Schrödinger equation i∂t u + △ u = | u | 4/n-2 ulogc ⁡ (log ⁡ (10 + | u|2), 0 < c n/2, radial data u (0) : =u0 ∈H˜k but with slightly different values of cn, i.e cn = 1/5772 if n = 3 and cn = 3/8024 if n = 4. We propose some corrections.

Well behaved anisotropic compact star models in general relativity

NASA Astrophysics Data System (ADS)

Jasim, M. K.; Maurya, S. K.; Gupta, Y. K.; Dayanandan, B.

2016-11-01

Anisotropic compact star models have been constructed by assuming a particular form of a metric function e^{λ}. We solved the Einstein field equations for determining the metric function e^{ν}. For this purpose we have assumed a physically valid expression of radial pressure (pr). The obtained anisotropic compact star model is representing the realistic compact objects such as PSR 1937 +21. We have done an extensive study about physical parameters for anisotropic models and found that these parameters are well behaved throughout inside the star. Along with these we have also determined the equation of state for compact star which gives the radial pressure is purely the function of density i.e. pr=f(ρ).

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.

Evolution of Turbulence in the Expanding Solar Wind, a Numerical Study

NASA Astrophysics Data System (ADS)

Dong, Yue; Verdini, Andrea; Grappin, Roland

2014-10-01

We study the evolution of turbulence in the solar wind by solving numerically the full three-dimensional (3D) magnetohydrodynamic (MHD) equations embedded in a radial mean wind. The corresponding equations (expanding box model or EBM) have been considered earlier but never integrated in 3D simulations. Here, we follow the development of turbulence from 0.2 AU up to about 1.5 AU. Starting with isotropic spectra scaling as k -1, we observe a steepening toward a k -5/3 scaling in the middle of the wave number range and formation of spectral anisotropies. The advection of a plasma volume by the expanding solar wind causes a non-trivial stretching of the volume in directions transverse to radial and the selective decay of the components of velocity and magnetic fluctuations. These two effects combine to yield the following results. (1) Spectral anisotropy: gyrotropy is broken, and the radial wave vectors have most of the power. (2) Coherent structures: radial streams emerge that resemble the observed microjets. (3) Energy spectra per component: they show an ordering in good agreement with the one observed in the solar wind at 1 AU. The latter point includes a global dominance of the magnetic energy over kinetic energy in the inertial and f -1 range and a dominance of the perpendicular-to-the-radial components over the radial components in the inertial range. We conclude that many of the above properties are the result of evolution during transport in the heliosphere, and not just the remnant of the initial turbulence close to the Sun.

The role of fluctuation-induced transport in a toroidal plasma with strong radial electric fields

NASA Technical Reports Server (NTRS)

Roth, J. R.; Krawczonek, W. M.; Powers, E. J.; Hong, J. Y.; Kim, Y. C.

1981-01-01

Previous work employing digitally implemented spectral analysis techniques is extended to demonstrate that radial fluctuation-induced transport is the dominant ion transport mechanism in an electric field dominated toroidal plasma. Such transport can be made to occur against a density gradient, and hence may have a very beneficial effect on confinement in toroidal plasmas of fusion interest. It is shown that Bohm or classical diffusion down a density gradient, the collisional Pedersen-current mechanism, and the collisionless electric field gradient mechanism described by Cole (1976) all played a minor role, if any, in the radial transport of this plasma.

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.

A simple scaling law for the equation of state and the radial distribution functions calculated by density-functional theory molecular dynamics

NASA Astrophysics Data System (ADS)

Danel, J.-F.; Kazandjian, L.

2018-06-01

It is shown that the equation of state (EOS) and the radial distribution functions obtained by density-functional theory molecular dynamics (DFT-MD) obey a simple scaling law. At given temperature, the thermodynamic properties and the radial distribution functions given by a DFT-MD simulation remain unchanged if the mole fractions of nuclei of given charge and the average volume per atom remain unchanged. A practical interest of this scaling law is to obtain an EOS table for a fluid from that already obtained for another fluid if it has the right characteristics. Another practical interest of this result is that an asymmetric mixture made up of light and heavy atoms requiring very different time steps can be replaced by a mixture of atoms of equal mass, which facilitates the exploration of the configuration space in a DFT-MD simulation. The scaling law is illustrated by numerical results.

