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

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

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

2011-02-15

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

Magnetically Driven Flows of Suspensions of Rods to Deliver Clot-Busting Drugs to Dead-End Arteries

NASA Astrophysics Data System (ADS)

Bonnecaze, Roger; Clements, Michael

2014-11-01

Suspensions of iron particles in the presence of a magnetic field create flows that could significantly increase the delivery of drugs to dissolve clots in stroke victims. An explanation of this flow rests on the foundation of the seminal works by Prof. Acrivos and his students on effective magnetic permittivity of suspensions of rods, hydrodynamic diffusion of particles, and the flow of suspensions. Intravenous administration of the clot dissolving tissue plasminogen activator (tPA) is the most used therapy for stroke. This therapy is often unsuccessful because the tPA delivery is diffusion-limited and too slow to be effective. Observations show that added iron particles in a rotating magnetic field form rotating rods along the wall of the occluded vessel, creating a convective flow that can carry tPA much faster than diffusion. We present a proposed mechanism for this magnetically driven flow in the form of coupled particle-scale and vessel-scale flow models. At the particle-scale, particles chain up to form rods that rotate, diffuse and translate in the presence of the flow and magnetic fields. Localized vorticity created by the rotating particles drives a macroscopic convective flow in the vessel. Suspension transport equations describe the flow at the vessel-scale. The flow affects the convection and diffusion of the suspension of particles, linking the two scales. The model equations are solved asymptotically and numerically to understand how to create convective flows in dead-end or blocked vessels.

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

A quasilinear operator retaining magnetic drift effects in tokamak geometry

NASA Astrophysics Data System (ADS)

Catto, Peter J.; Lee, Jungpyo; Ram, Abhay K.

2017-12-01

The interaction of radio frequency waves with charged particles in a magnetized plasma is usually described by the quasilinear operator that was originally formulated by Kennel & Engelmann (Phys. Fluids, vol. 9, 1966, pp. 2377-2388). In their formulation the plasma is assumed to be homogenous and embedded in a uniform magnetic field. In tokamak plasmas the Kennel-Engelmann operator does not capture the magnetic drifts of the particles that are inherent to the non-uniform magnetic field. To overcome this deficiency a combined drift and gyrokinetic derivation is employed to derive the quasilinear operator for radio frequency heating and current drive in a tokamak with magnetic drifts retained. The derivation requires retaining the magnetic moment to higher order in both the unperturbed and perturbed kinetic equations. The formal prescription for determining the perturbed distribution function then follows a novel procedure in which two non-resonant terms must be evaluated explicitly. The systematic analysis leads to a diffusion equation that is compact and completely expressed in terms of the drift kinetic variables. The equation is not transit averaged, and satisfies the entropy principle, while retaining the full poloidal angle variation without resorting to Fourier decomposition. As the diffusion equation is in physical variables, it can be implemented in any computational code. In the Kennel-Engelmann formalism, the wave-particle resonant delta function is either for the Landau resonance or the Doppler shifted cyclotron resonance. In the combined gyro and drift kinetic approach, a term related to the magnetic drift modifies the resonance condition.

ULF Waves and Diffusive Radial Transport of Charged Particles

NASA Astrophysics Data System (ADS)

Ali, Ashar Fawad

The Van Allen radiation belts contain highly energetic particles which interact with a variety of plasma and magnetohydrodynamic (MHD) waves. Waves in the ultra low-frequency (ULF) range play an important role in the loss and acceleration of energetic particles. Considering the geometry of the geomagnetic field, charged particles trapped in the inner magnetosphere undergo three distinct types of periodic motions; an adiabatic invariant is associated with each type of motion. The evolution of the phase space density of charged particles in the magnetosphere in the coordinate space of the three adiabatic invariants is modeled by the Fokker-Planck equation. If we assume that the first two adiabatic invariants are conserved while the third invariant is violated, then the general Fokker-Planck equation reduces to a radial diffusion equation with the radial diffusion coefficient quantifying the rate of the radial diffusion of charged particles, including contributions from perturbations in both the magnetic and the electric fields. This thesis investigates two unanswered questions about ULF wave-driven radial transport of charged particles. First, how important are the ULF fluctuations in the magnetic field compared with the ULF fluctuations in the electric field in driving the radial diffusion of charged particles in the Earth's inner magnetosphere? It has generally been accepted that magnetic field perturbations dominate over electric field perturbations, but several recently published studies suggest otherwise. Second, what is the distribution of ULF wave power in azimuth, and how does ULF wave power depend upon radial distance and the level of geomagnetic activity? Analytic treatments of the diffusion coefficients generally assume uniform distribution of power in azimuth, but in situ measurements suggest that this may not be the case. We used the magnetic field data from the Combined Release and Radiation Effects Satellite (CRRES) and the electric and the magnetic field data from the Radiation Belt Storm Probes (RBSP) to compute the electric and the magnetic component of the radial diffusion coefficient using the Fei et al. [2006] formulation. We conclude that contrary to prior notions, the electric component is dominant in driving radial diffusion of charged particles in the Earth's inner magnetosphere instead of the magnetic component. The electric component can be up to two orders of magnitude larger than the magnetic component. In addition, we see that ULF wave power in both the electric and the magnetic fields has a clear dependence on Kp with wave power decreasing as radial distance decreases. For both fields, the noon sectors generally contain more ULF wave power than the dawn, dusk, and the midnight magnetic local time (MLT) sectors. There is no significant difference between ULF wave power in the dawn, dusk, and the midnight sectors.

Diffusion coefficients of water in biobased hydrogel polymer matrices by nuclear magnetic resonance imaging

USDA-ARS?s Scientific Manuscript database

The diffusion coefficient of water in biobased hydrogels were measured utilizing a simple NMR method. This method tracks the migration of deuterium oxide through imaging data that is fit to a diffusion equation. The results show that a 5 wt% soybean oil based hydrogel gives aqueous diffusion of 1.37...

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.

2007-01-01

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Nguyen, Dang Van; Li, Jing-Rebecca; Grebenkov, Denis; Le Bihan, Denis

2014-04-01

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch-Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch-Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge-Kutta-Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.

Correlation Between the Field Line and Particle Diffusion Coefficients in the Stochastic Fields of a Tokamak

NASA Astrophysics Data System (ADS)

Calvin, Mark; Punjabi, Alkesh

1996-11-01

We use the method of quasi-magnetic surfaces to calculate the correlation between the field line and particle diffusion coefficients. The magnetic topology of a tokamak is perturbed by a spectrum of neighboring resonant resistive modes. The Hamiltonian equations of motion for the field line are integrated numerically. Poincare plots of the quasi-magnetic surfaces are generated initially and after the field line has traversed a considerable distance. From the areas of the quasi-magnetic surfaces and the field line distance, we estimate the field line diffusion coefficient. We start plasma particles on the initial quasi-surface, and calculate the particle diffusion coefficient from our Monte Carlo method (Punjabi A., Boozer A., Lam M., Kim H. and Burke K., J. Plasma Phys.), 44, 405 (1990). We then estimate the correlation between the particle and field diffusion as the strength of the resistive modes is varied.

Kinematic validation of a quasi-geostrophic model for the fast dynamics in the Earth's outer core

NASA Astrophysics Data System (ADS)

Maffei, S.; Jackson, A.

2017-09-01

We derive a quasi-geostrophic (QG) system of equations suitable for the description of the Earth's core dynamics on interannual to decadal timescales. Over these timescales, rotation is assumed to be the dominant force and fluid motions are strongly invariant along the direction parallel to the rotation axis. The diffusion-free, QG system derived here is similar to the one derived in Canet et al. but the projection of the governing equations on the equatorial disc is handled via vertical integration and mass conservation is applied to the velocity field. Here we carefully analyse the properties of the resulting equations and we validate them neglecting the action of the Lorentz force in the momentum equation. We derive a novel analytical solution describing the evolution of the magnetic field under these assumptions in the presence of a purely azimuthal flow and an alternative formulation that allows us to numerically solve the evolution equations with a finite element method. The excellent agreement we found with the analytical solution proves that numerical integration of the QG system is possible and that it preserves important physical properties of the magnetic field. Implementation of magnetic diffusion is also briefly considered.

Computational Diffusion Magnetic Resonance Imaging Based on Time-Dependent Bloch NMR Flow Equation and Bessel Functions.

PubMed

Awojoyogbe, Bamidele O; Dada, Michael O; Onwu, Samuel O; Ige, Taofeeq A; Akinwande, Ninuola I

2016-04-01

Magnetic resonance imaging (MRI) uses a powerful magnetic field along with radio waves and a computer to produce highly detailed "slice-by-slice" pictures of virtually all internal structures of matter. The results enable physicians to examine parts of the body in minute detail and identify diseases in ways that are not possible with other techniques. For example, MRI is one of the few imaging tools that can see through bones, making it an excellent tool for examining the brain and other soft tissues. Pulsed-field gradient experiments provide a straightforward means of obtaining information on the translational motion of nuclear spins. However, the interpretation of the data is complicated by the effects of restricting geometries as in the case of most cancerous tissues and the mathematical concept required to account for this becomes very difficult. Most diffusion magnetic resonance techniques are based on the Stejskal-Tanner formulation usually derived from the Bloch-Torrey partial differential equation by including additional terms to accommodate the diffusion effect. Despite the early success of this technique, it has been shown that it has important limitations, the most of which occurs when there is orientation heterogeneity of the fibers in the voxel of interest (VOI). Overcoming this difficulty requires the specification of diffusion coefficients as function of spatial coordinate(s) and such a phenomenon is an indication of non-uniform compartmental conditions which can be analyzed accurately by solving the time-dependent Bloch NMR flow equation analytically. In this study, a mathematical formulation of magnetic resonance flow sequence in restricted geometry is developed based on a general second order partial differential equation derived directly from the fundamental Bloch NMR flow equations. The NMR signal is obtained completely in terms of NMR experimental parameters. The process is described based on Bessel functions and properties that can make it possible to distinguish cancerous cells from normal cells. A typical example of liver distinguished from gray matter, white matter and kidney is demonstrated. Bessel functions and properties are specifically needed to show the direct effect of the instantaneous velocity on the NMR signal originating from normal and abnormal tissues.

Pattern formation in diffusive excitable systems under magnetic flow effects

NASA Astrophysics Data System (ADS)

Mvogo, Alain; Takembo, Clovis N.; Ekobena Fouda, H. P.; Kofané, Timoléon C.

2017-07-01

We study the spatiotemporal formation of patterns in a diffusive FitzHugh-Nagumo network where the effect of electromagnetic induction has been introduced in the standard mathematical model by using magnetic flux, and the modulation of magnetic flux on membrane potential is realized by using memristor coupling. We use the multi-scale expansion to show that the system equations can be reduced to a single differential-difference nonlinear equation. The linear stability analysis is performed and discussed with emphasis on the impact of magnetic flux. It is observed that the effect of memristor coupling importantly modifies the features of modulational instability. Our analytical results are supported by the numerical experiments, which reveal that the improved model can lead to nonlinear quasi-periodic spatiotemporal patterns with some features of synchronization. It is observed also the generation of pulses and rhythmics behaviors like breathing or swimming which are important in brain researches.

Diffusion of strongly magnetized cosmic ray particles in a turbulent medium

NASA Technical Reports Server (NTRS)

Ptuskin, V. S.

1985-01-01

Cosmic ray (CR) propagation in a turbulent medium is usually considered in the diffusion approximation. Here, the diffusion equation is obtained for strongly magnetized particles in the general form. The influence of a large-scale random magnetic field on CR propagation in interstellar medium is discussed. Cosmic rays are assumed to propagate in a medium with a regular field H and an ensemble of random MHD waves. The energy density of waves on scales smaller than the free path 1 of CR particles is small. The collision integral of the general form which describes interaction between relativistic particles and waves in the quasilinear approximation is used.

A two-dimensional kinematic dynamo model of the ionospheric magnetic field at Venus

NASA Technical Reports Server (NTRS)

Cravens, T. E.; Wu, D.; Shinagawa, H.

1990-01-01

The results of a high-resolution, two-dimensional, time dependent, kinematic dynamo model of the ionospheric magnetic field of Venus are presented. Various one-dimensional models are considered and the two-dimensional model is then detailed. In this model, the two-dimensional magnetic induction equation, the magnetic diffusion-convection equation, is numerically solved using specified plasma velocities. Origins of the vertical velocity profile and of the horizontal velocities are discussed. It is argued that the basic features of the vertical magnetic field profile remain unaltered by horizontal flow effects and also that horizontal plasma flow can strongly affect the magnetic field for altitudes above 300 km.

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

On axisymmetric resistive magnetohydrodynamic equilibria with flow free of Pfirsch-Schlüter diffusion

NASA Astrophysics Data System (ADS)

Throumoulopoulos, G. N.; Tasso, H.

2003-06-01

The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and incompressible flows parallel to the magnetic field is investigated within the framework of the magnetohydrodynamic (MHD) theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order elliptic partial differential equation for the poloidal magnetic flux function ψ along with a decoupled Bernoulli equation for the pressure identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the resistivities η∥ and η⊥ parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic resistivity and parallel flows [G. N. Throumoulopoulos and H. Tasso, J. Plasma Phys. 64, 601 (2000)] the equilibrium is compatible with nonvanishing poloidal current densities. Also, although exactly Spitzer resistivities either η∥(ψ) or η⊥(ψ) are not allowed, exact solutions with vanishing poloidal electric fields can be constructed with η∥ and η⊥ profiles compatible with roughly collisional resistivity profiles, i.e., profiles having a minimum close to the magnetic axis, taking very large values on the boundary and such that η⊥>η∥. For equilibria with vanishing flows satisfying the relation (dP/dψ)(dI2/dψ)>0, where P and I are the pressure and the poloidal current functions, the difference η⊥-η∥ for the reversed-field pinch scaling, Bp≈Bt, is nearly two times larger than that for the tokamak scaling, Bp≈0.1Bt (Bp and Bt are the poloidal and toroidal magnetic-field components). The particular resistive equilibrium solutions obtained in the present work, inherently free of—but not inconsistent with—Pfirsch-Schlüter diffusion, indicate that parallel flows might result in a reduction of the diffusion observed in magnetically confined plasmas.

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

NASA Technical Reports Server (NTRS)

Karimbadi, H.; Krauss-Varban, D.

1992-01-01

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

Magnetic field diffusion and dissipation in reversed-field plasmas

NASA Technical Reports Server (NTRS)

Drake, J. F.; Gladd, N. T.; Huba, J. D.

1981-01-01

A diffusion equation is derived which describes the evolution of a magnetic field in a plasma of arbitrary beta and resistivity. The equation is valid for a one-dimensional slab geometry, assumes the plasma remains in quasi-equilibrium throughout its evolution and does not include thermal transport. Scaling laws governing the rate of change of the magnetic energy, particle drift energy, and magnetic flux are calculated. It is found that the magnetic free energy can be substantially larger than the particle drift energy and can be an important energy reservoir in driving plasma instabilities (e.g., the lower-hybrid-drift instability). In addition, the effect of a spatially varying resistivity on the evolution of a reversed-field plasma is studied. The resistivity model used is based upon the anomalous transport properties associated with the nonlocal mode structure of the lower-hybrid-drift instability. The relevance of this research to laboratory plasmas (e.g., theta pinches, reversed-field theta pinches) and space plasmas (e.g., the earth's magnetotail) is discussed.

CRPropa 3.1—a low energy extension based on stochastic differential equations

NASA Astrophysics Data System (ADS)

Merten, Lukas; Becker Tjus, Julia; Fichtner, Horst; Eichmann, Björn; Sigl, Günter

2017-06-01

The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us to use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ∥ and perpendicular κ⊥ diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.

A finite elements method to solve the Bloch–Torrey equation applied to diffusion magnetic resonance imaging

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

Nguyen, Dang Van; NeuroSpin, Bat145, Point Courrier 156, CEA Saclay Center, 91191 Gif-sur-Yvette Cedex; Li, Jing-Rebecca, E-mail: jingrebecca.li@inria.fr

2014-04-15

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch–Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution atmore » the cell interfaces by using double nodes. Using a transformation of the Bloch–Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge–Kutta–Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.« less

Holographic estimate of heavy quark diffusion in a magnetic field

NASA Astrophysics Data System (ADS)

Dudal, David; Mertens, Thomas G.

2018-03-01

We study the influence of a background magnetic field on the J /ψ vector meson in a Dirac-Born-Infeld-extension of the soft wall model, building upon our earlier work [D. Dudal and T. G. Mertens Phys. Rev. D 91, 086002 (2015), 10.1103/PhysRevD.91.086002]. In this specific holographic QCD model, we discuss the heavy quark number susceptibility and diffusion constants of charm quarks and their dependence on the magnetic field by either a hydrodynamic expansion or by numerically solving the differential equation. This allows us to determine the response of these transport coefficients to the magnetic field. The effects of the latter are considered both from a direct as indirect (medium) viewpoint. As expected, we find a magnetic field induced anisotropic diffusion, with a stronger diffusion in the longitudinal direction compared to the transversal one. We backup, at least qualitatively, our findings with a hanging string analysis of heavy quark diffusion in a magnetic field. From the quark number susceptibility we can extract an estimate for the effective deconfinement temperature in the heavy quark sector, reporting consistency with the phenomenon of inverse magnetic catalysis.

Diffusive processes in a stochastic magnetic field

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

Wang, H.; Vlad, M.; Vanden Eijnden, E.

1995-05-01

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing,more » in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle`s trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works.« less

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Breaking The Ion Frozen-in Condition Via The Non-gyrotropic Pressure Effect In Magnetic Reconnection

NASA Astrophysics Data System (ADS)

Dai, L.; Wang, C.; Angelopoulos, V.; Glassmeier, K. H.

2016-12-01

For magnetic reconnection to proceed, the frozen-in condition for both ion fluid and electron fluid in a localized diffusion region must be violated. In the framework of fluid, the frozen-in can be broken by inertial effects, thermal pressure effects, or inter-species collisions. An essential question in reconnection physics is what effect breaks the ion/electron frozen-in in the diffusion region. We present clear in-situ evidence that the off-diagonal pressure tensor, which corresponds to a non-gyrotropic pressure effect, is mainly responsible for breaking the ion frozen-in condition in reconnection. The non-gyrotropic pressure tensor is a fluid manifestation of ion demagnetization in reconnection. As our experiences indicate, we feel the need to clarify several conceptual points regarding the approach to studying diffusion region. 1) Conceptually, the ion/electron momentum equations ("ion/electron Ohm's law"), rather than the generalized Ohm's law (Rossi and Olbert,1970, equation [12.25] ), are appropriate for investigating the fronzen-in or decoupling of individual fluid species. 2) The reconnection electric field is equally explainable in terms of ion momentum or electron momentum equation.

Relativistic theory of particles in a scattering flow I: basic equations, diffusion and drift.

NASA Astrophysics Data System (ADS)

Achterberg, A.; Norman, C. A.

2018-06-01

We reconsider the theory of particle transport in a scattering medium, allowing for relativistic flow velocities. The theory uses a mixed set of variables, with position and time measured in the Laboratory Frame, and particle energy and momentum measured in the Fluid Rest Frame, the reference frame where scattering is assumed to be elastic. We give a new derivation for the fictitious force terms in the equation of motion that are present if the Fluid Rest Frame is not an inertial frame. By using a 3+1 notation we discuss the physical interpretation of the different terms in the fictitious force. It is shown that different approaches to the problem of particle propagation in a magnetized medium due to Skilling (1975) and Kulsrud (1983) are largely equivalent. We extend known results for non-relativistic flows to include the effects of cross-field diffusion for cosmic rays in a magnetized plasma. We also carefully consider the correct form of the diffusion approximation for scattering, and show that the resulting equations can be cast in conservation form.

Anomalous transport and stochastic processes

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

Balescu, R.

1996-03-01

The relation between kinetic transport theory and theory of stochastic processes is reviewed. The Langevin equation formalism provides important, but rather limited information about diffusive processes. A quite promising new approach to modeling complex situations, such as transport in incompletely destroyed magnetic surfaces, is provided by the theory of Continuous Time Random Walks (CTRW), which is presented in some detail. An academic test problem is discussed in great detail: transport of particles in a fluctuating magnetic field, in the limit of infinite perpendicular correlation length. The well-known subdiffusive behavior of the Mean Square Displacement (MSD), proportional to t{sup 1/2}, ismore » recovered by a CTRW, but the complete density profile is not. However, the quasilinear approximation of the kinetic equation has the form of a non-Markovian diffusion equation and can thus be generated by a CTRW. 16 refs., 3 figs.« less

Magnetic resonance electrical impedance tomography (MREIT) based on the solution of the convection equation using FEM with stabilization.

PubMed

Oran, Omer Faruk; Ider, Yusuf Ziya

2012-08-21

Most algorithms for magnetic resonance electrical impedance tomography (MREIT) concentrate on reconstructing the internal conductivity distribution of a conductive object from the Laplacian of only one component of the magnetic flux density (∇²B(z)) generated by the internal current distribution. In this study, a new algorithm is proposed to solve this ∇²B(z)-based MREIT problem which is mathematically formulated as the steady-state scalar pure convection equation. Numerical methods developed for the solution of the more general convection-diffusion equation are utilized. It is known that the solution of the pure convection equation is numerically unstable if sharp variations of the field variable (in this case conductivity) exist or if there are inconsistent boundary conditions. Various stabilization techniques, based on introducing artificial diffusion, are developed to handle such cases and in this study the streamline upwind Petrov-Galerkin (SUPG) stabilization method is incorporated into the Galerkin weighted residual finite element method (FEM) to numerically solve the MREIT problem. The proposed algorithm is tested with simulated and also experimental data from phantoms. Successful conductivity reconstructions are obtained by solving the related convection equation using the Galerkin weighted residual FEM when there are no sharp variations in the actual conductivity distribution. However, when there is noise in the magnetic flux density data or when there are sharp variations in conductivity, it is found that SUPG stabilization is beneficial.

Electron magnetic resonance investigation of gadolinium diffusion in zircon powders

NASA Astrophysics Data System (ADS)

de Biasi, R. S.; Grillo, M. L. N.

2011-11-01

The electron magnetic resonance (EMR) technique was used to investigate the diffusion of gadolinium in zircon (ZrSiO4) powders. The EMR absorption intensity was measured for several annealing times and three different temperatures of isothermal annealing: 1273, 1323 and 1373 K. The activation energy for diffusion, calculated from the experimental data using a theoretical model based on the Fick equation, was found to be EA=506±5 kJ mol-1. This value is close to the ones for the diffusion of Gd in UO2 and CeO2, but much larger than for the diffusion of gadolinium in a compound with the same crystal structure as zircon, YVO4. This is attributed to a difference in the relative sizes of the ions involved in the diffusion process.

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.

Magnon spin transport driven by the magnon chemical potential in a magnetic insulator

NASA Astrophysics Data System (ADS)

Cornelissen, L. J.; Peters, K. J. H.; Bauer, G. E. W.; Duine, R. A.; van Wees, B. J.

2016-07-01

We develop a linear-response transport theory of diffusive spin and heat transport by magnons in magnetic insulators with metallic contacts. The magnons are described by a position-dependent temperature and chemical potential that are governed by diffusion equations with characteristic relaxation lengths. Proceeding from a linearized Boltzmann equation, we derive expressions for length scales and transport coefficients. For yttrium iron garnet (YIG) at room temperature we find that long-range transport is dominated by the magnon chemical potential. We compare the model's results with recent experiments on YIG with Pt contacts [L. J. Cornelissen et al., Nat. Phys. 11, 1022 (2015), 10.1038/nphys3465] and extract a magnon spin conductivity of σm=5 ×105 S/m. Our results for the spin Seebeck coefficient in YIG agree with published experiments. We conclude that the magnon chemical potential is an essential ingredient for energy and spin transport in magnetic insulators.

Notes and Discussion

ERIC Educational Resources Information Center

American Journal of Physics, 1978

1978-01-01

Describes experiments demonstrating the Josephson effect, single-file diffusion in biological membranes, refractive index of beer, lines of magnetic fields, indexing diffraction patterns, Maxwell's equations, and spherical aberration. (SL)

Texture formation mechanism and constitutive equation for anisotropic thermorheological rare-earth permanent magnets

NASA Astrophysics Data System (ADS)

Zhu, Minggang; Li, Wei

2017-05-01

The study investigates the mechanism and constitutive equations describing oriented texture formation in anisotropic thermorheological rare-earth permanent magnets. The thermorheological process cannot be considered as creep, since the related phenomena are not suitably explained by the diffusion creep model. A mathematical model describing the relationship between the rheological deformation rate and texture orientation was established, and a theoretical expression was obtained for the orientation factor of thermorheological magnets. In addition, nanocrystalline Nd-Fe-B magnets were fabricated, with intrinsic coercivity Hcj=760.1 kA/m, remanence Br=1.469 T, and maximum energy product (BH)max=427.1 kJ/m3.

Anomalous current in diffusive ferromagnetic Josephson junctions

NASA Astrophysics Data System (ADS)

Silaev, M. A.; Tokatly, I. V.; Bergeret, F. S.

2017-05-01

We demonstrate that in diffusive superconductor/ferromagnet/superconductor (S/F/S) junctions a finite, anomalous Josephson current can flow even at zero phase difference between the S electrodes. The conditions for the observation of this effect are noncoplanar magnetization distribution and a broken magnetization inversion symmetry of the superconducting current. The latter symmetry is intrinsic for the widely used quasiclassical approximation and prevented previous works based on this approximation from obtaining the Josephson anomalous current. We show that this symmetry can be removed by introducing spin-dependent boundary conditions for the quasiclassical equations at the superconducting/ferromagnet interfaces in diffusive systems. Using this recipe, we consider generic multilayer magnetic systems and determine the ideal experimental conditions in order to maximize the anomalous current.

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.

CRPropa 3.1—a low energy extension based on stochastic differential equations

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

Merten, Lukas; Tjus, Julia Becker; Eichmann, Björn

The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us tomore » use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ{sub ∥} and perpendicular κ{sub ⊥} diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.« less

Magnetic order at a single-crystal surface in the diffuse-scattering theory

NASA Astrophysics Data System (ADS)

Zasada, I.

2003-06-01

A theoretical description of incoherent spin-dependent multiple scattering of electrons at a magnetically disordered single-crystal surface is reported. A formalism in which the spin operators specify the magnetic state of a surface atom is used for the description of magnetic order at the surface. The theory is based upon the concepts used in multiple scattering spin-dependent diffuse LEED theory (DSPLEED) theory. In the present considerations, this theory is extended to the case of magnetic materials by using the time-independent Dirac equation with an effective magnetic field. Thus, an expression for incoherent spin-dependent intensity for magnetic material is obtained. It depends on the Fourier transform on the surface lattice of the spin-pair correlation function and, as a consequence, on the magnetic properties of the surface. The equations for the description of magnetization and various correlation functions in the frame of effective field theory are derived and the results of the numerical calculations are presented for the particular case of Ni(1 0 0) surface. The spin-orbit induced and exchange asymmetries are calculated. It is found that the magnetic DSPLEED is sensitive to the properties of the surface characterized by the spin-pair correlation functions. Thus, it is demonstrated that the magnetic DSPLEED can be an effective method in the investigation of critical behaviour of magnetic surfaces.

A thermodynamically consistent model of magneto-elastic materials under diffusion at large strains and its analysis

NASA Astrophysics Data System (ADS)

Roubíček, Tomáš; Tomassetti, Giuseppe

2018-06-01

A theory of elastic magnets is formulated under possible diffusion and heat flow governed by Fick's and Fourier's laws in the deformed (Eulerian) configuration, respectively. The concepts of nonlocal nonsimple materials and viscous Cahn-Hilliard equations are used. The formulation of the problem uses Lagrangian (reference) configuration while the transport processes are pulled back. Except the static problem, the demagnetizing energy is ignored and only local non-self-penetration is considered. The analysis as far as existence of weak solutions of the (thermo) dynamical problem is performed by a careful regularization and approximation by a Galerkin method, suggesting also a numerical strategy. Either ignoring or combining particular aspects, the model has numerous applications as ferro-to-paramagnetic transformation in elastic ferromagnets, diffusion of solvents in polymers possibly accompanied by magnetic effects (magnetic gels), or metal-hydride phase transformation in some intermetallics under diffusion of hydrogen accompanied possibly by magnetic effects (and in particular ferro-to-antiferromagnetic phase transformation), all in the full thermodynamical context under large strains.

Investigating Whistler Mode Wave Diffusion Coefficients at Mars

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Stability of wave processes in a rotating electrically conducting fluid

NASA Astrophysics Data System (ADS)

Peregudin, S. I.; Peregudina, E. S.; Kholodova, S. E.

2018-05-01

The paper puts forward a mathematical model of dynamics of spatial large-scale motions in a rotating layer of electrically conducting incompressible perfect fluid of variable depth with due account of dissipative effects. The resulting boundary-value problem is reduced to a vector system of partial differential equations for any values of the Reynolds number. Theoretical analysis of the so-obtained analytical solution reveals the effect of the magnetic field diffusion on the stability of the wave mode — namely, with the removed external magnetic field, the diffusion of the magnetic field promotes its damping. Besides, a criterion of stability of a wave mode is obtained.

Magnetic flux and heat losses by diffusive, advective, and Nernst effects in MagLIF-like plasma

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

Velikovich, A. L., E-mail: sasha.velikovich@nrl.navy.mil; Giuliani, J. L., E-mail: sasha.velikovich@nrl.navy.mil; Zalesak, S. T.

2014-12-15

The MagLIF approach to inertial confinement fusion involves subsonic/isobaric compression and heating of a DT plasma with frozen-in magnetic flux by a heavy cylindrical liner. The losses of heat and magnetic flux from the plasma to the liner are thereby determined by plasma advection and gradient-driven transport processes, such as thermal conductivity, magnetic field diffusion and thermomagnetic effects. Theoretical analysis based on obtaining exact self-similar solutions of the classical collisional Braginskii's plasma transport equations in one dimension demonstrates that the heat loss from the hot plasma to the cold liner is dominated by the transverse heat conduction and advection, andmore » the corresponding loss of magnetic flux is dominated by advection and the Nernst effect. For a large electron Hall parameter ω{sub e}τ{sub e} effective diffusion coefficients determining the losses of heat and magnetic flux are both shown to decrease with ω{sub e}τ{sub e} as does the Bohm diffusion coefficient, which is commonly associated with low collisionality and two-dimensional transport. This family of exact solutions can be used for verification of codes that model the MagLIF plasma dynamics.« less

On the resilience of helical magnetic fields to turbulent diffusion and the astrophysical implications

NASA Astrophysics Data System (ADS)

Blackman, Eric G.; Subramanian, Kandaswamy

2013-02-01

The extent to which large-scale magnetic fields are susceptible to turbulent diffusion is important for interpreting the need for in situ large-scale dynamos in astrophysics and for observationally inferring field strengths compared to kinetic energy. By solving coupled evolution equations for magnetic energy and magnetic helicity in a system initialized with isotropic turbulence and an arbitrarily helical large-scale field, we quantify the decay rate of the latter for a bounded or periodic system. The magnetic energy associated with the non-helical large-scale field decays at least as fast as the kinematically estimated turbulent diffusion rate, but the decay rate of the helical part depends on whether the ratio of its magnetic energy to the turbulent kinetic energy exceeds a critical value given by M1, c = (k1/k2)2, where k1 and k2 are the wavenumbers of the large and forcing scales. Turbulently diffusing helical fields to small scales while conserving magnetic helicity requires a rapid increase in total magnetic energy. As such, only when the helical field is subcritical can it so diffuse. When supercritical, it decays slowly, at a rate determined by microphysical dissipation even in the presence of macroscopic turbulence. In effect, turbulent diffusion of such a large-scale helical field produces small-scale helicity whose amplification abates further turbulent diffusion. Two curious implications are that (1) standard arguments supporting the need for in situ large-scale dynamos based on the otherwise rapid turbulent diffusion of large-scale fields require re-thinking since only the large-scale non-helical field is so diffused in a closed system. Boundary terms could however provide potential pathways for rapid change of the large-scale helical field. (2) Since M1, c ≪ 1 for k1 ≪ k2, the presence of long-lived ordered large-scale helical fields as in extragalactic jets do not guarantee that the magnetic field dominates the kinetic energy.

Proton-driven spin diffusion in rotating solids via reversible and irreversible quantum dynamics

PubMed Central

Veshtort, Mikhail; Griffin, Robert G.

2011-01-01

Proton-driven spin diffusion (PDSD) experiments in rotating solids have received a great deal of attention as a potential source of distance constraints in large biomolecules. However, the quantitative relationship between the molecular structure and observed spin diffusion has remained obscure due to the lack of an accurate theoretical description of the spin dynamics in these experiments. We start with presenting a detailed relaxation theory of PDSD in rotating solids that provides such a description. The theory applies to both conventional and radio-frequency-assisted PDSD experiments and extends to the non-Markovian regime to include such phenomena as rotational resonance (R2). The basic kinetic equation of the theory in the non-Markovian regime has the form of a memory function equation, with the role of the memory function played by the correlation function. The key assumption used in the derivation of this equation expresses the intuitive notion of the irreversible dissipation of coherences in macroscopic systems. Accurate expressions for the correlation functions and for the spin diffusion constants are given. The theory predicts that the spin diffusion constants governing the multi-site PDSD can be approximated by the constants observed in the two-site diffusion. Direct numerical simulations of PDSD dynamics via reversible Liouville-von Neumann equation are presented to support and compliment the theory. Remarkably, an exponential decay of the difference magnetization can be observed in such simulations in systems consisting of only 12 spins. This is a unique example of a real physical system whose typically macroscopic and apparently irreversible behavior can be traced via reversible microscopic dynamics. An accurate value for the spin diffusion constant can be usually obtained through direct simulations of PDSD in systems consisting of two 13C nuclei and about ten 1H nuclei from their nearest environment. Spin diffusion constants computed by this method are in excellent agreement with the spin diffusion constants obtained through equations given by the relaxation theory of PDSD. The constants resulting from these two approaches were also in excellent agreement with the results of 2D rotary resonance recoupling proton-driven spin diffusion (R3-PDSD) experiments performed in three model compounds, where magnetization exchange occurred over distances up to 4.9 Å. With the methodology presented, highly accurate internuclear distances can be extracted from such data. Relayed transfer of magnetization between distant nuclei appears to be the main (and apparently resolvable) source of uncertainty in such measurements. The non-Markovian kinetic equation was applied to the analysis of the R2 spin dynamics. The conventional semi-phenomenological treatment of relxation in R2 has been shown to be equivalent to the assumption of the Lorentzian spectral density function in the relaxatoin theory of PDSD. As this assumption is a poor approximation in real physical systems, the conventional R2 treatment is likely to carry a significant model error that has not been recognized previously. The relaxation theory of PDSD appears to provide an accurate, parameter-free alternative. Predictions of this theory agreed well with the full quantum mechanical simulations of the R2 dynamics in the few simple model systems we considered. PMID:21992326

Diffusion, Fluxes, Friction Forces, and Joule Heating in Two-Temperature Multicomponent Magnetohydrodynamics

NASA Technical Reports Server (NTRS)

Chang, C. H.

1999-01-01

The relationship between Joule heating, diffusion fluxes, and friction forces has been studied for both total and electron thermal energy equations, using general expressions for multicomponent diffusion in two-temperature plasmas with the velocity dependent Lorentz force acting on charged species in a magnetic field. It is shown that the derivation of Joule heating terms requires both diffusion fluxes and friction between species which represents the resistance experienced by the species moving at different relative velocities. It is also shown that the familiar Joule heating term in the electron thermal energy equation includes artificial effects produced by switching the convective velocity from the species velocity to the mass-weighted velocity, and thus should not be ignored even when there is no net energy dissipation.

The effect of the neutral sheet structure of the interplanetary magnetic field on cosmic ray distribution in space

NASA Technical Reports Server (NTRS)

Alania, M. V.; Aslamazashvili, R. G.; Bochorishvili, T.; Djapiashvili, T. V.; Tkemaladze, V. S.

1985-01-01

Results of the numerical solution of the anistoropic diffusion equation are presented. The modulation depth of galactic cosmic rays is defined by the degree of curvature of the neutral current sheet in the heliosphere. The effect of the regular interplanetary magnetic field (IMF) on cosmic ray anisotropy in the period of solar activity minimum (in 1976) is analyzed by the data of the neutron super-monitors of the world network, and the heliolatitudinal gradient and cosmic ray diffusion coefficient are defined.

Modeling weakly-ionized plasmas in magnetic field: A new computationally-efficient approach

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

Parent, Bernard, E-mail: parent@pusan.ac.kr; Macheret, Sergey O.; Shneider, Mikhail N.

2015-11-01

Despite its success at simulating accurately both non-neutral and quasi-neutral weakly-ionized plasmas, the drift-diffusion model has been observed to be a particularly stiff set of equations. Recently, it was demonstrated that the stiffness of the system could be relieved by rewriting the equations such that the potential is obtained from Ohm's law rather than Gauss's law while adding some source terms to the ion transport equation to ensure that Gauss's law is satisfied in non-neutral regions. Although the latter was applicable to multicomponent and multidimensional plasmas, it could not be used for plasmas in which the magnetic field was significant.more » This paper hence proposes a new computationally-efficient set of electron and ion transport equations that can be used not only for a plasma with multiple types of positive and negative ions, but also for a plasma in magnetic field. Because the proposed set of equations is obtained from the same physical model as the conventional drift-diffusion equations without introducing new assumptions or simplifications, it results in the same exact solution when the grid is refined sufficiently while being more computationally efficient: not only is the proposed approach considerably less stiff and hence requires fewer iterations to reach convergence but it yields a converged solution that exhibits a significantly higher resolution. The combined faster convergence and higher resolution is shown to result in a hundredfold increase in computational efficiency for some typical steady and unsteady plasma problems including non-neutral cathode and anode sheaths as well as quasi-neutral regions.« less

Unmagnetized diffusion for azimuthally symmetric wave and particle distributions

NASA Technical Reports Server (NTRS)

Dusenbery, P. B.; Lyons, L. R.

1988-01-01

The quasi-linear diffusion of particles from resonant interactions with a spectrum of electrostatic waves is investigated theoretically, extending results obtained for no magnetic field and for strong magnetic fields to cases where the ambient magnetic field which organizes azimuthally symmetric wave and particle distributions does not have to be taken into consideration in evaluating the local interaction. The derivation of the governing equations is explained, and numerical results are presented in extensive graphs and characterized in detail. Slow-mode ion-acoustic waves are shown to be unstable under the plasma conditions studied, and the dependence of resonant-ion diffusion rates with pitch angle, speed, and the distribution of wave energy in wavenumber space is explored. The implications of the present findings for theoretical models of the earth bow shock and plasma-sheet boundary layer are indicated.

Implementation of the full viscoresistive magnetohydrodynamic equations in a nonlinear finite element code

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

Haverkort, J.W.; Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven; Blank, H.J. de

Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. Amore » rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.« less

A 2D multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements

NASA Astrophysics Data System (ADS)

Qin, Shanlin; Liu, Fawang; Turner, Ian W.

2018-03-01

The consideration of diffusion processes in magnetic resonance imaging (MRI) signal attenuation is classically described by the Bloch-Torrey equation. However, many recent works highlight the distinct deviation in MRI signal decay due to anomalous diffusion, which motivates the fractional order generalization of the Bloch-Torrey equation. In this work, we study the two-dimensional multi-term time and space fractional diffusion equation generalized from the time and space fractional Bloch-Torrey equation. By using the Galerkin finite element method with a structured mesh consisting of rectangular elements to discretize in space and the L1 approximation of the Caputo fractional derivative in time, a fully discrete numerical scheme is derived. A rigorous analysis of stability and error estimation is provided. Numerical experiments in the square and L-shaped domains are performed to give an insight into the efficiency and reliability of our method. Then the scheme is applied to solve the multi-term time and space fractional Bloch-Torrey equation, which shows that the extra time derivative terms impact the relaxation process.

b matrix errors in echo planar diffusion tensor imaging

PubMed Central

Boujraf, Saïd; Luypaert, Robert; Osteaux, Michel

2001-01-01

Diffusion‐weighted magnetic resonance imaging (DW‐MRI) is a recognized tool for early detection of infarction of the human brain. DW‐MRI uses the signal loss associated with the random thermal motion of water molecules in the presence of magnetic field gradients to derive parameters that reflect the translational mobility of the water molecules in tissues. If diffusion‐weighted images with different values of b matrix are acquired during one individual investigation, it is possible to calculate apparent diffusion coefficient maps that are the elements of the diffusion tensor. The diffusion tensor elements represent the apparent diffusion coefficient of protons of water molecules in each pixel in the corresponding sample. The relation between signal intensity in the diffusion‐weighted images, diffusion tensor, and b matrix is derived from the Bloch equations. Our goal is to establish the magnitude of the error made in the calculation of the elements of the diffusion tensor when the imaging gradients are ignored. PACS number(s): 87.57. –s, 87.61.–c PMID:11602015

Non-Markovian renormalization of kinetic coefficients for drift-type turbulence in magnetized plasmas

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

Zagorodny, A.; Weiland, J.

2009-05-15

The problem of derivation of the kinetic equations for inhomogeneous plasma in an external magnetic field is considered. The Fokker-Planck-type equations with the non-Markovian kinetic coefficients are proposed. In the time-local limit (small correlation times with respect to the distribution function relaxation time) the relations obtained recover the results known from the appropriate quasilinear theory and the Dupree-Weinstock theory of plasma turbulence. Kinetic calculations of the dielectric response function are also performed with regard to the influence of turbulent fields on particle motion. The equations proposed are used to describe zonal flow generation and to estimate the diffusion coefficient formore » saturated turbulence.« less

Particle Acceleration via Reconnection Processes in the Supersonic Solar Wind

NASA Astrophysics Data System (ADS)

Zank, G. P.; le Roux, J. A.; Webb, G. M.; Dosch, A.; Khabarova, O.