Electron-pair-production cross section in the tip region of the positron spectrum

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

Sud, K.K.; Sharma, D.K.

1984-11-01

The radial integrals for electron-pair production in a point Coulomb potential have been expressed by Sud, Sharma, and Sud in terms of the matrix generalization of the GAMMA function. Two new partial differential equations in photon energy satisfied by the matrix GAMMA function are obtained. We have obtained, on integrating the partial differential equations, accurate radial integrals as a function of photon energy for the pair production by intermediate-energy photons. The cross section in the tip region of the spectrum are calculated for photons of energy 5.0 to 10.0 MeV for /sup 92/U. The new technique results in extensive savingmore » in computer time as the basic radial integrals in terms of the hypergeometric function F/sub 2/ are computed at one photon energy for each pair of partial waves. The results of our calculations are compared with plane-wave Born-approximation results and with the calculations of Dugne and of Deck, Moroi, and Alling.« less

Solution of the relativistic asymptotic equations in electron-ion scattering

NASA Astrophysics Data System (ADS)

Young, I. G.; Norrington, P. H.

1994-12-01

Two asymptotic expansions are suggested for the solution of the coupled equations for the radial channel wavefunctions arising from the treament of electron-ion scattering using the Dirac Hamiltonian. The recurrence relations obtained for the expansions coefficients are given. A method is suggested for calculation of the one-electron Dirac-Coulomb functions used in the second expansion using solutions of the non-relativistic Coulomb equation with complex arguments.

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.

The solitary wave solution of coupled Klein-Gordon-Zakharov equations via two different numerical methods

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Nikpour, Ahmad

2013-09-01

In this research, we propose two different methods to solve the coupled Klein-Gordon-Zakharov (KGZ) equations: the Differential Quadrature (DQ) and Globally Radial Basis Functions (GRBFs) methods. In the DQ method, the derivative value of a function with respect to a point is directly approximated by a linear combination of all functional values in the global domain. The principal work in this method is the determination of weight coefficients. We use two ways for obtaining these coefficients: cosine expansion (CDQ) and radial basis functions (RBFs-DQ), the former is a mesh-based method and the latter categorizes in the set of meshless methods. Unlike the DQ method, the GRBF method directly substitutes the expression of the function approximation by RBFs into the partial differential equation. The main problem in the GRBFs method is ill-conditioning of the interpolation matrix. Avoiding this problem, we study the bases introduced in Pazouki and Schaback (2011) [44]. Some examples are presented to compare the accuracy and easy implementation of the proposed methods. In numerical examples, we concentrate on Inverse Multiquadric (IMQ) and second-order Thin Plate Spline (TPS) radial basis functions. The variable shape parameter (exponentially and random) strategies are applied in the IMQ function and the results are compared with the constant shape parameter.

Two-body perturbation theory versus first order perturbation theory: A comparison based on the square-well fluid.

PubMed

Mercier Franco, Luís Fernando; Castier, Marcelo; Economou, Ioannis G

2017-12-07

We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior.

Coplanar Waveguide Radial Line Double Stub and Application to Filter Circuits

NASA Technical Reports Server (NTRS)

Simons, R. N.; Taub, S. R.

1993-01-01

Coplanar waveguide (CPW) and grounded coplanar waveguide (GCPW) radial line double stub resonators are experimentally characterized with respect to stub radius and sector angle. A simple closed-form design equation, which predicts the resonance radius of the stub, is presented. Use of a double stub resonator as a lowpass filter or as a harmonic suppression filter is demonstrated, and design rules are given.

On the exterior Dirichlet problem for Hessian quotient equations

NASA Astrophysics Data System (ADS)

Li, Dongsheng; Li, Zhisu

2018-06-01

In this paper, we establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for Hessian quotient equations with prescribed asymptotic behavior at infinity. This extends the previous related results on the Monge-Ampère equations and on the Hessian equations, and rearranges them in a systematic way. Based on the Perron's method, the main ingredient of this paper is to construct some appropriate subsolutions of the Hessian quotient equation, which is realized by introducing some new quantities about the elementary symmetric polynomials and using them to analyze the corresponding ordinary differential equation related to the generalized radially symmetric subsolutions of the original equation.

Transport of Solar Energetic Particles across the Parker field direction due to field line meandering

NASA Astrophysics Data System (ADS)

Laitinen, T. L.; Kopp, A.; Effenberger, F.; Dalla, S.; Marsh, M. S.

2014-12-01

Multi-spacecraft observations of Solar Energetic Particles (SEPs) show that the SEPs can spread large distances across the mean Parker spiral field. The SEPs accelerated during a solar eruption can be observed 360° around the Sun, and the dependence of SEP peak intensity on heliographic longitude at 1 AU has been fitted with Gaussian profiles with σ=30-50° for several events (e.g., Dresing et al 2014; Richardson et al 2014). SEP anisotropy measurements suggest that interplanetary transport is an important factor to the SEP cross-field extent (Dresing et al 2014). However, the currently used diffusive Fokker Planck (FP) description of SEP transport, with realistic diffusion coefficients, has been found insufficient to explain the SEP event cross-field extents. Recently Laitinen et al (2013) emphasised the importance of particle propagation along meandering field lines, which cannot be described as diffusion. They showed that early in an event field line meandering dominates particle cross-field transport and produces events wider than the FP description. They also introduced a new FP model that incorporates both field line meandering and SEP cross-field diffusion using stochastic differential equations and a constant background magnetic field. In this work, we implement the new FP model into Parker field geometry, to study the evolution of an SEP event in the interplanetary space. We compare the new model to the traditional FP approach by using particle and field line diffusion coefficients that are calculated consistently for both models using an assumed radial and spectral description of the turbulence evolution. We find that while the traditional SEP propagation modelling gives typically longitudinal extent with σ=10-20°, the new model results in values σ=30-50°, which is consistent with SEP observations. We conclude that field line meandering must be taken into account when modelling SEP propagation in the interplanetary space.

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

Reduced integrity of the left arcuate fasciculus is specifically associated with auditory verbal hallucinations in schizophrenia.

PubMed

McCarthy-Jones, Simon; Oestreich, Lena K L; Whitford, Thomas J

2015-03-01

Schizophrenia patients with auditory verbal hallucinations (AVH) have reduced structural integrity in the left arcuate fasciculus (AFL) compared to healthy controls. However, it is neither known whether these changes are specific to AVH, as opposed to hallucinations or schizophrenia per se, nor how radial and/or axial diffusivity are altered. This study aimed to test the hypothesis that reductions to the structural integrity of the AFL are specifically associated with AVH in schizophrenia. Diffusion tensor imaging scans and clinical data were obtained from the Australian Schizophrenia Research Bank for 39 schizophrenia patients with lifetime AVH (18 current, 21 remitted), 74 schizophrenia patients with no lifetime AVH (40 with lifetime hallucinations in other modalities, 34 no lifetime hallucinations) and 40 healthy controls. Fractional anisotropy was significantly reduced in the AFL of patients with lifetime AVH compared to both healthy controls (Cohen's d=1.24) and patients without lifetime AVH (d=.72), including compared to the specific subsets of patients without AVH who either had hallucinations in other modalities (d=.69) or no history of any hallucinations (d=.73). Radial, but not axial, diffusivity was significantly increased in patients with lifetime AVH compared to both healthy controls (d=.89) and patients without lifetime AVH (d=.39). Evidence was found for a non-linear relation between fractional anisotropy in the AFL and state AVH. Reduced integrity of the AFL is specifically associated with AVH, as opposed to schizophrenia in general or hallucinations in other modalities. Increased radial diffusivity suggests dysmyelination or demyelination of the AFL may play a role in AVH. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.