2014-12-01

An emerging paradigm for the dissipation of magnetic turbulence in the supersonic solar wind is via localized small-scale reconnection processes, essentially between quasi-2D interacting magnetic islands. Charged particles trapped in merging magnetic islands can be accelerated by the electric field generated by magnetic island merging and the contraction of magnetic islands. We derive a gyrophase-averaged transport equation for particles experiencing pitch-angle scattering and energization in a super-Alfvénic flowing plasma experiencing multiple small-scale reconnection events. A simpler advection-diffusion transport equation for a nearly isotropic particle distribution is derived. The dominant charged particle energization processes are (1) the electric field induced by quasi-2D magnetic island merging and (2) magnetic island contraction. The magnetic island topology ensures that charged particles are trapped in regions where they experience repeated interactions with the induced electric field or contracting magnetic islands. Steady-state solutions of the isotropic transport equation with only the induced electric field and a fixed source yield a power-law spectrum for the accelerated particles with index α = -(3 + MA )/2, where MA is the Alfvén Mach number. Considering only magnetic island contraction yields power-law-like solutions with index -3(1 + τ c /(8τdiff)), where τ c /τdiff is the ratio of timescales between magnetic island contraction and charged particle diffusion. The general solution is a power-law-like solution with an index that depends on the Alfvén Mach number and the timescale ratio τdiff/τ c . Observed power-law distributions of energetic particles observed in the quiet supersonic solar wind at 1 AU may be a consequence of particle acceleration associated with dissipative small-scale reconnection processes in a turbulent plasma, including the widely reported c -5 (c particle speed) spectra observed by Fisk & Gloeckler and Mewaldt et al.

Particle acceleration via reconnection processes in the supersonic solar wind

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

Zank, G. P.; Le Roux, J. A.; Webb, G. M.

An emerging paradigm for the dissipation of magnetic turbulence in the supersonic solar wind is via localized small-scale reconnection processes, essentially between quasi-2D interacting magnetic islands. Charged particles trapped in merging magnetic islands can be accelerated by the electric field generated by magnetic island merging and the contraction of magnetic islands. We derive a gyrophase-averaged transport equation for particles experiencing pitch-angle scattering and energization in a super-Alfvénic flowing plasma experiencing multiple small-scale reconnection events. A simpler advection-diffusion transport equation for a nearly isotropic particle distribution is derived. The dominant charged particle energization processes are (1) the electric field induced bymore » quasi-2D magnetic island merging and (2) magnetic island contraction. The magnetic island topology ensures that charged particles are trapped in regions where they experience repeated interactions with the induced electric field or contracting magnetic islands. Steady-state solutions of the isotropic transport equation with only the induced electric field and a fixed source yield a power-law spectrum for the accelerated particles with index α = –(3 + M{sub A} )/2, where M{sub A} is the Alfvén Mach number. Considering only magnetic island contraction yields power-law-like solutions with index –3(1 + τ {sub c}/(8τ{sub diff})), where τ {sub c}/τ{sub diff} is the ratio of timescales between magnetic island contraction and charged particle diffusion. The general solution is a power-law-like solution with an index that depends on the Alfvén Mach number and the timescale ratio τ{sub diff}/τ {sub c}. Observed power-law distributions of energetic particles observed in the quiet supersonic solar wind at 1 AU may be a consequence of particle acceleration associated with dissipative small-scale reconnection processes in a turbulent plasma, including the widely reported c {sup –5} (c particle speed) spectra observed by Fisk and Gloeckler and Mewaldt et al.« less

Steady motion of skyrmions and domains walls under diffusive spin torques

NASA Astrophysics Data System (ADS)

Elías, Ricardo Gabriel; Vidal-Silva, Nicolas; Manchon, Aurélien

2017-03-01

We explore the role of the spin diffusion of conducting electrons in two-dimensional magnetic textures (domain walls and skyrmions) with spatial variation of the order of the spin precession length λex. The effect of diffusion reflects in four additional torques that are third order in spatial derivatives of magnetization and bilinear in λex and in the nonadiabatic parameter β'. In order to study the dynamics of the solitons when these diffusive torques are present, we derive the Thiele equation in the limit of steady motion and we compare the results with the nondiffusive limit. When considering a homogenous current these torques increase the longitudinal velocity of transverse domain walls of width Δ by a factor (λex/Δ)2(α/3), α being the magnetic damping constant. In the case of single skyrmions with core radius r0these new contributions tend to increase the Magnus effect in an amount proportional to (λex/r0) 2(1 +2 α β') .

Magnon diffusion theory for the spin Seebeck effect in ferromagnetic and antiferromagnetic insulators

NASA Astrophysics Data System (ADS)

Rezende, Sergio M.; Azevedo, Antonio; Rodríguez-Suárez, Roberto L.

2018-05-01

In magnetic insulators, spin currents are carried by the elementary excitations of the magnetization: spin waves or magnons. In simple ferromagnetic insulators there is only one magnon mode, while in two-sublattice antiferromagnetic insulators (AFIs) there are two modes, which carry spin currents in opposite directions. Here we present a theory for the diffusive magnonic spin current generated in a magnetic insulator layer by a thermal gradient in the spin Seebeck effect. We show that the formulations describing magnonic perturbation using a position-dependent chemical potential and those using a magnon accumulation are completely equivalent. Then we develop a drift–diffusion formulation for magnonic spin transport treating the magnon accumulation governed by the Boltzmann transport and diffusion equations and considering the full boundary conditions at the surfaces and interfaces of an AFI/normal metal bilayer. The theory is applied to the ferrimagnetic yttrium iron garnet and to the AFIs MnF2 and NiO, providing good quantitative agreement with experimental data.

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

NASA Astrophysics Data System (ADS)

Arendt, V.; Shalchi, A.

2018-06-01

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker-Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.

Repeated-cascade theory of strong turbulence in a magnetized plasma

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1976-01-01

A two-dimensional Navier-Stokes equation of vorticity in fluid turbulence is used to model drift turbulence in a plasma with a strong constant magnetic field and a constant mean density gradient. The nonlinear eddy diffusivity is described by a time-integrated Lagrangian correlation of velocities, and the repeated-cascade method is employed to choose the rank accounting for nearest-neighbor interactions, to calculate the Lagrangian correlation, and to close the correlation hierarchy. As a result, the diffusivity becomes dependent on the plasma's induced diffusion and is represented by a memory chain that is cut off by similarity and inertial randomization. Spectral laws relating the kinetic-energy spectrum to the -5, -5/2, -3, and -11 powers of wavenumber are derived for the velocity subranges of production, approach to inertia, inertia, and dissipation, respectively. It is found that the diffusivity is proportional to some inverse power of the magnetic field, that power being 1, 2/3, 5/6, and 2, respectively, for the four velocity subranges.

Diffusive shock acceleration - Acceleration rate, magnetic-field direction and the diffusion limit

NASA Technical Reports Server (NTRS)

Jokipii, J. R.

1992-01-01

This paper reviews the concept of diffusive shock acceleration, showing that the acceleration of charged particles at a collisionless shock is a straightforward consequence of the standard cosmic-ray transport equation, provided that one treats the discontinuity at the shock correctly. This is true for arbitrary direction of the upstream magnetic field. Within this framework, it is shown that acceleration at perpendicular or quasi-perpendicular shocks is generally much faster than for parallel shocks. Paradoxically, it follows also that, for a simple scattering law, the acceleration is faster for less scattering or larger mean free path. Obviously, the mean free path can not become too large or the diffusion limit becomes inapplicable. Gradient and curvature drifts caused by the magnetic-field change at the shock play a major role in the acceleration process in most cases. Recent observations of the charge state of the anomalous component are shown to require the faster acceleration at the quasi-perpendicular solar-wind termination shock.

Semi-empirical equation of limiting current for cobalt electrodeposition in the presence of magnetic field and additive electrolyte

NASA Astrophysics Data System (ADS)

Sudibyo, Aziz, N.

2016-02-01

One of the available methods to solve a roughening in cobalt electrodeposition is magneto electrodeposition (MED) in the presence of additive electrolyte. Semi-empirical equation of limiting current under a magnetic field for cobalt MED in the presence of boric acid as an additive electrolyte was successfully developed. This semi empirical equation shows the effects of the electrode area (A), the concentration of the electro active species (C), the diffusion coefficient of the electro active species (D), the kinematic viscosity of the electrolyte (v), magnetic strength (B) and the number of electrons involved in the redox process (n). The presence of boric acid led to decrease in the limiting current, but the acid was found useful as a buffer to avoid the local pH rise caused by parallel hydrogen evolution reaction (HER).

Asymptotic-Preserving methods and multiscale models for plasma physics

NASA Astrophysics Data System (ADS)

Degond, Pierre; Deluzet, Fabrice

2017-05-01

The purpose of the present paper is to provide an overview of Asymptotic-Preserving methods for multiscale plasma simulations by addressing three singular perturbation problems. First, the quasi-neutral limit of fluid and kinetic models is investigated in the framework of non-magnetized as well as magnetized plasmas. Second, the drift limit for fluid descriptions of thermal plasmas under large magnetic fields is addressed. Finally efficient numerical resolutions of anisotropic elliptic or diffusion equations arising in magnetized plasma simulation are reviewed.

Evidence for equivalence of diffusion processes of passive scalar and magnetic fields in anisotropic Navier-Stokes turbulence.

PubMed

Jurčišinová, E; Jurčišin, M

2017-05-01

The influence of the uniaxial small-scale anisotropy on the kinematic magnetohydrodynamic turbulence is investigated by using the field theoretic renormalization group technique in the one-loop approximation of a perturbation theory. The infrared stable fixed point of the renormalization group equations, which drives the scaling properties of the model in the inertial range, is investigated as the function of the anisotropy parameters and it is shown that, at least at the one-loop level of approximation, the diffusion processes of the weak passive magnetic field in the anisotropically driven kinematic magnetohydrodynamic turbulence are completely equivalent to the corresponding diffusion processes of passively advected scalar fields in the anisotropic Navier-Stokes turbulent environments.

Magnetic flux and heat losses by diffusive, advective, and Nernst effects in magnetized liner inertial fusion-like plasma

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

Velikovich, A. L.; Giuliani, J. L.; Zalesak, S. T.

The magnetized liner inertial fusion (MagLIF) approach to inertial confinement fusion [Slutz et al., Phys. Plasmas 17, 056303 (2010); Cuneo et al., IEEE Trans. Plasma Sci. 40, 3222 (2012)] involves subsonic/isobaric compression and heating of a deuterium-tritium plasma with frozen-in magnetic flux by a heavy cylindrical liner. The losses of heat and magnetic flux from the plasma to the liner are thereby determined by plasma advection and gradient-driven transport processes, such as thermal conductivity, magnetic field diffusion, and thermomagnetic effects. Theoretical analysis based on obtaining exact self-similar solutions of the classical collisional Braginskii's plasma transport equations in one dimension demonstratesmore » that the heat loss from the hot compressed magnetized plasma to the cold liner is dominated by transverse heat conduction and advection, and the corresponding loss of magnetic flux is dominated by advection and the Nernst effect. For a large electron Hall parameter (ω{sub e}τ{sub e}≫1), the effective diffusion coefficients determining the losses of heat and magnetic flux to the liner wall are both shown to decrease with ω{sub e}τ{sub e} as does the Bohm diffusion coefficient cT/(16eB), which is commonly associated with low collisionality and two-dimensional transport. We demonstrate how this family of exact solutions can be used for verification of codes that model the MagLIF plasma dynamics.« less

EVOLUTION OF THE MAGNETIC FIELD LINE DIFFUSION COEFFICIENT AND NON-GAUSSIAN STATISTICS

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

Snodin, A. P.; Ruffolo, D.; Matthaeus, W. H.

The magnetic field line random walk (FLRW) plays an important role in the transport of energy and particles in turbulent plasmas. For magnetic fluctuations that are transverse or almost transverse to a large-scale mean magnetic field, theories describing the FLRW usually predict asymptotic diffusion of magnetic field lines perpendicular to the mean field. Such theories often depend on the assumption that one can relate the Lagrangian and Eulerian statistics of the magnetic field via Corrsin’s hypothesis, and additionally take the distribution of magnetic field line displacements to be Gaussian. Here we take an ordinary differential equation (ODE) model with thesemore » underlying assumptions and test how well it describes the evolution of the magnetic field line diffusion coefficient in 2D+slab magnetic turbulence, by comparisons to computer simulations that do not involve such assumptions. In addition, we directly test the accuracy of the Corrsin approximation to the Lagrangian correlation. Over much of the studied parameter space we find that the ODE model is in fairly good agreement with computer simulations, in terms of both the evolution and asymptotic values of the diffusion coefficient. When there is poor agreement, we show that this can be largely attributed to the failure of Corrsin’s hypothesis rather than the assumption of Gaussian statistics of field line displacements. The degree of non-Gaussianity, which we measure in terms of the kurtosis, appears to be an indicator of how well Corrsin’s approximation works.« less

Effects of anisotropic turbulent thermal diffusion on spherical magnetoconvection in the Earth's core

NASA Astrophysics Data System (ADS)

Ivers, D. J.; Phillips, C. G.

2018-03-01

We re-consider the plate-like model of turbulence in the Earth's core, proposed by Braginsky and Meytlis (1990), and show that it is plausible for core parameters not only in polar regions but extends to mid- and low-latitudes where rotation and gravity are not parallel, except in a very thin equatorial layer. In this model the turbulence is highly anisotropic with preferred directions imposed by the Earth's rotation and the magnetic field. Current geodynamo computations effectively model sub-grid scale turbulence by using isotropic viscous and thermal diffusion values significantly greater than the molecular values of the Earth's core. We consider a local turbulent dynamo model for the Earth's core in which the mean magnetic field, velocity and temperature satisfy the Boussinesq induction, momentum and heat equations with an isotropic turbulent Ekman number and Roberts number. The anisotropy is modelled only in the thermal diffusion tensor with the Earth's rotation and magnetic field as preferred directions. Nonlocal organising effects of gravity and rotation (but not aspect ratio in the Earth's core) such as an inverse cascade and nonlocal transport are assumed to occur at longer length scales, which computations may accurately capture with sufficient resolution. To investigate the implications of this anisotropy for the proposed turbulent dynamo model we investigate the linear instability of turbulent magnetoconvection on length scales longer than the background turbulence in a rotating sphere with electrically insulating exterior for no-slip and isothermal boundary conditions. The equations are linearised about an axisymmetric basic state with a conductive temperature, azimuthal magnetic field and differential rotation. The basic state temperature is a function of the anisotropy and the spherical radius. Elsasser numbers in the range 1-20 and turbulent Roberts numbers 0.01-1 are considered for both equatorial symmetries of the magnetic basic state. It is found that anisotropic turbulent thermal diffusivity has a strong destabilising effect on magneto-convective instabilities, which may relax the tight energy budget constraining geodynamo models. The enhanced instability is not due to a reduction of the total diffusivity. The anisotropy also strengthens instabilities which break the symmetry of the underlying state, which may facilitate magnetic field reversal. Geostrophic flow appears to suppress the symmetry breaking modes and magnetic instabilities. Through symmetry breaking and the geostrophic flow the anisotropy may provide a mechanism of magnetic field reversal and its suppression in computational dynamo models.

Langevin equation versus kinetic equation: Subdiffusive behavior of charged particles in a stochastic magnetic field

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

Balescu, R.; Wang, H.; Misguich, J.H.

1994-12-01

The running diffusion coefficient [ital D]([ital t]) is evaluated for a system of charged particles undergoing the effect of a fluctuating magnetic field and of their mutual collisions. The latter coefficient can be expressed either in terms of the mean square displacement (MSD) of a test particle, or in terms of a correlation between a fluctuating distribution function and the magnetic field fluctuation. In the first case a stochastic differential equation of Langevin type for the position of a test particle must be solved; the second problem requires the determination of the distribution function from a kinetic equation. Using suitablemore » simplifications, both problems are amenable to exact analytic solution. The conclusion is that the equivalence of the two approaches is by no means automatically guaranteed. A new type of object, the hybrid kinetic equation'' is constructed: it automatically ensures the equivalence with the Langevin results. The same conclusion holds for the generalized Fokker--Planck equation. The (Bhatnagar--Gross--Krook) (BGK) model for the collisions yields a completely wrong result. A linear approximation to the hybrid kinetic equation yields an inexact behavior, but represents an acceptable approximation in the strongly collisional limit.« less

On the local well-posedness and a Prodi-Serrin-type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion

NASA Astrophysics Data System (ADS)

Larios, Adam; Pei, Yuan

2017-07-01

We prove a Prodi-Serrin-type global regularity condition for the three-dimensional Magnetohydrodynamic-Boussinesq system (3D MHD-Boussinesq) without thermal diffusion, in terms of only two velocity and two magnetic components. To the best of our knowledge, this is the first Prodi-Serrin-type criterion for such a 3D hydrodynamic system which is not fully dissipative, and indicates that such an approach may be successful on other systems. In addition, we provide a constructive proof of the local well-posedness of solutions to the fully dissipative 3D MHD-Boussinesq system, and also the fully inviscid, irresistive, non-diffusive MHD-Boussinesq equations. We note that, as a special case, these results include the 3D non-diffusive Boussinesq system and the 3D MHD equations. Moreover, they can be extended without difficulty to include the case of a Coriolis rotational term.

Stochastic analysis of pitch angle scattering of charged particles by transverse magnetic waves

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

Lemons, Don S.; Liu Kaijun; Winske, Dan

2009-11-15

This paper describes a theory of the velocity space scattering of charged particles in a static magnetic field composed of a uniform background field and a sum of transverse, circularly polarized, magnetic waves. When that sum has many terms the autocorrelation time required for particle orbits to become effectively randomized is small compared with the time required for the particle velocity distribution to change significantly. In this regime the deterministic equations of motion can be transformed into stochastic differential equations of motion. The resulting stochastic velocity space scattering is described, in part, by a pitch angle diffusion rate that ismore » a function of initial pitch angle and properties of the wave spectrum. Numerical solutions of the deterministic equations of motion agree with the theory at all pitch angles, for wave energy densities up to and above the energy density of the uniform field, and for different wave spectral shapes.« less

Calculation of two-dimension radial electric field in boundary plasmas by using BOUT++

NASA Astrophysics Data System (ADS)

Li, N. M.; Xu, X. Q.; Rognlien, T. D.; Gui, B.; Sun, J. Z.; Wang, D. Z.

2018-07-01

The steady state radial electric field (Er) is calculated by coupling a plasma transport model with the quasi-neutrality constraint and the vorticity equation within the BOUT++ framework. Based on the experimentally measured plasma density and temperature profiles in Alcator C-Mod discharges, the effective radial particle and heat diffusivities are inferred from the set of plasma transport equations. The effective diffusivities are then extended into the scrape-off layer (SOL) to calculate the plasma density, temperature and flow profiles across the separatrix into the SOL with the electrostatic sheath boundary conditions (SBC) applied on the divertor plates. Given these diffusivities, the electric field can be calculated self-consistently across the separatrix from the vorticity equation with SBC coupled to the plasma transport equations. The sheath boundary conditions act to generate a large and positive Er in the SOL, which is consistent with experimental measurements. The effect of magnetic particle drifts is shown to play a significant role on local particle transport and Er by inducing a net particle flow in both the edge and SOL regions.

Topological Hall effect in diffusive ferromagnetic thin films with spin-flip scattering

DOE PAGES

Zhang, Steven S. -L.; Heinonen, Olle

2018-04-02

In this paper, we study the topological Hall (TH) effect in a diffusive ferromagnetic metal thin film by solving a Boltzmann transport equation in the presence of spin-flip scattering. A generalized spin-diffusion equation is derived which contains an additional source term associated with the gradient of the emergent magnetic field that arises from skyrmions. Because of the source term, spin accumulation may build up in the vicinity of the skyrmions. This gives rise to a spin-polarized diffusion current that in general suppresses the bulk TH current. Only when the spin-diffusion length is much smaller than the skyrmion size does themore » TH resistivity approach the value derived by Bruno et al. [Phys. Rev. Lett. 93, 096806 (2004)]. Finally, we derive a general expression of the TH resistivity that applies to thin-film geometries with spin-flip scattering, and show that the corrections to the TH resistivity become large when the size of room temperature skyrmions is further reduced to tens of nanometers.« less

Topological Hall effect in diffusive ferromagnetic thin films with spin-flip scattering

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

Zhang, Steven S. -L.; Heinonen, Olle

In this paper, we study the topological Hall (TH) effect in a diffusive ferromagnetic metal thin film by solving a Boltzmann transport equation in the presence of spin-flip scattering. A generalized spin-diffusion equation is derived which contains an additional source term associated with the gradient of the emergent magnetic field that arises from skyrmions. Because of the source term, spin accumulation may build up in the vicinity of the skyrmions. This gives rise to a spin-polarized diffusion current that in general suppresses the bulk TH current. Only when the spin-diffusion length is much smaller than the skyrmion size does themore » TH resistivity approach the value derived by Bruno et al. [Phys. Rev. Lett. 93, 096806 (2004)]. Finally, we derive a general expression of the TH resistivity that applies to thin-film geometries with spin-flip scattering, and show that the corrections to the TH resistivity become large when the size of room temperature skyrmions is further reduced to tens of nanometers.« less

Topological Hall effect in diffusive ferromagnetic thin films with spin-flip scattering

NASA Astrophysics Data System (ADS)

Zhang, Steven S.-L.; Heinonen, Olle

2018-04-01

We study the topological Hall (TH) effect in a diffusive ferromagnetic metal thin film by solving a Boltzmann transport equation in the presence of spin-flip scattering. A generalized spin-diffusion equation is derived which contains an additional source term associated with the gradient of the emergent magnetic field that arises from skyrmions. Because of the source term, spin accumulation may build up in the vicinity of the skyrmions. This gives rise to a spin-polarized diffusion current that in general suppresses the bulk TH current. Only when the spin-diffusion length is much smaller than the skyrmion size does the TH resistivity approach the value derived by Bruno et al. [Phys. Rev. Lett. 93, 096806 (2004), 10.1103/PhysRevLett.93.096806]. We derive a general expression of the TH resistivity that applies to thin-film geometries with spin-flip scattering, and show that the corrections to the TH resistivity become large when the size of room temperature skyrmions is further reduced to tens of nanometers.

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

Effects of Drift-Shell Splitting by Chorus Waves on Radiation Belt Electrons

NASA Astrophysics Data System (ADS)

Chan, A. A.; Zheng, L.; O'Brien, T. P., III; Tu, W.; Cunningham, G.; Elkington, S. R.; Albert, J.

2015-12-01

Drift shell splitting in the radiation belts breaks all three adiabatic invariants of charged particle motion via pitch angle scattering, and produces new diffusion terms that fully populate the diffusion tensor in the Fokker-Planck equation. Based on the stochastic differential equation method, the Radbelt Electron Model (REM) simulation code allows us to solve such a fully three-dimensional Fokker-Planck equation, and to elucidate the sources and transport mechanisms behind the phase space density variations. REM has been used to perform simulations with an empirical initial phase space density followed by a seed electron injection, with a Tsyganenko 1989 magnetic field model, and with chorus wave and ULF wave diffusion models. Our simulation results show that adding drift shell splitting changes the phase space location of the source to smaller L shells, which typically reduces local electron energization (compared to neglecting drift-shell splitting effects). Simulation results with and without drift-shell splitting effects are compared with Van Allen Probe measurements.

Particle Diffusion in Chaotic Magnetic Fields Generated by Asymmetric Current Configurations

NASA Astrophysics Data System (ADS)

Ram, A. K.; Dasgupta, B.

2008-12-01

The observed cross-field diffusion of charged particles in cosmic rays is assumed to be due to the chaotic nature of the interplanetary/intergalactic magnetic fields. Among the classic works on this subject have been those of Parker [1] and Jokipii [2]. Parker considered the passage of cosmic ray particles and energetic solar particles in a large scale magnetic field containing small scale irregularities. In the context of cosmic ray propagation, Jokipii considered a small fluctuating component, added on to a uniform magnetic field, to study the spatial transport of particles. In these studies the irregular component of the magnetic field is prescribed in an ad hoc fashion. In contrast, we consider asymmetric, nonlinear, steady-state magnetic fields, in three spatial dimensions, generated by currents flowing in circular loops and straight lines [3]. These magnetic fields are completely deterministic and, for certain range of parameters, chaotic. We will present analytical and numerical studies on the spatial characteristics of these fields. The motion of charged particles in the nonlinear and chaotic magnetic fields is determined using the Lorentz equation. A particle moving in a deterministic chaotic magnetic field superposed on a uniform background magnetic field is found to undergo spatial transport. This shows that chaotic magnetic fields generated by simple current configurations can produce cross-field diffusion. A detailed analysis of particle motion and diffusion along with application to space plasmas will be presented. [1] E.N. Parker, Planet. Space Sci. 13, 9 (1965). [2] J.R. Jokipii, Astrophys. J. 146, 480 (1966), and J.R. Jokipii, Astrophys. J. 149, 405 (1967). [3] A.K. Ram and B. Dasgupta, Eos Trans. AGU 87 (52), Fall Meet. Suppl. Abstract NG31B-1593 (2006); and Eos Trans. AGU 88 (52), Fall Meet. Suppl. Abstract NG21B-0522 (2007).

A GLOBAL GALACTIC DYNAMO WITH A CORONA CONSTRAINED BY RELATIVE HELICITY

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

Prasad, A.; Mangalam, A., E-mail: avijeet@iiap.res.in, E-mail: mangalam@iiap.res.in

We present a model for a global axisymmetric turbulent dynamo operating in a galaxy with a corona that treats the parameters of turbulence driven by supernovae and by magneto-rotational instability under a common formalism. The nonlinear quenching of the dynamo is alleviated by the inclusion of small-scale advective and diffusive magnetic helicity fluxes, which allow the gauge-invariant magnetic helicity to be transferred outside the disk and consequently to build up a corona during the course of dynamo action. The time-dependent dynamo equations are expressed in a separable form and solved through an eigenvector expansion constructed using the steady-state solutions ofmore » the dynamo equation. The parametric evolution of the dynamo solution allows us to estimate the final structure of the global magnetic field and the saturated value of the turbulence parameter α{sub m}, even before solving the dynamical equations for evolution of magnetic fields in the disk and the corona, along with α-quenching. We then solve these equations simultaneously to study the saturation of the large-scale magnetic field, its dependence on the small-scale magnetic helicity fluxes, and the corresponding evolution of the force-free field in the corona. The quadrupolar large-scale magnetic field in the disk is found to reach equipartition strength within a timescale of 1 Gyr. The large-scale magnetic field in the corona obtained is much weaker than the field inside the disk and has only a weak impact on the dynamo operation.« less

A variational image-based approach to the correction of susceptibility artifacts in the alignment of diffusion weighted and structural MRI.

PubMed

Tao, Ran; Fletcher, P Thomas; Gerber, Samuel; Whitaker, Ross T

2009-01-01

This paper presents a method for correcting the geometric and greyscale distortions in diffusion-weighted MRI that result from inhomogeneities in the static magnetic field. These inhomogeneities may due to imperfections in the magnet or to spatial variations in the magnetic susceptibility of the object being imaged--so called susceptibility artifacts. Echo-planar imaging (EPI), used in virtually all diffusion weighted acquisition protocols, assumes a homogeneous static field, which generally does not hold for head MRI. The resulting distortions are significant, sometimes more than ten millimeters. These artifacts impede accurate alignment of diffusion images with structural MRI, and are generally considered an obstacle to the joint analysis of connectivity and structure in head MRI. In principle, susceptibility artifacts can be corrected by acquiring (and applying) a field map. However, as shown in the literature and demonstrated in this paper, field map corrections of susceptibility artifacts are not entirely accurate and reliable, and thus field maps do not produce reliable alignment of EPIs with corresponding structural images. This paper presents a new, image-based method for correcting susceptibility artifacts. The method relies on a variational formulation of the match between an EPI baseline image and a corresponding T2-weighted structural image but also specifically accounts for the physics of susceptibility artifacts. We derive a set of partial differential equations associated with the optimization, describe the numerical methods for solving these equations, and present results that demonstrate the effectiveness of the proposed method compared with field-map correction.

Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas

NASA Astrophysics Data System (ADS)

Ren, Zhigang; Xu, Chao; Lin, Qun; Loxton, Ryan; Teo, Kok Lay

2016-03-01

Establishing a good current spatial profile in tokamak fusion reactors is crucial to effective steady-state operation. The evolution of the current spatial profile is related to the evolution of the poloidal magnetic flux, which can be modeled in the normalized cylindrical coordinates using a parabolic partial differential equation (PDE) called the magnetic diffusion equation. In this paper, we consider the dynamic optimization problem of attaining the best possible current spatial profile during the ramp-up phase of the tokamak. We first use the Galerkin method to obtain a finite-dimensional ordinary differential equation (ODE) model based on the original magnetic diffusion PDE. Then, we combine the control parameterization method with a novel time-scaling transformation to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques such as sequential quadratic programming (SQP). This control parameterization approach involves approximating the tokamak input signals by piecewise-linear functions whose slopes and break-points are decision variables to be optimized. We show that the gradient of the objective function with respect to the decision variables can be computed by solving an auxiliary dynamic system governing the state sensitivity matrix. Finally, we conclude the paper with simulation results for an example problem based on experimental data from the DIII-D tokamak in San Diego, California.

Diffusion of chemically reactive species in MHD oscillatory flow with thermal radiation in the presence of constant suction and injection

NASA Astrophysics Data System (ADS)

Sasikumar, J.; Bhuvaneshwari, S.; Govindarajan, A.

2018-04-01

In this project, it is proposed to investigate the effect of suction/injection on the unsteady oscillatory flow of an incompressible viscous electrically conducting fluid through a channel filled with porous medium and non-uniform wall temperature. The fluid is subjected to a uniform magnetic field normal to the channel and the velocity slip at the cold plate is taken into consideration. With the assumption of magnetic Reynolds number to be very small, the induced magnetic field is neglected. Assuming pressure gradient to be oscillatory across the ends of the channel, resulting flow as unsteady oscillatory flow. Under the usual Bousinessq approximation, a mathematical model representing this fluid flow consisting of governing equations with boundary conditions will be developed. Closed form solutions of the dimensionless governing equations of the fluid flow, namely momentum equation, energy equation and species concentration can be obtained . The effects of heat radiation and chemical reaction with suction and injection on temperature, velocity and species concentration profiles will be analysed with tables and graphs.

A joined model for solar dynamo and differential rotation

NASA Astrophysics Data System (ADS)

Kitchatinov, L. L.; Nepomnyashchikh, A. A.

2017-05-01

A model for the solar dynamo, consistent in global flow and numerical method employed with the differential rotation model, is developed. The magnetic turbulent diffusivity is expressed in terms of the entropy gradient, which is controlled by the model equations. The magnetic Prandtl number and latitudinal profile of the alpha-effect are specified by fitting the computed period of the activity cycle and the equatorial symmetry of magnetic fields to observations. Then, the instants of polar field reversals and time-latitude diagrams of the fields also come into agreement with observations. The poloidal field has a maximum amplitude of about 10 Gs in the polar regions. The toroidal field of several thousand Gauss concentrates near the base of the convection zone and is transported towards the equator by the meridional flow. The model predicts a value of about 1037 erg for the total magnetic energy of large-scale fields in the solar convection zone.

Verification and Validation of a Coordinate Transformation Method in Axisymmetric Transient Magnetics.

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

Ashcraft, C. Chace; Niederhaus, John Henry; Robinson, Allen C.

We present a verification and validation analysis of a coordinate-transformation-based numerical solution method for the two-dimensional axisymmetric magnetic diffusion equation, implemented in the finite-element simulation code ALEGRA. The transformation, suggested by Melissen and Simkin, yields an equation set perfectly suited for linear finite elements and for problems with large jumps in material conductivity near the axis. The verification analysis examines transient magnetic diffusion in a rod or wire in a very low conductivity background by first deriving an approximate analytic solution using perturbation theory. This approach for generating a reference solution is shown to be not fully satisfactory. A specializedmore » approach for manufacturing an exact solution is then used to demonstrate second-order convergence under spatial refinement and tem- poral refinement. For this new implementation, a significant improvement relative to previously available formulations is observed. Benefits in accuracy for computed current density and Joule heating are also demonstrated. The validation analysis examines the circuit-driven explosion of a copper wire using resistive magnetohydrodynamics modeling, in comparison to experimental tests. The new implementation matches the accuracy of the existing formulation, with both formulations capturing the experimental burst time and action to within approximately 2%.« less

Presence of time-dependent diffusion in the brachial plexus.

PubMed

Mahbub, Zaid B; Peters, Andrew M; Gowland, Penny A

2018-02-01

This work describes the development of a method to measure the variation of apparent diffusion coefficient (ADC) with diffusion time (Δ) in the brachial plexus, as a potential method of probing microstructure. Diffusion-weighted MRI with body signal suppression was used to highlight the nerves from surrounding tissues, and sequence parameters were optimized for sensitivity to change with diffusion time. A porous media-restricted diffusion model based on the Latour-Mitra equation was fitted to the diffusion time-dependent ADC data from the brachial plexus nerves and cord. The ADC was observed to reduce at long diffusion times, confirming that diffusion was restricted in the nerves and cord in healthy subjects. T2 of the nerves was measured to be 80 ± 5 ms, the diffusion coefficient was found to vary from (1.5 ± 0.1) × 10 -3 mm 2 /s at a diffusion time of 18.3 ms to (1.0 ± 0.2) × 10 -3 mm 2 /s at a diffusion time of 81.3 ms. A novel method of probing restricted diffusion in the brachial plexus was developed. Resulting parameters were comparable with values obtained previously on biological systems. Magn Reson Med 79:789-795, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Mixed convection peristaltic flow of third order nanofluid with an induced magnetic field.

PubMed

Noreen, Saima

2013-01-01

This research is concerned with the peristaltic flow of third order nanofluid in an asymmetric channel. The governing equations of third order nanofluid are modelled in wave frame of reference. Effect of induced magnetic field is considered. Long wavelength and low Reynolds number situation is tackled. Numerical solutions of the governing problem are computed and analyzed. The effects of Brownian motion and thermophoretic diffusion of nano particles are particularly emphasized. Physical quantities such as velocity, pressure rise, temperature, induced magnetic field and concentration distributions are discussed.

Cosmic Ray Propagation through the Magnetic Fields of the Galaxy with Extended Halo

NASA Technical Reports Server (NTRS)

Zhang, Ming

2005-01-01

In this project we perform theoretical studies of 3-dimensional cosmic ray propagation in magnetic field configurations of the Galaxy with an extended halo. We employ our newly developed Markov stochastic process methods to solve the diffusive cosmic ray transport equation. We seek to understand observations of cosmic ray spectra, composition under the constraints of the observations of diffuse gamma ray and radio emission from the Galaxy. The model parameters are directly are related to properties of our Galaxy, such as the size of the Galactic halo, particle transport in Galactic magnetic fields, distribution of interstellar gas, primary cosmic ray source distribution and their confinement in the Galaxy. The core of this investigation is the development of software for cosmic ray propagation models with the Markov stochastic process approach. Values of important model parameters for the halo diffusion model are examined in comparison with observations of cosmic ray spectra, composition and the diffuse gamma-ray background. This report summarizes our achievement in the grant period at the Florida Institute of Technology. Work at the co-investigator's institution, the University of New Hampshire, under a companion grant, will be covered in detail by a separate report.

Self-propulsion of a planar electric or magnetic microbot immersed in a polar viscous fluid

NASA Astrophysics Data System (ADS)

Felderhof, B. U.

2011-05-01

A planar sheet immersed in an electrically polar liquid like water can propel itself by means of a plane wave charge density propagating in the sheet. The corresponding running electric wave polarizes the fluid and causes an electrical torque density to act on the fluid. The sheet is convected by the fluid motion resulting from the conversion of rotational particle motion, generated by the torque density, into translational fluid motion by the mechanism of friction and spin diffusion. Similarly, a planar sheet immersed in a magnetic ferrofluid can propel itself by means of a plane wave current density in the sheet and the torque density acting on the fluid corresponding to the running wave magnetic field and magnetization. The effect is studied on the basis of the micropolar fluid equations of motion and Maxwell’s equations of electrostatics or magnetostatics, respectively. An analytic expression is derived for the velocity of the sheet by perturbation theory to second order in powers of the amplitude of the driving charge or current density. Under the assumption that the equilibrium magnetic equation of state may be used in linearized form and that higher harmonics than the first may be neglected, a set of self-consistent integral equations is derived which can be solved numerically by iteration. In typical situations the second-order perturbation theory turns out to be quite accurate.

Plasma Equilibria With Stochastic Magnetic Fields

NASA Astrophysics Data System (ADS)

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

2009-05-01

Plasma equilibria that include regions of stochastic magnetic fields are of interest in a variety of applications, including tokamaks with ergodic limiters and high-pressure stellarators. Such equilibria are examined theoretically, and a numerical algorithm for their construction is described.^2,3 % The balance between stochastic diffusion of magnetic lines and small effects^2 omitted from the simplest MHD description can support pressure and current profiles that need not be flattened in stochastic regions. The diffusion can be described analytically by renormalizing stochastic Langevin equations for pressure and parallel current j, with particular attention being paid to the satisfaction of the periodicity constraints in toroidal configurations with sheared magnetic fields. The equilibrium field configuration can then be constructed by coupling the prediction for j to Amp'ere's law, which is solved numerically. A. Reiman et al., Pressure-induced breaking of equilibrium flux surfaces in the W7AS stellarator, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes and A. H. Reiman, Plasma equilibrium in a magnetic field with stochastic regions, submitted to Phys. Plasmas. J. A. Krommes, Fundamental statistical theories of plasma turbulence in magnetic fields, Phys. Reports 360, 1--351.

Magnetoconvection dynamics in a stratified layer. 1: Two-dimensional simulations and visualization

NASA Astrophysics Data System (ADS)

Lantz, Steven R.; Sudan, R. N.

1995-03-01

To gain insight in the problem of fluid convection below solar photosphere, time-dependent magnetohydrodynamic convection is studied by numerical simulation to the magneto-anelastic equations, a model appropiate for low Mach numbers. Numerical solutions to the equations are generated on a two-dimensional Cartesian mesh by a finite-difference, predictor-corrector algorithm. The thermodynamic properties of the fluid are held constant at the rigid, stress-free top and bottom boundaries of the computational box, while lateral boundaries are treated as periodic. In most runs the background polytropic fluid configuration is held fixed at Rayleigh number R = 5.44 times the critical value, Prandtl number P = 1.8, and aspect ratio a = 1, while the magnetic parameters are allowed to vary. The resulting dynamical behavior is shown to be strongly influenced by a horizontal magnetic field which is imposed at the bottom boundary. As the field strength increases from zero, an initially unsteady 'single-roll' state, featuring complex time dependence is replaced by a steady 'traveling-wave tilted state; then, an oscillatory or 'sloshing' state; then, a steady two-poll state with no tilting; and finally, a stationary state. Because the magnetic field is matched onto a potential field at the top boundary, it can penetrate into the nonconducting region above. By varying a magnetic diffusivity, the concentrations of weak magnetic fields at the top of these flows can be shown to be explainable in terms of an advection-diffusion balance.

SMALL-SCALE ANISOTROPIES OF COSMIC RAYS FROM RELATIVE DIFFUSION

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

Ahlers, Markus; Mertsch, Philipp

2015-12-10

The arrival directions of multi-TeV cosmic rays show significant anisotropies at small angular scales. It has been argued that this small-scale structure can naturally arise from cosmic ray scattering in local turbulent magnetic fields that distort a global dipole anisotropy set by diffusion. We study this effect in terms of the power spectrum of cosmic ray arrival directions and show that the strength of small-scale anisotropies is related to properties of relative diffusion. We provide a formalism for how these power spectra can be inferred from simulations and motivate a simple analytic extension of the ensemble-averaged diffusion equation that canmore » account for the effect.« less

Dynamical onset of superconductivity and retention of magnetic fields in cooling neutron stars

NASA Astrophysics Data System (ADS)

Ho, Wynn C. G.; Andersson, Nils; Graber, Vanessa

2017-12-01

A superconductor of paired protons is thought to form in the core of neutron stars soon after their birth. Minimum energy conditions suggest magnetic flux is expelled from the superconducting region due to the Meissner effect, such that the neutron star core is largely devoid of magnetic fields for some nuclear equation of state and proton pairing models. We show via neutron star cooling simulations that the superconducting region expands faster than flux is expected to be expelled because cooling timescales are much shorter than timescales of magnetic field diffusion. Thus magnetic fields remain in the bulk of the neutron star core for at least 106-107yr . We estimate the size of flux free regions at 107yr to be ≲100 m for a magnetic field of 1011G and possibly smaller for stronger field strengths. For proton pairing models that are narrow, magnetic flux may be completely expelled from a thin shell of approximately the above size after 105yr . This shell may insulate lower conductivity outer layers, where magnetic fields can diffuse and decay faster, from fields maintained in the highly conducting deep core.

Dynamics of the magnetization of single domain particles having triaxial anisotropy subjected to a uniform dc magnetic field

NASA Astrophysics Data System (ADS)

Ouari, Bachir; Kalmykov, Yury P.

2006-12-01

Thermally induced relaxation of the magnetization of single domain ferromagnetic particles with triaxial (orthorhombic) anisotropy in the presence of a uniform external magnetic field H0 is considered in the context of Brown's continuous diffusion model. Simple analytic equations, which allow one to describe qualitatively the field effects in the relaxation behavior of the system for wide ranges of the field strength and damping parameters are derived. It is shown that these formulas are in complete agreement with the exact matrix continued fraction solution of the infinite hierarchy of linear differential-recurrence equations for the statistical moments, which governs the magnetization dynamics of an individual particle (this hierarchy is derived by averaging the underlying stochastic Landau-Lifshitz-Gilbert equation over its realizations). It is also demonstrated that in strong fields the longitudinal relaxation of the magnetization is essentially modified by the contribution of the high-frequency "intrawell" modes to the relaxation process. This effect discovered for uniaxial particles by Coffey et al. [Phys. Rev. B 51, 15947 (1995)] is the natural consequence of the depletion of population of the shallow potential well. However, in contrast to uniaxial anisotropy, for orthorhombic crystals there is an inherent geometric dependence of the complex magnetic susceptibility and the relaxation time on the damping parameter α arising from the coupling of longitudinal and transverse relaxation modes.