The fate of solid particles in the Jovian circumplanetary disk : Implications for the formation of the Galilean satellites

NASA Astrophysics Data System (ADS)

Ronnet, Thomas; Mousis, Olivier; Vernazza, Pierre

2016-10-01

The Galilean satellites are thought to have formed within an accretion disk surrounding Jupiter at the late stages of its formation. However, the structure of the gaseous disk, as well as the size and origin of the solids that eventually formed the satellites are yet to be constrained.Here we model an evolving gaseous disk around Jupiter and investigate the fate of solid particles of different sizes submitted to aerodynamic drag, turbulent diffusion, and heated by the surrounding gas. The motion of the solid particles is integrated in the (r-z) plane, taking into account dust settling and radial drift. The evolution of their ice-to-rock ratio is tracked when they cross the snowline and start to sublimate. Sublimation is coupled to the equations of motion as it changes the radius of the particle and consequently acts on the drag force. The I/R ratio then serves as a comparison to the observed bulk compositions of Io and Europa.

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.

Filamentation effect in a gas attenuator for high-repetition-rate X-ray FELs

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

Feng, Yiping; Krzywinski, Jacek; Schafer, Donald W.

A sustained filamentation or density depression phenomenon in an argon gas attenuator servicing a high-repetition femtosecond X-ray free-electron laser has been studied using a finite-difference method applied to the thermal diffusion equation for an ideal gas. A steady-state solution was obtained by assuming continuous-wave input of an equivalent time-averaged beam power and that the pressure of the entire gas volume has reached equilibrium. Both radial and axial temperature/density gradients were found and describable as filamentation or density depression previously reported for a femtosecond optical laser of similar attributes. The effect exhibits complex dependence on the input power, the desired attenuation,more » and the geometries of the beam and the attenuator. Time-dependent simulations were carried out to further elucidate the evolution of the temperature/density gradients in between pulses, from which the actual attenuation received by any given pulse can be properly calculated.« less

A first look at resistive MHD stability differences between NSTX and NSTX-U high beta discharges

NASA Astrophysics Data System (ADS)

Morton, L. A.; La Haye, R. J.; Berkery, J. W.; Menard, J. E.; Ferraro, N. M.; Brennan, D. P.; Sabbagh, S. A.; Delgado-Aparicio, L. F.; Tritz, K.

2017-10-01

Comparison is made of the onset, growth rate and saturation of m/n = 2/1 tearing modes in NSTX and NSTX-U high beta discharges. NSTX-U has stronger toroidal field, higher electron temperature (thus longer resistive diffusion time) and a larger aspect ratio (due to the expansion of the center stack). Experimental identification of the mode helicity, radial location, and width is accomplished by synergistically combining information from soft x-ray emission, Thomson scattering (Te profile), Charge Exchange Recombination (Ti profile) and Mirnov diagnostics. Fitting the generalized Rutherford equation to the time-evolution of the island width allows evaluation of the different drive and stabilizing terms. Linear stability calculations have also been performed with M3D-C1. The possibility of a reduction in the stabilizing interchange effect due to curvature at somewhat larger aspect ratio in NSTX-U is one focus of the analysis. This work is supported by the US DOE under Grant DE-FG02-99ER54522.

Influence of hot and cold neutrals on scrape-off layer tokamak plasma turbulence

NASA Astrophysics Data System (ADS)

Bisai, N.; Kaw, P. K.

2018-01-01

The modification of interchange plasma turbulence in the scrape-off layer (SOL) region by the presence of hot and cold neutral gas molecules has been studied. The nonlinear equations have been solved numerically using two different simulations ("uniform-Te" and "varying-Te"), and the results obtained from both of the models have been compared. The hot neutrals, responsible for the increase in the electron density in the SOL, also account for more ionization of the cold molecules. The effect of hot and cold neutrals on the interchange turbulence is almost similar in the "uniform-Te" model, but in the "varying-Te" model, the influence of the hot neutrals is very small, specifically in the far SOL region. The neutral gas in the "varying Te" model decreases the heat load on the material walls by about 7%. A reduction in the radial velocity by about 25% and effective diffusion coefficient of the plasma particles has been found by the influence of the neutral gas.