Surface flux transport simulations: Effect of inflows toward active regions and random velocities on the evolution of the Sun's large-scale magnetic field

NASA Astrophysics Data System (ADS)

Martin-Belda, D.; Cameron, R. H.

2016-02-01

Aims: We aim to determine the effect of converging flows on the evolution of a bipolar magnetic region (BMR), and to investigate the role of these inflows in the generation of poloidal flux. We also discuss whether the flux dispersal due to turbulent flows can be described as a diffusion process. Methods: We developed a simple surface flux transport model based on point-like magnetic concentrations. We tracked the tilt angle, the magnetic flux and the axial dipole moment of a BMR in simulations with and without inflows and compared the results. To test the diffusion approximation, simulations of random walk dispersal of magnetic features were compared against the predictions of the diffusion treatment. Results: We confirm the validity of the diffusion approximation to describe flux dispersal on large scales. We find that the inflows enhance flux cancellation, but at the same time affect the latitudinal separation of the polarities of the bipolar region. In most cases the latitudinal separation is limited by the inflows, resulting in a reduction of the axial dipole moment of the BMR. However, when the initial tilt angle of the BMR is small, the inflows produce an increase in latitudinal separation that leads to an increase in the axial dipole moment in spite of the enhanced flux destruction. This can give rise to a tilt of the BMR even when the BMR was originally aligned parallel to the equator.

Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion

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

Mohandas, Gopakumar; Pessah, Martin E., E-mail: gopakumar@nbi.ku.dk, E-mail: mpessah@nbi.ku.dk

The effect of magnetic field diffusion on the stability of accretion disks is a problem that has attracted considerable interest of late. In particular, the Hall effect has the potential to bring about remarkable changes in the dynamical behavior of disks that are without parallel. In this paper, we conduct a systematic examination of the linear eigenmodes in a weakly magnetized differentially rotating gas with a special focus on Hall diffusion. We first develop a geometrical representation of the eigenmodes and provide a detailed quantitative description of the polarization properties of the oscillatory modes under the combined influence of themore » Coriolis and Hall effects. We also analyze the effects of magnetic diffusion on the structure of the unstable modes and derive analytical expressions for the kinetic and magnetic stresses and energy densities associated with the non-ideal magnetorotational instability (MRI). Our analysis explicitly demonstrates that, if the dissipative effects are relatively weak, the kinetic stresses and energies make up the dominant contribution to the total stress and energy density when the equilibrium angular momentum and magnetic field vectors are anti-parallel. This is in sharp contrast to what is observed in the case of the ideal or dissipative MRI. We conduct shearing box simulations and find very good agreement with the results derived from linear theory. Because the modes under consideration are also exact solutions of the nonlinear equations, the unconventional nature of the kinetic and magnetic stresses may have significant implications for the nonlinear evolution in some regions of protoplanetary disks.« less

Hall-Effect Thruster Simulations with 2-D Electron Transport and Hydrodynamic Ions

NASA Technical Reports Server (NTRS)

Mikellides, Ioannis G.; Katz, Ira; Hofer, Richard H.; Goebel, Dan M.

2009-01-01

A computational approach that has been used extensively in the last two decades for Hall thruster simulations is to solve a diffusion equation and energy conservation law for the electrons in a direction that is perpendicular to the magnetic field, and use discrete-particle methods for the heavy species. This "hybrid" approach has allowed for the capture of bulk plasma phenomena inside these thrusters within reasonable computational times. Regions of the thruster with complex magnetic field arrangements (such as those near eroded walls and magnets) and/or reduced Hall parameter (such as those near the anode and the cathode plume) challenge the validity of the quasi-one-dimensional assumption for the electrons. This paper reports on the development of a computer code that solves numerically the 2-D axisymmetric vector form of Ohm's law, with no assumptions regarding the rate of electron transport in the parallel and perpendicular directions. The numerical challenges related to the large disparity of the transport coefficients in the two directions are met by solving the equations in a computational mesh that is aligned with the magnetic field. The fully-2D approach allows for a large physical domain that extends more than five times the thruster channel length in the axial direction, and encompasses the cathode boundary. Ions are treated as an isothermal, cold (relative to the electrons) fluid, accounting for charge-exchange and multiple-ionization collisions in the momentum equations. A first series of simulations of two Hall thrusters, namely the BPT-4000 and a 6-kW laboratory thruster, quantifies the significance of ion diffusion in the anode region and the importance of the extended physical domain on studies related to the impact of the transport coefficients on the electron flow field.

Modulation of pure spin currents with a ferromagnetic insulator

NASA Astrophysics Data System (ADS)

Villamor, Estitxu; Isasa, Miren; Vélez, Saül; Bedoya-Pinto, Amilcar; Vavassori, Paolo; Hueso, Luis E.; Bergeret, F. Sebastián; Casanova, Fèlix

2015-01-01

We propose and demonstrate spin manipulation by magnetically controlled modulation of pure spin currents in cobalt/copper lateral spin valves, fabricated on top of the magnetic insulator Y3F e5O12 (YIG). The direction of the YIG magnetization can be controlled by a small magnetic field. We observe a clear modulation of the nonlocal resistance as a function of the orientation of the YIG magnetization with respect to the polarization of the spin current. Such a modulation can only be explained by assuming a finite spin-mixing conductance at the Cu/YIG interface, as it follows from the solution of the spin-diffusion equation. These results open a path towards the development of spin logics.

Brownian diffusion and thermophoresis mechanisms in Casson fluid over a moving wedge

NASA Astrophysics Data System (ADS)

Ullah, Imran; Shafie, Sharidan; Khan, Ilyas; Hsiao, Kai Long

2018-06-01

The effect of Brownian diffusion and thermophoresis on electrically conducting mixed convection flow of Casson fluid induced by moving wedge is investigated in this paper. It is assumed that the wedge is saturated in a porous medium and experiences the thermal radiation and chemical reaction effects. The transformed nonlinear governing equations are solved numerically by Keller box scheme. Findings reveal that increase in Casson and magnetic parameters reduced the boundary layer thickness. The effect of Brownian motion and thermophoresis parameters are more pronounced on temperature profile as compared to nanoparticles concentration. The presence of thermal radiation assisted the heat transfer rate significantly. The influence of magnetic parameter is observed less significant on temperature and nanoparticles concentration.

CFD-ACE+: a CAD system for simulation and modeling of MEMS

NASA Astrophysics Data System (ADS)

Stout, Phillip J.; Yang, H. Q.; Dionne, Paul; Leonard, Andy; Tan, Zhiqiang; Przekwas, Andrzej J.; Krishnan, Anantha

1999-03-01

Computer aided design (CAD) systems are a key to designing and manufacturing MEMS with higher performance/reliability, reduced costs, shorter prototyping cycles and improved time- to-market. One such system is CFD-ACE+MEMS, a modeling and simulation environment for MEMS which includes grid generation, data visualization, graphical problem setup, and coupled fluidic, thermal, mechanical, electrostatic, and magnetic physical models. The fluid model is a 3D multi- block, structured/unstructured/hybrid, pressure-based, implicit Navier-Stokes code with capabilities for multi- component diffusion, multi-species transport, multi-step gas phase chemical reactions, surface reactions, and multi-media conjugate heat transfer. The thermal model solves the total enthalpy from of the energy equation. The energy equation includes unsteady, convective, conductive, species energy, viscous dissipation, work, and radiation terms. The electrostatic model solves Poisson's equation. Both the finite volume method and the boundary element method (BEM) are available for solving Poisson's equation. The BEM method is useful for unbounded problems. The magnetic model solves for the vector magnetic potential from Maxwell's equations including eddy currents but neglecting displacement currents. The mechanical model is a finite element stress/deformation solver which has been coupled to the flow, heat, electrostatic, and magnetic calculations to study flow, thermal electrostatically, and magnetically included deformations of structures. The mechanical or structural model can accommodate elastic and plastic materials, can handle large non-linear displacements, and can model isotropic and anisotropic materials. The thermal- mechanical coupling involves the solution of the steady state Navier equation with thermoelastic deformation. The electrostatic-mechanical coupling is a calculation of the pressure force due to surface charge on the mechanical structure. Results of CFD-ACE+MEMS modeling of MEMS such as cantilever beams, accelerometers, and comb drives are discussed.

Simulations of high Mach number perpendicular shocks with resistive electrons

NASA Technical Reports Server (NTRS)

Quest, K. B.

1986-01-01

A simulation code which models the ions as microparticles and the electrons as a resistive massless fluid is employed to study the structure of high Mach number perpendicular shocks. It is found that stable stationary shock solutions can be obtained for Alfven Mach numbers (M sub A) between 5 and 60 for upstream plasmas where the ratio of the plasma pressure to the magnetic pressure is 1, providing that the upstream resistive diffusion length is much smaller than the ion inertial length. For much larger resistive diffusion lengths, the magnetic field overshoot is damped, and the imbalance in the electron momentum equation results in a periodic fluctuation of the fraction of reflected ions. In the limit of M sub A of less than 10, the magnetic overshoot and the fraction of reflected ions increase with increasing M sub A, while at higher Mach numbers the fraction of reflected ions peaks at about 40 percent and the magnetic field overshoot increases at a much slower rate. Electron inertial effects are also considered.

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

NASA Astrophysics Data System (ADS)

Denissenkov, Pavel A.

2010-08-01

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

On axisymmetric resistive MHD equilibria with flow free of Pfirsch-Schlüter diffusion

NASA Astrophysics Data System (ADS)

Throumoulopoulos, George N.; Tasso, Henri

2002-11-01

The equilibrium of an axisymmetric magnetically confined plasma with anisotropic electrical conductivity and flows parallel to the magnetic field is investigated within the framework of the MHD theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order partial differential equation for the poloidal magnetic flux function along with a Bernoulli equation for the density identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the conductivities σ_allel and σ_⊥ parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic conductivity and parallel flows (see [1]) the equilibrium is compatible with non-vanishing poloidal currents. For incompressible flows exact solutions of the above mentioned set of equations can be constructed with σ_allel and σ_⊥ profiles compatible with collisional conductivity profiles, i.e. profiles peaked close to the magnetic axis, vanishing on the boundary and such that σ_allel> σ_⊥. In particular, an exact equilibrium describing a toroidal plasma of arbitrary aspect ratio being contained within a perfectly conducting boundary of rectangular cross-section and peaked toroidal current density profile vanishing on the boundary is further considered. For this equilibrium in the case of vanishing flows the difference σ_allel-σ_⊥ for the reversed field pinch scaling Bp Bt (where Bp and Bt are the poloidal and toroidal magnetic field components) is nearly two times larger than that for the tokamak scaling B_p 0.1 B_t. [1] G. N. Throumoulopoulos, H. Tasso, J. Plasma Physics 64, 601 (2000).

The loss rates of O+ in the inner magnetosphere caused by both magnetic field line curvature scattering and charge exchange reactions

NASA Astrophysics Data System (ADS)

Ji, Y.; Shen, C.

2014-03-01

With consideration of magnetic field line curvature (FLC) pitch angle scattering and charge exchange reactions, the O+ (>300 keV) in the inner magnetosphere loss rates are investigated by using an eigenfunction analysis. The FLC scattering provides a mechanism for the ring current O+ to enter the loss cone and influence the loss rates caused by charge exchange reactions. Assuming that the pitch angle change is small for each scattering event, the diffusion equation including a charge exchange term is constructed and solved; the eigenvalues of the equation are identified. The resultant loss rates of O+ are approximately equal to the linear superposition of the loss rate without considering the charge exchange reactions and the loss rate associated with charge exchange reactions alone. The loss time is consistent with the observations from the early recovery phases of magnetic storms.

Theoretical and Experimental Investigation of the Translational Diffusion of Proteins in the Vicinity of Temperature-Induced Unfolding Transition.

PubMed

Molchanov, Stanislav; Faizullin, Dzhigangir A; Nesmelova, Irina V

2016-10-06

Translational diffusion is the most fundamental form of transport in chemical and biological systems. The diffusion coefficient is highly sensitive to changes in the size of the diffusing species; hence, it provides important information on the variety of macromolecular processes, such as self-assembly or folding-unfolding. Here, we investigate the behavior of the diffusion coefficient of a macromolecule in the vicinity of heat-induced transition from folded to unfolded state. We derive the equation that describes the diffusion coefficient of the macromolecule in the vicinity of the transition and use it to fit the experimental data from pulsed-field-gradient nuclear magnetic resonance (PFG NMR) experiments acquired for two globular proteins, lysozyme and RNase A, undergoing temperature-induced unfolding. A very good qualitative agreement between the theoretically derived diffusion coefficient and experimental data is observed.

Field Line Random Walk in Isotropic Magnetic Turbulence up to Infinite Kubo Number

NASA Astrophysics Data System (ADS)

Sonsrettee, W.; Wongpan, P.; Ruffolo, D. J.; Matthaeus, W. H.; Chuychai, P.; Rowlands, G.

2013-12-01

In astrophysical plasmas, the magnetic field line random walk (FLRW) plays a key role in the transport of energetic particles. In the present, we consider isotropic magnetic turbulence, which is a reasonable model for interstellar space. Theoretical conceptions of the FLRW have been strongly influenced by studies of the limit of weak fluctuations (or a strong mean field) (e.g, Isichenko 1991a, b). In this case, the behavior of FLRW can be characterized by the Kubo number R = (b/B0)(l_∥ /l_ \\bot ) , where l∥ and l_ \\bot are turbulence coherence scales parallel and perpendicular to the mean field, respectively, and b is the root mean squared fluctuation field. In the 2D limit (R ≫ 1), there has been an apparent conflict between concepts of Bohm diffusion, which is based on the Corrsin's independence hypothesis, and percolative diffusion. Here we have used three non-perturbative analytic techniques based on Corrsin's independence hypothesis for B0 = 0 (R = ∞ ): diffusive decorrelation (DD), random ballistic decorrelation (RBD) and a general ordinary differential equation (ODE), and compared them with direct computer simulations. All the analytical models and computer simulations agree that isotropic turbulence for R = ∞ has a field line diffusion coefficient that is consistent with Bohm diffusion. Partially supported by the Thailand Research Fund, NASA, and NSF.

Single-shot spiral imaging enabled by an expanded encoding model: Demonstration in diffusion MRI.

PubMed

Wilm, Bertram J; Barmet, Christoph; Gross, Simon; Kasper, Lars; Vannesjo, S Johanna; Haeberlin, Max; Dietrich, Benjamin E; Brunner, David O; Schmid, Thomas; Pruessmann, Klaas P

2017-01-01

The purpose of this work was to improve the quality of single-shot spiral MRI and demonstrate its application for diffusion-weighted imaging. Image formation is based on an expanded encoding model that accounts for dynamic magnetic fields up to third order in space, nonuniform static B 0 , and coil sensitivity encoding. The encoding model is determined by B 0 mapping, sensitivity mapping, and concurrent field monitoring. Reconstruction is performed by iterative inversion of the expanded signal equations. Diffusion-tensor imaging with single-shot spiral readouts is performed in a phantom and in vivo, using a clinical 3T instrument. Image quality is assessed in terms of artefact levels, image congruence, and the influence of the different encoding factors. Using the full encoding model, diffusion-weighted single-shot spiral imaging of high quality is accomplished both in vitro and in vivo. Accounting for actual field dynamics, including higher orders, is found to be critical to suppress blurring, aliasing, and distortion. Enhanced image congruence permitted data fusion and diffusion tensor analysis without coregistration. Use of an expanded signal model largely overcomes the traditional vulnerability of spiral imaging with long readouts. It renders single-shot spirals competitive with echo-planar readouts and thus deploys shorter echo times and superior readout efficiency for diffusion imaging and further prospective applications. Magn Reson Med 77:83-91, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

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

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

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

2017-09-20

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

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

New Quantum Diffusion Monte Carlo Method for strong field time dependent problems

NASA Astrophysics Data System (ADS)

Kalinski, Matt

2017-04-01

We have recently formulated the Quantum Diffusion Quantum Monte Carlo (QDMC) method for the solution of the time-dependent Schrödinger equation when it is equivalent to the reaction-diffusion system coupled by the highly nonlinear potentials of the type of Shay. Here we formulate a new Time Dependent QDMC method free of the nonlinearities described by the constant stochastic process of the coupled diffusion with transmutation. As before two kinds of diffusing particles (color walkers) are considered but which can further also transmute one into the other. Each of the species undergoes the hypothetical Einstein random walk progression with transmutation. The progressed particles transmute into the particles of the other kind before contributing to or annihilating the other particles density. This fully emulates the Time Dependent Schrödinger equation for any number of quantum particles. The negative sign of the real and the imaginary parts of the wave function is handled by the ``spinor'' densities carrying the sign as the degree of freedom. We apply the method for the exact time-dependent observation of our discovered two-electron Langmuir configurations in the magnetic and circularly polarized fields.

Etude de la physico-chime d'un magnetoplasma de chlore pour la gravure sous-micrometrique

NASA Astrophysics Data System (ADS)

Pauna, Olivier Daniel

The aim of this thesis is to achieve a better understanding of physical and chemical phenomena occurring in a high-density plasma designed for sub-micron etching of thin films. The plasma is produced in chlorine by means of an electromagnetic surface wave and it can be confined by a uniform static magnetic field. The flexibility offered by the reactor in terms of operating conditions makes possible a parametric study of the influence of the magnetic confinement on the plasma characteristics. Thus, we have examined the plasma properties by means of several diagnostics techniques, including electrostatic probes, laser photodetachment of negative ions, ion acoustic wave propagation and optical emission spectroscopy. First, we investigated the influence of the operating conditions on the spatial properties of the plasma; this includes electric characteristics (electrons, positive and negative ions) as well as chemical characteristics (reactive neutrals). Second, we studied the impact of the reactor aspect ratio (i.e. reactor length/radius ratio) on both electrical and chemical characteristics. Together with these experimental studies, we have developed a bidimensional fluid model, by solving self-consistently the first two moments of Bolzmann equation and Poisson's equation. Using a semi-implicit scheme, it was possible to maintain a short computation time and to use this model to investigate a diffusion plasma in an electropositive gas. We were thus able to estimate the value of the diffusion coefficient in the direction perpendicular to the magnetic field. The results thus obtained are in good qualitative agreement with the diffusion coefficient proposed by Liebermann and Lichtenberg.

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.

Magnetic Damping of g-Jitter Induced Double-Diffusive Convection

NASA Technical Reports Server (NTRS)

Shu, Y.; Li, B. Q.; deGroh, H. C.

2001-01-01

This paper describes a numerical study of the g-jitter driven double diffusive convective flows, thermal and concentration distributions in binary alloy melt systems subject to an external magnetic field. The study is based on the finite element solution of transient magnetohydrodynamic equations governing the momentum, thermal and solutal transport in the melt pool. Numerical simulations are conducted using the synthesized single- and multi- frequency g-jitter as well as the real g-jitter data taken during space flights with or without an applied magnetic field. It is found that for the conditions studied, the main melt flow follows approximately a lineal- superposition of velocity components induced by individual g-jitter components, regardless of whether a magnetic field exists or not. The flow field is characterized by a recirculating double diffusive convection loop oscillating in time with a defined frequency equal to that of the driving g-jitter force. An applied magnetic field has little effect on the oscillating recirculating pattern, except around the moment in time when the flow reverses its direction. The field has no effect on the oscillation period, but it changes the phase angle. It is very effective in suppressing the flow intensity and produces a notable reduction of the solutal striation and time fluctuations in the melt. For a given magnetic field strength, the magnetic damping effect is more pronounced on the velocity associated with the largest g-jitter component present and/or the g-jitter spiking peaks. A stronger magnetic field is more effective in suppressing the melt convection and also is more helpful in bringing the convection in phase with the g-jitter driving force. The applied field is particularly useful in suppressing the effect of real g-jitter spikes on both flow and solutal distributions. With appropriately selected magnetic fields, the convective flows caused by g-jitter can be reduced sufficiently and diffusion dominant. solutal transport in the melt is possible.

Chaotic Motion of Relativistic Electrons Driven by Whistler Waves

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Telnikhin, A. A.; Kronberg, Tatiana K.

2007-01-01

Canonical equations governing an electron motion in electromagnetic field of the whistler mode waves propagating along the direction of an ambient magnetic field are derived. The physical processes on which the equations of motion are based .are identified. It is shown that relativistic electrons interacting with these fields demonstrate chaotic motion, which is accompanied by the particle stochastic heating and significant pitch angle diffusion. Evolution of distribution functions is described by the Fokker-Planck-Kolmogorov equations. It is shown that the whistler mode waves could provide a viable mechanism for stochastic energization of electrons with energies up to 50 MeV in the Jovian magnetosphere.

Microscopic Lagrangian description of warm plasmas. III - Nonlinear wave-particle interaction

NASA Technical Reports Server (NTRS)

Galloway, J. J.; Crawford, F. W.

1977-01-01

The averaged-Lagrangian method is applied to nonlinear wave-particle interactions in an infinite, homogeneous, magnetic-field-free plasma. The specific example of Langmuir waves is considered, and the combined effects of four-wave interactions and wave-particle interactions are treated. It is demonstrated how the latter lead to diffusion in velocity space, and the quasilinear diffusion equation is derived. The analysis is generalized to the random phase approximation. The paper concludes with a summary of the method as applied in Parts 1-3 of the paper.

Accelerated ions and self-excited Alfvén waves at the Earth's bow shock

NASA Astrophysics Data System (ADS)

Berezhko, E. G.; Taneev, S. N.; Trattner, K. J.

2011-07-01

The diffuse energetic ion event and related Alfvén waves upstream of the Earth's bow shock, measured by AMPTE/IRM satellite on 29 September 1984, 06:42-07:22 UT, was studied using a self-consistent quasi-linear theory of ion diffusive shock acceleration and associated Alfvén wave generation. The wave energy density satisfies a wave kinetic equation, and the ion distribution function satisfies the diffusive transport equation. These coupled equations are solved numerically, and calculated ion and wave spectra are compared with observations. It is shown that calculated steady state ion and Alfvén wave spectra are established during the time period of about 1000 s. Alfvén waves excited by accelerated ions are confined within the frequency range (10-2 to 1) Hz, and their spectral peak with the wave amplitude δB ≈ B comparable to the interplanetary magnetic field value B corresponds to the frequency 2 × 10-2 Hz. The high-frequency part of the wave spectrum undergoes absorption by thermal protons. It is shown that the observed ion spectra and the associated Alfvén wave spectra are consistent with the theoretical prediction.

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.

Luminosity and cooling of highly magnetized white dwarfs: suppression of luminosity by strong magnetic fields

NASA Astrophysics Data System (ADS)

Bhattacharya, Mukul; Mukhopadhyay, Banibrata; Mukerjee, Subroto

2018-06-01

We investigate the luminosity and cooling of highly magnetized white dwarfs with electron-degenerate cores and non-degenerate surface layers where cooling occurs by diffusion of photons. We find the temperature and density profiles in the surface layers or envelope of white dwarfs by solving the magnetostatic equilibrium and photon diffusion equations in a Newtonian framework. We also obtain the properties of white dwarfs at the core-envelope interface, when the core is assumed to be practically isothermal. With the increase in magnetic field, the interface temperature increases whereas the interface radius decreases. For a given age of the white dwarf and for fixed interface radius or interface temperature, we find that the luminosity decreases significantly from about 10-6 to 10-9 L⊙ as the magnetic field strength increases from about 109 to 1012 G at the interface and hence the envelope. This is remarkable because it argues that magnetized white dwarfs are fainter and can be practically hidden in an observed Hertzsprung-Russell diagram. We also find the cooling rates corresponding to these luminosities. Interestingly, the decrease in temperature with time, for the fields under consideration, is not found to be appreciable.

Dissipative particle dynamics of diffusion-NMR requires high Schmidt-numbers

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

Azhar, Mueed; Greiner, Andreas; Korvink, Jan G., E-mail: jan.korvink@kit.edu, E-mail: david.kauzlaric@imtek.uni-freiburg.de

We present an efficient mesoscale model to simulate the diffusion measurement with nuclear magnetic resonance (NMR). On the level of mesoscopic thermal motion of fluid particles, we couple the Bloch equations with dissipative particle dynamics (DPD). Thereby we establish a physically consistent scaling relation between the diffusion constant measured for DPD-particles and the diffusion constant of a real fluid. The latter is based on a splitting into a centre-of-mass contribution represented by DPD, and an internal contribution which is not resolved in the DPD-level of description. As a consequence, simulating the centre-of-mass contribution with DPD requires high Schmidt numbers. Aftermore » a verification for fundamental pulse sequences, we apply the NMR-DPD method to NMR diffusion measurements of anisotropic fluids, and of fluids restricted by walls of microfluidic channels. For the latter, the free diffusion and the localisation regime are considered.« less

CONTRIBUTIONS OF CHEMICAL AND DIFFUSIVE EXCHANGE TO T1ρ DISPERSION

PubMed Central

Cobb, Jared Guthrie; Xie, Jingping; Gore, John C.

2012-01-01

Variations in local magnetic susceptibility may induce magnetic field gradients that affect the signals acquired for MR imaging. Under appropriate diffusion conditions, such fields produce effects similar to slow chemical exchange. These effects may also be found in combination with other chemical exchange processes at multiple time scales. We investigate these effects with simulations and measurements to determine their contributions to rotating frame (R1ρ) relaxation in model systems. Simulations of diffusive and chemical exchange effects on R1ρ dispersion were performed using the Bloch equations. Additionally, R1ρ dispersion was measured in suspensions of Sephadex and latex beads with varying spin locking fields at 9.4T. A novel analysis method was used to iteratively fit for apparent chemical and diffusive exchange rates with a model by Chopra et al. Single- and double-inflection points in R1ρ dispersion profiles were observed, respectively, in simulations of slow diffusive exchange alone and when combined with rapid chemical exchange. These simulations were consistent with measurements of R1ρ in latex bead suspensions and small-diameter Sephadex beads that showed single- and double-inflection points, respectively. These observations, along with measurements following changes in temperature and pH, are consistent with the combined effects of slow diffusion and rapid −OH exchange processes. PMID:22791589

Traveling waves in Hall-magnetohydrodynamics and the ion-acoustic shock structure

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

Hagstrom, George I.; Hameiri, Eliezer

Hall-magnetohydrodynamics (HMHD) is a mixed hyperbolic-parabolic partial differential equation that describes the dynamics of an ideal two fluid plasma with massless electrons. We study the only shock wave family that exists in this system (the other discontinuities being contact discontinuities and not shocks). We study planar traveling wave solutions and we find solutions with discontinuities in the hydrodynamic variables, which arise due to the presence of real characteristics in Hall-MHD. We introduce a small viscosity into the equations and use the method of matched asymptotic expansions to show that solutions with a discontinuity satisfying the Rankine-Hugoniot conditions and also anmore » entropy condition have continuous shock structures. The lowest order inner equations reduce to the compressible Navier-Stokes equations, plus an equation which implies the constancy of the magnetic field inside the shock structure. We are able to show that the current is discontinuous across the shock, even as the magnetic field is continuous, and that the lowest order outer equations, which are the equations for traveling waves in inviscid Hall-MHD, are exactly integrable. We show that the inner and outer solutions match, which allows us to construct a family of uniformly valid continuous composite solutions that become discontinuous when the diffusivity vanishes.« less

Theoretical investigation of discharge parameters in magnetized radio frequency excited CO2 lasers

NASA Astrophysics Data System (ADS)

Tavassoli, H.; Sohbatzadeh, F.; Latifi, H.

2003-06-01

In the present paper the magnetic field effects on discharge parameters in rf excited CO2 lasers are calculated. A rf generated plasma imbedded in an external, constant, and homogeneous magnetic field is considered. The continuity equation is used to derive the electron density. Quasineutrality condition and ambipolar diffusion are used. Electron attachment coefficient is neglected. Local electric field, local electron density, and thickness of charge layers are derived as a function of distance from the electrodes and magnetic field. The thickness of charge layers in the presence of magnetic field is always smaller than one without the magnetic field. When the magnetic field increases, the electron density increases in all regions of discharge, and the electric field reduces in the charge layers but increases in the middle part of discharge.

Anisotropic Thermal Diffusion

NASA Astrophysics Data System (ADS)

Gardiner, Thomas

2013-10-01

Anisotropic thermal diffusion in magnetized plasmas is an important physical phenomena for a diverse set of physical conditions ranging from astrophysical plasmas to MFE and ICF. Yet numerically simulating this phenomenon accurately poses significant challenges when the computational mesh is misaligned with respect to the magnetic field. Particularly when the temperature gradients are unresolved, one frequently finds entropy violating solutions with heat flowing from cold to hot zones for χ∥ /χ⊥ >=102 which is substantially smaller than the range of interest which can reach 1010 or higher. In this talk we present a new implicit algorithm for solving the anisotropic thermal diffusion equations and demonstrate its characteristics on what has become a fairly standard set of test problems in the literature. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. SAND2013-5687A.

Electromotive force and large-scale magnetic dynamo in a turbulent flow with a mean shear.

PubMed

Rogachevskii, Igor; Kleeorin, Nathan

2003-09-01

An effect of sheared large-scale motions on a mean electromotive force in a nonrotating turbulent flow of a conducting fluid is studied. It is demonstrated that in a homogeneous divergence-free turbulent flow the alpha effect does not exist, however a mean magnetic field can be generated even in a nonrotating turbulence with an imposed mean velocity shear due to a "shear-current" effect. A mean velocity shear results in an anisotropy of turbulent magnetic diffusion. A contribution to the electromotive force related to the symmetric parts of the gradient tensor of the mean magnetic field (the kappa effect) is found in nonrotating turbulent flows with a mean shear. The kappa effect and turbulent magnetic diffusion reduce the growth rate of the mean magnetic field. It is shown that a mean magnetic field can be generated when the exponent of the energy spectrum of the background turbulence (without the mean velocity shear) is less than 2. The shear-current effect was studied using two different methods: the tau approximation (the Orszag third-order closure procedure) and the stochastic calculus (the path integral representation of the solution of the induction equation, Feynman-Kac formula, and Cameron-Martin-Girsanov theorem). Astrophysical applications of the obtained results are discussed.

Spin-orbit torque in a thin film of the topological insulator Bi2Se3: Crossover from the ballistic to diffusive regime

NASA Astrophysics Data System (ADS)

Ren, Y. J.; Deng, W. Y.; Geng, H.; Shen, R.; Shao, L. B.; Sheng, L.; Xing, D. Y.

2017-12-01

The spin-orbit torque provides an efficient method for switching the direction of a magnetization by using an electric field. Owing to the spin-orbit coupling, when an electric field is applied, a nonequilibrium spin density is generated, which exerts a torque on the local magnetization. Here, we investigate the spin-orbit torque in a thin film of topological insulator \\text{Bi}2\\text{Se}3 based upon a Boltzmann equation, with proper boundary conditions, which is applicable from the ballistic regime to the diffusive regime. It is shown that due to the spin-momentum interlocking of the electron surface states, the magnitude of the field-like torque is simply in linear proportion to the longitudinal electrical current. For a fixed electric field, the spin-orbit torque is proportional to the sample length in the ballistic limit, and saturates to a constant in the diffusive limit. The dependence of the torque on the magnetization direction and exchange coupling strength is also studied. Our theory may offer useful guidance for experimental investigations of the spin-orbit torque in finite-size systems.

Mixed Convection Flow of Nanofluid in Presence of an Inclined Magnetic Field

PubMed Central

Noreen, Saima; Ahmed, Bashir; Hayat, Tasawar

2013-01-01

This research is concerned with the mixed convection peristaltic flow of nanofluid in an inclined asymmetric channel. The fluid is conducting in the presence of inclined magnetic field. The governing equations are modelled. Mathematical formulation is completed through long wavelength and low Reynolds number approach. Numerical solution to the nonlinear analysis is made by shooting technique. Attention is mainly focused to the effects of Brownian motion and thermophoretic diffusion of nanoparticle. Results for velocity, temperature, concentration, pumping and trapping are obtained and analyzed in detail. PMID:24086276

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

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

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

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

Modification of the parallel scattering mean free path of cosmic rays in the presence of adiabatic focusing

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

He, H.-Q.; Schlickeiser, R., E-mail: hqhe@mail.iggcas.ac.cn, E-mail: rsch@tp4.rub.de

The cosmic ray mean free path in a large-scale nonuniform guide magnetic field with superposed magnetostatic turbulence is calculated to clarify some conflicting results in the literature. A new, exact integro-differential equation for the cosmic-ray anisotropy is derived from the Fokker-Planck transport equation. A perturbation analysis of this integro-differential equation leads to an analytical expression for the cosmic ray anisotropy and the focused transport equation for the isotropic part of the cosmic ray distribution function. The derived parallel spatial diffusion coefficient and the associated cosmic ray mean free path include the effect of adiabatic focusing and reduce to the standardmore » forms in the limit of a uniform guide magnetic field. For the illustrative case of isotropic pitch angle scattering, the derived mean free path agrees with the earlier expressions of Beeck and Wibberenz, Bieber and Burger, Kota, and Litvinenko, but disagrees with the result of Shalchi. The disagreement with the expression of Shalchi is particularly strong in the limit of strong adiabatic focusing.« less

The behaviors of ferromagnetic nano-particles in and around blood vessels under applied magnetic fields

NASA Astrophysics Data System (ADS)

Nacev, A.; Beni, C.; Bruno, O.; Shapiro, B.

2011-03-01

In magnetic drug delivery, therapeutic magnetizable particles are typically injected into the blood stream and magnets are then used to concentrate them to disease locations. The behavior of such particles in-vivo is complex and is governed by blood convection, diffusion (in blood and in tissue), extravasation, and the applied magnetic fields. Using physical first-principles and a sophisticated vessel-membrane-tissue (VMT) numerical solver, we comprehensively analyze in detail the behavior of magnetic particles in blood vessels and surrounding tissue. For any blood vessel (of any size, depth, and blood velocity) and tissue properties, particle size and applied magnetic fields, we consider a Krogh tissue cylinder geometry and solve for the resulting spatial distribution of particles. We find that there are three prototypical behaviors (blood velocity dominated, magnetic force dominated, and boundary-layer formation) and that the type of behavior observed is uniquely determined by three non-dimensional numbers (the magnetic-Richardson number, mass Péclet number, and Renkin reduced diffusion coefficient). Plots and equations are provided to easily read out which behavior is found under which circumstances (Figs. 5-8). We compare our results to previously published in-vitro and in-vivo magnetic drug delivery experiments. Not only do we find excellent agreement between our predictions and prior experimental observations, but we are also able to qualitatively and quantitatively explain behavior that was previously not understood.

Anisotropic rotational diffusion studied by passage saturation transfer electron paramagnetic resonance

NASA Astrophysics Data System (ADS)

Robinson, Bruce H.; Dalton, Larry R.

1980-01-01

The stochastic Liouville equation for the spin density matrix is modified to consider the effects of Brownian anisotropic rotational diffusion upon electron paramagnetic resonance (EPR) and saturation transfer electron paramagnetic resonance (ST-EPR) spectra. Spectral shapes and the ST-EPR parameters L″/L, C'/C, and H″/H defined by Thomas, Dalton, and Hyde at X-band microwave frequencies [J. Chem. Phys. 65, 3006 (1976)] are examined and discussed in terms of the rotational times τ∥ and τ⊥ and in terms of other defined correlation times for systems characterized by magnetic tensors of axial symmetry and for systems characterized by nonaxially symmetric magnetic tensors. For nearly axially symmetric magnetic tensors, such as nitroxide spin labels studied employing 1-3 GHz microwaves, ST-EPR spectra for systems undergoing anisotropic rotational diffusion are virtually indistinguishable from spectra for systems characterized by isotropic diffusion. For nonaxially symmetric magnetic tensors, such as nitroxide spin labels studied employing 8-35 GHz microwaves, the high field region of the ST-EPR spectra, and hence the H″/H parameter, will be virtually indistinguishable from spectra, and parameter values, obtained for isotropic diffusion. On the other hand, the central spectral region at x-band microwave frequencies, and hence the C'/C parameter, is sensitive to the anisotropic diffusion model provided that a unique and static relationship exists between the magnetic and diffusion tensors. Random labeling or motion of the spin label relative to the biomolecule whose hydrodynamic properties are to be investigated will destroy spectral sensitivity to anisotropic motion. The sensitivity to anisotropic motion is enhanced in proceeding to 35 GHz with the increased sensitivity evident in the low field half of the EPR and ST-EPR spectra. The L″/L parameter is thus a meaningful indicator of anisotropic motion when compared with H″/H parameter analysis. However, consideration of spectral shapes suggests that the C'/C parameter definition is not meaningfully extended from 9.5 to 35 GHz. Alternative definitions of the L″/L and C'/C parameters are proposed for those microwave frequencies for which the electron Zeeman anisotropy is comparable to or greater than the electron-nitrogen nuclear hyperfine anisotropy.

Transport of solar electrons in the turbulent interplanetary magnetic field

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

Ablaßmayer, J.; Tautz, R. C., E-mail: robert.c.tautz@gmail.com; Dresing, N., E-mail: dresing@physik.uni-kiel.de

2016-01-15

The turbulent transport of solar energetic electrons in the interplanetary magnetic field is investigated by means of a test-particle Monte-Carlo simulation. The magnetic fields are modeled as a combination of the Parker field and a turbulent component. In combination with the direct calculation of diffusion coefficients via the mean-square displacements, this approach allows one to analyze the effect of the initial ballistic transport phase. In that sense, the model complements the main other approach in which a transport equation is solved. The major advancement is that, by recording the flux of particles arriving at virtual detectors, intensity and anisotropy-time profilesmore » can be obtained. Observational indications for a longitudinal asymmetry can thus be explained by tracing the diffusive spread of the particle distribution. The approach may be of future help for the systematic interpretation of observations for instance by the solar terrestrial relations observatory (STEREO) and advanced composition explorer (ACE) spacecrafts.« less

A theoretical study of the global F region for June solstice, solar maximum, and low magnetic activity

NASA Technical Reports Server (NTRS)

Sojka, J. J.; Schunk, R. W.

1985-01-01

A time-dependent, three-dimensional, multi-ion model of the ionospheric F region at 120-800 km altitude is presented. Account is taken of field-aligned diffusion, cross-field electrodynamic drifts in equatorial and high latitude regions, interhemispheric flow, thermospheric winds, polar wind escape, energy-dependent chemical reactions and neutral composition changes. Attention is also given to the effects of ion production by solar EUV radiation and auroral precipitation, thermal conduction, diffusion-thermal heat flow, local heating and cooling processes, offsets between the geomagnetic and geographic poles, and bending of field lines near the magnetic equator. The model incorporates all phenomena described by previous models and can be applied to tracing magnetic storm and substorm disturbances from high to low latitudes on a global scale. Sample results are provided for ionospheric features during a June solstice, the solar maximum and in a period of low geomagnetic activity. The model will eventually be used to study coupled ionosphere-thermosphere activity.

Effect of magnetic helicity upon rectilinear propagation of charged particles in random magnetic fields

NASA Technical Reports Server (NTRS)

Earl, James A.

1992-01-01

When charged particles spiral along a large constant magnetic field, their trajectories are scattered by any random field components that are superposed on the guiding field. If the random field configuration embodies helicity, the scattering is asymmetrical with respect to a plane perpendicular to the guiding field, for particles moving into the forward hemisphere are scattered at different rates from those moving into the backward hemisphere. This asymmetry gives rise to new terms in the transport equations that describe propagation of charged particles. Helicity has virtually no impact on qualitative features of the diffusive mode of propagation. However, characteristic velocities of the coherent modes that appear after a highly anisotropic injection exhibit an asymmetry related to helicity. Explicit formulas, which embody the effects of helicity, are given for the anisotropies, the coefficient diffusion, and the coherent velocities. Predictions derived from these expressions are in good agreement with Monte Carlo simulations of particle transport, but the simulations reveal certain phenomena whose explanation calls for further analytical work.

Stochastic flux freezing and magnetic dynamo.

PubMed

Eyink, Gregory L

2011-05-01

Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr(m)) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr(m)=1 and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered. © 2011 American Physical Society

Pitch Angle Scattering of Upgoing Electron Beams in Jupiter's Polar Regions by Whistler Mode Waves

NASA Astrophysics Data System (ADS)

Elliott, S. S.; Gurnett, D. A.; Kurth, W. S.; Clark, G.; Mauk, B. H.; Bolton, S. J.; Connerney, J. E. P.; Levin, S. M.

2018-02-01

The Juno spacecraft's Jupiter Energetic-particle Detector Instrument has observed field-aligned, unidirectional (upgoing) electron beams throughout most of Jupiter's entire polar cap region. The Waves instrument detected intense broadband whistler mode emissions occurring in the same region. In this paper, we investigate the pitch angle scattering of the upgoing electron beams due to interactions with the whistler mode waves. Profiles of intensity versus pitch angle for electron beams ranging from 2.53 to 7.22 Jovian radii show inconsistencies with the expected adiabatic invariant motion of the electrons. It is believed that the observed whistler mode waves perturb the electron motion and scatter them away from the magnetic field line. The diffusion equation has been solved by using diffusion coefficients which depend on the magnetic intensity of the whistler mode waves.

Thermodiffusion in concentrated ferrofluids: A review and current experimental and numerical results on non-magnetic thermodiffusion

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

Sprenger, Lisa, E-mail: Lisa.Sprenger@tu-dresden.de; Lange, Adrian; Odenbach, Stefan

2013-12-15

Ferrofluids are colloidal suspensions consisting of magnetic nanoparticles dispersed in a carrier liquid. Their thermodiffusive behaviour is rather strong compared to molecular binary mixtures, leading to a Soret coefficient (S{sub T}) of 0.16 K{sup −1}. Former experiments with dilute magnetic fluids have been done with thermogravitational columns or horizontal thermodiffusion cells by different research groups. Considering the horizontal thermodiffusion cell, a former analytical approach has been used to solve the phenomenological diffusion equation in one dimension assuming a constant concentration gradient over the cell's height. The current experimental work is based on the horizontal separation cell and emphasises the comparison ofmore » the concentration development in different concentrated magnetic fluids and at different temperature gradients. The ferrofluid investigated is the kerosene-based EMG905 (Ferrotec) to be compared with the APG513A (Ferrotec), both containing magnetite nanoparticles. The experiments prove that the separation process linearly depends on the temperature gradient and that a constant concentration gradient develops in the setup due to the separation. Analytical one dimensional and numerical three dimensional approaches to solve the diffusion equation are derived to be compared with the solution used so far for dilute fluids to see if formerly made assumptions also hold for higher concentrated fluids. Both, the analytical and numerical solutions, either in a phenomenological or a thermodynamic description, are able to reproduce the separation signal gained from the experiments. The Soret coefficient can then be determined to 0.184 K{sup −1} in the analytical case and 0.29 K{sup −1} in the numerical case. Former theoretical approaches for dilute magnetic fluids underestimate the strength of the separation in the case of a concentrated ferrofluid.« less

Nuclear magnetic resonance signal dynamics of liquids in the presence of distant dipolar fields, revisited

PubMed Central

Barros, Wilson; Gochberg, Daniel F.; Gore, John C.

2009-01-01

The description of the nuclear magnetic resonance magnetization dynamics in the presence of long-range dipolar interactions, which is based upon approximate solutions of Bloch–Torrey equations including the effect of a distant dipolar field, has been revisited. New experiments show that approximate analytic solutions have a broader regime of validity as well as dependencies on pulse-sequence parameters that seem to have been overlooked. In order to explain these experimental results, we developed a new method consisting of calculating the magnetization via an iterative formalism where both diffusion and distant dipolar field contributions are treated as integral operators incorporated into the Bloch–Torrey equations. The solution can be organized as a perturbative series, whereby access to higher order terms allows one to set better boundaries on validity regimes for analytic first-order approximations. Finally, the method legitimizes the use of simple analytic first-order approximations under less demanding experimental conditions, it predicts new pulse-sequence parameter dependencies for the range of validity, and clarifies weak points in previous calculations. PMID:19425789

Modeling Particle Acceleration and Transport at a 2-D CME-Driven Shock

NASA Astrophysics Data System (ADS)

Hu, Junxiang; Li, Gang; Ao, Xianzhi; Zank, Gary P.; Verkhoglyadova, Olga

2017-11-01

We extend our earlier Particle Acceleration and Transport in the Heliosphere (PATH) model to study particle acceleration and transport at a coronal mass ejection (CME)-driven shock. We model the propagation of a CME-driven shock in the ecliptic plane using the ZEUS-3D code from 20 solar radii to 2 AU. As in the previous PATH model, the initiation of the CME-driven shock is simplified and modeled as a disturbance at the inner boundary. Different from the earlier PATH model, the disturbance is now longitudinally dependent. Particles are accelerated at the 2-D shock via the diffusive shock acceleration mechanism. The acceleration depends on both the parallel and perpendicular diffusion coefficients κ|| and κ⊥ and is therefore shock-obliquity dependent. Following the procedure used in Li, Shalchi, et al. (k href="#jgra53857-bib-0045"/>), we obtain the particle injection energy, the maximum energy, and the accelerated particle spectra at the shock front. Once accelerated, particles diffuse and convect in the shock complex. The diffusion and convection of these particles are treated using a refined 2-D shell model in an approach similar to Zank et al. (k href="#jgra53857-bib-0089"/>). When particles escape from the shock, they propagate along and across the interplanetary magnetic field. The propagation is modeled using a focused transport equation with the addition of perpendicular diffusion. We solve the transport equation using a backward stochastic differential equation method where adiabatic cooling, focusing, pitch angle scattering, and cross-field diffusion effects are all included. Time intensity profiles and instantaneous particle spectra as well as particle pitch angle distributions are shown for two example CME shocks.

Mirror instability near the threshold: Hybrid simulations

NASA Astrophysics Data System (ADS)

Hellinger, P.; Trávníček, P.; Passot, T.; Sulem, P.; Kuznetsov, E. A.; Califano, F.

2007-12-01

Nonlinear behavior of the mirror instability near the threshold is investigated using 1-D hybrid simulations. The simulations demonstrate the presence of an early phase where quasi-linear effects dominate [ Shapiro and Shevchenko, 1964]. The quasi-linear diffusion is however not the main saturation mechanism. A second phase is observed where the mirror mode is linearly stable (the stability is evaluated using the instantaneous ion distribution function) but where the instability nevertheless continues to develop, leading to nonlinear coherent structures in the form of magnetic humps. This regime is well modeled by a nonlinear equation for the magnetic field evolution, derived from a reductive perturbative expansion of the Vlasov-Maxwell equations [ Kuznetsov et al., 2007] with a phenomenological term which represents local variations of the ion Larmor radius. In contrast with previous models where saturation is due to the cooling of a population of trapped particles, the resulting equation correctly reproduces the development of magnetic humps from an initial noise. References Kuznetsov, E., T. Passot and P. L. Sulem (2007), Dynamical model for nonlinear mirror modes near threshold, Phys. Rev. Lett., 98, 235003. Shapiro, V. D., and V. I. Shevchenko (1964), Sov. JETP, 18, 1109.

A hybrid numerical fluid dynamics code for resistive magnetohydrodynamics

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

Johnson, Jeffrey

2006-04-01

Spasmos is a computational fluid dynamics code that uses two numerical methods to solve the equations of resistive magnetohydrodynamic (MHD) flows in compressible, inviscid, conducting media[1]. The code is implemented as a set of libraries for the Python programming language[2]. It represents conducting and non-conducting gases and materials with uncomplicated (analytic) equations of state. It supports calculations in 1D, 2D, and 3D geometry, though only the 1D configuation has received significant testing to date. Because it uses the Python interpreter as a front end, users can easily write test programs to model systems with a variety of different numerical andmore » physical parameters. Currently, the code includes 1D test programs for hydrodynamics (linear acoustic waves, the Sod weak shock[3], the Noh strong shock[4], the Sedov explosion[5], magnetic diffusion (decay of a magnetic pulse[6], a driven oscillatory "wine-cellar" problem[7], magnetic equilibrium), and magnetohydrodynamics (an advected magnetic pulse[8], linear MHD waves, a magnetized shock tube[9]). Spasmos current runs only in a serial configuration. In the future, it will use MPI for parallel computation.« less

Analytic treatment of nuclear spin-lattice relaxation for diffusion in a cone model

NASA Astrophysics Data System (ADS)

Sitnitsky, A. E.

2011-12-01

We consider nuclear spin-lattice relaxation rate resulted from a diffusion equation for rotational wobbling in a cone. We show that the widespread point of view that there are no analytical expressions for correlation functions for wobbling in a cone model is invalid and prove that nuclear spin-lattice relaxation in this model is exactly tractable and amenable to full analytical description. The mechanism of relaxation is assumed to be due to dipole-dipole interaction of nuclear spins and is treated within the framework of the standard Bloemberger, Purcell, Pound-Solomon scheme. We consider the general case of arbitrary orientation of the cone axis relative the magnetic field. The BPP-Solomon scheme is shown to remain valid for systems with the distribution of the cone axes depending only on the tilt relative the magnetic field but otherwise being isotropic. We consider the case of random isotropic orientation of cone axes relative the magnetic field taking place in powders. Also we consider the cases of their predominant orientation along or opposite the magnetic field and that of their predominant orientation transverse to the magnetic field which may be relevant for, e.g., liquid crystals. Besides we treat in details the model case of the cone axis directed along the magnetic field. The latter provides direct comparison of the limiting case of our formulas with the textbook formulas for free isotropic rotational diffusion. The dependence of the spin-lattice relaxation rate on the cone half-width yields results similar to those predicted by the model-free approach.

A practical approach to calculate the time evolutions of magnetic field effects on photochemical reactions in nano-structured materials.

PubMed

Yago, Tomoaki; Wakasa, Masanobu

2015-04-21

A practical method to calculate time evolutions of magnetic field effects (MFEs) on photochemical reactions involving radical pairs is developed on the basis of the theory of the chemically induced dynamic spin polarization proposed by Pedersen and Freed. In theory, the stochastic Liouville equation (SLE), including the spin Hamiltonian, diffusion motions of the radical pair, chemical reactions, and spin relaxations, is solved by using the Laplace and the inverse Laplace transformation technique. In our practical approach, time evolutions of the MFEs are successfully calculated by applying the Miller-Guy method instead of the final value theorem to the inverse Laplace transformation process. Especially, the SLE calculations are completed in a short time when the radical pair dynamics can be described by the chemical kinetics consisting of diffusions, reactions and spin relaxations. The SLE analysis with a short calculation time enables one to examine the various parameter sets for fitting the experimental date. Our study demonstrates that simultaneous fitting of the time evolution of the MFE and of the magnetic field dependence of the MFE provides valuable information on the diffusion motions of the radical pairs in nano-structured materials such as micelles where the lifetimes of radical pairs are longer than hundreds of nano-seconds and the magnetic field dependence of the spin relaxations play a major role for the generation of the MFE.

New technique for excitation of bulk and surface spin waves in ferromagnets

NASA Astrophysics Data System (ADS)

Bogacz, S. A.; Ketterson, J. B.

1985-09-01

A meander-line magnetic transducer is discussed in the context of bulk and surface spin-wave generation in ferromagnets. The magnetic field created by the transducer was calculated in closed analytic form for this model. The linear response of the ferromagnet to the inhomogenous surface disturbance of arbitrary ω and k was obtained as a self-consistent solution to the Bloch equation of motion and the Maxwell equations, subject to appropriate boundary condition. In particular, the energy flux through the boundary displays a sharp resonantlike absorption maximum concentrated at the frequency of the magnetostatic Damon-Eshbach (DE) surface mode; furthermore, the energy transfer spectrum is cut off abruptly below the threshold frequency of the bulk spin waves. The application of the meander line to the spin diffusion problem in NMR is also discussed.

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.

A three-dimensional spin-diffusion model for micromagnetics

PubMed Central

Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Hrkac, Gino; Praetorius, Dirk; Suess, Dieter

2015-01-01

We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation. PMID:26442796

The Behaviors of Ferro-Magnetic Nano-Particles In and Around Blood Vessels under Applied Magnetic Fields

PubMed Central

Nacev, A.; Beni, C.; Bruno, O.; Shapiro, B.

2010-01-01

In magnetic drug delivery, therapeutic magnetizable particles are typically injected into the blood stream and magnets are then used to concentrate them to disease locations. The behavior of such particles in-vivo is complex and is governed by blood convection, diffusion (in blood and in tissue), extravasation, and the applied magnetic fields. Using physical first-principles and a sophisticated vessel-membrane-tissue (VMT) numerical solver, we comprehensively analyze in detail the behavior of magnetic particles in blood vessels and surrounding tissue. For any blood vessel (of any size, depth, and blood velocity) and tissue properties, particle size and applied magnetic fields, we consider a Krogh tissue cylinder geometry and solve for the resulting spatial distribution of particles. We find that there are three prototypical behaviors (blood velocity dominated, magnetic force dominated, and boundary-layer formation) and that the type of behavior observed is uniquely determined by three non-dimensional numbers (the magnetic-Richardson number, mass Péclet number, and Renkin reduced diffusion coefficient). Plots and equations are provided to easily read out which behavior is found under which circumstances (Figures 5, 6, 7, and 8). We compare our results to previously published in-vitro and in-vivo magnetic drug delivery experiments. Not only do we find excellent agreement between our predictions and prior experimental observations, but we are also able to qualitatively and quantitatively explain behavior that was previously not understood. PMID:21278859

Contributions of chemical and diffusive exchange to T1ρ dispersion.

PubMed

Cobb, Jared Guthrie; Xie, Jingping; Gore, John C

2013-05-01

Variations in local magnetic susceptibility may induce magnetic field gradients that affect the signals acquired for MR imaging. Under appropriate diffusion conditions, such fields produce effects similar to slow chemical exchange. These effects may also be found in combination with other chemical exchange processes at multiple time scales. We investigate these effects with simulations and measurements to determine their contributions to rotating frame (R1ρ ) relaxation in model systems. Simulations of diffusive and chemical exchange effects on R1ρ dispersion were performed using the Bloch equations. Additionally, R1ρ dispersion was measured in suspensions of Sephadex and latex beads with varying spin locking fields at 9.4 T. A novel analysis method was used to iteratively fit for apparent chemical and diffusive exchange rates with a model by Chopra et al. Single- and double-inflection points in R1ρ dispersion profiles were observed, respectively, in simulations of slow diffusive exchange alone and when combined with rapid chemical exchange. These simulations were consistent with measurements of R1ρ in latex bead suspensions and small-diameter Sephadex beads that showed single- and double-inflection points, respectively. These observations, along with measurements following changes in temperature and pH, are consistent with the combined effects of slow diffusion and rapid -OH exchange processes. Copyright © 2012 Wiley Periodicals, Inc.

Energy absorption by a magnetic nanoparticle suspension in a rotating field

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

Raikher, Yu. L.; Stepanov, V. I., E-mail: stepanov@icmm.ru

Heat generation by viscous dissipation in a dilute suspension of single-domain ferromagnetic particles in a rotating magnetic field is analyzed by assuming that the suspended particles have a high magnetic rigidity. The problem is solved by using a kinetic approach based on a rotational diffusion equation. Behavior of specific loss power (SLP) as a function of field strength H and frequency {omega} is examined at constant temperature. SLP increases as either of these parameters squared when the other is constant, eventually approaching a saturation value. The function SLP(H, {omega}) can be used to determine optimal and admissible ranges of magneticallymore » induced heating.« less

Anomalous transport in turbulent plasmas and continuous time random walks

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

Balescu, R.

1995-05-01

The possibility of a model of anomalous transport problems in a turbulent plasma by a purely stochastic process is investigated. The theory of continuous time random walks (CTRW`s) is briefly reviewed. It is shown that a particular class, called the standard long tail CTRW`s is of special interest for the description of subdiffusive transport. Its evolution is described by a non-Markovian diffusion equation that is constructed in such a way as to yield exact values for all the moments of the density profile. The concept of a CTRW model is compared to an exact solution of a simple test problem:more » transport of charged particles in a fluctuating magnetic field in the limit of infinite perpendicular correlation length. Although the well-known behavior of the mean square displacement proportional to {ital t}{sup 1/2} is easily recovered, the exact density profile cannot be modeled by a CTRW. However, the quasilinear approximation of the kinetic equation has the form of a non-Markovian diffusion equation and can thus be generated by a CTRW.« less

An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation

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

Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.

2014-09-01

We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while themore » second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X ⊥ /X ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L 2 ∥/X1L 2 ⊥ → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.« less

B2.5-Eirene modeling of radial transport in the MAGPIE linear plasma device

NASA Astrophysics Data System (ADS)

Owen, L. W.; Caneses, J. F.; Canik, J.; Lore, J. D.; Corr, C.; Blackwell, B.; Bonnin, X.; Rapp, J.

2017-05-01

Radial transport in helicon heated hydrogen plasmas in the MAGnetized Plasma Interaction Experiment (MAGPIE) is studied with the B2.5-Eirene (SOLPS5.0) code. Radial distributions of plasma density, temperature and ambipolar potential are computed for several magnetic field configurations and compared to double Langmuir probe measurements. Evidence for an unmagnetized ion population is seen in the requirement for a convective pinch term in the continuity equation in order to fit the centrally peaked density profile data. The measured slightly hollow electron temperature profiles are reproduced with combinations of on-axis and edge heating which can be interpreted as helicon and Trivelpiece-Gould wave absorption, respectively. Pressure gradient driven radial charged particle diffusion is chosen to describe the diffusive particle flux since the hollowness of the temperature profiles assists the establishment of on-axis density peaking.

Magnetic conjugate observation of the F3 layer using the SEALION ionosonde network

NASA Astrophysics Data System (ADS)

Uemoto, Jyunpei; Ono, Takayuki; Maruyama, Takashi; Saito, Susumu; Iizima, Masahide; Kumamoto, Atsushi

2007-01-01

Results from the meridional ionosonde network located in Southeast Asia (SEALION) demonstrate the interesting nature of the F 3 layer, showing its generation mechanism. Ionograms obtained on 16 November 2004 and 31 March 2005 at Chiang Mai (CMU; geographic latitude 18.8°N, geographic longitude 98.9°E, and magnetic latitude 13.2°N), Chumphon (CPN; 10.7°N, 99.4°E, and 3.2°N) and Kototabang (KTB; 0.2°S, 100.3°E, and 10.1°S) showed significant differences between CPN near the magnetic equator, and CMU and KTB in the magnetic low-latitude region. The simultaneous magnetic conjugate observations of the F 3 layer achieved using the SEALION ionosonde network data showed clear dependences of the F 3 layer on the magnetic latitude. It is suggested that these magnetic latitude dependences of the F 3 layer can be explained by considering the plasma diffusion effects along the magnetic field lines in the magnetic low-latitude region.

Mixed convection of magnetohydrodynamic nanofluids inside microtubes at constant wall temperature

NASA Astrophysics Data System (ADS)

Moshizi, S. A.; Zamani, M.; Hosseini, S. J.; Malvandi, A.

2017-05-01

Laminar fully developed mixed convection of magnetohydrodynamic nanofluids inside microtubes at a constant wall temperature (CWT) under the effects of a variable directional magnetic field is investigated numerically. Nanoparticles are assumed to have slip velocities relative to the base fluid owing to thermophoretic diffusion (temperature gradient driven force) and Brownian diffusion (concentration gradient driven force). The no-slip boundary condition is avoided at the fluid-solid mixture to assess the non-equilibrium region at the fluid-solid interface. A scale analysis is performed to estimate the relative significance of the pertaining parameters that should be included in the governing equations. After the effects of pertinent parameters on the pressure loss and heat transfer enhancement were considered, the figure of merit (FoM) is employed to evaluate and optimize the thermal performance of heat exchange equipment. The results indicate the optimum thermal performance is obtained when the thermophoresis overwhelms the Brownian diffusion, which is for larger nanoparticles. This enhancement boosts when the buoyancy force increases. In addition, increasing the magnetic field strength and slippage at the fluid-solid interface enhances the thermal performance.

Magnetic pumping of the solar wind

NASA Astrophysics Data System (ADS)

Egedal, Jan; Lichko, Emily; Daughton, William

2015-11-01

The transport of matter and radiation in the solar wind and terrestrial magnetosphere is a complicated problem involving competing processes of charged particles interacting with electric and magnetic fields. Given the rapid expansion of the solar wind, it would be expected that superthermal electrons originating in the corona would cool rapidly as a function of distance to the Sun. However, this is not observed, and various models have been proposed as candidates for heating the solar wind. In the compressional pumping mechanism explored by Fisk and Gloeckler particles are accelerated by random compressions by the interplanetary wave turbulence. This theory explores diffusion due to spatial non-uniformities and provides a mechanism for redistributing particle. For investigation of a related but different heating mechanism, magnetic pumping, in our work we include diffusion of anisotropic features that develops in velocity space. The mechanism allows energy to be transferred to the particles directly from the turbulence. Guided by kinetic simulations a theory is derived for magnetic pumping. At the heart of this work is a generalization of the Parker Equation to capture the role of the pressure anisotropy during the pumping process. Supported by NASA grant NNX15AJ73G.

Modulated wave formation in myocardial cells under electromagnetic radiation

NASA Astrophysics Data System (ADS)

Takembo, Clovis N.; Mvogo, A.; Ekobena Fouda, H. P.; Kofané, T. C.

2018-06-01

We exclusively analyze the onset and condition of formation of modulated waves in a diffusive FitzHugh-Nagumo model for myocardial cell excitations. The cells are connected through gap junction coupling. An additive magnetic flux variable is used to describe the effect of electromagnetic induction, while electromagnetic radiation is imposed on the magnetic flux variable as a periodic forcing. We used the discrete multiple scale expansion and obtained, from the model equations, a single differential-difference amplitude nonlinear equation. We performed the linear stability analysis of this equation and found that instability features are importantly influenced by the induced electromagnetic gain. We present the unstable and stable regions of modulational instability (MI). The resulting analytic predictions are confirmed by numerical experiments of the generic equations. The results reveal that due to MI, an initial steady state that consisted of a plane wave with low amplitude evolves into a modulated localized wave patterns, soliton-like in shape, with features of synchronization. Furthermore, the formation of periodic pulse train with breathing motion presents a disappearing pattern in the presence of electromagnetic radiation. This could provide guidance and better understanding of sudden heart failure exposed to heavily electromagnetic radiation.

Neutral gas rotation in magnetron discharge

NASA Astrophysics Data System (ADS)

Pal, A. F.; Ryabinkin, A. N.; Serov, A. O.; Filippov, A. V.

2014-12-01

We have experimentally established the existence and determined the velocity of motion of the neutral component of plasma in a planar magnetron discharge, which takes place in the direction of drift of the charged plasma component in crossed electric and magnetic ( E × B) fields. For this purpose, we have studied the propagation of a small gaseous additive over the plasma ring of dc magnetron discharge in the diffusion regime. The obtained temporal dependences of the intensity of atomic emission spectra of the additive in various regions of the plasma ring are compared to the results of numerical solution of the diffusion equation for the experimental conditions studied.

Radial Diffusion study of the 1 June 2013 CME event using MHD simulations.

NASA Astrophysics Data System (ADS)

Patel, M.; Hudson, M.; Wiltberger, M. J.; Li, Z.; Boyd, A. J.

2016-12-01

The June 1, 2013 storm was a CME-shock driven geomagnetic storm (Dst = -119 nT) that caused a dropout affecting all radiation belt electron energies measured by the Energetic Particle, Composition and Thermal Plasma Suite (ECT) instrument on Van Allen Probes at higher L-shells following dynamic pressure enhancement in the solar wind. Lower energies (up to about 700 keV) were enhanced by the storm while MeV electrons were depleted throughout the belt. We focus on depletion through radial diffusion caused by the enhanced ULF wave activity due to the CME-shock. This study utilities the Lyon-Fedder-Mobarry (LFM) model, a 3D global magnetospheric simulation code based on the ideal MHD equations, coupled with the Magnetosphere Ionosphere Coupler (MIX) and Rice Convection Model (RCM). The MHD electric and magnetic fields with equations described by Fei et al. [JGR, 2006] are used to calculate radial diffusion coefficients (DLL). These DLL values are input into a radial diffusion code to recreate the dropouts observed by the Van Allen Probes. The importance of understanding the complex role that ULF waves play in radial transport and the effects of CME-driven storms on the relativistic energy electrons in the radiation belts can be accomplished using MHD simulations to obtain diffusion coefficients, initial phase space density and the outer boundary condition from the ECT instrument suite and a radial diffusion model to reproduce observed fluxes which compare favorably with Van Allen Probes ECT measurements.

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

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

Clark, S. E.; Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu

2017-05-20

The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg–Landau equation. We further find that the Ginzburg–Landau equation will arise for the local MRI system with shear-periodic boundary conditions,more » when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg–Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.« less

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 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.

Spin diffusion from an inhomogeneous quench in an integrable system.

PubMed

Ljubotina, Marko; Žnidarič, Marko; Prosen, Tomaž

2017-07-13

Generalized hydrodynamics predicts universal ballistic transport in integrable lattice systems when prepared in generic inhomogeneous initial states. However, the ballistic contribution to transport can vanish in systems with additional discrete symmetries. Here we perform large scale numerical simulations of spin dynamics in the anisotropic Heisenberg XXZ spin 1/2 chain starting from an inhomogeneous mixed initial state which is symmetric with respect to a combination of spin reversal and spatial reflection. In the isotropic and easy-axis regimes we find non-ballistic spin transport which we analyse in detail in terms of scaling exponents of the transported magnetization and scaling profiles of the spin density. While in the easy-axis regime we find accurate evidence of normal diffusion, the spin transport in the isotropic case is clearly super-diffusive, with the scaling exponent very close to 2/3, but with universal scaling dynamics which obeys the diffusion equation in nonlinearly scaled time.

Effects of pressure on the magnetic properties of FeO: A diffusion Monte Carlo study

NASA Astrophysics Data System (ADS)

Townsend, Joshua; Shulenburger, Luke; Mattsson, Thomas; Esler, Ken; Cohen, Ronald

While simple in terms of structure and composition, both experimental and computational investigations have demonstrated that FeO has a rich phase diagram of structural phase transformations, electronic spin transitions, insulator-metal transitions, and magnetic ordering transitions, due to the open-shell occupation of the Fe 3d electrons. We investigated the magnetic and electronic structures of FeO under ambient and high pressure conditions using diffusion Quantum Monte Carlo (QMC) within the fixed-node approximation. QMC techniques are especially well suited to the study of strongly correlated systems because they explicitly include correlation into the ground-state wave function. Here we report on the effects of the choice of trial wave function on the ambient pressure lattice distortion due to AFM ordering, as well as the equation of state, spin collapse, and metal-insulator transitions. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE.

Hot spot model of MagLIF implosions: Nernst term effect on magnetic flux losses

NASA Astrophysics Data System (ADS)

Garcia Rubio, Fernando; Sanz Recio, Javier; Betti, Riccardo

2016-10-01

An analytical model of a collisional plasma being compressed by a cylindrical liner is proposed and solved in a magnetized liner inertial fusion-like context. The implosion is assumed to be isobaric, and the magnetic diffusion is confined to a thin layer near the liner. Both unmagnetized and magnetized plasma cases are considered. The model reduces to a system of two partial differential equations for temperature and magnetic field. Special attention is given to the effect of the Nernst term on the evolution of the magnetic field. Scaling laws for temperature, magnetic field, hot spot mass increase and magnetic field losses are obtained. The temperature and magnetic field spatial profiles tend to a self-similar state. It is found that when the Nernst term is taken into account, the magnetic field is advected towards the liner, and the magnetic flux losses are independent of the magnetic Lewis number. Research supported by the Spanish Ministerio de Economía y Competitividad, Project No. ENE2014-54960R. Acknowledgements to the Laboratory of Laser Energetics (Rochester) for its hospitality.

EIGENMODES OF THREE-DIMENSIONAL MAGNETIC ARCADES IN THE SUN’S CORONA

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

Hindman, Bradley W.; Jain, Rekha, E-mail: hindman@solarz.colorado.edu

We develop a model of coronal-loop oscillations that treats the observed bright loops as an integral part of a larger three-dimensional (3D) magnetic structure comprised of the entire magnetic arcade. We demonstrate that magnetic arcades within the solar corona can trap MHD fast waves in a 3D waveguide. This is accomplished through the construction of a cylindrically symmetric model of a magnetic arcade with a potential magnetic field. For a magnetically dominated plasma, we derive a governing equation for MHD fast waves and from this equation we show that the magnetic arcade forms a 3D waveguide if the Alfvén speedmore » increases monotonically beyond a fiducial radius. Both magnetic pressure and tension act as restoring forces, instead of just tension as is generally assumed in 1D models. Since magnetic pressure plays an important role, the eigenmodes involve propagation both parallel and transverse to the magnetic field. Using an analytic solution, we derive the specific eigenfrequencies and eigenfunctions for an arcade possessing a discontinuous density profile. The discontinuity separates a diffuse cylindrical cavity and an overlying shell of denser plasma that corresponds to the bright loops. We emphasize that all of the eigenfunctions have a discontinuous axial velocity at the density interface; hence, the interface can give rise to the Kelvin–Helmholtz instability. Further, we find that all modes have elliptical polarization with the degree of polarization changing with height. However, depending on the line of sight, only one polarization may be clearly visible.« less

Stochastic layer scaling in the two-wire model for divertor tokamaks

NASA Astrophysics Data System (ADS)

Ali, Halima; Punjabi, Alkesh; Boozer, Allen

2009-06-01

The question of magnetic field structure in the vicinity of the separatrix in divertor tokamaks is studied. The authors have investigated this problem earlier in a series of papers, using various mathematical techniques. In the present paper, the two-wire model (TWM) [Reiman, A. 1996 Phys. Plasmas 3, 906] is considered. It is noted that, in the TWM, it is useful to consider an extra equation expressing magnetic flux conservation. This equation does not add any more information to the TWM, since the equation is derived from the TWM. This equation is useful for controlling the step size in the numerical integration of the TWM equations. The TWM with the extra equation is called the flux-preserving TWM. Nevertheless, the technique is apparently still plagued by numerical inaccuracies when the perturbation level is low, resulting in an incorrect scaling of the stochastic layer width. The stochastic broadening of the separatrix in the flux-preserving TWM is compared with that in the low mn (poloidal mode number m and toroidal mode number n) map (LMN) [Ali, H., Punjabi, A., Boozer, A. and Evans, T. 2004 Phys. Plasmas 11, 1908]. The flux-preserving TWM and LMN both give Boozer-Rechester 0.5 power scaling of the stochastic layer width with the amplitude of magnetic perturbation when the perturbation is sufficiently large [Boozer, A. and Rechester, A. 1978, Phys. Fluids 21, 682]. The flux-preserving TWM gives a larger stochastic layer width when the perturbation is low, while the LMN gives correct scaling in the low perturbation region. Area-preserving maps such as the LMN respect the Hamiltonian structure of field line trajectories, and have the added advantage of computational efficiency. Also, for a $1\\frac12$ degree of freedom Hamiltonian system such as field lines, maps do not give Arnold diffusion.

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.

Development of Numerical Tools for the Investigation of Plasma Detachment from Magnetic Nozzles

NASA Technical Reports Server (NTRS)

Sankaran, Kamesh; Polzin, Kurt A.

2007-01-01

A multidimensional numerical simulation framework aimed at investigating the process of plasma detachment from a magnetic nozzle is introduced. An existing numerical code based on a magnetohydrodynamic formulation of the plasma flow equations that accounts for various dispersive and dissipative processes in plasmas was significantly enhanced to allow for the modeling of axisymmetric domains containing three.dimensiunai momentum and magnetic flux vectors. A separate magnetostatic solver was used to simulate the applied magnetic field topologies found in various nozzle experiments. Numerical results from a magnetic diffusion test problem in which all three components of the magnetic field were present exhibit excellent quantitative agreement with the analytical solution, and the lack of numerical instabilities due to fluctuations in the value of del(raised dot)B indicate that the conservative MHD framework with dissipative effects is well-suited for multi-dimensional analysis of magnetic nozzles. Further studies will focus on modeling literature experiments both for the purpose of code validation and to extract physical insight regarding the mechanisms driving detachment.

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.

Effects of a parallel electric field and the geomagnetic field in the topside ionosphere on auroral and photoelectron energy distributions

NASA Technical Reports Server (NTRS)

Min, Q.-L.; Lummerzheim, D.; Rees, M. H.; Stamnes, K.

1993-01-01

The consequences of electric field acceleration and an inhomogeneous magnetic field on auroral electron energy distributions in the topside ionosphere are investigated. The one-dimensional, steady state electron transport equation includes elastic and inelastic collisions, an inhomogeneous magnetic field, and a field-aligned electric field. The case of a self-consistent polarization electric field is considered first. The self-consistent field is derived by solving the continuity equation for all ions of importance, including diffusion of O(+) and H(+), and the electron and ion energy equations to derive the electron and ion temperatures. The system of coupled electron transport, continuity, and energy equations is solved numerically. Recognizing observations of parallel electric fields of larger magnitude than the baseline case of the polarization field, the effect of two model fields on the electron distribution function is investigated. In one case the field is increased from the polarization field magnitude at 300 km to a maximum at the upper boundary of 800 km, and in another case a uniform field is added to the polarization field. Substantial perturbations of the low energy portion of the electron flux are produced: an upward directed electric field accelerates the downward directed flux of low-energy secondary electrons and decelerates the upward directed component. Above about 400 km the inhomogeneous magnetic field produces anisotropies in the angular distribution of the electron flux. The effects of the perturbed energy distributions on auroral spectral emission features are noted.

Effects of a Parallel Electric Field and the Geomagnetic Field in the Topside Ionosphere on Auroral and Photoelectron Energy Distributions

NASA Technical Reports Server (NTRS)

Min, Q.-L.; Lummerzheim, D.; Rees, M. H.; Stamnes, K.

1993-01-01

The consequences of electric field acceleration and an inhomogencous magnetic field on auroral electron energy distributions in the topside ionosphere are investigated. The one- dimensional, steady state electron transport equation includes elastic and inelastic collisions, an inhomogencous magnetic field, and a field-aligned electric field. The case of a self-consistent polarization electric field is considered first. The self-consistent field is derived by solving the continuity equation for all ions of importance, including diffusion of 0(+) and H(+), and the electron and ion energy equations to derive the electron and ion temperatures. The system of coupled electron transport, continuity, and energy equations is solved numerically. Recognizing observations of parallel electric fields of larger magnitude than the baseline case of the polarization field, the effect of two model fields on the electron distribution function in investigated. In one case the field is increased from the polarization field magnitude at 300 km to a maximum at the upper boundary of 800 km, and in another case a uniform field is added to the polarization field. Substantial perturbations of the low energy portion of the electron flux are produced: an upward directed electric field accelerates the downward directed flux of low-energy secondary electrons and decelerates the upward directed component. Above about 400 km the inhomogencous magnetic field produces anisotropies in the angular distribution of the electron flux. The effects of the perturbed energy distributions on auroral spectral emission features are noted.

Cosmic-ray streaming perpendicular to the mean magnetic field. II - The gyrophase distribution function

NASA Technical Reports Server (NTRS)

Forman, M. A.; Jokipii, J. R.

1978-01-01

The distribution function of cosmic rays streaming perpendicular to the mean magnetic field in a turbulent medium is reexamined. Urch's (1977) discovery that in quasi-linear theory, the flux is due to particles at 90 deg pitch angle is discussed and shown to be consistent with previous formulations of the theory. It is pointed out that this flux of particles at 90 deg cannot be arbitrarily set equal to zero, and hence the alternative theory which proceeds from this premise is dismissed. A further, basic inconsistency in Urch's transport equation is demonstrated, and the connection between quasi-linear theory and compound diffusion is discussed.

On the interpretation of continuous wave electron spin resonance spectra of tempo-palmitate in 5-cyanobiphenyl.

PubMed

Zerbetto, Mirco; Polimeno, Antonino; Cimino, Paola; Barone, Vincenzo

2008-01-14

Electron spin resonance (ESR) measurements are highly informative on the dynamic behavior of molecules, which is of fundamental importance to understand their stability, biological functions and activities, and catalytic action. The wealth of dynamic information which can be extracted from a continuous wave electron spin resonance (cw-ESR) spectrum can be inferred by a basic theoretical approach defined within the stochastic Liouville equation formalism, i.e., the direct inclusion of motional dynamics in the form of stochastic (Fokker-Planck/diffusive) operators in the super Hamiltonian H governing the time evolution of the system. Modeling requires the characterization of magnetic parameters (e.g., hyperfine and Zeeman tensors) and the calculation of ESR observables in terms of spectral densities. The magnetic observables can be pursued by the employment of density functional theory which is apt, provided that hybrid functionals are employed, for the accurate computation of structural properties of molecular systems. Recently, an ab initio integrated computational approach to the in silico interpretation of cw-ESR spectra of multilabeled systems in isotropic fluids has been discussed. In this work we present the extension to the case of nematic liquid crystalline environments by performing simulations of the ESR spectra of the prototypical nitroxide probe 4-(hexadecanoyloxy)-2,2,6,6-tetramethylpiperidine-1-oxy in isotropic and nematic phases of 5-cyanobiphenyl. We first discuss the basic ingredients of the integrated approach, i.e., (1) determination of geometric and local magnetic parameters by quantum-mechanical calculations, taking into account the solvent and, when needed, the vibrational averaging contributions; (2) numerical solution of a stochastic Liouville equation in the presence of diffusive rotational dynamics, based on (3) parameterization of diffusion rotational tensor provided by a hydrodynamic model. Next we present simulated spectra with minimal resorting to fitting procedures, proving that the combination of sensitive ESR spectroscopy and sophisticated modeling can be highly helpful in providing three-dimensional structural and dynamic information on molecular systems in anisotropic environments.

Kinematic dynamo, supersymmetry breaking, and chaos

NASA Astrophysics Data System (ADS)

Ovchinnikov, Igor V.; Enßlin, Torsten A.

2016-04-01

The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an important model system for understanding astrophysical magnetism. Here, the mathematical correspondence between the KD and a specific stochastic differential equation (SDE) viewed from the perspective of the supersymmetric theory of stochastics (STS) is discussed. The STS is a novel, approximation-free framework to investigate SDEs. The correspondence reported here permits insights from the STS to be applied to the theory of KD and vice versa. It was previously known that the fast KD in the idealistic limit of no magnetic diffusion requires chaotic flows. The KD-STS correspondence shows that this is also true for the diffusive KD. From the STS perspective, the KD possesses a topological supersymmetry, and the dynamo effect can be viewed as its spontaneous breakdown. This supersymmetry breaking can be regarded as the stochastic generalization of the concept of dynamical chaos. As this supersymmetry breaking happens in both the diffusive and the nondiffusive cases, the necessity of the underlying SDE being chaotic is given in either case. The observed exponentially growing and oscillating KD modes prove physically that dynamical spectra of the STS evolution operator that break the topological supersymmetry exist with both real and complex ground state eigenvalues. Finally, we comment on the nonexistence of dynamos for scalar quantities.

A generalized spin diffusion equation with four electrochemical potentials for channels with spin-orbit coupling

NASA Astrophysics Data System (ADS)

Sayed, Shehrin; Hong, Seokmin; Datta, Supriyo

We will present a general semiclassical theory for an arbitrary channel with spin-orbit coupling (SOC), that uses four electrochemical potential (U + , D + , U - , and D -) depending on the sign of z-component of the spin (up (U) , down (D)) and the sign of the x-component of the group velocity (+ , -) . This can be considered as an extension of the standard spin diffusion equation that uses two electrochemical potentials for up and down spin states, allowing us to take into account the unique coupling between charge and spin degrees of freedom in channels with SOC. We will describe applications of this model to answer a number of interesting questions in this field such as: (1) whether topological insulators can switch magnets, (2) how the charge to spin conversion is influenced by the channel resistivity, and (3) how device structures can be designed to enhance spin injection. This work was supported by FAME, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.

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.

Effect of CO2 absorption on ion and water mobility in an anion exchange membrane

NASA Astrophysics Data System (ADS)

Peng, Jing; Roy, Asa L.; Greenbaum, Steve G.; Zawodzinski, Thomas A.

2018-03-01

We report the measured water uptake, density, ionic conductivity and water transport properties in Tokuyama A201 membrane in OH-, HCO3- and Cl- forms. The water uptake of the AEM varies with anion type in the order λ(OH-) > λ(HCO3-) > λ(Cl-) for samples equilibrated with the same water vapor activity (aw). The conductivity of the AEM is reduced by absorption of CO2. Pulsed-field gradient nuclear magnetic resonance (PFG-NMR) measurements were utilized to characterize the diffusivity of water and HCO3- ion. The anion diffusion coefficient and membrane conductivity are used to probe the applicability of the Nernst-Einstein equation in these AEMs.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

PubMed

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

2017-02-01

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

Photon emission from melanoma cells during brief stimulation by patterned magnetic fields: is the source coupled to rotational diffusion within the membrane?

PubMed

Dotta, Blake T; Lafrenie, Robert M; Karbowski, Lukasz M; Persinger, Michael A

2014-01-01

If parameters for lateral diffusion of lipids within membranes are macroscopic metaphors of the angular magnetic moment of the Bohr magneton then the energy emission should be within the visible wavelength for applied ~1 µT magnetic fields. Single or paired digital photomultiplier tubes (PMTs) were placed near dishes of ~1 million B16 mouse melanoma cells that had been removed from incubation. In very dark conditions (10(-11) W/m(2)) different averaged (RMS) intensities between 5 nT and 3.5 µT were applied randomly in 4 min increments. Numbers of photons were recorded directly over or beside the cell dishes by PMTs placed in pairs within various planes. Spectral analyses were completed for photon power density. The peak photon emissions occurred around 1 µT as predicted by the equation. Spectra analyses showed reliable discrete peaks between 0.9 and 1.8 µT but not for lesser or greater intensities; these peak frequencies corresponded to the energy difference of the orbital-spin magnetic moment of the electron within the applied range of magnetic field intensities and the standard solution for Rydberg atoms. Numbers of photons from cooling cells can be modified by applying specific intensities of temporally patterned magnetic fields. There may be a type of "cellular" magnetic moment that, when stimulated by intensity-tuned magnetic fields, results in photon emissions whose peak frequencies reflect predicted energies for fundamental orbital/spin properties of the electron and atomic aggregates with large principal quantum numbers.

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

On turbulent diffusion of magnetic fields and the loss of magnetic flux from stars

NASA Technical Reports Server (NTRS)

Vainshtein, Samuel I.; Rosner, Robert

1991-01-01

The turbulent diffusion of magnetic fields in astrophysical objects, and the processes leading to magnetic field flux loss from such objects are discussed with attention to the suppression of turbulent diffusion by back-reaction of magnetic fields on small spatial scales, and on the constraint imposed on magnetic flux loss by flux-freezing within stars. Turbulent magnetic diffusion can be suppressed even for very weak large-scale magnetic fields, so that 'standard' turbulent diffusion is incapable of significant magnetic flux destruction within a star. Finally, magnetic flux loss via winds is shown to be generally ineffective, no matter what the value of the effective magnetic Reynolds number is.

Magnetic field of jupiter and its interaction with the solar wind.

PubMed

Smith, E J; Davis, L; Jones, D E; Colburn, D S; Coleman, P J; Dyal, P; Sonett, C P

1974-01-25

Jupiter's magnetic field and its interaction with the magnetized solar wind were observed with the Pioneer 10 vector helium magnetometer. The magnetic dipole is directed opposite to that of the earth with a moment of 4.0 gauss R(J)(3) (R(J), Jupiter radius), and an inclination of 15 degrees lying in a system III meridian of 230 degrees . The dipole is offset about 0.1 R(J) north of the equatorial plane and about 0.2 R(J) toward longitude 170 degrees . There is severe stretching of the planetary field parallel to the equator throughout the outer magnetosphere, accompanied by a systematic departure from meridian planes. The field configuration implies substantial plasma effects inside the magnetosphere, such as thermal pressure, centrifugal forces, and differential rotation. As at the earth, the outer boundary is thin, nor diffuse, and there is a detached bow shock.