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.

Genetic relatedness of axial and radial diffusivity indices of cerebral white matter microstructure in late middle age.

PubMed

Hatton, Sean N; Panizzon, Matthew S; Vuoksimaa, Eero; Hagler, Donald J; Fennema-Notestine, Christine; Rinker, Daniel; Eyler, Lisa T; Franz, Carol E; Lyons, Michael J; Neale, Michael C; Tsuang, Ming T; Dale, Anders M; Kremen, William S

2018-05-01

Two basic neuroimaging-based characterizations of white matter tracts are the magnitude of water diffusion along the principal tract orientation (axial diffusivity, AD) and water diffusion perpendicular to the principal orientation (radial diffusivity, RD). It is generally accepted that decreases in AD reflect disorganization, damage, or loss of axons, whereas increases in RD are indicative of disruptions to the myelin sheath. Previous reports have detailed the heritability of individual AD and RD measures, but have not examined the extent to which the same or different genetic or environmental factors influence these two phenotypes (except for corpus callosum). We implemented bivariate twin analyses to examine the shared and independent genetic influences on AD and RD. In the Vietnam Era Twin Study of Aging, 393 men (mean age = 61.8 years, SD = 2.6) underwent diffusion-weighted magnetic resonance imaging. We derived fractional anisotropy (FA), mean diffusivity (MD), AD, and RD estimates for 11 major bilateral white matter tracts and the mid-hemispheric corpus callosum, forceps major, and forceps minor. Separately, AD and RD were each highly heritable. In about three-quarters of the tracts, genetic correlations between AD and RD were >.50 (median = .67) and showed both unique and common variance. Genetic variance of FA and MD were predominately explained by RD over AD. These findings are important for informing genetic association studies of axonal coherence/damage and myelination/demyelination. Thus, genetic studies would benefit from examining the shared and unique contributions of AD and RD. © 2018 Wiley Periodicals, Inc.

Segmentation of the canine corpus callosum using diffusion-tensor imaging tractography.

PubMed

Pierce, Theodore T; Calabrese, Evan; White, Leonard E; Chen, Steven D; Platt, Simon R; Provenzale, James M

2014-01-01

We set out to determine functional white matter (WM) connections passing through the canine corpus callosum; these WM connections would be useful for subsequent studies of canine brains that serve as models for human WM pathway disease. Based on prior studies, we anticipated that the anterior corpus callosum would send projections to the anterior cerebral cortex whereas progressively posterior segments would send projections to more posterior cortex. A postmortem canine brain was imaged using a 7-T MRI system producing 100-μm-isotropic-resolution diffusion-tensor imaging analyzed by tractography. Using regions of interest (ROIs) within cortical locations, which were confirmed by a Nissl stain that identified distinct cortical architecture, we successfully identified six important WM pathways. We also compared fractional anisotropy (FA), apparent diffusion coefficient (ADC), radial diffusivity, and axial diffusivity in tracts passing through the genu and splenium. Callosal fibers were organized on the basis of cortical destination (e.g., fibers from the genu project to the frontal cortex). Histologic results identified the motor cortex on the basis of cytoarchitectonic criteria that allowed placement of ROIs to discriminate between frontal and parietal lobes. We also identified cytoarchitecture typical of the orbital frontal, anterior frontal, and occipital regions and placed ROIs accordingly. FA, ADC, radial diffusivity, and axial diffusivity values were all higher in posterior corpus callosum fiber tracts. Using six cortical ROIs, we identified six major WM tracts that reflect major functional divisions of the cerebral hemispheres, and we derived quantitative values that can be used for study of canine models of human WM pathologic states.

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.