A partial differential equation-based general framework adapted to Rayleigh's, Rician's and Gaussian's distributed noise for restoration and enhancement of magnetic resonance image.

PubMed

Yadav, Ram Bharos; Srivastava, Subodh; Srivastava, Rajeev

2016-01-01

The proposed framework is obtained by casting the noise removal problem into a variational framework. This framework automatically identifies the various types of noise present in the magnetic resonance image and filters them by choosing an appropriate filter. This filter includes two terms: the first term is a data likelihood term and the second term is a prior function. The first term is obtained by minimizing the negative log likelihood of the corresponding probability density functions: Gaussian or Rayleigh or Rician. Further, due to the ill-posedness of the likelihood term, a prior function is needed. This paper examines three partial differential equation based priors which include total variation based prior, anisotropic diffusion based prior, and a complex diffusion (CD) based prior. A regularization parameter is used to balance the trade-off between data fidelity term and prior. The finite difference scheme is used for discretization of the proposed method. The performance analysis and comparative study of the proposed method with other standard methods is presented for brain web dataset at varying noise levels in terms of peak signal-to-noise ratio, mean square error, structure similarity index map, and correlation parameter. From the simulation results, it is observed that the proposed framework with CD based prior is performing better in comparison to other priors in consideration.

Scalable explicit implementation of anisotropic diffusion with Runge-Kutta-Legendre super-time stepping

NASA Astrophysics Data System (ADS)

Vaidya, Bhargav; Prasad, Deovrat; Mignone, Andrea; Sharma, Prateek; Rickler, Luca

2017-12-01

An important ingredient in numerical modelling of high temperature magnetized astrophysical plasmas is the anisotropic transport of heat along magnetic field lines from higher to lower temperatures. Magnetohydrodynamics typically involves solving the hyperbolic set of conservation equations along with the induction equation. Incorporating anisotropic thermal conduction requires to also treat parabolic terms arising from the diffusion operator. An explicit treatment of parabolic terms will considerably reduce the simulation time step due to its dependence on the square of the grid resolution (Δx) for stability. Although an implicit scheme relaxes the constraint on stability, it is difficult to distribute efficiently on a parallel architecture. Treating parabolic terms with accelerated super-time-stepping (STS) methods has been discussed in literature, but these methods suffer from poor accuracy (first order in time) and also have difficult-to-choose tuneable stability parameters. In this work, we highlight a second-order (in time) Runge-Kutta-Legendre (RKL) scheme (first described by Meyer, Balsara & Aslam 2012) that is robust, fast and accurate in treating parabolic terms alongside the hyperbolic conversation laws. We demonstrate its superiority over the first-order STS schemes with standard tests and astrophysical applications. We also show that explicit conduction is particularly robust in handling saturated thermal conduction. Parallel scaling of explicit conduction using RKL scheme is demonstrated up to more than 104 processors.

A first principles kinetic Monte Carlo investigation of the adsorption and mobility of gadolinium on the (100) surface of tungsten

NASA Astrophysics Data System (ADS)

Samin, Adib J.; Zhang, Jinsuo

2017-05-01

An accurate characterization of lanthanide adsorption and mobility on tungsten surfaces is important for pyroprocessing. In the present study, the adsorption and diffusion of gadolinium on the (100) surface of tungsten was investigated. It was found that the hollow sites were the most energetically favorable for the adsorption. It was further observed that a magnetic moment was induced following the adsorption of gadolinium on the tungsten surface and that the system with adsorbed hollow sites had the largest magnetization. A pathway for the surface diffusion of gadolinium was determined to occur by hopping between the nearest neighbor hollow sites via the bridge site and the activation energy for the hop was calculated to be 0.75 eV. The surface diffusion process was further assessed using two distinct kinetic Monte Carlo models; one that accounted for lateral adsorbate interactions up to the second nearest neighbor and one that did not account for such interatomic interactions in the adlayer. When the lateral interactions were included in the simulations, the diffusivity was observed to have a strong dependence on coverage (for the coverage values being studied). The effects of lateral interactions were further observed in a one-dimensional simulation of the diffusion equation where the asymmetry in the surface coverage profile upon its approach to a steady state distribution was clear in comparison with the simulations which did not account for those interactions.

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.

Substorms: The Attempt at Magnetospheric Dynamic Equilibrium between Magnetically-Driven Frontside Reconnection and Particle-Driven Reconnection in a Multiple-Current-Sheet Magnetotail

NASA Astrophysics Data System (ADS)

Sofko, G. J.; Hussey, G. C.; McWilliams, K. A.; Reimer, A. S.

2016-12-01

We propose a multi-current-sheet model for magnetic substorms. Those storms are normally driven by frontside magnetically-driven reconnection (MDRx), in which the diffusion zone current JD and the electric field E have a "load" relationship JD*E >0, indicating transfer if magnetic energy to the particles in the "reconnection jets". As a result of lobe field line transport over the north and south poles, polar cap particles are subject to parallel energization as they flow upward out of the ionosphere. These particles convectively drift toward the equator and subsequently mirror near the Neutral Sheet (NSh) region, forming an extended westward NSh current sheet which is unstable and "tears up" into multiple current sheets. Each current sheet has very different behaviour at its ends: (a) strong magnetic pressure and weak particle pressure at its tailward end; (b) strong particle pressure and weak magnetic field at its earthward end. Therefore, in each Separation Zone (SZ) between current sheets, a strong eastward magnetic curl develops. The associated eastward SZ current, caused by diamagnetic electron drift, is squeezed by the repulsion of the westward currents tailward and earthward. That current becomes intense enough to act as a diffusion zone for "generator-type" or Particle-driven reconnection (PDRx) for which JD*E<0, indicating that the particles return energy to the magnetic field. The PDRx produces a Dipolarization Front (DF) on the earthward side of the SZ and a Plasmoid (PMD) on the tailward side. Such DF-PMD pairs form successively in time and radial downtail SZ distance. In this way, the magnetosphere attempts to achieve a dynamic equilibrium between magnetic and particle energy.

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

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.

Modeling bioluminescent photon transport in tissue based on Radiosity-diffusion model

NASA Astrophysics Data System (ADS)

Sun, Li; Wang, Pu; Tian, Jie; Zhang, Bo; Han, Dong; Yang, Xin

2010-03-01

Bioluminescence tomography (BLT) is one of the most important non-invasive optical molecular imaging modalities. The model for the bioluminescent photon propagation plays a significant role in the bioluminescence tomography study. Due to the high computational efficiency, diffusion approximation (DA) is generally applied in the bioluminescence tomography. But the diffusion equation is valid only in highly scattering and weakly absorbing regions and fails in non-scattering or low-scattering tissues, such as a cyst in the breast, the cerebrospinal fluid (CSF) layer of the brain and synovial fluid layer in the joints. A hybrid Radiosity-diffusion model is proposed for dealing with the non-scattering regions within diffusing domains in this paper. This hybrid method incorporates a priori information of the geometry of non-scattering regions, which can be acquired by magnetic resonance imaging (MRI) or x-ray computed tomography (CT). Then the model is implemented using a finite element method (FEM) to ensure the high computational efficiency. Finally, we demonstrate that the method is comparable with Mont Carlo (MC) method which is regarded as a 'gold standard' for photon transportation simulation.

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

Morales, George J.; Maggs, James E.

The project expanded and developed mathematical descriptions, and corresponding numerical modeling, of non-diffusive transport to incorporate new perspectives derived from basic transport experiments performed in the LAPD device at UCLA, and at fusion devices throughout the world. By non-diffusive it is meant that the transport of fundamental macroscopic parameters of a system, such as temperature and density, does not follow the standard diffusive behavior predicted by a classical Fokker-Planck equation. The appearance of non-diffusive behavior is often related to underlying microscopic processes that cause the value of a system parameter, at one spatial position, to be linked to distant events,more » i.e., non-locality. In the LAPD experiments the underlying process was traced to large amplitude, coherent drift-waves that give rise to chaotic trajectories. Significant advances were made in this project. The results have lead to a new perspective about the fundamentals of edge transport in magnetically confined plasmas; the insight has important consequences for worldwide studies in fusion devices. Progress was also made in advancing the mathematical techniques used to describe fractional diffusion.« less

Pickup protons and water ions at Comet Halley - Comparisons with Giotto observations

NASA Astrophysics Data System (ADS)

Ye, G.; Cravens, T. E.; Gombosi, T. I.

1993-02-01

The cometary ion pickup process along the sun-comet line at Comet Halley is investigated using a quasi-linear diffusion model including both pitch angle and energy diffusion, adiabatic compression, and convective motion with the solar wind flow. The model results are compared with energetic ion distributions observed by instruments on board the Giotto spacecraft. The observed power spectrum index of magnetic turbulence (gamma) is 2-2.5. The present simulation shows that when gamma was 2, the calculated proton distributions were much more isotropic than the observed ones. The numerical solutions of the quasi-linear diffusion equations show that the isotropization of the pickup ion distribution, particularly at the pickup velocity, is not complete even close to the bow shock. Given the observed turbulence level, quasi-linear theory yields pickup ion energy distributions that agree with the observed ones quite well and easily produces energetic ions with energies up to hundreds of keV.

Nuclear quadrupole resonance lineshape analysis for different motional models: Stochastic Liouville approach

NASA Astrophysics Data System (ADS)

Kruk, D.; Earle, K. A.; Mielczarek, A.; Kubica, A.; Milewska, A.; Moscicki, J.

2011-12-01

A general theory of lineshapes in nuclear quadrupole resonance (NQR), based on the stochastic Liouville equation, is presented. The description is valid for arbitrary motional conditions (particularly beyond the valid range of perturbation approaches) and interaction strengths. It can be applied to the computation of NQR spectra for any spin quantum number and for any applied magnetic field. The treatment presented here is an adaptation of the "Swedish slow motion theory," [T. Nilsson and J. Kowalewski, J. Magn. Reson. 146, 345 (2000), 10.1006/jmre.2000.2125] originally formulated for paramagnetic systems, to NQR spectral analysis. The description is formulated for simple (Brownian) diffusion, free diffusion, and jump diffusion models. The two latter models account for molecular cooperativity effects in dense systems (such as liquids of high viscosity or molecular glasses). The sensitivity of NQR slow motion spectra to the mechanism of the motional processes modulating the nuclear quadrupole interaction is discussed.

Spin dynamics of antiferromagnets in the presence of a homogeneous magnetization

NASA Astrophysics Data System (ADS)

Kirkpatrick, T. R.; Belitz, D.

2017-06-01

We use general hydrodynamic equations to determine the long-wavelength spin excitations in isotropic antiferromagnets in the presence of a homogeneous magnetization. The latter may be induced, such as in antiferromagnets in an external magnetic field, or spontaneous, such as in ferrimagnetic or canted phases that are characterized by the coexistence of antiferromagnetic and ferromagnetic order. Depending on the physical situation, we find propagating spin waves that are gapped in some cases and gapless in others, diffusive modes, or relaxational modes. The excitation spectra turn out to be qualitatively different depending on whether or not the homogeneous magnetization is a conserved quantity. The results lay the foundation for a description of a variety of quantum phase transitions, including the transition from a ferromagnetic metal to an antiferromagnetic one, and the spin-flop transitions that are observed in some antiferromagnets. They also are crucial for incorporating weak localization and Altshuler-Aronov effects into the descriptions of quantum phases in both clean and disordered magnetic metals.

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.

Phase formation kinetics, hardness and magnetocaloric effect of sub-rapidly solidified LaFe11.6Si1.4 plates during isothermal annealing

NASA Astrophysics Data System (ADS)

Dai, Yuting; Xu, Zhishuai; Luo, Zhiping; Han, Ke; Zhai, Qijie; Zheng, Hongxing

2018-05-01

High-temperature phase transition behavior and intrinsic brittleness of NaZn13-type τ1 phase in La-Fe-Si magnetocaloric materials are two key problems from the viewpoint of materials production and practical applications. In the present work, the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation was introduced to quantitatively characterize the formation kinetics of τ1 phase in sub-rapidly solidified LaFe11.6Si1.4 plates during the isothermal annealing process. Avrami index was estimated to be 0.43 (∼0.5), which suggests that the formation of τ1 phase is in a diffusion-controlled one-dimensional growth mode. Meanwhile, it is found that the Vickers hardness as a function of annealing time for sub-rapidly solidified plates also agrees well with the JMAK equation. The Vickers hardness of τ1 phase was estimated to be about 754. Under a magnetic field change of 30 kOe, the maximum magnetic entropy change was about 22.31 J/(kg·K) for plates annealed at 1323 K for 48 h, and the effective magnetic refrigeration capacity reached 191 J/kg.

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

Effect of magnetic islands on the localization of kinetic Alfvén wave

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

Rai, Rajesh Kumar, E-mail: rajanraj.rai7@gmail.com; Sharma, Swati, E-mail: swati.sharma704@gmail.com; Yadav, Nitin

2015-12-15

Recent studies have revealed an intimate link between magnetic reconnection and turbulence. Observations show that kinetic Alfvén waves (KAWs) play a very crucial role in magnetic reconnection and have been a topic of interest from decades in the context of turbulence and particle heating. In the present paper, we study the role that KAW plays in the formation of coherent structures/current sheets when KAW is propagating in the pre-existing fully developed chain of magnetic islands. We derived the dynamical equation of KAW in the presence of chain of magnetic islands and solved it using numerical simulations well as analytic tools.more » Due to pre-existing chain of magnetic islands, KAW splits into coherent structures and the scale size of these structures along transverse directions (with respect to background magnetic field) comes out to be either less than or greater than ion gyro radius. Therefore, the present work may be the first step towards understanding how magnetic reconnection generated islands may affect the KAW localization and eventually contribute to magnetic turbulence. In this way the present approach may be helpful to understand the interplay between magnetic reconnection and turbulence in ion diffusion region.« less

Reconnection Diffusion in Turbulent Fluids and Its Implications for Star Formation

NASA Astrophysics Data System (ADS)

Lazarian, A.

2014-05-01

Astrophysical fluids are turbulent a fact which changes the dynamics of many key processes, including magnetic reconnection. Fast reconnection of magnetic field in turbulent fluids allows the field to change its topology and connections. As a result, the traditional concept of magnetic fields being frozen into the plasma is no longer applicable. Plasma associated with a given magnetic field line at one instant is distributed along a different set of magnetic field lines at the next instant. This diffusion of plasmas and magnetic field is enabled by reconnection and therefore is termed "reconnection diffusion". The astrophysical implications of this concept include heat transfer in plasmas, advection of heavy elements in interstellar medium, magnetic field generation etc. However, the most dramatic implications of the concept are related to the star formation process. The reason is that magnetic fields are dynamically important for most of the stages of star formation. The existing theory of star formation has been developed ignoring the possibility of reconnection diffusion. Instead, it appeals to the decoupling of mass and magnetic field arising from neutrals drifting in respect to ions entrained on magnetic field lines, i.e. through the process that is termed "ambipolar diffusion". The predictions of ambipolar diffusion and reconnection diffusion are very different. For instance, if the ionization of media is high, ambipolar diffusion predicts that the coupling of mass and magnetic field is nearly perfect. At the same time, reconnection diffusion is independent of the ionization but depends on the scale of the turbulent eddies and on the turbulent velocities. In the paper we explain the physics of reconnection diffusion both from macroscopic and microscopic points of view, i.e. appealing to the reconnection of flux tubes and to the diffusion of magnetic field lines. We make use of the Lazarian and Vishniac (Astrophys. J. 517:700, 1999) theory of magnetic reconnection and show that this theory is applicable to the partially ionized gas. We quantify the reconnection diffusion rate both for weak and strong MHD turbulence and address the problem of reconnection diffusion acting together with ambipolar diffusion. In addition, we provide a criterion for correctly representing the magnetic diffusivity in simulations of star formation. We discuss the intimate relation between the processes of reconnection diffusion, field wandering and turbulent mixing of a magnetized media and show that the role of the plasma effects is limited to "breaking up lines" on small scales and does not affect the rate of reconnection diffusion. We address the existing observational results and demonstrate how reconnection diffusion can explain the puzzles presented by observations, in particular, the observed higher magnetization of cloud cores in comparison with the magnetization of envelopes. We also outline a possible set of observational tests of the reconnection diffusion concept and discuss how the application of the new concept changes our understanding of star formation and its numerical modeling. Finally, we outline the differences of the process of reconnection diffusion and the process of accumulation of matter along magnetic field lines that is frequently invoked to explain the results of numerical simulations.

Thermal diffusion effect on MHD mixed convective flow along a vertically inclined plate: A casson fluid flow

NASA Astrophysics Data System (ADS)

Prasad, D. V. V. Krishna; Chaitanya, G. S. Krishna; Raju, R. Srinivasa

2018-05-01

The nature of Casson fluid on MHD free convective flow of over an impulsively started infinite vertically inclined plate in presence of thermal diffusion (Soret), thermal radiation, heat and mass transfer effects is studied. The basic governing nonlinear coupled partial differential equations are solved numerically using finite element method. The relevant physical parameters appearing in velocity, temperature and concentration profiles are analyzed and discussed through graphs. Finally, the results for velocity profiles and the reduced Nusselt and Sherwood numbers are obtained and compared with previous results in the literature and are found to be in excellent agreement. Applications of the present study would be useful in magnetic material processing and chemical engineering systems.

Rotation and magnetism in intermediate-mass stars

NASA Astrophysics Data System (ADS)

Quentin, Léo G.; Tout, Christopher A.

2018-06-01

Rotation and magnetism are increasingly recognized as important phenomena in stellar evolution. Surface magnetic fields from a few to 20 000 G have been observed and models have suggested that magnetohydrodynamic transport of angular momentum and chemical composition could explain the peculiar composition of some stars. Stellar remnants such as white dwarfs have been observed with fields from a few to more than 109 G. We investigate the origin of and the evolution, on thermal and nuclear rather than dynamical time-scales, of an averaged large-scale magnetic field throughout a star's life and its coupling to stellar rotation. Large-scale magnetic fields sustained until late stages of stellar evolution with conservation of magnetic flux could explain the very high fields observed in white dwarfs. We include these effects in the Cambridge stellar evolution code using three time-dependant advection-diffusion equations coupled to the structural and composition equations of stars to model the evolution of angular momentum and the two components of the magnetic field. We present the evolution in various cases for a 3 M_{⊙} star from the beginning to the late stages of its life. Our particular model assumes that turbulent motions, including convection, favour small-scale field at the expense of large-scale field. As a result, the large-scale field concentrates in radiative zones of the star and so is exchanged between the core and the envelope of the star as it evolves. The field is sustained until the end of the asymptotic giant branch, when it concentrates in the degenerate core.

A conservative MHD scheme on unstructured Lagrangian grids for Z-pinch hydrodynamic simulations

NASA Astrophysics Data System (ADS)

Wu, Fuyuan; Ramis, Rafael; Li, Zhenghong

2018-03-01

A new algorithm to model resistive magnetohydrodynamics (MHD) in Z-pinches has been developed. Two-dimensional axisymmetric geometry with azimuthal magnetic field Bθ is considered. Discretization is carried out using unstructured meshes made up of arbitrarily connected polygons. The algorithm is fully conservative for mass, momentum, and energy. Matter energy and magnetic energy are managed separately. The diffusion of magnetic field is solved using a derivative of the Symmetric-Semi-Implicit scheme, Livne et al. (1985) [23], where unconditional stability is obtained without needing to solve large sparse systems of equations. This MHD package has been integrated into the radiation-hydrodynamics code MULTI-2D, Ramis et al. (2009) [20], that includes hydrodynamics, laser energy deposition, heat conduction, and radiation transport. This setup allows to simulate Z-pinch configurations relevant for Inertial Confinement Fusion.

Study of diffusion of wave packets in a square lattice under external fields along the discrete nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

de Brito, P. E.; Nazareno, H. N.

2012-09-01

The object of the present work is to analyze the effect of nonlinearity on wave packet propagation in a square lattice subject to a magnetic and an electric field in the Hall configuration, by using the Discrete Nonlinear Schrödinger Equation (DNLSE). In previous works we have shown that without the nonlinear term, the presence of the magnetic field induces the formation of vortices that remain stationary, while a wave packet is introduced in the system. As for the effect of an applied electric field, it was shown that the vortices propagate in a direction perpendicular to the electric field, similar behavior as presented in the classical treatment, we provide a quantum mechanics explanation for that. We have performed the calculations considering first the action of the magnetic field as well as the nonlinearity. The results indicate that for low values of the nonlinear parameter U the vortices remain stationary while preserving the form. For greater values of the parameter the picture gets distorted, the more so, the greater the nonlinearity. As for the inclusion of the electric field, we note that for small U, the wave packet propagates perpendicular to the applied field, until for greater values of U the wave gets partially localized in a definite region of the lattice. That is, for strong nonlinearity the wave packet gets partially trapped, while the tail of it can propagate through the lattice. Note that this tail propagation is responsible for the over-diffusion for long times of the wave packet under the action of an electric field. We have produced short films that show clearly the time evolution of the wave packet, which can add to the understanding of the dynamics.

Collapse and Fragmentation of Molecular Cloud Cores. VII. Magnetic Fields and Multiple Protostar Formation

NASA Astrophysics Data System (ADS)

Boss, Alan P.

2002-04-01

Recent observations of star-forming regions suggest that binary and multiple young stars are the rule rather than the exception and implicate fragmentation as the likely mechanism for their formation. Most numerical hydrodynamic calculations of fragmentation have neglected the possibly deleterious effects of magnetic fields, despite ample evidence for the importance of magnetic support of precollapse clouds. We present here the first numerical hydrodynamic survey of the collapse and fragmentation of initially magnetically supported clouds that takes into account several magnetic field effects in an approximate manner. The models are calculated with a three-dimensional, finite differences code that solves the equations of hydrodynamics, gravitation, and radiative transfer in the Eddington and diffusion approximations. Magnetic field effects are included through two simple approximations: magnetic pressure is added to the gas pressure, and magnetic tension is approximated by gravity dilution once collapse is well underway. Ambipolar diffusion of the magnetic field leading to cloud collapse is treated approximately as well. Models are calculated for a variety of initial cloud density profiles, shapes, and rotation rates. We find that in spite of the inclusion of magnetic field effects, dense cloud cores are capable of fragmenting into binary and multiple protostar systems. Initially prolate clouds tend to fragment into binary protostars, while initially oblate clouds tend to fragment into multiple protostar systems containing a small number (of the order of 4) of fragments. The latter are likely to be subject to rapid orbital evolution, with close encounters possibly leading to the ejection of fragments. Contrary to expectation, magnetic tension effects appear to enhance fragmentation, allowing lower mass fragments to form than would otherwise be possible, because magnetic tension helps to prevent a central density singularity from forming and producing a dominant single object. Magnetically supported dense cloud cores thus seem to be capable of collapsing and fragmenting into sufficient numbers of binary and multiple protostar systems to be compatible with observations of the relative rarity of single protostars.

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

Penetration of Cosmic Rays into Dense Molecular Clouds: Role of Diffuse Envelopes

NASA Astrophysics Data System (ADS)

Ivlev, A. V.; Dogiel, V. A.; Chernyshov, D. O.; Caselli, P.; Ko, C.-M.; Cheng, K. S.

2018-03-01

A flux of cosmic rays (CRs) propagating through a diffuse ionized gas can excite MHD waves, thus generating magnetic disturbances. We propose a generic model of CR penetration into molecular clouds through their diffuse envelopes, and identify the leading physical processes controlling their transport on the way from a highly ionized interstellar medium to the dense interior of the cloud. The model allows us to describe a transition between a free streaming of CRs and their diffusive propagation, determined by the scattering on the self-generated disturbances. A self-consistent set of equations, governing the diffusive transport regime in an envelope and the MHD turbulence generated by the modulated CR flux, is characterized by two dimensionless numbers. We demonstrate a remarkable mutual complementarity of different mechanisms leading to the onset of the diffusive regime, which results in a universal energy spectrum of the modulated CRs. In conclusion, we briefly discuss implications of our results for several fundamental astrophysical problems, such as the spatial distribution of CRs in the Galaxy as well as the ionization, heating, and chemistry in dense molecular clouds. This paper is dedicated to the memory of Prof. Vadim Tsytovich.

Hydrodynamic theory of diffusion in two-temperature multicomponent plasmas

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

Ramshaw, J.D.; Chang, C.H.

Detailed numerical simulations of multicomponent plasmas require tractable expressions for species diffusion fluxes, which must be consistent with the given plasma current density J{sub q} to preserve local charge neutrality. The common situation in which J{sub q} = 0 is referred to as ambipolar diffusion. The use of formal kinetic theory in this context leads to results of formidable complexity. We derive simple tractable approximations for the diffusion fluxes in two-temperature multicomponent plasmas by means of a generalization of the hydrodynamical approach used by Maxwell, Stefan, Furry, and Williams. The resulting diffusion fluxes obey generalized Stefan-Maxwell equations that contain drivingmore » forces corresponding to ordinary, forced, pressure, and thermal diffusion. The ordinary diffusion fluxes are driven by gradients in pressure fractions rather than mole fractions. Simplifications due to the small electron mass are systematically exploited and lead to a general expression for the ambipolar electric field in the limit of infinite electrical conductivity. We present a self-consistent effective binary diffusion approximation for the diffusion fluxes. This approximation is well suited to numerical implementation and is currently in use in our LAVA computer code for simulating multicomponent thermal plasmas. Applications to date include a successful simulation of demixing effects in an argon-helium plasma jet, for which selected computational results are presented. Generalizations of the diffusion theory to finite electrical conductivity and nonzero magnetic field are currently in progress.« less

Development of numerical techniques for simulation of magnetogasdynamics and hypersonic chemistry

NASA Astrophysics Data System (ADS)

Damevin, Henri-Marie

Magnetogasdynamics, the science concerned with the mutual interaction between electromagnetic field and flow of electrically conducting gas, offers promising advances in flow control and propulsion of future hypersonic vehicles. Numerical simulations are essential for understanding phenomena, and for research and development. The current dissertation is devoted to the development and validation of numerical algorithms for the solution of multidimensional magnetogasdynamic equations and the simulation of hypersonic high-temperature effects. Governing equations are derived, based on classical magnetogasdynamic assumptions. Two sets of equations are considered, namely the full equations and equations in the low magnetic Reynolds number approximation. Equations are expressed in a suitable formulation for discretization by finite differences in a computational space. For the full equations, Gauss law for magnetism is enforced using Powell's methodology. The time integration method is a four-stage modified Runge-Kutta scheme, amended with a Total Variation Diminishing model in a postprocessing stage. The eigensystem, required for the Total Variation Diminishing scheme, is derived in generalized three-dimensional coordinate system. For the simulation of hypersonic high-temperature effects, two chemical models are utilized, namely a nonequilibrium model and an equilibrium model. A loosely coupled approach is implemented to communicate between the magnetogasdynamic equations and the chemical models. The nonequilibrium model is a one-temperature, five-species, seventeen-reaction model solved by an implicit flux-vector splitting scheme. The chemical equilibrium model computes thermodynamics properties using curve fit procedures. Selected results are provided, which explore the different features of the numerical algorithms. The shock-capturing properties are validated for shock-tube simulations using numerical solutions reported in the literature. The computations of superfast flows over corners and in convergent channels demonstrate the performances of the algorithm in multiple dimensions. The implementation of diffusion terms is validated by solving the magnetic Rayleigh problem and Hartmann problem, for which analytical solutions are available. Prediction of blunt-body type flow are investigated and compared with numerical solutions reported in the literature. The effectiveness of the chemical models for hypersonic flow over blunt body is examined in various flow conditions. It is shown that the proposed schemes perform well in a variety of test cases, though some limitations have been identified.

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.

Magnetic Fields and Multiple Protostar Formation

NASA Astrophysics Data System (ADS)

Boss, A. P.

2001-12-01

Recent observations of star-forming regions suggest that binary and multiple young stars are the rule rather than the exception, and implicate fragmentation as the likely mechanism for their formation. Most numerical hydrodynamical calculations of fragmentation have neglected the possibly deleterious effects of magnetic fields, in spite of ample evidence for the importance of magnetic support of pre-collapse clouds. We present here the first numerical hydrodynamical survey of the full effects of magnetic fields on the collapse and fragmentation of dense cloud cores. The models are calculated with a three dimensional, finite differences code which solves the equations of hydrodynamics, gravitation, and radiative transfer in the Eddington and diffusion approximations. Magnetic field effects are included through two simple approximations: magnetic pressure is added to the gas pressure, and magnetic tension is approximated by gravity dilution once collapse is well underway. Ambipolar diffusion of the magnetic field leading to cloud collapse is treated approximately as well. Models are calculated for a variety of initial cloud density profiles, shapes, and rotation rates. We find that in spite of the inclusion of magnetic field effects, dense cloud cores are capable of fragmenting into binary and multiple protostar systems. Initially prolate clouds tend to fragment into binary protostars, while initially oblate clouds tend to fragment into multiple protostar systems containing a small number (of order four) of fragments. The latter are likely to be subject to rapid orbital evolution, with close encounters possibly leading to the ejection of fragments. Contrary to expectation, magnetic tension effects appear to enhance fragmentation, allowing lower mass fragments to form than would otherwise be possible, because magnetic tension helps to prevent a central density singularity from forming and producing a dominant single object. Magnetically-supported dense cloud cores thus seem to be capable of collapsing and fragmenting into sufficient numbers of binary and multiple protostar systems to be compatible with observations of the relative rarity of single protostars. This work was partially supported by NSF grants AST-9983530 and MRI-9976645.

Cosmic-ray streaming and anisotropies

NASA Technical Reports Server (NTRS)

Forman, M. A.; Gleeson, L. J.

1975-01-01

The paper is concerned with the differential current densities and anisotropies that exist in the interplanetary cosmic-ray gas, and in particular with a correct formulation and simple interpretation of the momentum equation that describes these on a local basis. Two examples of the use of this equation in the interpretation of previous data are given. It is demonstrated that in interplanetary space, the electric-field drifts and convective flow parallel to the magnetic field of cosmic-ray particles combine as a simple convective flow with the solar wind, and that there exist diffusive currents and transverse gradient drift currents. Thus direct reference to the interplanetary electric-field drifts is eliminated, and the study of steady-state and transient cosmic-ray anisotropies is both more systematic and simpler.

Double Diffusive Magnetohydrodynamic (MHD) Mixed Convective Slip Flow along a Radiating Moving Vertical Flat Plate with Convective Boundary Condition

PubMed Central

Rashidi, Mohammad M.; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J.; Freidoonimehr, Navid

2014-01-01

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables. PMID:25343360

Grating formation by a high power radio wave in near-equator ionosphere

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

Singh, Rohtash; Sharma, A. K.; Tripathi, V. K.

2011-11-15

The formation of a volume grating in the near-equator regions of ionosphere due to a high power radio wave is investigated. The radio wave, launched from a ground based transmitter, forms a standing wave pattern below the critical layer, heating the electrons in a space periodic manner. The thermal conduction along the magnetic lines of force inhibits the rise in electron temperature, limiting the efficacy of heating to within a latitude of few degrees around the equator. The space periodic electron partial pressure leads to ambipolar diffusion creating a space periodic density ripple with wave vector along the vertical. Suchmore » a volume grating is effective to cause strong reflection of radio waves at a frequency one order of magnitude higher than the maximum plasma frequency in the ionosphere. Linearly mode converted plasma wave could scatter even higher frequency radio waves.« less

The Nonisothermal Stage of Magnetic Star Formation. I. Formulation of the Problem and Method of Solution

NASA Astrophysics Data System (ADS)

Kunz, Matthew W.; Mouschovias, Telemachos Ch.

2009-03-01

We formulate the problem of the formation and subsequent evolution of fragments (or cores) in magnetically supported, self-gravitating molecular clouds in two spatial dimensions. The six-fluid (neutrals, electrons, molecular and atomic ions, positively charged, negatively charged, and neutral grains) physical system is governed by the radiation, nonideal magnetohydrodynamic equations. The magnetic flux is not assumed to be frozen in any of the charged species. Its evolution is determined by a newly derived generalized Ohm's law, which accounts for the contributions of both elastic and inelastic collisions to ambipolar diffusion and Ohmic dissipation. The species abundances are calculated using an extensive chemical-equilibrium network. Both MRN and uniform grain size distributions are considered. The thermal evolution of the protostellar core and its effect on the dynamics are followed by employing the gray flux-limited diffusion approximation. Realistic temperature-dependent grain opacities are used that account for a variety of grain compositions. We have augmented the publicly available Zeus-MP code to take into consideration all these effects and have modified several of its algorithms to improve convergence, accuracy, and efficiency. Results of magnetic star formation simulations that accurately track the evolution of a protostellar fragment from a density sime103 cm-3 to a density sime1015 cm-3, while rigorously accounting for both nonideal MHD processes and radiative transfer, are presented in a separate paper.

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.

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

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-05-01

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

A parallel algorithm for nonlinear convection-diffusion equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1990-01-01

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

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

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

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

Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights

NASA Astrophysics Data System (ADS)

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

2008-08-01

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

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?

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.

Magnetic Turbulence, Fast Magnetic Field line Diffusion and Small Magnetic Structures in the Solar Wind

NASA Astrophysics Data System (ADS)

Zimbardo, G.; Pommois, P.; Veltri, P.

2003-09-01

The influence of magnetic turbulence on magnetic field line diffusion has been known since the early days of space and plasma physics. However, the importance of ``stochastic diffusion'' for energetic particles has been challenged on the basis of the fact that sharp gradients of either energetic particles or ion composition are often observed in the solar wind. Here we show that fast transverse field line and particle diffusion can coexist with small magnetic structures, sharp gradients, and with long lived magnetic flux tubes. We show, by means of a numerical realization of three dimensional magnetic turbulence and by use of the concepts of deterministic chaos and turbulent transport, that turbulent diffusion is different from Gaussian diffusion, and that transport can be inhomogeneous even if turbulence homogeneously fills the heliosphere. Several diagnostics of field line transport and flux tube evolution are shown, and the size of small magnetic structures in the solar wind, like gradient scales and flux tube thickness, are estimated and compared to the observations.

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.

A theoretical model of the variation of the meridional circulation with the solar cycle

NASA Astrophysics Data System (ADS)

Hazra, Gopal; Choudhuri, Arnab Rai

2017-12-01

Observations of the meridional circulation of the Sun, which plays a key role in the operation of the solar dynamo, indicate that its speed varies with the solar cycle, becoming faster during the solar minima and slower during the solar maxima. To explain this variation of the meridional circulation with the solar cycle, we construct a theoretical model by coupling the equation of the meridional circulation (the ϕ component of the vorticity equation within the solar convection zone) with the equations of the flux transport dynamo model. We consider the back reaction due to the Lorentz force of the dynamo-generated magnetic fields and study the perturbations produced in the meridional circulation due to it. This enables us to model the variations of the meridional circulation without developing a full theory of the meridional circulation itself. We obtain results which reproduce the observational data of solar cycle variations of the meridional circulation reasonably well. We get the best results on assuming the turbulent viscosity acting on the velocity field to be comparable to the magnetic diffusivity (i.e. on assuming the magnetic Prandtl number to be close to unity). We have to assume an appropriate bottom boundary condition to ensure that the Lorentz force cannot drive a flow in the subadiabatic layers below the bottom of the tachocline. Our results are sensitive to this bottom boundary condition. We also suggest a hypothesis on how the observed inward flow towards the active regions may be produced.

Space Flows and Disturbances Due to Bodies in Motion Through the Magnetoplasma

NASA Astrophysics Data System (ADS)

Ponomarjov, Maxim G.

2000-10-01

In this paper a method is concerned which makes it possible to describe numerically and analytically the most famous structures in the non-equilibrium ionosphere, such as stratified and yacht sail like structures, flute jets, wakes and clouds. These problems are of practical interest in space sciences, astrophysics and in turbulence theory, and also of fundamental interest since they enable one to concentrate on the effects of the ambient electric and magnetic fields. Disturbances of charged particle flows due to the ambient flow interactions with bodies are simulated with taking into account the ambient magnetic field effect. The effects of interactions between solid surfaces and the flows was simulated by making use of an original image method. The flow disturbances were described by the Boltzmann equation. In the case of the ambient homogeneous magnetic field the Boltzmann equation is solved analytically. The case of diffuse reflection of particles by surface is considered in detail. The disturbances of charged particle concentration are calculated in 3D space. The contours of constant particle concentration obtained from numerical simulations illustrate the dynamics of developing stratifications and flute structures in charged particle jets and wakes under the ambient magnetic field effect. The basic goal of this paper is to present the method and to demonstate its possibility for simulations of turbulence, plasma jets, wakes and clouds in the ionosphere and Space when effects of electric and magnetic fields are taken into account.

A Green's function method for local and non-local parallel transport in general magnetic fields

NASA Astrophysics Data System (ADS)

Del-Castillo-Negrete, Diego; Chacón, Luis

2009-11-01

The study of transport in magnetized plasmas is a problem of fundamental interest in controlled fusion and astrophysics research. Three issues make this problem particularly challenging: (i) The extreme anisotropy between the parallel (i.e., along the magnetic field), χ, and the perpendicular, χ, conductivities (χ/χ may exceed 10^10 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 the local and non-local parallel transport equation applicable to integrable and chaotic magnetic fields. The numerical implementation employs a volume-preserving field-line integrator [Finn and Chac'on, Phys. Plasmas, 12 (2005)] for an accurate representation of the magnetic field lines regardless of the level of stochasticity. The general formalism and its algorithmic properties are discussed along with illustrative analytical and numerical examples. Problems of particular interest include: the departures from the Rochester--Rosenbluth diffusive scaling in the weak magnetic chaos regime, the interplay between non-locality and chaos, and the robustness of transport barriers in reverse shear configurations.

Fractional order analysis of Sephadex gel structures: NMR measurements reflecting anomalous diffusion

NASA Astrophysics Data System (ADS)

Magin, Richard L.; Akpa, Belinda S.; Neuberger, Thomas; Webb, Andrew G.

2011-12-01

We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[-( bD) α], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch-Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0 < b < 4000 s mm -2). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.

The Evolution of the Solar Magnetic Field: A Comparative Analysis of Two Models

NASA Astrophysics Data System (ADS)

McMichael, K. D.; Karak, B. B.; Upton, L.; Miesch, M. S.; Vierkens, O.

2017-12-01

Understanding the complexity of the solar magnetic cycle is a task that has plagued scientists for decades. However, with the help of computer simulations, we have begun to gain more insight into possible solutions to the plethora of questions inside the Sun. STABLE (Surface Transport and Babcock Leighton) is a newly developed 3D dynamo model that can reproduce features of the solar cycle. In this model, the tilted bipolar sunspots are formed on the surface (based on the toroidal field at the bottom of the convection zone) and then decay and disperse, producing the poloidal field. Since STABLE is a 3D model, it is able to solve the full induction equation in the entirety of the solar convection zone as well as incorporate many free parameters (such as spot depth and turbulent diffusion) which are difficult to observe. In an attempt to constrain some of these free parameters, we compare STABLE to a surface flux transport model called AFT (Advective Flux Transport) which solves the radial component of the magnetic field on the solar surface. AFT is a state-of-the-art surface flux transport model that has a proven record of being able to reproduce solar observations with great accuracy. In this project, we implement synthetic bipolar sunspots into both models, using identical surface parameters, and run the models for comparison. We demonstrate that the 3D structure of the sunspots in the interior and the vertical diffusion of the sunspot magnetic field play an important role in establishing the surface magnetic field in STABLE. We found that when a sufficient amount of downward magnetic pumping is included in STABLE, the surface magnetic field from this model becomes insensitive to the internal structure of the sunspot and more consistent with that of AFT.

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.

The Dynamics of Fibril Magnetic Fields - Part Two - the Mean Field Equations

NASA Astrophysics Data System (ADS)

Parker, E. N.

1982-05-01

A variety of scenarios for the origin and activity of magnetic fields in the convective zone of the Sun have been put forth in recent years. In particular, a number of authors have urged that the magnetic field is in a generally fibril state, much as observed at the surface, with a variety of suggestions as to the consequences. The present paper works out the mean field equations for intense thin fibrils of fixed cross section under the assumption of some significant local ordering. The aim is to establish to what degree new effects may arise as a result of the fibril state. It is shown that the fibril state of a mean field B enhances the tension in the field and the buoyancy of the field by the compression factor m of the field in the individual fibrils. New qualitative effects appear in the slip velocity u of the fibrils through the ambient fluid and in the neutral point reconnection of neighboring fibrils. Some of the novel features are illustrated in later papers in this series. One of the most important consequences is the simplification of the theory of turbulent diffusion by eliminating the looping and tangling that arises when a continuum field is carried in a chaotic turbulent flow. We have been unable to find any effects that would admit of a new concept for the origin of the solar magnetic fields.

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

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

The exit-time problem for a Markov jump process

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

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

2014-12-15

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

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

PubMed

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

2002-04-01

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

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

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

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

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

PubMed

Horowitz, Jordan M

2015-07-28

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

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

NASA Astrophysics Data System (ADS)

Frank, T. D.

2008-02-01

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

Magnetic damping of thermocapillary convection in the floating-zone growth of semiconductor crystals

NASA Astrophysics Data System (ADS)

Morthland, Timothy Edward

The floating zone is one process used to grow high purity semiconductor single crystals. In the floating-zone process, a liquid bridge of molten semiconductor, or melt, is held by surface tension between the upper, melting polycrystalline feed rod and the lower, solidifying single crystal. A perfect crystal would require a quiescent melt with pure diffusion of dopants during the entire period needed to grow the crystal. However, temperature variations along the free surface of the melt lead to gradients of the temperature-dependent surface tension, driving a strong and unsteady flow in the melt, commonly labeled thermocapillary or Marangoni convection. For small temperature differences along the free surface, unsteady thermocapillary convection occurs, disrupting the diffusion controlled solidification and creating undesirable dopant concentration variations in the semiconductor single crystal. Since molten semiconductors are good electrical conductors, an externally applied, steady magnetic field can eliminate the unsteadiness in the melt and can reduce the magnitude of the residual steady motion. Crystal growers hope that a strong enough magnetic field will lead to diffusion controlled solidification, but the magnetic field strengths needed to damp the unsteady thermocapillary convection as a function of floating-zone process parameters is unknown. This research has been conducted in the area of the magnetic damping of thermocapillary convection in floating zones. Both steady and unsteady flows have been investigated. Due to the added complexities in solving Maxwells equations in these magnetohydrodynamic problems and due to the thin boundary layers in these flows, a direct numerical simulation of the fluid and heat transfer in the floating zone is virtually impossible, and it is certainly impossible to run enough simulations to search for neutral stability as a function of magnetic field strength over the entire parameter space. To circumvent these difficulties, we have used matched asymptotic expansions, linear stability theory and numerics to characterize these flows. Some fundamental aspects of the heat transfer and fluid mechanics in these magnetohydrodynamic flows are elucidated in addition to the calculation of the magnetic field strengths required to damp unsteady thermocapillary convection as a function of process parameters.

Sharp-front wave of strong magnetic field diffusion in solid metal

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

Xiao, Bo; Gu, Zhuo-wei; Kan, Ming-xian

When a strong magnetic field diffuses into a solid metal, if the metal's resistance possesses an abrupt rise at some critical temperature and the magnetic field strength is above some critical value, the magnetic field will diffuse into the metal in the form of a sharp-front wave. Formulas for the critical conditions under which a sharp-front magnetic diffusion wave emerges and a formula for the wave-front velocity are derived in this work.

Laser surface modification of medical grade alloys for reduced heating in a magnetic resonance imaging environment

NASA Astrophysics Data System (ADS)

Benafan, O.; Chen, S.-Y.; Kar, A.; Vaidyanathan, R.

2015-12-01

Nanoscale surface modification of medical grade metallic alloys was conducted using a neodymium-doped yttrium aluminum garnet laser-based dopant diffusion technique. The objective of this approach was to minimize the induction heating by reducing the absorbed radio frequency field. Such an approach is advantageous in that the dopant is diffused into the alloy and is not susceptible to detachment or spallation as would an externally applied coating, and is expected to not deteriorate the mechanical and electrical properties of the base alloy or device. Experiments were conducted using a controlled environment laser system with the ability to control laser properties (i.e., laser power, spot size, and irradiation time) and dopant characteristics (i.e., temperature, concentration, and pressure). The reflective and transmissive properties of both the doped and untreated samples were measured in a radio frequency (63.86 MHz) magnetic field using a system comprising a high power signal generator, a localized magnetic field source and sensor, and a signal analyzer. The results indicate an increase in the reflectivity of the laser-treated samples compared to untreated samples. The effect of reflectivity on the heating of the alloys is investigated through a mathematical model incorporating Maxwell's equations and heat conduction.

Stellar differential rotation and coronal time-scales

NASA Astrophysics Data System (ADS)

Gibb, G. P. S.; Jardine, M. M.; Mackay, D. H.

2014-10-01

We investigate the time-scales of evolution of stellar coronae in response to surface differential rotation and diffusion. To quantify this, we study both the formation time and lifetime of a magnetic flux rope in a decaying bipolar active region. We apply a magnetic flux transport model to prescribe the evolution of the stellar photospheric field, and use this to drive the evolution of the coronal magnetic field via a magnetofrictional technique. Increasing the differential rotation (i.e. decreasing the equator-pole lap time) decreases the flux rope formation time. We find that the formation time is dependent upon the lap time and the surface diffusion time-scale through the relation τ_Form ∝ √{τ_Lapτ_Diff}. In contrast, the lifetimes of flux ropes are proportional to the lap time (τLife∝τLap). With this, flux ropes on stars with a differential rotation of more than eight times the solar value have a lifetime of less than 2 d. As a consequence, we propose that features such as solar-like quiescent prominences may not be easily observable on such stars, as the lifetimes of the flux ropes which host the cool plasma are very short. We conclude that such high differential rotation stars may have very dynamical coronae.

Multilayer integral method for simulation of eddy currents in thin volumes of arbitrary geometry produced by MRI gradient coils.

PubMed

Sanchez Lopez, Hector; Freschi, Fabio; Trakic, Adnan; Smith, Elliot; Herbert, Jeremy; Fuentes, Miguel; Wilson, Stephen; Liu, Limei; Repetto, Maurizio; Crozier, Stuart

2014-05-01

This article aims to present a fast, efficient and accurate multi-layer integral method (MIM) for the evaluation of complex spatiotemporal eddy currents in nonmagnetic and thin volumes of irregular geometries induced by arbitrary arrangements of gradient coils. The volume of interest is divided into a number of layers, wherein the thickness of each layer is assumed to be smaller than the skin depth and where one of the linear dimensions is much smaller than the remaining two dimensions. The diffusion equation of the current density is solved both in time-harmonic and transient domain. The experimentally measured magnetic fields produced by the coil and the induced eddy currents as well as the corresponding time-decay constants were in close agreement with the results produced by the MIM. Relevant parameters such as power loss and force induced by the eddy currents in a split cryostat were simulated using the MIM. The proposed method is capable of accurately simulating the current diffusion process inside thin volumes, such as the magnet cryostat. The method permits the priori-calculation of optimal pre-emphasis parameters. The MIM enables unified designs of gradient coil-magnet structures for an optimal mitigation of deleterious eddy current effects. Copyright © 2013 Wiley Periodicals, Inc.

Focused transport of energetic particles along magnetic field lines draped around a coronal mass ejection

NASA Technical Reports Server (NTRS)

Tan, L. C.; Mason, G. M.; Lee, M. A.; Klecker, B.; Ipavich, F. M.

1992-01-01

Evidence is presented for focused transport of energetic particles along magnetic field lines draped around a coronal mass ejection. This evidence was obtained with the University of Maryland/Max-Planck-Institute experiment on the ISEE-3 spacecraft during the decay phase of the June 6, 1979, solar particle event. During the early portion of the decay phase of this event, interplanetary magnetic field lines were apparently draped around a coronal mass ejection, leading to a small focusing length on the western flank where ISEE 3 was located. A period of very slow decrease of particle intensity was observed, along with large sunward anisotropy in the solar wind frame, which is inconsistent with predictions of the standard Fokker-Planck equation models for diffusive transport. It was found possible to fit the observations, assuming that focused transport dominates and that the particle pitch angle scattering is isotropic.

Pre-earthquake Magnetic Pulses

NASA Astrophysics Data System (ADS)

Scoville, J.; Heraud, J. A.; Freund, F. T.

2015-12-01

A semiconductor model of rocks is shown to describe unipolar magnetic pulses, a phenomenon that has been observed prior to earthquakes. These pulses are suspected to be generated deep in the Earth's crust, in and around the hypocentral volume, days or even weeks before earth quakes. Their extremely long wavelength allows them to pass through kilometers of rock. Interestingly, when the sources of these pulses are triangulated, the locations coincide with the epicenters of future earthquakes. We couple a drift-diffusion semiconductor model to a magnetic field in order to describe the electromagnetic effects associated with electrical currents flowing within rocks. The resulting system of equations is solved numerically and it is seen that a volume of rock may act as a diode that produces transient currents when it switches bias. These unidirectional currents are expected to produce transient unipolar magnetic pulses similar in form, amplitude, and duration to those observed before earthquakes, and this suggests that the pulses could be the result of geophysical semiconductor processes.

Pre-earthquake magnetic pulses

NASA Astrophysics Data System (ADS)

Scoville, J.; Heraud, J.; Freund, F.

2015-08-01

A semiconductor model of rocks is shown to describe unipolar magnetic pulses, a phenomenon that has been observed prior to earthquakes. These pulses are suspected to be generated deep in the Earth's crust, in and around the hypocentral volume, days or even weeks before earthquakes. Their extremely long wavelength allows them to pass through kilometers of rock. Interestingly, when the sources of these pulses are triangulated, the locations coincide with the epicenters of future earthquakes. We couple a drift-diffusion semiconductor model to a magnetic field in order to describe the electromagnetic effects associated with electrical currents flowing within rocks. The resulting system of equations is solved numerically and it is seen that a volume of rock may act as a diode that produces transient currents when it switches bias. These unidirectional currents are expected to produce transient unipolar magnetic pulses similar in form, amplitude, and duration to those observed before earthquakes, and this suggests that the pulses could be the result of geophysical semiconductor processes.

Evolution of a magnetic flux tube in two-dimensional penetrative convection

NASA Technical Reports Server (NTRS)

Jennings, R. L.; Brandenburg, A.; Nordlund, A.; Stein, R. F.

1992-01-01

Highly supercritical compressible convection is simulated in a two-dimensional domain in which the upper half is unstable to convection while the lower half is stably stratified. This configuration is an idealization of the layers near the base of the solar convection zone. Once the turbulent flow is well developed, a toroidal magnetic field B sub tor is introduced to the stable layer. The field's evolution is governed by an advection-diffusion-type equation, and the Lorentz force does not significantly affect the flow. After many turnover times the field is stratified such that the absolute value of B sub tor/rho is approximately constant in the convective layer, where rho is density, while in the stable layer this ratio decreases linearly with depth. Consequently most of the magnetic flux is stored in the overshoot layer. The inclusion of rotation leads to travelling waves which transport magnetic flux latitudinally in a manner reminiscent of the migrations seen during the solar cycle.

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.

A study of tablet dissolution by magnetic resonance electric current density imaging.

PubMed

Mikac, Ursa; Demsar, Alojz; Demsar, Franci; Sersa, Igor

2007-03-01

The electric current density imaging technique (CDI) was used to monitor the dissolution of ion releasing tablets (made of various carboxylic acids and of sodium chloride) by following conductivity changes in an agar-agar gel surrounding the tablet. Conductivity changes in the sample were used to calculate spatial and temporal changes of ionic concentrations in the sample. The experimental data for ion migration were compared to a mathematical model based on a solution of the diffusion equation with moving boundary conditions for the tablet geometry. Diffusion constants for different acids were determined by fitting the model to the experimental data. The experiments with dissolving tablets were used to demonstrate the potential of the CDI technique for measurement of ion concentration in the vicinity of ion releasing samples.

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.

Demonstration of Anisotropic Fluid Closure Capturing the Kinetic Structure of Magnetic Reconnection

NASA Astrophysics Data System (ADS)

Ohia, Obioma

2012-10-01

Magnetic reconnection in collisionless plasmas plays an important role in space and laboratory plasmas. Allowing magnetic stress to be reduced by a rearrangement of magnetic line topology, this process is often accompanied by a large release of magnetic field energy, which can heat the plasma, drive large scale flows, or accelerate particles. Reconnection has been widely studied through fluid models and kinetic simulations. While two-fluid models often reproduce the fast reconnection that is observed in nature and seen in kinetic simulations, it is found that the structure surrounding the electron diffusion region and the electron current layer differ vastly between fluid models and kinetic simulations [1]. Recently, using an adiabatic solution of the Vlasov equation, a new fluid closure has been obtained for electrons that relate parallel and perpendicular pressures to the density and magnetic field [2]. Here we present the results of fluid simulation, developed using the HiFi framework [3], that implements new equations of state for guide-field reconnection. The new fluid closure accurately accounts for the anisotropic electron pressure that builds in the reconnection region due to electric and magnetic trapping of electrons. In contrast to previous fluid models, our fluid simulation reproduces the detailed reconnection region as observed in fully kinetic simulations [4]. We hereby demonstrate that the new fluid closure self-consistently captures all the physics relevant to the structure of the reconnection region, providing a gateway to a renewed and deeper theoretical understanding for reconnection in weakly collisional regimes.[4pt] [1] Daughton W et al., Phys. Plasmas 13, 072101 (2006).[0pt] [2] Le A et al., Phys. Rev. Lett. 102, 085001 (2009). [0pt] [3] Lukin VS, Linton MG, Nonlinear Proc. Geoph. 18, 871 (2011). [0pt] [4] Ohia O, et al., Phys. Rev. Lett. In Press (2012).

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

Magnetic orientation of nontronite clay in aqueous dispersions and its effect on water diffusion.

PubMed

Abrahamsson, Christoffer; Nordstierna, Lars; Nordin, Matias; Dvinskikh, Sergey V; Nydén, Magnus

2015-01-01

The diffusion rate of water in dilute clay dispersions depends on particle concentration, size, shape, aggregation and water-particle interactions. As nontronite clay particles magnetically align parallel to the magnetic field, directional self-diffusion anisotropy can be created within such dispersion. Here we study water diffusion in exfoliated nontronite clay dispersions by diffusion NMR and time-dependant 1H-NMR-imaging profiles. The dispersion clay concentration was varied between 0.3 and 0.7 vol%. After magnetic alignment of the clay particles in these dispersions a maximum difference of 20% was measured between the parallel and perpendicular self-diffusion coefficients in the dispersion with 0.7 vol% clay. A method was developed to measure water diffusion within the dispersion in the absence of a magnetic field (random clay orientation) as this is not possible with standard diffusion NMR. However, no significant difference in self-diffusion coefficient between random and aligned dispersions could be observed. Copyright © 2014 Elsevier Inc. All rights reserved.

Preparation and characterization of corn cob activated carbon coated with nano-sized magnetite particles for the removal of Cr(VI).

PubMed

Nethaji, S; Sivasamy, A; Mandal, A B

2013-04-01

Activated carbon prepared from corn cob biomass, magnetized by magnetite nanoparticles (MCCAC) was used for the adsorption of hexavalent chromium from aqueous solution. The adsorbent was characterized by SEM, TEM, XRD, VSM, surface functionality and zero-point charge. The iron oxide nanoparticles were of 50 nm sizes and the saturation magnetization value for the adsorbent is 48.43 emu/g. Adsorption was maximum at pH 2. Isotherm data were modeled using Langmuir, Freundlich and Temkin isotherm. The prepared MCCAC had a heterogeneous surface. The maximum monolayer adsorption capacity was 57.37 mg/g. Kinetic studies were carried out and the data fitted the pseudo second-order equation. The mechanism of the adsorption process was studied by incorporating the kinetic data with intraparticle diffusion model, Bangham equation and Boyd plot. The adsorption was by chemisorption and the external mass transfer was the rate-determining step. A micro column was designed and the basic column parameters were estimated. Copyright © 2013 Elsevier Ltd. All rights reserved.

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.

Effect of Structure on Transport Properties (Viscosity, Ionic Conductivity, and Self-Diffusion Coefficient) of Aprotic Heterocyclic Anion (AHA) Room Temperature Ionic Liquids. 2. Variation of Alkyl Chain Length in the Phosphonium Cation.

PubMed

Sun, Liyuan; Morales-Collazo, Oscar; Xia, Han; Brennecke, Joan F

2016-06-30

A series of room-temperature ionic liquids (ILs) composed of triethyl(alkyl)phosphonium cations paired with three different aprotic heterocyclic anions (AHAs) (alkyl = butyl ([P2224](+)) and octyl ([P2228](+))) were prepared to investigate the effect of cationic alkyl chain length on transport properties. The transport properties and density of these ILs were measured from 283.15 to 343.15 K at ambient pressure. The dependence of the transport properties (viscosity, ionic conductivity, diffusivity, and molar conductivity) on temperature can be described by the Vogel-Fulcher-Tamman (VFT) equation. The ratio of the molar conductivity obtained from the molar concentration and ionic conductivity measurements to that calculated from self-diffusion coefficients (measured by pulsed gradient spin-echo nuclear magnetic resonance spectroscopy) using the Nernst-Einstein equation was used to quantify the ionicity of these ILs. The molar conductivity ratio decreases with increasing number of carbon atoms in the alkyl chain, indicating that the reduced Coulombic interactions resulting from lower density are more than balanced by the increased van der Waals interactions between the alkyl chains. The results of this study may provide insight into the design of ILs with enhanced dynamics that may be suitable as electrolytes in lithium ion batteries and other electrochemical applications.

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

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

Stochastic Reconnection for Large Magnetic Prandtl Numbers

NASA Astrophysics Data System (ADS)

Jafari, Amir; Vishniac, Ethan T.; Kowal, Grzegorz; Lazarian, Alex

2018-06-01

We consider stochastic magnetic reconnection in high-β plasmas with large magnetic Prandtl numbers, Pr m > 1. For large Pr m , field line stochasticity is suppressed at very small scales, impeding diffusion. In addition, viscosity suppresses very small-scale differential motions and therefore also the local reconnection. Here we consider the effect of high magnetic Prandtl numbers on the global reconnection rate in a turbulent medium and provide a diffusion equation for the magnetic field lines considering both resistive and viscous dissipation. We find that the width of the outflow region is unaffected unless Pr m is exponentially larger than the Reynolds number Re. The ejection velocity of matter from the reconnection region is also unaffected by viscosity unless Re ∼ 1. By these criteria the reconnection rate in typical astrophysical systems is almost independent of viscosity. This remains true for reconnection in quiet environments where current sheet instabilities drive reconnection. However, if Pr m > 1, viscosity can suppress small-scale reconnection events near and below the Kolmogorov or viscous damping scale. This will produce a threshold for the suppression of large-scale reconnection by viscosity when {\\Pr }m> \\sqrt{Re}}. In any case, for Pr m > 1 this leads to a flattening of the magnetic fluctuation power spectrum, so that its spectral index is ∼‑4/3 for length scales between the viscous dissipation scale and eddies larger by roughly {{\\Pr }}m3/2. Current numerical simulations are insensitive to this effect. We suggest that the dependence of reconnection on viscosity in these simulations may be due to insufficient resolution for the turbulent inertial range rather than a guide to the large Re limit.

The diffusion and conduction of lithium in poly(ethylene oxide)-based sulfonate ionomers

NASA Astrophysics Data System (ADS)

LaFemina, Nikki H.; Chen, Quan; Colby, Ralph H.; Mueller, Karl T.

2016-09-01

Pulsed field gradient nuclear magnetic resonance spectroscopy and dielectric relaxation spectroscopy have been utilized to investigate lithium dynamics within poly(ethylene oxide) (PEO)-based lithium sulfonate ionomers of varying ion content. The ion content is set by the fraction of sulfonated phthalates and the molecular weight of the PEO spacer, both of which can be varied independently. The molecular level dynamics of the ionomers are dominated by either Vogel-Fulcher-Tammann or Arrhenius behavior depending on ion content, spacer length, temperature, and degree of ionic aggregation. In these ionomers the main determinants of the self-diffusion of lithium and the observed conductivities are the ion content and ionic states of the lithium ion, which are profoundly affected by the interactions of the lithium ions with the ether oxygens of the polymer. Since many lithium ions move by segmental polymer motion in the ion pair state, their diffusion is significantly larger than that estimated from conductivity using the Nernst-Einstein equation.

Grain boundary diffusion behaviors in hot-deformed Nd2Fe14B magnets by PrNd-Cu low eutectic alloys

NASA Astrophysics Data System (ADS)

Tang, Xu; Chen, Renjie; Li, Ming; Jin, Chaoxiang; Yin, Wenzong; Lee, Don; Yan, Aru

2018-01-01

High coercivity of hot-deformed Nd2Fe14B magnets was obtained by grain boundary diffusion. Comparable squareness and similar magnetic properties for samples diffusing from side and pole surfaces show little discrepancies if quantities of the infiltrated PrNd-Cu low eutectic alloys is enough to obtain sufficient diffusion. However, the microstructures and higher characteristic peak ratios show preferable orientation of grains near surfaces of the sample diffused from side surfaces than that from pole surfaces. Amorphous Nd-rich phases and crystal Fe-rich phases were both observed in the diffused magnets. The enhancement of coercivity is considered to be resulted from grain boundary optimization and magnetic isolation which is caused by the thickened nonmagnetic intergranular phases.

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...

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

NASA Astrophysics Data System (ADS)

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

2014-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

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

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

A moving mesh finite difference method for equilibrium radiation diffusion equations

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

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

2015-10-01

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

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

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

2017-07-27

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

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

PubMed Central

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

2012-01-01

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

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.

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

Measuring restriction sizes using diffusion weighted magnetic resonance imaging: a review.

PubMed

Martin, Melanie

2013-01-01

This article reviews a new concept in magnetic resonance as applied to cellular and biological systems. Diffusion weighted magnetic resonance imaging can be used to infer information about restriction sizes of samples being measured. The measurements rely on the apparent diffusion coefficient changing with diffusion times as measurements move from restricted to free diffusion regimes. Pulsed gradient spin echo (PGSE) measurements are limited in the ability to shorten diffusion times and thus are limited in restriction sizes which can be probed. Oscillating gradient spin echo (OGSE) measurements could provide shorter diffusion times so smaller restriction sizes could be probed.

Diffusion weighted magnetic resonance imaging and its recent trend—a survey

PubMed Central

Chilla, Geetha Soujanya; Tan, Cher Heng

2015-01-01

Since its inception in 1985, diffusion weighted magnetic resonance imaging has been evolving and is becoming instrumental in diagnosis and investigation of tissue functions in various organs including brain, cartilage, and liver. Even though brain related pathology and/or investigation remains as the main application, diffusion weighted magnetic resonance imaging (DWI) is becoming a standard in oncology and in several other applications. This review article provides a brief introduction of diffusion weighted magnetic resonance imaging, challenges involved and recent advancements. PMID:26029644

The Effect of Bioturbation on Relative Paleointenstiy Records

NASA Astrophysics Data System (ADS)

Egli, R.; Zhao, X.; Gilder, S. A.

2015-12-01

Bioturbation is one of the key factors affecting the acquisition of a natural remanent magnetization (NRM) in sediments featuring a top mixed layer. In this case, a rotational diffusion process controls the acquisition timing, which is described in terms of a lock-in function, and NRM intensity. In general terms, NRM acquisition by rotational diffusion is described by a Smoluchowski-Debye differential equation, which yields analytical solutions describing how an initially acquired depositional remanent magnetization (DRM) is progressively replaced by a post-depositional remanent magnetization (PDRM) [Egli and Mao, Geochem. Geophys. Geosyst. 16, 995-1016, 2015]. These solutions in turn support the calculation of lock-in functions. Results are controlled by the following parameters: (1) a rotation diffusivity constant γ = 2DrL/ω, where Dr is the rotational diffusion coefficient, L the thickness of the mixed layer, and ω the sedimentation rate, and (2) the ratio between magnetic aligning torques τm = mB and the torques τp associated with mechanical interactions between sediment particles and with the action of perturbing forces. The PDRM acquisition rate and the extent of DRM replacement is controlled by γ, while PDRM intensity is a Langevin function of τm/ τp. Associated lock-in functions range from a constant (NRM is acquired only at the sediment surface) to the classical lock-in function starting below the mixed layer, though intermediate situations where PDRM is partially acquired in the mixed layer. This model has been confirmed by redeposition experiments performed with fresh sediment containing living microorganisms. Redeposition experiments show that the intensity of bioturbation-driven PDRMs can reach ~50% of the originally acquired DRM. Our model has profound consequences for the evaluation of relative paleointensity records, where variations can be driven by changes of the depositional environment. While this knowledge is not new, we provide for the first time a key for understanding, in a quantitative manner, how the NRM acquisition efficiency is controlled by bioturbation. A combination of proxies leading to estimates of the bioturbation activity might provide a new path for improving the reliability of relative paleointensity records.

A diffusive atmospheric pressure glow discharge in a coaxial pin-to-ring gap with a transverse magnetic field

NASA Astrophysics Data System (ADS)

Wang, YongSheng; Ding, WeiDong; Yan, JiaQi; Wang, YaNan

2017-09-01

Atmospheric pressure glow discharge (APGD) has been widely used in the industrial field. The industrial applications are based on achieving stable and diffusive APGD in a relatively large space. The existing sources only achieved stable and diffusive APGD between a short inter-electrode distance within 5 millimeters. In this paper, the effect of a transverse stationary magnetic field on the diffusion of filamentary APGD was studied in a pin-to-ring coaxial gap. The APGD was driven by a high-voltage resonant power supply, and the stationary magnetic field was supplied by a permanent magnet. The stable and diffusive APGD was achieved in the circular area, which diameter was 20 millimeters. The experimental results revealed that more collision ionization occurred and the plasma was distributed diffusively in the discharge gap by applying the external transverse magnetic field. Besides, it is likely to obtain more stable and diffusive APGD in the coaxial pin-to-ring discharge gap when adjusting the input voltage, transverse magnetic flux density and resonant frequency of the power supply.

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.

Double diffusive magnetohydrodynamic (MHD) mixed convective slip flow along a radiating moving vertical flat plate with convective boundary condition.

PubMed

Rashidi, Mohammad M; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J; Freidoonimehr, Navid

2014-01-01

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, [Formula: see text], local Nusselt number, [Formula: see text], and local Sherwood number [Formula: see text] are shown and explained through tables.

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.

Global diffusion of cosmic rays in random magnetic fields

NASA Astrophysics Data System (ADS)

Snodin, A. P.; Shukurov, A.; Sarson, G. R.; Bushby, P. J.; Rodrigues, L. F. S.

2016-04-01

The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particle's Larmor radius RL and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g. there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of the order of 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least 106 times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to 10-2 ≲ RL/lc ≲ 103, where lc is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for RL/lc ≪ 1, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.

Role of collateral paths in long-range diffusion in lungs

PubMed Central

Bartel, Seth-Emil T.; Haywood, Susan E.; Woods, Jason C.; Chang, Yulin V.; Menard, Christopher; Yablonskiy, Dmitriy A.; Gierada, David S.; Conradi, Mark S.

2010-01-01

The long-range apparent diffusion coefficient (LRADC) of 3He gas in lungs, measured over times of several seconds and distances of 1–3 cm, probes the connections between the airways. Previous work has shown the LRADC to be small in health and substantially elevated in emphysema, reflecting tissue destruction, which is known to create collateral pathways. To better understand what controls LRADC, we report computer simulations and measurements of 3He gas diffusion in healthy lungs. The lung is generated with a random algorithm using well-defined rules, yielding a three-dimensional set of nodes or junctions, each connected by airways to one parent node and two daughters; airway dimensions are taken from published values. Spin magnetization in the simulated lung is modulated sinusoidally, and the diffusion equation is solved to 1,000 s. The modulated magnetization decays with a time constant corresponding to an LRADC of ~0.001 cm2/s, which is smaller by a factor of ~20 than the values in healthy lungs measured here and previously in vivo and in explanted lungs. It appears that collateral gas pathways, not present in the simulations, are functional in healthy lungs; they provide additional and more direct routes for long-range motion than the canonical airway tree. This is surprising, inasmuch as collateral ventilation is believed to be physiologically insignificant in healthy lungs. We discuss the effect on LRADC of small collateral connections through airway walls and rule out other possible mechanisms. The role of collateral paths is supported by measurements of smaller LRADC in pigs, where collateral ventilation is known to be smaller. PMID:18292298

Fractional diffusion on bounded domains

DOE PAGES

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

2015-03-13

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

Mathematics of thermal diffusion in an exponential temperature field

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

NASA Technical Reports Server (NTRS)

Ceccobello, C.; Farinelli, R.; Titarchuk, L.

2014-01-01

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the ordinary photons, under the approximation of large angle and large optical depth. These assumptions allow the equation to be treated using a diffusion-like approximation.

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.

Thermal coupling effect on the vortex dynamics of superconducting thin films: time-dependent Ginzburg–Landau simulations

NASA Astrophysics Data System (ADS)

Jing, Ze; Yong, Huadong; Zhou, Youhe

2018-05-01

In this paper, vortex dynamics of superconducting thin films are numerically investigated by the generalized time-dependent Ginzburg–Landau (TDGL) theory. Interactions between vortex motion and the motion induced energy dissipation is considered by solving the coupled TDGL equation and the heat diffusion equation. It is found that thermal coupling has significant effects on the vortex dynamics of superconducting thin films. Branching in the vortex penetration path originates from the coupling between vortex motion and the motion induced energy dissipation. In addition, the environment temperature, the magnetic field ramp rate and the geometry of the superconducting film also greatly influence the vortex dynamic behaviors. Our results provide new insights into the dynamics of superconducting vortices, and give a mesoscopic understanding on the channeling and branching of vortex penetration paths during flux avalanches.

Evidence for Particle Inward Transport, Theoretical prediction and Importance for Reacting Plasmas

NASA Astrophysics Data System (ADS)

Sharky, N.; Coppi, B.; Mazzotta, C.

2017-10-01

The fact that particle transport cannot be described by a diffusion equation but by one that would include an inflow term, involving transport in the direction of the density gradient, was evidenced by experiments on magnetically confined plasmas in which the central plasma density was observed to increase as a result of gas injection at the edge of the plasma column. The validity of the proposed equation has been repeatedly confirmed over the years and limitations for the occurrence of particle inflow in a variety of experimental conditions have been uncovered. The direct experimental observation of the inward propagating particle cloud leading to a profile peaking is described and the effects of different degrees of density peaking in fusion burning plasmas are analyzed. Sponsored in part by the U.S. DoE.

Correction of spin diffusion during iterative automated NOE assignment

NASA Astrophysics Data System (ADS)

Linge, Jens P.; Habeck, Michael; Rieping, Wolfgang; Nilges, Michael

2004-04-01

Indirect magnetization transfer increases the observed nuclear Overhauser enhancement (NOE) between two protons in many cases, leading to an underestimation of target distances. Wider distance bounds are necessary to account for this error. However, this leads to a loss of information and may reduce the quality of the structures generated from the inter-proton distances. Although several methods for spin diffusion correction have been published, they are often not employed to derive distance restraints. This prompted us to write a user-friendly and CPU-efficient method to correct for spin diffusion that is fully integrated in our program ambiguous restraints for iterative assignment (ARIA). ARIA thus allows automated iterative NOE assignment and structure calculation with spin diffusion corrected distances. The method relies on numerical integration of the coupled differential equations which govern relaxation by matrix squaring and sparse matrix techniques. We derive a correction factor for the distance restraints from calculated NOE volumes and inter-proton distances. To evaluate the impact of our spin diffusion correction, we tested the new calibration process extensively with data from the Pleckstrin homology (PH) domain of Mus musculus β-spectrin. By comparing structures refined with and without spin diffusion correction, we show that spin diffusion corrected distance restraints give rise to structures of higher quality (notably fewer NOE violations and a more regular Ramachandran map). Furthermore, spin diffusion correction permits the use of tighter error bounds which improves the distinction between signal and noise in an automated NOE assignment scheme.

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.

A new diffusion matrix for whistler mode chorus waves

NASA Astrophysics Data System (ADS)

Horne, Richard B.; Kersten, Tobias; Glauert, Sarah A.; Meredith, Nigel P.; Boscher, Daniel; Sicard-Piet, Angelica; Thorne, Richard M.; Li, Wen

2013-10-01

Global models of the Van Allen radiation belts usually include resonant wave-particle interactions as a diffusion process, but there is a large uncertainty over the diffusion rates. Here we present a new diffusion matrix for whistler mode chorus waves that can be used in such models. Data from seven satellites are used to construct 3536 power spectra for upper and lower band chorus for 1.5≤L∗≤10 MLT, magnetic latitude 0°≤|λm|≤60° and five levels of Kp. Five density models are also constructed from the data. Gaussian functions are fitted to the spectra and capture typically 90% of the wave power. The frequency maxima of the power spectra vary with L∗ and are typically lower than that used previously. Lower band chorus diffusion increases with geomagnetic activity and is largest between 21:00 and 12:00 MLT. Energy diffusion extends to a few megaelectron volts at large pitch angles >60° and at high energies exceeds pitch angle diffusion at the loss cone. Most electron diffusion occurs close to the geomagnetic equator (<12°). Pitch angle diffusion rates for lower band chorus increase with L∗ and are significant at L∗=8 even for low levels of geomagnetic activity, while upper band chorus is restricted to mainly L∗<6. The combined drift and bounce averaged diffusion rates for upper and lower band chorus extend from a few kiloelectron volts near the loss cone up to several megaelectron volts at large pitch angles indicating loss at low energies and net acceleration at high energies.

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

Understanding the effects of diffusion and relaxation in magnetic resonance imaging using computational modeling

NASA Astrophysics Data System (ADS)

Russell, Greg

The work described in this dissertation was motivated by a desire to better understand the cellular pathology of ischemic stroke. Two of the three bodies of research presented herein address and issue directly related to the investigation of ischemic stroke through the use of diffusion weighted magnetic resonance imaging (DWMRI) methods. The first topic concerns the development of a computationally efficient finite difference method, designed to evaluate the impact of microscopic tissue properties on the formation of DWMRI signal. For the second body of work, the effect of changing the intrinsic diffusion coefficient of a restricted sample on clinical DWMRI experiments is explored. The final body of work, while motivated by the desire to understand stroke, addresses the issue of acquiring large amounts of MRI data well suited for quantitative analysis in reduced scan time. In theory, the method could be used to generate quantitative parametric maps, including those depicting information gleaned through the use of DWMRI methods. Chapter 1 provides an introduction to several topics. A description of the use of DWMRI methods in the study of ischemic stroke is covered. An introduction to the fundamental physical principles at work in MRI is also provided. In this section the means by which magnetization is created in MRI experiments, how MRI signal is induced, as well as the influence of spin-spin and spin-lattice relaxation are discussed. Attention is also given to describing how MRI measurements can be sensitized to diffusion through the use of qualitative and quantitative descriptions of the process. Finally, the reader is given a brief introduction to the use of numerical methods for solving partial differential equations. In Chapters 2, 3 and 4, three related bodies of research are presented in terms of research papers. In Chapter 2, a novel computational method is described. The method reduces the computation resources required to simulate DWMRI experiments. In Chapter 3, a detailed study on how changes in the intrinsic intracellular diffusion coefficient may influence clinical DWMRI experiments is described. In Chapter 4, a novel, non-steady state quantitative MRI method is described.

Spin diffusion in the Mn2+ ion system of II-VI diluted magnetic semiconductor heterostructures

NASA Astrophysics Data System (ADS)

Maksimov, A. A.; Yakovlev, D. R.; Debus, J.; Tartakovskii, I. I.; Waag, A.; Karczewski, G.; Wojtowicz, T.; Kossut, J.; Bayer, M.

2010-07-01

The magnetization dynamics in diluted magnetic semiconductor heterostructures based on (Zn,Mn)Se and (Cd,Mn)Te were studied optically and simulated numerically. In samples with inhomogeneous magnetic ion distribution, these dynamics are contributed by spin-lattice relaxation and spin diffusion in the Mn spin system. A spin-diffusion coefficient of 7×10-8cm2/s was evaluated for Zn0.99Mn0.01Se from comparison of experiment and theory. Calculations of the exciton giant Zeeman splitting and the magnetization dynamics in ordered alloys and digitally grown parabolic quantum wells show perfect agreement with the experimental data. In both structure types, spin diffusion contributes essentially to the magnetization dynamics.

Influence of annealing temperature on the Dy diffusion process in NdFeB magnets

NASA Astrophysics Data System (ADS)

Hu, Sheng-qing; Peng, Kun; Chen, Hong

2017-03-01

Sintered NdFeB magnets were coated with a layer of Dy metal using electron beam evaporation method and then annealed at various temperatures to investigate the temperature dependence of Dy diffusion process in NdFeB magnets. A Dy-rich phase was observed along the grain boundaries after the grain boundary diffusion process, the diffusion coefficients of various temperatures were obtained, the diffusion coefficients of Dy along the grain boundaries at 800 °C and 900 °C were determined to be 9.8×10-8 cm2 s-1 and 2.4×10-7 cm2 s-1, respectively. The diffusion length depended on the annealing temperature and the maximum diffusion length of approximately 1.8 mm and 3.0 mm can be obtained after annealing at 800 °C and 900 °C for 8 h. Higher diffusion temperature results in the diffusion not only along the grain boundaries but also into grains and then decrease in magnetic properties. The optimum annealing conditions can be determined as 900 °C for 8 h. The coercivity was improved from 1040 kA/m to 1450 kA/m and its magnetization has no significant reduction after the grain boundary diffusion process at the optimum annealing conditions.

Fluctuation dynamo based on magnetic reconnections

NASA Astrophysics Data System (ADS)

Baggaley, A. W.; Shukurov, A.; Barenghi, C. F.; Subramanian, K.

2010-01-01

We develop a new model of the fluctuation dynamo in which the magnetic field is confined to thin flux ropes advected by a multi-scale flow which models turbulence. Magnetic dissipation occurs only via reconnections of flux ropes. The model is particularly suitable for rarefied plasma, such as the solar corona or galactic halos. We investigate the kinetic energy release into heat, mediated by dynamo action, both in our model and by solving the induction equation with the same flow. We find that the flux rope dynamo is more than an order of magnitude more efficient at converting mechanical energy into heat. The probability density of the magnetic energy released during reconnections has a power-law form with the slope -3, consistent with the solar corona heating by nanoflares. We also present a nonlinear extension of the model. This shows that a plausible saturation mechanism of the fluctuation dynamo is the suppression of turbulent magnetic diffusivity, due to suppression of random stretching at the location of the flux ropes. We confirm that the probability distribution function of the magnetic line curvature has a power-law form suggested by \\citet{Sheck:2002b}. We argue, however, using our results that this does not imply a persistent folded structure of magnetic field, at least in the nonlinear stage.

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.

Enhanced diffusion weighting generated by selective adiabatic pulse trains

NASA Astrophysics Data System (ADS)

Sun, Ziqi; Bartha, Robert

2007-09-01

A theoretical description and experimental validation of the enhanced diffusion weighting generated by selective adiabatic full passage (AFP) pulse trains is provided. Six phantoms (Ph-1-Ph-6) were studied on a 4 T Varian/Siemens whole body MRI system. Phantoms consisted of 2.8 cm diameter plastic tubes containing a mixture of 10 μm ORGASOL polymer beads and 2 mM Gd-DTPA dissolved in 5% agar (Ph-1) or nickel(II) ammonium sulphate hexahydrate doped (56.3-0.8 mM) water solutions (Ph-2-Ph-6). A customized localization by adiabatic selective refocusing (LASER) sequence containing slice selective AFP pulse trains and pulsed diffusion gradients applied in the phase encoding direction was used to measure 1H 2O diffusion. The b-value associated with the LASER sequence was derived using the Bloch-Torrey equation. The apparent diffusion coefficients measured by LASER were comparable to those measured by a conventional pulsed gradient spin-echo (PGSE) sequence for all phantoms. Image signal intensity increased in Ph-1 and decreased in Ph-2-Ph-6 as AFP pulse train length increased while maintaining a constant echo-time. These experimental results suggest that such AFP pulse trains can enhance contrast between regions containing microscopic magnetic susceptibility variations and homogeneous regions in which dynamic dephasing relaxation mechanisms are dominant.

Perturbative studies of toroidal momentum transport in KSTAR H-mode and the effect of ion temperature perturbation

NASA Astrophysics Data System (ADS)

Yang, S. M.; Na, Yong-Su; Na, D. H.; Park, J.-K.; Shi, Y. J.; Ko, W. H.; Lee, S. G.; Hahm, T. S.

2018-06-01

Perturbative experiments have been carried out using tangential neutral beam injection (NBI) and non-resonant magnetic perturbation (NRMP) to analyze the momentum transport properties in KSTAR H-modes. Diffusive and non-diffusive terms of momentum transport are evaluated from the transient analysis. Although the operating conditions and methodologies applied in the two cases are similar, the momentum transport properties obtained show clear differences. The estimated momentum diffusivity and pinch obtained in the NBI modulation experiments is larger than that in the NRMP modulation experiments. We found that this discrepancy could be a result of uncertainties in the assumption for the analysis. By introducing time varying momentum transport coefficients depending on the temperature gradient, the linearized equation shows that if the temperature perturbation exists, the evolution of toroidal rotation perturbation could be faster than the transport rate of mean quantity, since the evolution of toroidal rotation perturbation is related to , a momentum diffusivity from perturbative analysis. This could explain the estimated higher momentum diffusivity using time independent transport coefficients in NBI experiments with higher ion temperature perturbation compared to that in NRMP modulation experiments. The differences in the momentum transport coefficient with NRMP and NBI are much reduced by considering time varying momentum transport coefficients in the time dependent transport simulation.

Quasi-linear diffusion coefficients for highly oblique whistler mode waves

NASA Astrophysics Data System (ADS)

Albert, J. M.

2017-05-01

Quasi-linear diffusion coefficients are considered for highly oblique whistler mode waves, which exhibit a singular "resonance cone" in cold plasma theory. The refractive index becomes both very large and rapidly varying as a function of wave parameters, making the diffusion coefficients difficult to calculate and to characterize. Since such waves have been repeatedly observed both outside and inside the plasmasphere, this problem has received renewed attention. Here the diffusion equations are analytically treated in the limit of large refractive index μ. It is shown that a common approximation to the refractive index allows the associated "normalization integral" to be evaluated in closed form and that this can be exploited in the numerical evaluation of the exact expression. The overall diffusion coefficient formulas for large μ are then reduced to a very simple form, and the remaining integral and sum over resonances are approximated analytically. These formulas are typically written for a modeled distribution of wave magnetic field intensity, but this may not be appropriate for highly oblique whistlers, which become quasi-electrostatic. Thus, the analysis is also presented in terms of wave electric field intensity. The final results depend strongly on the maximum μ (or μ∥) used to model the wave distribution, so realistic determination of these limiting values becomes paramount.

Scaling laws of passive-scalar diffusion in the interstellar medium

NASA Astrophysics Data System (ADS)

Colbrook, Matthew J.; Ma, Xiangcheng; Hopkins, Philip F.; Squire, Jonathan

2017-05-01

Passive-scalar mixing (metals, molecules, etc.) in the turbulent interstellar medium (ISM) is critical for abundance patterns of stars and clusters, galaxy and star formation, and cooling from the circumgalactic medium. However, the fundamental scaling laws remain poorly understood in the highly supersonic, magnetized, shearing regime relevant for the ISM. We therefore study the full scaling laws governing passive-scalar transport in idealized simulations of supersonic turbulence. Using simple phenomenological arguments for the variation of diffusivity with scale based on Richardson diffusion, we propose a simple fractional diffusion equation to describe the turbulent advection of an initial passive scalar distribution. These predictions agree well with the measurements from simulations, and vary with turbulent Mach number in the expected manner, remaining valid even in the presence of a large-scale shear flow (e.g. rotation in a galactic disc). The evolution of the scalar distribution is not the same as obtained using simple, constant 'effective diffusivity' as in Smagorinsky models, because the scale dependence of turbulent transport means an initially Gaussian distribution quickly develops highly non-Gaussian tails. We also emphasize that these are mean scalings that apply only to ensemble behaviours (assuming many different, random scalar injection sites): individual Lagrangian 'patches' remain coherent (poorly mixed) and simply advect for a large number of turbulent flow-crossing times.

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

Complete fourier direct magnetic resonance imaging (CFD-MRI) for diffusion MRI

PubMed Central

Özcan, Alpay

2013-01-01

The foundation for an accurate and unifying Fourier-based theory of diffusion weighted magnetic resonance imaging (DW–MRI) is constructed by carefully re-examining the first principles of DW–MRI signal formation and deriving its mathematical model from scratch. The derivations are specifically obtained for DW–MRI signal by including all of its elements (e.g., imaging gradients) using complex values. Particle methods are utilized in contrast to conventional partial differential equations approach. The signal is shown to be the Fourier transform of the joint distribution of number of the magnetic moments (at a given location at the initial time) and magnetic moment displacement integrals. In effect, the k-space is augmented by three more dimensions, corresponding to the frequency variables dual to displacement integral vectors. The joint distribution function is recovered by applying the Fourier transform to the complete high-dimensional data set. In the process, to obtain a physically meaningful real valued distribution function, phase corrections are applied for the re-establishment of Hermitian symmetry in the signal. Consequently, the method is fully unconstrained and directly presents the distribution of displacement integrals without any assumptions such as symmetry or Markovian property. The joint distribution function is visualized with isosurfaces, which describe the displacement integrals, overlaid on the distribution map of the number of magnetic moments with low mobility. The model provides an accurate description of the molecular motion measurements via DW–MRI. The improvement of the characterization of tissue microstructure leads to a better localization, detection and assessment of biological properties such as white matter integrity. The results are demonstrated on the experimental data obtained from an ex vivo baboon brain. PMID:23596401

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

NASA Astrophysics Data System (ADS)

Li, Huicong; Wang, Xuefeng; Wu, Yanxia

2014-11-01

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

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

PubMed

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

2018-03-01

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

Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods

DTIC Science & Technology

2002-05-06

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

Role of Multiple Atmospheric Reflections in Formation of Electron Distribution Function in the Diffuse Aurora Region. Chapter 9

NASA Technical Reports Server (NTRS)

Khazanov, George V.; Himwich, Elizabeth W.; Glocer, Alex; Sibeck, David G.

2015-01-01

The precipitation of high-energy magnetospheric electrons (E greater than 500-600 electronvolts) in the diffuse aurora contributes significant energy flux into Earth's ionosphere. In the diffuse aurora, precipitating electrons initially injected from the plasmasheet via wave-particle interaction processes degrade in the atmosphere toward lower energies and produce secondary electrons via impact ionization of the neutral atmosphere. These initially precipitating electrons of magnetospheric origin can be additionally reflected back into the magnetosphere by the two magnetically conjugated atmospheres, leading to a series of multiple reflections that can greatly influence the initially precipitating flux at the upper ionospheric boundary (700-800 kilometers) and the resultant population of secondary electrons and electrons cascading toward lower energies. We present the solution of the Boltzmann.Landau kinetic equation that uniformly describes the entire electron distribution function in the diffuse aurora, including the affiliated production of secondary electrons (E is less than or equal to 600 electronvolts) and their energy interplay in the magnetosphere and two conjugated ionospheres. This solution takes into account the role of multiple atmospheric reflections of the precipitated electrons that were initially moved into the loss cone via wave.particle interaction processes in Earth's plasmasheet.

Evaluation of the toroidal torque driven by external non-resonant non-axisymmetric magnetic field perturbations in a tokamak

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

Kasilov, Sergei V.; Institute of Plasma Physics National Science Center “Kharkov Institute of Physics and Technology” ul. Akademicheskaya 1, 61108 Kharkov; Kernbichler, Winfried

2014-09-15

The toroidal torque driven by external non-resonant magnetic perturbations (neoclassical toroidal viscosity) is an important momentum source affecting the toroidal plasma rotation in tokamaks. The well-known force-flux relation directly links this torque to the non-ambipolar neoclassical particle fluxes arising due to the violation of the toroidal symmetry of the magnetic field. Here, a quasilinear approach for the numerical computation of these fluxes is described, which reduces the dimension of a standard neoclassical transport problem by one without model simplifications of the linearized drift kinetic equation. The only limiting condition is that the non-axisymmetric perturbation field is small enough such thatmore » the effect of the perturbation field on particle motion within the flux surface is negligible. Therefore, in addition to most of the transport regimes described by the banana (bounce averaged) kinetic equation also such regimes as, e.g., ripple-plateau and resonant diffusion regimes are naturally included in this approach. Based on this approach, a quasilinear version of the code NEO-2 [W. Kernbichler et al., Plasma Fusion Res. 3, S1061 (2008).] has been developed and benchmarked against a few analytical and numerical models. Results from NEO-2 stay in good agreement with results from these models in their pertinent range of validity.« less

Diffusion of magnetic field via turbulent reconnection

NASA Astrophysics Data System (ADS)

Santos de Lima, Reinaldo; Lazarian, Alexander; de Gouveia Dal Pino, Elisabete M.; Cho, Jungyeon

2010-05-01

The diffusion of astrophysical magnetic fields in conducting fluids in the presence of turbulence depends on whether magnetic fields can change their topology via reconnection in highly conducting media. Recent progress in understanding fast magnetic reconnection in the presence of turbulence is reassuring that the magnetic field behavior in computer simulations and turbulent astrophysical environments is similar, as far as magnetic reconnection is concerned. This makes it meaningful to perform MHD simulations of turbulent flows in order to understand the diffusion of magnetic field in astrophysical environments. Our studies of magnetic field diffusion in turbulent medium reveal interesting new phenomena. First of all, our 3D MHD simulations initiated with anti-correlating magnetic field and gaseous density exhibit at later times a de-correlation of the magnetic field and density, which corresponds well to the observations of the interstellar media. While earlier studies stressed the role of either ambipolar diffusion or time-dependent turbulent fluctuations for de-correlating magnetic field and density, we get the effect of permanent de-correlation with one fluid code, i.e. without invoking ambipolar diffusion. In addition, in the presence of gravity and turbulence, our 3D simulations show the decrease of the magnetic flux-to-mass ratio as the gaseous density at the center of the gravitational potential increases. We observe this effect both in the situations when we start with equilibrium distributions of gas and magnetic field and when we follow the evolution of collapsing dynamically unstable configurations. Thus the process of turbulent magnetic field removal should be applicable both to quasi-static subcritical molecular clouds and cores and violently collapsing supercritical entities. The increase of the gravitational potential as well as the magnetization of the gas increases the segregation of the mass and magnetic flux in the saturated final state of the simulations, supporting the notion that the reconnection-enabled diffusivity relaxes the magnetic field + gas system in the gravitational field to its minimal energy state. This effect is expected to play an important role in star formation, from its initial stages of concentrating interstellar gas to the final stages of the accretion to the forming protostar.

Modulation of GCR in Various Types of Helispheric Magnetic Field

NASA Astrophysics Data System (ADS)

Kobylinski, Z.; Bochorishvili, T.

We make an attempt to compare the modulation of galactic cosmic rays (GCR) as the result of various assumptions referred to heliospheric magnetic field (HMF). The steady state version of 3D Parker cosmic ray transport equation (TPE), with drift included, is solved num erically in the spherically symmetric heliosphere. We take into account four cases of the possible magnetic field configuration: standard Parker HMF, Parker field with modifications in polar direction done by Jokippi and K ta (2) and Smith ando Bieber (3) , Fisk type of field (4). In the last one we assume the existence north and south polar coronal holes in the inner corona with central point inclined from the rotation of the Sun. At the polar regions of the heliosphere the isotropic diffusion of GCR is assumed. The results of calculation s will be discussed in detail. The (4) model more reduces an acces s of galactic particles from polar direction into solar system than others.

Depletion of solar wind plasma near a planetary boundary

NASA Technical Reports Server (NTRS)

Zwan, B. J.; Wolf, R. A.

1976-01-01

A mathematical model is presented that describes the squeezing of solar wind plasma out along interplanetary magnetic field lines in the region between the bow shock and the effective planetary boundary (in the case of the earth, the magnetopause). In the absence of local magnetic merging the squeezing process should create a 'depletion layer', a region of very low plasma density just outside the magnetopause. Numerical solutions are obtained for the dimensionless magnetohydrodynamic equations describing this depletion process for the case where the solar wind magnetic field is perpendicular to the solar wind flow direction. For the case of the earth, the theory predicts that the density should be reduced by a factor exceeding 2 in a layer about 700-1300 km thick if the Alfven Mach number in the solar wind, is equal to 8. Scaling of the model calculations to Venus and Mars suggests layer thicknesses about 1/10 and 1/15 those of the earth, respectively, neglecting diffusion and ionospheric effects.

Calculating Pressure-Driven Current Near Magnetic Islands for 3D MHD Equilibria

NASA Astrophysics Data System (ADS)

Radhakrishnan, Dhanush; Reiman, Allan

2016-10-01

In general, 3D MHD equilibria in toroidal plasmas do not result in nested pressure surfaces. Instead, islands and chaotic regions appear in the equilibrium. Near small magnetic islands, the pressure varies within the flux surfaces, which has a significant effect on the pressure-driven current, introducing singularities. Previously, the MHD equilibrium current near a magnetic island was calculated, including the effect of ``stellarator symmetry,'' wherein the singular components of the pressure-driven current vanish [A. H. Reiman, Phys. Plasmas 23, 072502 (2016)]. Here we first solve for pressure in a cylindrical plasma from the heat diffusion equation, after adding a helical perturbation. We then numerically calculate the corresponding Pfirsch-Schluter current. At the small island limit, we compare the pressure-driven current with the previously calculated solution, and far from the island, we recover the solution for nested flux surfaces. Lastly, we compute the current for a toroidal plasma for symmetric and non-symmetric geometries.

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.

Micromagnetic simulation of anisotropic grain boundary diffusion for sintered Nd-Fe-B magnets

NASA Astrophysics Data System (ADS)

Li, W.; Zhou, Q.; Zhao, L. Z.; Wang, Q. X.; Zhong, X. C.; Liu, Z. W.

2018-04-01

A systematic investigation on the anisotropic grain boundary diffusion in sintered Nd-Fe-B magnets is carried out by micromagnetic simulation. The results indicate that the critical reason for the anisotropic diffusion effect is not the difference in the amount of Dy diffused along different directions but the macroscopic demagnetizing field. The diffusion parallel to the easy axis from both pole surfaces of the magnet can increase the nucleation fields in the two major regions with large macroscopic demagnetizing fields, where the reverse domains can nucleate easily. As a consequence, the grain boundary diffusion along the directions parallel to the easy axis from two pole surfaces is more effective to improve the coercivity of the magnets than that along other directions. It is also found that, to enhance the coercivity, only a limited diffusion depth is required. The present result is in good agreement with the recent experimental findings.

Magnetization of Cloud Cores and Envelopes and Other Observational Consequences of Reconnection Diffusion

NASA Astrophysics Data System (ADS)

Lazarian, A.; Esquivel, A.; Crutcher, R.

2012-10-01

Recent observational results for magnetic fields in molecular clouds reviewed by Crutcher seem to be inconsistent with the predictions of the ambipolar diffusion theory of star formation. These include the measured decrease in mass to flux ratio between envelopes and cores, the failure to detect any self-gravitating magnetically subcritical clouds, the determination of the flat probability distribution function (PDF) of the total magnetic field strengths implying that there are many clouds with very weak magnetic fields, and the observed scaling Bvpropρ2/3 that implies gravitational contraction with weak magnetic fields. We consider the problem of magnetic field evolution in turbulent molecular clouds and discuss the process of magnetic field diffusion mediated by magnetic reconnection. For this process that we termed "reconnection diffusion," we provide a simple physical model and explain that this process is inevitable in view of the present-day understanding of MHD turbulence. We address the issue of the expected magnetization of cores and envelopes in the process of star formation and show that reconnection diffusion provides an efficient removal of magnetic flux that depends only on the properties of MHD turbulence in the core and the envelope. We show that as the amplitude of turbulence as well as the scale of turbulent motions decrease from the envelope to the core of the cloud, the diffusion of the magnetic field is faster in the envelope. As a result, the magnetic flux trapped during the collapse in the envelope is being released faster than the flux trapped in the core, resulting in much weaker fields in envelopes than in cores, as observed. We provide simple semi-analytical model calculations which support this conclusion and qualitatively agree with the observational results. Magnetic reconnection is also consistent with the lack of subcritical self-gravitating clouds, with the observed flat PDF of field strengths, and with the scaling of field strength with density. In addition, we demonstrate that the reconnection diffusion process can account for the empirical Larson relations and list a few other implications of the reconnection diffusion concept. We argue that magnetic reconnection provides a solution to the magnetic flux problem of star formation that agrees better with observations than the long-standing ambipolar diffusion paradigm. Due to the illustrative nature of our simplified model we do not seek quantitative agreement, but discuss the complementary nature of our approach to the three-dimensional MHD numerical simulations.

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.

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.

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.

Short-Term Forecasting of Radiation Belt and Ring Current

NASA Technical Reports Server (NTRS)

Fok, Mei-Ching

2007-01-01

A computer program implements a mathematical model of the radiation-belt and ring-current plasmas resulting from interactions between the solar wind and the Earth s magnetic field, for the purpose of predicting fluxes of energetic electrons (10 keV to 5 MeV) and protons (10 keV to 1 MeV), which are hazardous to humans and spacecraft. Given solar-wind and interplanetary-magnetic-field data as inputs, the program solves the convection-diffusion equations of plasma distribution functions in the range of 2 to 10 Earth radii. Phenomena represented in the model include particle drifts resulting from the gradient and curvature of the magnetic field; electric fields associated with the rotation of the Earth, convection, and temporal variation of the magnetic field; and losses along particle-drift paths. The model can readily accommodate new magnetic- and electric-field submodels and new information regarding physical processes that drive the radiation-belt and ring-current plasmas. Despite the complexity of the model, the program can be run in real time on ordinary computers. At present, the program can calculate present electron and proton fluxes; after further development, it should be able to predict the fluxes 24 hours in advance

The physical foundation of the reconnection electric field

NASA Astrophysics Data System (ADS)

Hesse, M.; Liu, Y.-H.; Chen, L.-J.; Bessho, N.; Wang, S.; Burch, J. L.; Moretto, T.; Norgren, C.; Genestreti, K. J.; Phan, T. D.; Tenfjord, P.

2018-03-01

Magnetic reconnection is a key charged particle transport and energy conversion process in environments ranging from astrophysical systems to laboratory plasmas [Yamada et al., Rev. Mod. Phys. 82, 603-664 (2010)]. Magnetic reconnection facilitates plasma transport by establishing new connections of magnetic flux tubes, and it converts, often explosively, energy stored in the magnetic field to kinetic energy of charged particles [J. L. Burch and J. F. Drake, Am. Sci. 97, 392-299 (2009)]. The intensity of the magnetic reconnection process is measured by the reconnection electric field, which regulates the rate of flux tube connectivity changes. The change of magnetic connectivity occurs in the current layer of the diffusion zone, where the plasma transport is decoupled from the transport of magnetic flux. Here we report on computer simulations and analytic theory to provide a self-consistent understanding of the role of the reconnection electric field, which extends substantially beyond the simple change of magnetic connections. Rather, we find that the reconnection electric field is essential to maintain the current density in the diffusion region, which would otherwise be dissipated by a set of processes. Natural candidates for current dissipation are the average convection of current carriers away from the reconnection region by the outflow of accelerated particles, or the average rotation of the current density by the magnetic field reversal in the vicinity. Instead, we show here that the current dissipation is the result of thermal effects, underlying the statistical interaction of current-carrying particles with the adjacent magnetic field. We find that this interaction serves to redirect the directed acceleration of the reconnection electric field to thermal motion. This thermalization manifests itself in form of quasi-viscous terms in the thermal energy balance of the current layer. This collisionless viscosity, found in the pressure evolution equation, dominates near the x-line. These quasi-viscous terms act to increase the average thermal energy. Our predictions regarding current and thermal energy balance are readily amenable to exploration in the laboratory or by satellite missions, in particular, by NASA's Magnetospheric Multiscale mission.

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.

Radio Emission from a Young Supernova Remnant Interacting with an Interstellar Cloud: Magnetohydrodynamic Simulation with Relativistic Electrons

NASA Astrophysics Data System (ADS)

Jun, Byung-Il; Jones, T. W.

1999-02-01

We present two-dimensional MHD simulations of the evolution of a young Type Ia supernova remnant (SNR) during its interaction with an interstellar cloud of comparable size at impact. We include for the first time in such simulations explicit relativistic electron transport. This was done using a simplified treatment of the diffusion-advection equation, thus allowing us to model injection and acceleration of cosmic-ray electrons at shocks and their subsequent transport. From this information we also model radio synchrotron emission, including spectral information. The simulations were carried out in spherical coordinates with azimuthal symmetry and compare three different situations, each incorporating an initially uniform interstellar magnetic field oriented in the polar direction on the grid. In particular, we modeled the SNR-cloud interactions for a spherical cloud on the polar axis, a toroidal cloud whose axis is aligned with the polar axis, and, for comparison, a uniform medium with no cloud. We find that the evolution of the overrun cloud qualitatively resembles that seen in simulations of simpler but analogous situations: that is, the cloud is crushed and begins to be disrupted by Rayleigh-Taylor and Kelvin-Helmholtz instabilities. However, we demonstrate here that, in addition, the internal structure of the SNR is severely distorted as such clouds are engulfed. This has important dynamical and observational implications. The principal new conclusions we draw from these experiments are the following. (1) Independent of the cloud interaction, the SNR reverse shock can be an efficient site for particle acceleration in a young SNR. (2) The internal flows of the SNR become highly turbulent once it encounters a large cloud. (3) An initially uniform magnetic field is preferentially amplified along the magnetic equator of the SNR, primarily because of biased amplification in that region by Rayleigh-Taylor instabilities. A similar bias produces much greater enhancement to the magnetic energy in the SNR during an encounter with a cloud when the interstellar magnetic field is partially transverse to the expansion of the SNR. The enhanced magnetic fields have a significant radial component, independent of the field orientation external to the SNR. This leads to a strong equatorial bias in synchrotron brightness that could easily mask any enhancements to electron-acceleration efficiency near the magnetic equator of the SNR. Thus, to establish the latter effect, it will be essential to establish that the magnetic field in the brightest regions are actually tangential to the blast wave. (4) The filamentary radio structures correlate well with ``turbulence-enhanced'' magnetic structures, while the diffuse radio emission more closely follows the gas-density distribution within the SNR. (5) At these early times, the synchrotron spectral index due to electrons accelerated at the primary shocks should be close to 0.5 unless those shocks are modified by cosmic-ray proton pressures. While that result is predictable, we find that this simple result can be significantly complicated in practice by SNR interactions with clouds. Those events can produce regions with significantly steeper spectra. Especially if there are multiple cloud encounters, this interaction can lead to nonuniform spatial spectral distributions or, through turbulent mixing, produce a spectrum that is difficult to relate to the actual strength of the blast wave. (6) Interaction with the cloud enhances the nonthermal electron population in the SNR in our simulations because of additional electron injection taking place in the shocks associated with the cloud. Together with point 3, this means that SNR-cloud encounters can significantly increase the radio emission from the SNR.

Dynamics of a magnetic active Brownian particle under a uniform magnetic field.

PubMed

Vidal-Urquiza, Glenn C; Córdova-Figueroa, Ubaldo M

2017-11-01

The dynamics of a magnetic active Brownian particle undergoing three-dimensional Brownian motion, both translation and rotation, under the influence of a uniform magnetic field is investigated. The particle self-propels at a constant speed along its magnetic dipole moment, which reorients due to the interplay between Brownian and magnetic torques, quantified by the Langevin parameter α. In this work, the time-dependent active diffusivity and the crossover time (τ^{cross})-from ballistic to diffusive regimes-are calculated through the time-dependent correlation function of the fluctuations of the propulsion direction. The results reveal that, for any value of α, the particle undergoes a directional (or ballistic) propulsive motion at very short times (t≪τ^{cross}). In this regime, the correlation function decreases linearly with time, and the active diffusivity increases with it. It the opposite time limit (t≫τ^{cross}), the particle moves in a purely diffusive regime with a correlation function that decays asymptotically to zero and an active diffusivity that reaches a constant value equal to the long-time active diffusivity of the particle. As expected in the absence of a magnetic field (α=0), the crossover time is equal to the characteristic time scale for rotational diffusion, τ_{rot}. In the presence of a magnetic field (α>0), the correlation function, the active diffusivity, and the crossover time decrease with increasing α. The magnetic field regulates the regimes of propulsion of the particle. Here, the field reduces the period of time at which the active particle undergoes a directional motion. Consequently, the active particle rapidly reaches a diffusive regime at τ^{cross}≪τ_{rot}. In the limit of weak fields (α≪1), the crossover time decreases quadratically with α, while in the limit of strong fields (α≫1) it decays asymptotically as α^{-1}. The results are in excellent agreement with those obtained by Brownian dynamics simulations.

Dynamics of a magnetic active Brownian particle under a uniform magnetic field

NASA Astrophysics Data System (ADS)

Vidal-Urquiza, Glenn C.; Córdova-Figueroa, Ubaldo M.

2017-11-01

The dynamics of a magnetic active Brownian particle undergoing three-dimensional Brownian motion, both translation and rotation, under the influence of a uniform magnetic field is investigated. The particle self-propels at a constant speed along its magnetic dipole moment, which reorients due to the interplay between Brownian and magnetic torques, quantified by the Langevin parameter α . In this work, the time-dependent active diffusivity and the crossover time (τcross)—from ballistic to diffusive regimes—are calculated through the time-dependent correlation function of the fluctuations of the propulsion direction. The results reveal that, for any value of α , the particle undergoes a directional (or ballistic) propulsive motion at very short times (t ≪τcross ). In this regime, the correlation function decreases linearly with time, and the active diffusivity increases with it. It the opposite time limit (t ≫τcross ), the particle moves in a purely diffusive regime with a correlation function that decays asymptotically to zero and an active diffusivity that reaches a constant value equal to the long-time active diffusivity of the particle. As expected in the absence of a magnetic field (α =0 ), the crossover time is equal to the characteristic time scale for rotational diffusion, τrot. In the presence of a magnetic field (α >0 ), the correlation function, the active diffusivity, and the crossover time decrease with increasing α . The magnetic field regulates the regimes of propulsion of the particle. Here, the field reduces the period of time at which the active particle undergoes a directional motion. Consequently, the active particle rapidly reaches a diffusive regime at τcross≪τrot . In the limit of weak fields (α ≪1 ), the crossover time decreases quadratically with α , while in the limit of strong fields (α ≫1 ) it decays asymptotically as α-1. The results are in excellent agreement with those obtained by Brownian dynamics simulations.

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.

Improved image reconstruction of low-resolution multichannel phase contrast angiography

PubMed Central

P. Krishnan, Akshara; Joy, Ajin; Paul, Joseph Suresh

2016-01-01

Abstract. In low-resolution phase contrast magnetic resonance angiography, the maximum intensity projected channel images will be blurred with consequent loss of vascular details. The channel images are enhanced using a stabilized deblurring filter, applied to each channel prior to combining the individual channel images. The stabilized deblurring is obtained by the addition of a nonlocal regularization term to the reverse heat equation, referred to as nonlocally stabilized reverse diffusion filter. Unlike reverse diffusion filter, which is highly unstable and blows up noise, nonlocal stabilization enhances intensity projected parallel images uniformly. Application to multichannel vessel enhancement is illustrated using both volunteer data and simulated multichannel angiograms. Robustness of the filter applied to volunteer datasets is shown using statistically validated improvement in flow quantification. Improved performance in terms of preserving vascular structures and phased array reconstruction in both simulated and real data is demonstrated using structureness measure and contrast ratio. PMID:26835501

The influence of non-Gaussian distribution functions on the time-dependent perpendicular transport of energetic particles

NASA Astrophysics Data System (ADS)

Lasuik, J.; Shalchi, A.

2018-06-01

In the current paper we explore the influence of the assumed particle statistics on the transport of energetic particles across a mean magnetic field. In previous work the assumption of a Gaussian distribution function was standard, although there have been known cases for which the transport is non-Gaussian. In the present work we combine a kappa distribution with the ordinary differential equation provided by the so-called unified non-linear transport theory. We then compute running perpendicular diffusion coefficients for different values of κ and turbulence configurations. We show that changing the parameter κ slightly increases or decreases the perpendicular diffusion coefficient depending on the considered turbulence configuration. Since these changes are small, we conclude that the assumed statistics is less significant in particle transport theory. The results obtained in the current paper support to use a Gaussian distribution function as usually done in particle transport theory.

Coronal ``Wave'': Magnetic Footprint of a Coronal Mass Ejection?

NASA Astrophysics Data System (ADS)

Attrill, Gemma D. R.; Harra, Louise K.; van Driel-Gesztelyi, Lidia; Démoulin, Pascal

2007-02-01

We investigate the properties of two ``classical'' EUV Imaging Telescope (EIT) coronal waves. The two source regions of the associated coronal mass ejections (CMEs) possess opposite helicities, and the coronal waves display rotations in opposite senses. We observe deep core dimmings near the flare site and also widespread diffuse dimming, accompanying the expansion of the EIT wave. We also report a new property of these EIT waves, namely, that they display dual brightenings: persistent ones at the outermost edge of the core dimming regions and simultaneously diffuse brightenings constituting the leading edge of the coronal wave, surrounding the expanding diffuse dimmings. We show that such behavior is consistent with a diffuse EIT wave being the magnetic footprint of a CME. We propose a new mechanism where driven magnetic reconnections between the skirt of the expanding CME magnetic field and quiet-Sun magnetic loops generate the observed bright diffuse front. The dual brightenings and the widespread diffuse dimming are identified as innate characteristics of this process.

Non-kinematic Flux-transport Dynamos Including the Effects of Diffusivity Quenching

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

Ichimura, Chiaki; Yokoyama, Takaaki

2017-04-10

Turbulent magnetic diffusivity is quenched when strong magnetic fields suppress turbulent motion in a phenomenon known as diffusivity quenching. Diffusivity quenching can provide a mechanism for amplifying magnetic field and influencing global velocity fields through Lorentz force feedback. To investigate this effect, we conducted mean field flux-transport dynamo simulations that included the effects of diffusivity quenching in a non-kinematic regime. We found that toroidal magnetic field strength is amplified by up to approximately 1.5 times in the convection zone as a result of diffusivity quenching. This amplification is much weaker than that in kinematic cases as a result of Lorentzmore » force feedback on the system’s differential rotation. While amplified toroidal fields lead to the suppression of equatorward meridional flow locally near the base of the convection zone, large-scale equatorward transport of magnetic flux via meridional flow, which is the essential process of the flux-transport dynamo, is sustainable in our calculations.« less

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.

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.

Bounce- and MLT-averaged diffusion coefficients in a physics-based magnetic field geometry obtained from RAM-SCB for the March 17 2013 storm

DOE PAGES

Zhao, Lei; Yu, Yiqun; Delzanno, Gian Luca; ...

2015-04-01

Local acceleration via whistler wave and particle interaction plays a significant role in particle dynamics in the radiation belt. In this work we explore gyro-resonant wave-particle interaction and quasi-linear diffusion in different magnetic field configurations related to the March 17 2013 storm. We consider the Earth's magnetic dipole field as a reference and compare the results against non-dipole field configurations corresponding to quiet and stormy conditions. The latter are obtained with the ring current-atmosphere interactions model with a self-consistent magnetic field RAM-SCB, a code that models the Earth's ring current and provides a realistic modeling of the Earth's magnetic field.more » By applying quasi-linear theory, the bounce- and MLT-averaged electron pitch angle, mixed term, and energy diffusion coefficients are calculated for each magnetic field configuration. For radiation belt (~1 MeV) and ring current (~100 keV) electrons, it is shown that at some MLTs the bounce-averaged diffusion coefficients become rather insensitive to the details of the magnetic field configuration, while at other MLTs storm conditions can expand the range of equatorial pitch angles where gyro-resonant diffusion occurs and significantly enhance the diffusion rates. When MLT average is performed at drift shell L = 4.25 (a good approximation to drift average), the diffusion coefficients become quite independent of the magnetic field configuration for relativistic electrons, while the opposite is true for lower energy electrons. These results suggest that, at least for the March 17 2013 storm and for L ≲ 4.25, the commonly adopted dipole approximation of the Earth's magnetic field can be safely used for radiation belt electrons, while a realistic modeling of the magnetic field configuration is necessary to describe adequately the diffusion rates of ring current electrons.« less

Bounce- and MLT-averaged diffusion coefficients in a physics-based magnetic field geometry obtained from RAM-SCB for the March 17 2013 storm

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

Zhao, Lei; Yu, Yiqun; Delzanno, Gian Luca

Local acceleration via whistler wave and particle interaction plays a significant role in particle dynamics in the radiation belt. In this work we explore gyro-resonant wave-particle interaction and quasi-linear diffusion in different magnetic field configurations related to the March 17 2013 storm. We consider the Earth's magnetic dipole field as a reference and compare the results against non-dipole field configurations corresponding to quiet and stormy conditions. The latter are obtained with the ring current-atmosphere interactions model with a self-consistent magnetic field RAM-SCB, a code that models the Earth's ring current and provides a realistic modeling of the Earth's magnetic field.more » By applying quasi-linear theory, the bounce- and MLT-averaged electron pitch angle, mixed term, and energy diffusion coefficients are calculated for each magnetic field configuration. For radiation belt (~1 MeV) and ring current (~100 keV) electrons, it is shown that at some MLTs the bounce-averaged diffusion coefficients become rather insensitive to the details of the magnetic field configuration, while at other MLTs storm conditions can expand the range of equatorial pitch angles where gyro-resonant diffusion occurs and significantly enhance the diffusion rates. When MLT average is performed at drift shell L = 4.25 (a good approximation to drift average), the diffusion coefficients become quite independent of the magnetic field configuration for relativistic electrons, while the opposite is true for lower energy electrons. These results suggest that, at least for the March 17 2013 storm and for L ≲ 4.25, the commonly adopted dipole approximation of the Earth's magnetic field can be safely used for radiation belt electrons, while a realistic modeling of the magnetic field configuration is necessary to describe adequately the diffusion rates of ring current electrons.« less

Photospheric Magnetic Diffusion by Measuring Moments of Active Regions

NASA Astrophysics Data System (ADS)

Engell, Alexander; Longcope, D.

2013-07-01

Photospheric magnetic surface diffusion is an important constraint for the solar dynamo. The HMI Active Region Patches (HARPs) program automatically identify all magnetic regions above a certain flux. In our study we measure the moments of ARs that are no longer actively emerging and can thereby give us good statistical constraints on photospheric diffusion. We also present the diffusion properties as a function of latitude, flux density, and single polarity (leading or following) within each HARP.

Large-scale magnetic fields at high Reynolds numbers in magnetohydrodynamic simulations.

PubMed

Hotta, H; Rempel, M; Yokoyama, T

2016-03-25

The 11-year solar magnetic cycle shows a high degree of coherence in spite of the turbulent nature of the solar convection zone. It has been found in recent high-resolution magnetohydrodynamics simulations that the maintenance of a large-scale coherent magnetic field is difficult with small viscosity and magnetic diffusivity (≲10 (12) square centimenters per second). We reproduced previous findings that indicate a reduction of the energy in the large-scale magnetic field for lower diffusivities and demonstrate the recovery of the global-scale magnetic field using unprecedentedly high resolution. We found an efficient small-scale dynamo that suppresses small-scale flows, which mimics the properties of large diffusivity. As a result, the global-scale magnetic field is maintained even in the regime of small diffusivities-that is, large Reynolds numbers. Copyright © 2016, American Association for the Advancement of Science.

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

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

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

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

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

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

Obstructions to Existence in Fast-Diffusion Equations

NASA Astrophysics Data System (ADS)

Rodriguez, Ana; Vazquez, Juan L.

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

Diffusion of Magnetic Field and Removal of Magnetic Flux from Clouds Via Turbulent Reconnection

NASA Astrophysics Data System (ADS)

Santos-Lima, R.; Lazarian, A.; de Gouveia Dal Pino, E. M.; Cho, J.

2010-05-01

The diffusion of astrophysical magnetic fields in conducting fluids in the presence of turbulence depends on whether magnetic fields can change their topology via reconnection in highly conducting media. Recent progress in understanding fast magnetic reconnection in the presence of turbulence reassures that the magnetic field behavior in computer simulations and turbulent astrophysical environments is similar, as far as magnetic reconnection is concerned. This makes it meaningful to perform MHD simulations of turbulent flows in order to understand the diffusion of magnetic field in astrophysical environments. Our studies of magnetic field diffusion in turbulent medium reveal interesting new phenomena. First of all, our three-dimensional MHD simulations initiated with anti-correlating magnetic field and gaseous density exhibit at later times a de-correlation of the magnetic field and density, which corresponds well to the observations of the interstellar media. While earlier studies stressed the role of either ambipolar diffusion or time-dependent turbulent fluctuations for de-correlating magnetic field and density, we get the effect of permanent de-correlation with one fluid code, i.e., without invoking ambipolar diffusion. In addition, in the presence of gravity and turbulence, our three-dimensional simulations show the decrease of the magnetic flux-to-mass ratio as the gaseous density at the center of the gravitational potential increases. We observe this effect both in the situations when we start with equilibrium distributions of gas and magnetic field and when we follow the evolution of collapsing dynamically unstable configurations. Thus, the process of turbulent magnetic field removal should be applicable both to quasi-static subcritical molecular clouds and cores and violently collapsing supercritical entities. The increase of the gravitational potential as well as the magnetization of the gas increases the segregation of the mass and magnetic flux in the saturated final state of the simulations, supporting the notion that the reconnection-enabled diffusivity relaxes the magnetic field + gas system in the gravitational field to its minimal energy state. This effect is expected to play an important role in star formation, from its initial stages of concentrating interstellar gas to the final stages of the accretion to the forming protostar. In addition, we benchmark our codes by studying the heat transfer in magnetized compressible fluids and confirm the high rates of turbulent advection of heat obtained in an earlier study.

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.

Charged Particle Diffusion in Isotropic Random Static Magnetic Fields

NASA Astrophysics Data System (ADS)

Subedi, P.; Sonsrettee, W.; Matthaeus, W. H.; Ruffolo, D. J.; Wan, M.; Montgomery, D.

2013-12-01

Study of the transport and diffusion of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here we consider Diffusion of charged particles in fully three dimensional statistically isotropic magnetic field turbulence with no mean field which is pertinent to many astrophysical situations. We classify different regions of particle energy depending upon the ratio of Larmor radius of the charged particle to the characteristic outer length scale of turbulence. We propose three different theoretical models to calculate the diffusion coefficient each applicable to a distinct range of particle energies. The theoretical results are compared with those from computer simulations, showing very good agreement.

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.

FLiT: a field line trace code for magnetic confinement devices

NASA Astrophysics Data System (ADS)

Innocente, P.; Lorenzini, R.; Terranova, D.; Zanca, P.

2017-04-01

This paper presents a field line tracing code (FLiT) developed to study particle and energy transport as well as other phenomena related to magnetic topology in reversed-field pinch (RFP) and tokamak experiments. The code computes magnetic field lines in toroidal geometry using curvilinear coordinates (r, ϑ, ϕ) and calculates the intersections of these field lines with specified planes. The code also computes the magnetic and thermal diffusivity due to stochastic magnetic field in the collisionless limit. Compared to Hamiltonian codes, there are no constraints on the magnetic field functional formulation, which allows the integration of whichever magnetic field is required. The code uses the magnetic field computed by solving the zeroth-order axisymmetric equilibrium and the Newcomb equation for the first-order helical perturbation matching the edge magnetic field measurements in toroidal geometry. Two algorithms are developed to integrate the field lines: one is a dedicated implementation of a first-order semi-implicit volume-preserving integration method, and the other is based on the Adams-Moulton predictor-corrector method. As expected, the volume-preserving algorithm is accurate in conserving divergence, but slow because the low integration order requires small amplitude steps. The second algorithm proves to be quite fast and it is able to integrate the field lines in many partially and fully stochastic configurations accurately. The code has already been used to study the core and edge magnetic topology of the RFX-mod device in both the reversed-field pinch and tokamak magnetic configurations.

Magnetic performance change of multi-main-phase Nd-Ce-Fe-B magnets by diffusing (Nd, Pr)H x

NASA Astrophysics Data System (ADS)

Ma, Tianyu; Zhang, Wenying; Peng, Baixing; Liu, Yongsheng; Chen, Yongjie; Wang, Xinhua; Yan, Mi

2018-02-01

The grain boundary diffusion process (GBDP) is effective to enhance coercivity of the single-main-phase (SMP) RE2Fe14B (rare earth (RE)) magnets through forming magnetic hardening shells surrounding the hard grain cores. Here, the GBDP was applied to the multi-main-phase (MMP) (Nd, Pr)22.3Ce8.24FebalM1.0B1.0 (wt.%) magnets prepared by sintering the mixture of Ce-free and Ce-containing 2:14:1 powders, which have shown superior magnetic properties, especially coercivity, to the SMP ones at the same average composition. The remanence of the (Nd, Pr)H x diffused magnets increases gradually with the increase of diffusion temperature from 480 to 880 °C, the coercivity, however, slightly decreases. The highest (BH)max of 350.1 kJ m-3 is achieved when diffusing at 680 °C, which is 9.2% higher than 320.7 kJ m-3 for the as-prepared magnet. The remanence increment is due to the diffusion of Nd/Pr into the 2:14:1 phase grains, enlarging the intrinsic saturation magnetic polarization. The slight coercivity reduction is due to the gradual homogenization of RE distribution within the 2:14:1 grains of the undiffused parts, i.e. approaching the ‘close to equilibrium (or SMP)’ state, which offsets the positive contributions from the enrichment of Nd/Pr in the Ce-rich 2:14:1 phase and the formation of continuous RE-rich intergranular phase. These findings suggest that the GBDP effect on coercivity of the MMP Nd-Ce-Fe-B magnets is distinctly different from the SMP ones, and that the chemical heterogeneity should be carefully controlled to improve the magnetic properties of such high cost-performance permanent magnets.

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.

Quantum approach of mesoscopic magnet dynamics with spin transfer torque

NASA Astrophysics Data System (ADS)

Wang, Yong; Sham, L. J.

2013-05-01

We present a theory of magnetization dynamics driven by spin-polarized current in terms of the quantum master equation. In the spin coherent state representation, the master equation becomes a Fokker-Planck equation, which naturally includes the spin transfer and quantum fluctuation. The current electron scattering state is correlated to the magnet quantum states, giving rise to quantum correction to the electron transport properties in the usual semiclassical theory. In the large-spin limit, the magnetization dynamics is shown to obey the Hamilton-Jacobi equation or the Hamiltonian canonical equations.

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

NASA Astrophysics Data System (ADS)

Kalinay, Pavol; Slanina, František

2018-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, H. C.

2003-01-01

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

Cosmic Rays in Intermittent Magnetic Fields

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

Shukurov, Anvar; Seta, Amit; Bushby, Paul J.

The propagation of cosmic rays in turbulent magnetic fields is a diffusive process driven by the scattering of the charged particles by random magnetic fluctuations. Such fields are usually highly intermittent, consisting of intense magnetic filaments and ribbons surrounded by weaker, unstructured fluctuations. Studies of cosmic-ray propagation have largely overlooked intermittency, instead adopting Gaussian random magnetic fields. Using test particle simulations, we calculate cosmic-ray diffusivity in intermittent, dynamo-generated magnetic fields. The results are compared with those obtained from non-intermittent magnetic fields having identical power spectra. The presence of magnetic intermittency significantly enhances cosmic-ray diffusion over a wide range of particlemore » energies. We demonstrate that the results can be interpreted in terms of a correlated random walk.« less

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.

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.

Theoretical investigations of plasma processes in the ion bombardment thruster

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.

1975-01-01

A physical model for a thruster discharge was developed, consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field. The associated boundary-value problem for the coupled partial differential equations with mixed boundary conditions, which describe the electric potential and the plasma velocity fields, was solved in closed form. By means of quantum-mechanical perturbation theory, a formula for the number S(E) of atoms sputtered on the average by an ion of energy E was derived from first principles. The boundary-value problem describing the diffusion of the sputtered atoms through the surrounding rarefied electron-ion plasma to the system surfaces of ion propulsion systems was formulated and treated analytically. It is shown that outer boundary-value problems of this type lead to a complex integral equation, which requires numerical resolution.

Simultaneous Observations of Lower Band Chorus Emissions at the Equator and Microburst Precipitating Electrons in the Ionosphere

NASA Astrophysics Data System (ADS)

Mozer, F. S.; Agapitov, O. V.; Blake, J. B.; Vasko, I. Y.

2018-01-01

On 11 December 2016 at 00:12:30 UT, Van Allen Probe-B, at the equator and near midnight, and AC6-B, in the ionosphere, were on magnetic field lines whose 100 km altitude foot points were separated by 600 km. Van Allen Probe-B observed a 30 s burst of lower band chorus waves (with maximum amplitudes >1 nT) at the same time that AC6-B observed intense microburst electrons in the loss cone. One second averaged variations of the chorus intensity and the microburst electron flux were well correlated. The low-altitude electron flux expected from quasi-linear diffusion of the equatorial electrons by the equatorial chorus is in excellent agreement with the observed, 1 s averaged, low-altitude electron flux. However, the large-amplitude, <0.5 s duration, low-altitude electron pulses require nonlinear processes for their explanation.

Source and identification of heavy ions in the equatorial F layer.

NASA Technical Reports Server (NTRS)

Hanson, W. B.; Sterling, D. L.; Woodman, R. F.

1972-01-01

Further evidence is presented to show that the interpretation of some Ogo 6 retarding potential analyzer (RPA) results in terms of ambient Fe+ ions is correct. The Fe+ ions are observed only within dip latitudes of plus or minus 30 deg, and the reason for this latitudinal specificity is discussed in terms of a low-altitude source region and F region diffusion and electrodynamic drift. It is shown that the polarization field associated with the equatorial electrojet will raise ions to 160 km out of a chemical source region below 100 km but it will do so only in a narrow region centered on the dip equator. Subsequent vertical ExB drift, coupled with motions along the magnetic fields, can move the ions to greater heights and greater latitudes. There should be a resultant fountain of metallic ions rising near the equator that subsequently descends back to the E and D layers at tropical latitudes.

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

Magnetic Fields Recorded by Chondrules Formed in Nebular Shocks

NASA Astrophysics Data System (ADS)

Mai, Chuhong; Desch, Steven J.; Boley, Aaron C.; Weiss, Benjamin P.

2018-04-01

Recent laboratory efforts have constrained the remanent magnetizations of chondrules and the magnetic field strengths to which the chondrules were exposed as they cooled below their Curie points. An outstanding question is whether the inferred paleofields represent the background magnetic field of the solar nebula or were unique to the chondrule-forming environment. We investigate the amplification of the magnetic field above background values for two proposed chondrule formation mechanisms, large-scale nebular shocks and planetary bow shocks. Behind large-scale shocks, the magnetic field parallel to the shock front is amplified by factors of ∼10–30, regardless of the magnetic diffusivity. Therefore, chondrules melted in these shocks probably recorded an amplified magnetic field. Behind planetary bow shocks, the field amplification is sensitive to the magnetic diffusivity. We compute the gas properties behind a bow shock around a 3000 km radius planetary embryo, with and without atmospheres, using hydrodynamics models. We calculate the ionization state of the hot, shocked gas, including thermionic emission from dust, thermal ionization of gas-phase potassium atoms, and the magnetic diffusivity due to Ohmic dissipation and ambipolar diffusion. We find that the diffusivity is sufficiently large that magnetic fields have already relaxed to background values in the shock downstream where chondrules acquire magnetizations, and that these locations are sufficiently far from the planetary embryos that chondrules should not have recorded a significant putative dynamo field generated on these bodies. We conclude that, if melted in planetary bow shocks, chondrules probably recorded the background nebular field.

Ionic Channels as Natural Nanodevices

DTIC Science & Technology

2006-05-01

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

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

NASA Astrophysics Data System (ADS)

Cairoli, Andrea; Baule, Adrian

2017-04-01

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

FDM study of ion exchange diffusion equation in glass

NASA Astrophysics Data System (ADS)

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

2009-05-01

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

Gas-induced friction and diffusion of rigid rotors

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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.

Cosmic-Ray Transport in Heliospheric Magnetic Structures. II. Modeling Particle Transport through Corotating Interaction Regions

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

Kopp, Andreas; Wiengarten, Tobias; Fichtner, Horst

The transport of cosmic rays (CRs) in the heliosphere is determined by the properties of the solar wind plasma. The heliospheric plasma environment has been probed by spacecraft for decades and provides a unique opportunity for testing transport theories. Of particular interest for the three-dimensional (3D) heliospheric CR transport are structures such as corotating interaction regions (CIRs), which, due to the enhancement of the magnetic field strength and magnetic fluctuations within and due to the associated shocks as well as stream interfaces, do influence the CR diffusion and drift. In a three-fold series of papers, we investigate these effects bymore » modeling inner-heliospheric solar wind conditions with the numerical magnetohydrodynamic (MHD) framework Cronos (Wiengarten et al., referred as Paper I), and the results serve as input to a transport code employing a stochastic differential equation approach (this paper). While, in Paper I, we presented results from 3D simulations with Cronos, the MHD output is now taken as an input to the CR transport modeling. We discuss the diffusion and drift behavior of Galactic cosmic rays using the example of different theories, and study the effects of CIRs on these transport processes. In particular, we point out the wide range of possible particle fluxes at a given point in space resulting from these different theories. The restriction of this variety by fitting the numerical results to spacecraft data will be the subject of the third paper of this series.« less

Grain boundary diffusion of Dy films prepared by magnetron sputtering for sintered Nd–Fe–B magnets

NASA Astrophysics Data System (ADS)

Chen, W.; Luo, J. M.; Guan, Y. W.; Huang, Y. L.; Chen, M.; Hou, Y. H.

2018-05-01

Dy films, deposited on the surface of sintered Nd–Fe–B magnets by magnetron sputtering, were employed for grain boundary diffusion source. High coercivity sintered Nd–Fe–B magnets were successfully prepared. Effects of sputtering power and grain boundary diffusion processes (GBDP) on the microstructure and magnetic properties were investigated in detail. The dense and uniform Dy films were beneficial to prepare high coercivity magnets by GBDP. The maximum coercivity value of 1189 kA m‑1 could be shown, which was an amplification of 22.3%, compared with that of as-prepared Nd–Fe–B magnet. Furthermore, the improved remanence and maximum energy product were also achieved through tuning grain boundary diffusion processes. Our results demonstrated that the formation of (Nd, Dy)2Fe14B shell surrounding Nd2Fe14B grains and fine, uniform and continuous intergranular RE-rich phases jointly contribute to the improved coercivity.

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

Role of Magnetic Diffusion Induced by Turbulent Magnetic Reconnection for Star Formation

NASA Astrophysics Data System (ADS)

Lazarian, Alex; Santos de Lima, R.; de Gouveia Dal Pino, E.

2010-01-01

The diffusion of astrophysical magnetic fields in conducting fluids in the presence of turbulence depends on whether magnetic fields can change their topology or reconnect in highly conducting media. Recent progress in understanding fast magnetic reconnection in the presence of turbulence is reassuring that the magnetic field behavior in the computer simulations and turbulent astrophysical environments is similar, as far as the magnetic reconnection is concerned. This makes it meaningful to perform MHD simulations of turbulent flows in order to understand the diffusion of magnetic field in astrophysical environments. Our study of magnetic field diffusion reveals important propertie s of the process. First of all, our 3D MHD simulations initiated with anti-correlating magnetic field and gaseous density exhibit at later times a decorrelation of the magnetic field and density, which corresponds well to the observations of the interstellar media. In the presence of gravity, our 3D simulations show the decrease of the flux to mass ratio with density concentration when turbulence is present. We observe this effect both in the situations when we start with the equilibrium distributions of gas and magnetic field and when we start with collapsing dynamically unstable configurations. Thus the process of turbulent magnetic field removal should be applicable both to quasistatic subcritical molecular clouds and cores and violently collapsing supercritical entities. The increase of the gravitational potential as well as the magnetization of the gas increases the segregation of the mass and flux in the saturated final state of simulations, supporting the notion that turbulent diffusivity relaxes the magnetic field + gas system in the gravitational field to its minimal energy state. At the same time, turbulence of high level may get the system unbound making the flux to mass ratio more uniform through the simulation box.

Paramagnetic particles and mixing in micro-scale flows.

PubMed

Calhoun, R; Yadav, A; Phelan, P; Vuppu, A; Garcia, A; Hayes, M

2006-02-01

Mixing in microscale flows with rotating chains of paramagnetic particles can be enhanced by adjusting the ratio of viscous to magnetic forces so that chains dynamically break and reform. Lattice Boltzmann (LB) simulations were used to calculate the interaction between the fluid and suspended paramagnetic particles under the influence of a rotating magnetic field. Fluid velocities obtained from the LB simulations are used to solve the advection diffusion equation for massless tracer particles. At relatively high Mason numbers, small chains result in low edge velocities, and hence mixing is slower than at other Mason numbers. At low Mason numbers, long, stable chains form and produce little mixing toward the center of the chains. A peak in mixing rate is observed when chains break and reform. The uniformity of mixing is greater at higher Mason numbers because more small chains result in a larger number of small mixing areas.

Nonlinear restrictions on dynamo action. [in magnetic fields of astrophysical objects

NASA Technical Reports Server (NTRS)

Vainshtein, Samuel I.; Cattaneo, Fausto

1992-01-01

Astrophysical dynamos operate in the limit of small magnetic diffusivity. In order for magnetic reconnection to occur, very small magnetic structures must form so that diffusion becomes effective. The formation of small-scale fields is accompanied by the stretching of the field lines and therefore by an amplification of the magnetic field strength. The back reaction of the magnetic field on the motions leads to the eventual saturation of the dynamo process, thus posing a constraint on the amount of magnetic flux that can be generated by dynamo action, It is argued that in the limit of small diffusivity only a small amount of flux, many orders of magnitude less than the observed fluxes, can be created by dynamo processes.

Local turbulence simulations for the multiphase ISM

NASA Astrophysics Data System (ADS)

Kissmann, R.; Kleimann, J.; Fichtner, H.; Grauer, R.

2008-12-01

In this paper, we show results of numerical simulations for the turbulence in the interstellar medium (ISM). These results were obtained using a Riemann solver-free numerical scheme for high-Mach number hyperbolic equations. Here, we especially concentrate on the physical properties of the ISM. That is, we do not present turbulence simulations trimmed to be applicable to the ISM. The simulations are rather based on physical estimates for the relevant parameters of the interstellar gas. Applying our code to simulate the turbulent plasma motion within a typical interstellar molecular cloud, we investigate the influence of different equations of state (isothermal and adiabatic) on the statistical properties of the resulting turbulent structures. We find slightly different density power spectra and dispersion maps, while both cases yield qualitatively similar dissipative structures, and exhibit a departure from the classical Kolmogorov case towards a scaling described by the She-Leveque model. Solving the full energy equation with realistic heating/cooling terms appropriate for the diffuse interstellar gas (DIG), we are able to reproduce a realistic two-phase distribution of cold and warm plasma. When extracting maps of polarized intensity from our simulation data, we find encouraging similarity to actual observations. Finally, we compare the actual magnetic field strength of our simulations to its value inferred from the rotation measure. We find these to be systematically different by a factor of about 1.15, thus highlighting the often-underestimated influence of varying line-of-sight particle densities on the magnetic field strength derived from observed rotation measures.

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.

Rotating magnetic shallow water waves and instabilities in a sphere

NASA Astrophysics Data System (ADS)

Márquez-Artavia, X.; Jones, C. A.; Tobias, S. M.

2017-07-01

Waves in a thin layer on a rotating sphere are studied. The effect of a toroidal magnetic field is considered, using the shallow water ideal MHD equations. The work is motivated by suggestions that there is a stably stratified layer below the Earth's core mantle boundary, and the existence of stable layers in stellar tachoclines. With an azimuthal background field known as the Malkus field, ?, ? being the co-latitude, a non-diffusive instability is found with azimuthal wavenumber ?. A necessary condition for instability is that the Alfvén speed exceeds ? where ? is the rotation rate and ? the sphere radius. Magneto-inertial gravity waves propagating westward and eastward occur, and become equatorially trapped when the field is strong. Magneto-Kelvin waves propagate eastward at low field strength, but a new westward propagating Kelvin wave is found when the field is strong. Fast magnetic Rossby waves travel westward, whilst the slow magnetic Rossby waves generally travel eastward, except for some ? modes at large field strength. An exceptional very slow westward ? magnetic Rossby wave mode occurs at all field strengths. The current-driven instability occurs for ? when the slow and fast magnetic Rossby waves interact. With strong field the magnetic Rossby waves become trapped at the pole. An asymptotic analysis giving the wave speed and wave form in terms of elementary functions is possible both in polar trapped and equatorially trapped cases.

Magnetothermal Convection of Water with the Presence or Absence of a Magnetic Force Acting on the Susceptibility Gradient.

PubMed

Maki, Syou

2016-01-01

Heat transfer of magnetothermal convection with the presence or absence of the magnetic force acting on the susceptibility gradient (fsc) was examined by three-dimensional numerical computations. Thermal convection of water enclosed in a shallow cylindrical vessel (diameter over vessel height = 6.0) with the Rayleigh-Benard model was adopted as the model, under the conditions of Prandtl number 6.0 and Ra number 7000, respectively. The momentum equations of convection were nondimensionalized, which involved the term of fsc and the term of magnetic force acting on the magnetic field gradient (fb). All the computations resulted in axisymmetric steady rolls. The values of the averaged Nu, the averaged velocity components U, V, and W, and the isothermal distributions and flow patterns were almost completely the same, regardless of the presence or absence of the term of fsc. As a result, we found that the effect of fsc was extremely small, although much previous research emphasized the effect with paramagnetic solutions under an unsteady state. The magnitude of fsc depends not only on magnetic conditions (magnitudes of magnetic susceptibility and magnetic flux density), but also on the thermal properties of the solution (thermal conductivity, thermal diffusivity, and viscosity). Therefore the effect of fb becomes dominant on the magnetothermal convection. Active control over the density gradient with temperature will be required to advance heat transfer with the effect of fsc.

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.

Magnetic diffusion and flare energy buildup

NASA Technical Reports Server (NTRS)

Wu, S. T.; Yin, C. L.; Yang, W.-H.

1992-01-01

Photospheric motion shears or twists solar magnetic fields to increase magnetic energy in the corona, because this process may change a current-free state of a coronal field to force-free states which carry electric current. This paper analyzes both linear and nonlinear 2D force-free magnetic field models and derives relations of magnetic energy buildup with photospheric velocity field. When realistic data of solar magnetic field and photospheric velocity field are used, it is found that 3-4 hours are needed to create an amount of free magnetic energy which is of the order of the current-free field energy. Furthermore, the paper studies situations in which finite magnetic diffusivities in photospheric plasma are introduced. The shearing motion increases coronal magnetic energy, while the photospheric diffusion reduces the energy. The variation of magnetic energy in the coronal region, then, depends on which process dominates.

Spin effects induced by thermal perturbation in a normal metal/magnetic insulator system

NASA Astrophysics Data System (ADS)

Lyapilin, I. I.; Okorokov, M. S.; Ustinov, V. V.

2015-05-01

Using one of the methods of quantum nonequilibrium statistical physics, we have investigated the spin transport transverse to the normal metal/ferromagnetic insulator interface in hybrid nanostructures. An approximation of the effective parameters, when each of the interacting subsystems (electron spin, magnon, and phonon) is characterized by its own effective temperature, has been considered. The generalized Bloch equations which describe the spin-wave current propagation in the dielectric have been derived. Finally, two sides of the spin transport "coin" have been revealed: the diffusive nature of the magnon motion and magnon relaxation processes, responsible for the spin pumping, and the spin-torque effect.

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.

Toroidal magnetized plasma device with sheared magnetic field lines using an internal ring conductor.

PubMed

Pierre, Th

2013-01-01

In a new toroidal laboratory plasma device including a poloidal magnetic field created by an internal circular conductor, the confinement efficiency of the magnetized plasma and the turbulence level are studied in different situations. The plasma density is greatly enhanced when a sufficiently large poloidal magnetic field is established. Moreover, the instabilities and the turbulence usually found in toroidal devices without sheared magnetic field lines are suppressed by the finite rotational transform. The particle confinement time is estimated from the measurement of the plasma decay time. It is compared to the Bohm diffusion time and to the value predicted by different diffusion models, in particular neoclassical diffusion involving trapped particles.

Incomplete initial nutation diffusion imaging: An ultrafast, single-scan approach for diffusion mapping.

PubMed

Ianuş, Andrada; Shemesh, Noam

2018-04-01

Diffusion MRI is confounded by the need to acquire at least two images separated by a repetition time, thereby thwarting the detection of rapid dynamic microstructural changes. The issue is exacerbated when diffusivity variations are accompanied by rapid changes in T 2 . The purpose of the present study is to accelerate diffusion MRI acquisitions such that both reference and diffusion-weighted images necessary for quantitative diffusivity mapping are acquired in a single-shot experiment. A general methodology termed incomplete initial nutation diffusion imaging (INDI), capturing two diffusion contrasts in a single shot, is presented. This methodology creates a longitudinal magnetization reservoir that facilitates the successive acquisition of two images separated by only a few milliseconds. The theory behind INDI is presented, followed by proof-of-concept studies in water phantom, ex vivo, and in vivo experiments at 16.4 and 9.4 T. Mean diffusivities extracted from INDI were comparable with diffusion tensor imaging and the two-shot isotropic diffusion encoding in the water phantom. In ex vivo mouse brain tissues, as well as in the in vivo mouse brain, mean diffusivities extracted from conventional isotropic diffusion encoding and INDI were in excellent agreement. Simulations for signal-to-noise considerations identified the regimes in which INDI is most beneficial. The INDI method accelerates diffusion MRI acquisition to single-shot mode, which can be of great importance for mapping dynamic microstructural properties in vivo without T 2 bias. Magn Reson Med 79:2198-2204, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

Exact Magnetic Diffusion Solutions for Magnetohydrodynamic Code Verification

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

Miller, D S

In this paper, the authors present several new exact analytic space and time dependent solutions to the problem of magnetic diffusion in R-Z geometry. These problems serve to verify several different elements of an MHD implementation: magnetic diffusion, external circuit time integration, current and voltage energy sources, spatially dependent conductivities, and ohmic heating. The exact solutions are shown in comparison with 2D simulation results from the Ares code.

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.

Numerical Solution of the Electron Heat Transport Equation and Physics-Constrained Modeling of the Thermal Conductivity via Sequential Quadratic Programming Optimization in Nuclear Fusion Plasmas

NASA Astrophysics Data System (ADS)

Paloma, Cynthia S.

The plasma electron temperature (Te) plays a critical role in a tokamak nu- clear fusion reactor since temperatures on the order of 108K are required to achieve fusion conditions. Many plasma properties in a tokamak nuclear fusion reactor are modeled by partial differential equations (PDE's) because they depend not only on time but also on space. In particular, the dynamics of the electron temperature is governed by a PDE referred to as the Electron Heat Transport Equation (EHTE). In this work, a numerical method is developed to solve the EHTE based on a custom finite-difference technique. The solution of the EHTE is compared to temperature profiles obtained by using TRANSP, a sophisticated plasma transport code, for specific discharges from the DIII-D tokamak, located at the DIII-D National Fusion Facility in San Diego, CA. The thermal conductivity (also called thermal diffusivity) of the electrons (Xe) is a plasma parameter that plays a critical role in the EHTE since it indicates how the electron temperature diffusion varies across the minor effective radius of the tokamak. TRANSP approximates Xe through a curve-fitting technique to match experimentally measured electron temperature profiles. While complex physics-based model have been proposed for Xe, there is a lack of a simple mathematical model for the thermal diffusivity that could be used for control design. In this work, a model for Xe is proposed based on a scaling law involving key plasma variables such as the electron temperature (Te), the electron density (ne), and the safety factor (q). An optimization algorithm is developed based on the Sequential Quadratic Programming (SQP) technique to optimize the scaling factors appearing in the proposed model so that the predicted electron temperature and magnetic flux profiles match predefined target profiles in the best possible way. A simulation study summarizing the outcomes of the optimization procedure is presented to illustrate the potential of the proposed modeling method.

Three-dimensional wideband electromagnetic modeling on massively parallel computers

NASA Astrophysics Data System (ADS)

Alumbaugh, David L.; Newman, Gregory A.; Prevost, Lydie; Shadid, John N.

1996-01-01

A method is presented for modeling the wideband, frequency domain electromagnetic (EM) response of a three-dimensional (3-D) earth to dipole sources operating at frequencies where EM diffusion dominates the response (less than 100 kHz) up into the range where propagation dominates (greater than 10 MHz). The scheme employs the modified form of the vector Helmholtz equation for the scattered electric fields to model variations in electrical conductivity, dielectric permitivity and magnetic permeability. The use of the modified form of the Helmholtz equation allows for perfectly matched layer ( PML) absorbing boundary conditions to be employed through the use of complex grid stretching. Applying the finite difference operator to the modified Helmholtz equation produces a linear system of equations for which the matrix is sparse and complex symmetrical. The solution is obtained using either the biconjugate gradient (BICG) or quasi-minimum residual (QMR) methods with preconditioning; in general we employ the QMR method with Jacobi scaling preconditioning due to stability. In order to simulate larger, more realistic models than has been previously possible, the scheme has been modified to run on massively parallel (MP) computer architectures. Execution on the 1840-processor Intel Paragon has indicated a maximum model size of 280 × 260 × 200 cells with a maximum flop rate of 14.7 Gflops. Three different geologic models are simulated to demonstrate the use of the code for frequencies ranging from 100 Hz to 30 MHz and for different source types and polarizations. The simulations show that the scheme is correctly able to model the air-earth interface and the jump in the electric and magnetic fields normal to discontinuities. For frequencies greater than 10 MHz, complex grid stretching must be employed to incorporate absorbing boundaries while below this normal (real) grid stretching can be employed.

Modeling boundary measurements of scattered light using the corrected diffusion approximation

PubMed Central

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

2012-01-01

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

Optical Oversampled Analog-to-Digital Conversion

DTIC Science & Technology

1992-06-29

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

Modelling the radiotherapy effect in the reaction-diffusion equation.

PubMed

Borasi, Giovanni; Nahum, Alan

2016-09-01

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

Magnetic reconnection in numerical simulations of the Bastille day flare

NASA Astrophysics Data System (ADS)

Vincent, A. P.; Charbonneau, P.

2011-12-01

If neither waves nor adiabatic heating due to compression are taken into account, coronal heating may be obtained in numerical simulations from current dissipation inside solar flares. To increase Joule heating locally we used a model for hyper resistivity (Klimas et al., 2004: Journal of Geophysical Research, 109, 2218-2231). Here the change in resistivity is due to small scale (less than 1Mm in our simulations) current density fluctuations. Whenever the current exceeds a cut-off value, magnetic resistivity jumps sharply to reach a maximum locally thus increasing magnetic gradients at the border of the flare. In this way, not only the current increases but also the maximum is slowly displaced and simulations of the full set of 3-D MHD equations show a progression westward as can be seen in SOHO-EIT images of the ''slinky''. In our simulations of the Bastille day flare, most of the reconnection events take place just above the transition and mostly follow the neutral line but it is Spitzer thermal diffusivity together with radiative cooling that illuminates magnetic arcades in a way similar to what can be seen in extreme ultra-violet animations of the slinky.

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

PubMed

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

2013-03-01

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

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

PubMed Central

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

2013-01-01

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

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

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

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

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

2009-07-01

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

Nature of self-diffusion in two-dimensional fluids

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

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

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

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

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

2017-12-18

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

The rotation of discs around neutron stars: dependence on the Hall diffusion

NASA Astrophysics Data System (ADS)

Faghei, Kazem; Salehi, Fatemeh

2018-01-01

In this paper, we study the dynamics of a geometrically thin, steady and axisymmetric accretion disc surrounding a rotating and magnetized star. The magnetic field lines of star penetrate inside the accretion disc and are twisted due to the differential rotation between the magnetized star and the disc. We apply the Hall diffusion effect in the accreting plasma, because of the Hall diffusion plays an important role in both fully ionized plasma and weakly ionized medium. In the current research, we show that the Hall diffusion is also an important mechanism in accreting plasma around neutron stars. For the typical system parameter values associated with the accreting X-ray binary pulsar, the angular velocity of the inner regions of disc departs outstandingly from Keplerian angular velocity, due to coupling between the magnetic field of neutron star and the rotating plasma of disc. We found that the Hall diffusion is very important in inner disc and increases the coupling between the magnetic field of neutron star and accreting plasma. On the other word, the rotational velocity of inner disc significantly decreases in the presence of the Hall diffusion. Moreover, the solutions imply that the fastness parameter decreases and the angular velocity transition zone becomes broad for the accreting plasma including the Hall diffusion.

Effect of the magnetism of impurities on their diffusion in metals: Bulk diffusion of iron, cobalt, and rhodium in iridium single crystals

NASA Astrophysics Data System (ADS)

Klotsman, S. M.; Tatarinova, G. N.

2008-12-01

The coefficients and parameters of the temperature dependences of the coefficients of bulk diffusion of Fe, Co, Rh, and Au atomic probes (APs) in iridium single crystals (mono-Ir) have been determined from the diffusion profiles obtained using secondary-ion mass spectrometry of the diffusion zones. The enthalpies of activation of diffusion of Fe, Co, and Rh APs are considerably lower than the enthalpy of activation of selfdiffusion in mono-Ir. This is caused by the negative contributions of the intraatomic exchange energy and energy of relaxation of the environment of the d transition APs to the enthalpy of interaction of magnetically active APs with the vacancies in the iridium lattice. The interaction energy of partners in such complexes and the relationships between the magnetic moments of d transition APs in complexes with vacancies have been estimated. The Rh APs in complexes with vacancies in iridium possess stable magnetic moments.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

The Role of Fluid Compression in Particle Energization during Magnetic Reconnection

NASA Astrophysics Data System (ADS)

Li, X.; Guo, F.; Li, H.; Li, S.

2017-12-01

Theories of particle transport and acceleration have shown that fluid compression is the leading mechanism for particle energization. However, the role of compression in particle energization during magnetic reconnection is unclear. We present a cluster of studies to clarify and show the effect of fluid compression in accelerating particles to high energies during magnetic reconnection. Using fully kinetic reconnection simulations, we show that fluid compression is the leading mechanism for high-energy particle energization. We find that the compressional energization is more important in a low-beta plasma or in a reconnection layer with a weak guide field (the magnetic field component perpendicular to the reconnecting magnetic field), which are relevant to solar flares. Our analysis on 3D kinetic simulations shows that the self-generated turbulence scatters particles and enhances the particle diffusion processes in the acceleration regions. Based on these results, we then study large-scale reconnection acceleration by solving the particle transport equation in a large-scale reconnection layer evolved with MHD simulations. Due to the compressional effect, particles are accelerated to high energies and develop power-law energy distributions. This study clarifies the nature of particle acceleration in reconnection layer and is important to understand particle energization during large-scale acceleration such as solar flares.

The generation and amplification of intergalactic magnetic fields in analogue laboratory experiments with high power lasers

NASA Astrophysics Data System (ADS)

Gregori, G.; Reville, B.; Miniati, F.

2015-11-01

The advent of high-power laser facilities has, in the past two decades, opened a new field of research where astrophysical environments can be scaled down to laboratory dimensions, while preserving the essential physics. This is due to the invariance of the equations of magneto-hydrodynamics to a class of similarity transformations. Here we review the relevant scaling relations and their application in laboratory astrophysics experiments with a focus on the generation and amplification of magnetic fields in cosmic environment. The standard model for the origin of magnetic fields is a multi stage process whereby a vanishing magnetic seed is first generated by a rotational electric field and is then amplified by turbulent dynamo action to the characteristic values observed in astronomical bodies. We thus discuss the relevant seed generation mechanisms in cosmic environment including resistive mechanism, collision-less and fluid instabilities, as well as novel laboratory experiments using high power laser systems aimed at investigating the amplification of magnetic energy by magneto-hydrodynamic (MHD) turbulence. Future directions, including efforts to model in the laboratory the process of diffusive shock acceleration are also discussed, with an emphasis on the potential of laboratory experiments to further our understanding of plasma physics on cosmic scales.

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

NASA Astrophysics Data System (ADS)

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

2013-08-01

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

Mechanisms of Stochastic Diffusion of Energetic Ions in Spherical Tori

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

Ya.I. Kolesnichenko; R.B. White; Yu.V. Yakovenko

Stochastic diffusion of the energetic ions in spherical tori is considered. The following issues are addressed: (I) Goldston-White-Boozer diffusion in a rippled field; (ii) cyclotron-resonance-induced diffusion caused by the ripple; (iii) effects of non-conservation of the magnetic moment in an axisymmetric field. It is found that the stochastic diffusion in spherical tori with a weak magnetic field has a number of peculiarities in comparison with conventional tokamaks; in particular, it is characterized by an increased role of mechanisms associated with non-conservation of the particle magnetic moment. It is concluded that in current experiments on National Spherical Torus eXperiment (NSTX) themore » stochastic diffusion does not have a considerable influence on the confinement of energetic ions.« less

Recent developments in the understanding of equatorial ionization anomaly: A review

NASA Astrophysics Data System (ADS)

Balan, N.; Souza, J.; Bailey, G. J.

2018-06-01

A brief review of the recent developments in the understanding of the equatorial plasma fountain (EPF) and equatorial ionization anomaly (EIA) under quiet and active conditions is presented. It is clarified that (1) the EPF is not upward ExB plasma drift at the equator followed by downward plasma diffusion, but it is field perpendicular ExB plasma drift and field-aligned plasma diffusion acting together all along the field lines at all altitudes and plasma flowing in the direction of the resultant. (2) The EIA is formed not from the accumulation of plasma at the crests but mainly from the removal of plasma from around the equator by the upward ExB drift with small accumulations when the crests are within approximately ±20° magnetic latitude. The accumulations reduce with increasing latitude and become zero by approximately ±25°. (3) An asymmetric neutral wind makes EPF and EIA asymmetric with stronger fountain and stronger crest usually occurring in opposite hemispheres especially at equinoxes when winter anomaly is absent. (4) During the early stages of daytime main phase of major geomagnetic storms, the plasma fountain becomes a super fountain and the EIA becomes strong not due to the eastward prompt penetration electric field (PPEF) alone but due to the combined effect of eastward PPEF and storm-time equatorward winds (SEW). (5) During the later stages of the storms when EIA gets inhibited a peak sometimes occurs around the equator not due to westward electric fields but mainly due to the convergence of plasma from both hemispheres due to SEW.

Kappa Distribution in a Homogeneous Medium: Adiabatic Limit of a Super-diffusive Process?

NASA Astrophysics Data System (ADS)

Roth, I.

2015-12-01

The classical statistical theory predicts that an ergodic, weakly interacting system like charged particles in the presence of electromagnetic fields, performing Brownian motions (characterized by small range deviations in phase space and short-term microscopic memory), converges into the Gibbs-Boltzmann statistics. Observation of distributions with a kappa-power-law tails in homogeneous systems contradicts this prediction and necessitates a renewed analysis of the basic axioms of the diffusion process: characteristics of the transition probability density function (pdf) for a single interaction, with a possibility of non-Markovian process and non-local interaction. The non-local, Levy walk deviation is related to the non-extensive statistical framework. Particles bouncing along (solar) magnetic field with evolving pitch angles, phases and velocities, as they interact resonantly with waves, undergo energy changes at undetermined time intervals, satisfying these postulates. The dynamic evolution of a general continuous time random walk is determined by pdf of jumps and waiting times resulting in a fractional Fokker-Planck equation with non-integer derivatives whose solution is given by a Fox H-function. The resulting procedure involves the known, although not frequently used in physics fractional calculus, while the local, Markovian process recasts the evolution into the standard Fokker-Planck equation. Solution of the fractional Fokker-Planck equation with the help of Mellin transform and evaluation of its residues at the poles of its Gamma functions results in a slowly converging sum with power laws. It is suggested that these tails form the Kappa function. Gradual vs impulsive solar electron distributions serve as prototypes of this description.

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

NASA Astrophysics Data System (ADS)

Padrino, Juan C.; Zhang, Duan Z.

2016-11-01

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

Electron heat transport measured in a stochastic magnetic field.

PubMed

Biewer, T M; Forest, C B; Anderson, J K; Fiksel, G; Hudson, B; Prager, S C; Sarff, J S; Wright, J C; Brower, D L; Ding, W X; Terry, S D

2003-07-25

New profile measurements have allowed the electron thermal diffusivity profile to be estimated from power balance in the Madison Symmetric Torus where magnetic islands overlap and field lines are stochastic. The measurements show that (1) the electron energy transport is conductive not convective, (2) the measured thermal diffusivities are in good agreement with numerical simulations of stochastic transport, and (3) transport is greatly reduced near the reversal surface where magnetic diffusion is small.

Stochastic field-line wandering in magnetic turbulence with shear. II. Decorrelation trajectory method

NASA Astrophysics Data System (ADS)

Negrea, M.; Petrisor, I.; Shalchi, A.

2017-11-01

We study the diffusion of magnetic field lines in turbulence with magnetic shear. In the first part of the series, we developed a quasi-linear theory for this type of scenario. In this article, we employ the so-called DeCorrelation Trajectory method in order to compute the diffusion coefficients of stochastic magnetic field lines. The magnetic field configuration used here contains fluctuating terms which are described by the dimensionless functions bi(X, Y, Z), i = (x, y) and they are assumed to be Gaussian processes and are perpendicular with respect to the main magnetic field B0. Furthermore, there is also a z-component of the magnetic field depending on radial coordinate x (representing the gradient of the magnetic field) and a poloidal average component. We calculate the diffusion coefficients for magnetic field lines for different values of the magnetic Kubo number K, the dimensionless inhomogeneous magnetic parallel and perpendicular Kubo numbers KB∥, KB⊥ , as well as Ka v=bya vKB∥/KB⊥ .

Star Formation and the Hall Effect

NASA Astrophysics Data System (ADS)

Braiding, Catherine

2011-10-01

Magnetic fields play an important role in star formation by regulating the removal of angular momentum from collapsing molecular cloud cores. Hall diffusion is known to be important to the magnetic field behaviour at many of the intermediate densities and field strengths encountered during the gravitational collapse of molecular cloud cores into protostars, and yet its role in the star formation process is not well-studied. This thesis describes a semianalytic self-similar model of the collapse of rotating isothermal molecular cloud cores with both Hall and ambipolar diffusion, presenting similarity solutions that demonstrate that the Hall effect has a profound influence on the dynamics of collapse. ... Hall diffusion also determines the strength of the magnetic diffusion and centrifugal shocks that bound the pseudo and rotationally-supported discs, and can introduce subshocks that further slow accretion onto the protostar. In cores that are not initially rotating Hall diffusion can even induce rotation, which could give rise to disc formation and resolve the magnetic braking catastrophe. The Hall effect clearly influences the dynamics of gravitational collapse and its role in controlling the magnetic braking and radial diffusion of the field would be worth exploring in future numerical simulations of star formation.

The Role of Diffusivity Quenching in Flux-transport Dynamo Models

NASA Astrophysics Data System (ADS)

Guerrero, Gustavo; Dikpati, Mausumi; de Gouveia Dal Pino, Elisabete M.

2009-08-01

In the nonlinear phase of a dynamo process, the back-reaction of the magnetic field upon the turbulent motion results in a decrease of the turbulence level and therefore in a suppression of both the magnetic field amplification (the α-quenching effect) and the turbulent magnetic diffusivity (the η-quenching effect). While the former has been widely explored, the effects of η-quenching in the magnetic field evolution have rarely been considered. In this work, we investigate the role of the suppression of diffusivity in a flux-transport solar dynamo model that also includes a nonlinear α-quenching term. Our results indicate that, although for α-quenching the dependence of the magnetic field amplification with the quenching factor is nearly linear, the magnetic field response to η-quenching is nonlinear and spatially nonuniform. We have found that the magnetic field can be locally amplified in this case, forming long-lived structures whose maximum amplitude can be up to ~2.5 times larger at the tachocline and up to ~2 times larger at the center of the convection zone than in models without quenching. However, this amplification leads to unobservable effects and to a worse distribution of the magnetic field in the butterfly diagram. Since the dynamo cycle period increases when the efficiency of the quenching increases, we have also explored whether the η-quenching can cause a diffusion-dominated model to drift into an advection-dominated regime. We have found that models undergoing a large suppression in η produce a strong segregation of magnetic fields that may lead to unsteady dynamo-oscillations. On the other hand, an initially diffusion-dominated model undergoing a small suppression in η remains in the diffusion-dominated regime.

Plasma processes in inert gas thrusters

NASA Technical Reports Server (NTRS)

Kaufman, H. R.; Robinson, R. S.

1979-01-01

Inert gas thrusters, particularly with large diameters, have continued to be of interest for space propulsion applications. Two plasma processes are treated in this study: electron diffusion across magnetic fields and double ion production in inert-gas thrusters. A model is developed to describe electron diffusion across a magnetic field that is driven by both density and potential gradients, with Bohm diffusion used to predict the diffusion rate. This model has applications to conduction across magnetic fields inside a discharge chamber, as well as through a magnetic baffle region used to isolate a hollow cathode from the main chamber. A theory for double ion production is presented, which is not as complete as the electron diffusion theory described, but it should be a useful tool for predicting double ion sputter erosion. Correlations are developed that may be used, without experimental data, to predict double ion densities for the design of new and especially larger ion thrusters.

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

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

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

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

PubMed

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

2018-02-01

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

The Fokker-Planck equation for coupled Brown-Néel-rotation.

PubMed

Weizenecker, Jürgen

2018-01-22

Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker-Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker-Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker-Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.

The Fokker-Planck equation for coupled Brown-Néel-rotation

NASA Astrophysics Data System (ADS)

Weizenecker, Jürgen

2018-02-01

Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker-Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker-Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker-Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.

Void Formation during Diffusion - Two-Dimensional Approach

NASA Astrophysics Data System (ADS)

Wierzba, Bartek

2016-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

The generation and dissipation of solar and galactic magnetic fields.

NASA Technical Reports Server (NTRS)

Parker, E. N.

1973-01-01

Turbulent diffusion of magnetic field plays an essential role in the generation of magnetic field in most astrophysical bodies. Review of what can be proved and what can be believed about the turbulent diffusion of magnetic field. Observations indicate the dissipation of magnetic field at rates that can be understood only in terms of turbulent diffusion. Theory shows that a large-scale weak magnetic field diffuses in a turbulent flow in the same way that smoke is mixed throughout the fluid by the turbulence. The small-scale fields (produced from the large-scale field by the turbulence) are limited in their growth by reconnection of field lines at neutral points, so that the turbulent mixing of field and fluid is not halted by them. Altogether, it appears that the mixing of field and fluid in the observed turbulent motions in the sun and in the Galaxy is unavoidable. Turbulent diffusion causes decay of the general solar fields in a decade or so, and of the galactic field in 100 m.y. to 1 b.y. It is concluded that continual dynamo action is implied by the observed existence of the fields.

EM Diffusion for a Time-Domain Airborne EM System

NASA Astrophysics Data System (ADS)

Yin, C.; Qiu, C.; Liu, Y.; Cai, J.

2014-12-01

Visualization of EM diffusion for an airborne EM (AEM) system is important for understanding the transient procedure of EM diffusion. The current distribution and diffusion features also provide effective means to evaluate EM footprint, depth of exploration and further help AEM system design and data interpretation. Most previous studies on EM diffusion (or "smoke ring" effect) are based on the static presentation of EM field, where the dynamic features of EM diffusion were not visible. For visualizing the dynamic feature of EM diffusion, we first calculate in this paper the frequency-domain EM field by downward continuation of the EM field at the EM receiver to the deep earth. After that, we transform the results to time-domain via a Fourier transform. We take a homogeneous half-space and a two-layered earth induced by a step pulse to calculate the EM fields and display the EM diffusion in the earth as 3D animated vectors or time-varying contours. The "smoke ring" effect of EM diffusion, dominated by the resistivity distribution of the earth, is clearly observed. The numerical results for an HCP (vertical magnetic dipole) and a VCX (horizontal magnetic dipole) transmitting coil above a homogeneous half-space of 100 ohm-m are shown in Fig.1. We display as example only the distribution of EM field inside the earth for the diffusion time of 0.05ms. The detailed EM diffusion will be shown in our future presentation. From the numerical experiments for different models, we find that 1) the current for either an HCP or a VCX transmitting dipole propagates downward and outward with time, becoming wider and more diffuse, forming a "smoke ring"; 2) for a VCX transmitter, the underground current forms two ellipses, corresponding to the two polarities of the magnetic flux of a horizontal magnetic dipole, injecting into or ejected from the earth; 3) for a HCP transmitter, however, the underground current forms only one circle, corresponding to the polarity of the magnetic flux for a vertical magnetic dipole, injecting into the earth; 4) there exists no vertical current in an isotropic homogeneous half-space. The currents for both HCP and VCX transmitting dipole flow horizontally.

A Least-Squares Transport Equation Compatible with Voids

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

Hansen, Jon; Peterson, Jacob; Morel, Jim

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

High-throughput ab-initio dilute solute diffusion database.

PubMed

Wu, Henry; Mayeshiba, Tam; Morgan, Dane

2016-07-19

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

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Finite-volume scheme for anisotropic diffusion

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

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

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

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

The dynamics of oceanic fronts. I - The Gulf Stream

NASA Technical Reports Server (NTRS)

Kao, T. W.

1980-01-01

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

Holographic Interferometry and Laminar Jet Diffusion Flames in the Presence of Non-Uniform Magnetic Fields

NASA Technical Reports Server (NTRS)

Baker, J.; Calvert, M. E.; Saito, K.; VanderWal, R.

2001-01-01

Magnetic fields impact combustion processes in a manner analogous to that of buoyancy, i.e., as a body force. It is well known that in a terrestrial environment buoyancy is one of the principal transport mechanisms associated with diffusion flame behavior. Unfortunately, in a terrestrial environment it is difficult if not impossible to isolate flame behavior due magnetic fields from the behavior associated with buoyancy. A micro-, or reduced, gravity environment is ideally suited for studying the impact of magnetic fields on diffusion flames due to the decreased impact of buoyancy on flame behavior.

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

DTIC Science & Technology

1979-02-01

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

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

PubMed

Sánchez-Garduño, Faustino; Pérez-Velázquez, Judith

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

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

PubMed Central

Sánchez-Garduño, Faustino

2016-01-01

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

Self-learning kinetic Monte Carlo simulations of diffusion in ferromagnetic α-Fe-Si alloys

NASA Astrophysics Data System (ADS)

Nandipati, Giridhar; Jiang, Xiujuan; Vemuri, Rama S.; Mathaudhu, Suveen; Rohatgi, Aashish

2018-01-01

Diffusion of Si atom and vacancy in the A2-phase of α-Fe-Si alloys in the ferromagnetic state, with and without magnetic order and in various temperature ranges, are studied using AKSOME, an on-lattice self-learning KMC code. Diffusion of the Si atom and the vacancy are studied in the dilute limit and up to 12 at.% Si, respectively, in the temperature range 350-700 K. Local Si neighborhood dependent activation energies for vacancy hops were calculated on-the-fly using a broken-bond model based on pairwise interaction. The migration barrier and prefactor for the Si diffusion in the dilute limit were obtained and found to agree with published data within the limits of uncertainty. Simulations results show that the prefactor and the migration barrier for the Si diffusion are approximately an order of magnitude higher, and a tenth of an electron-volt higher, respectively, in the magnetic disordered state than in the fully ordered state. However, the net result is that magnetic disorder does not have a significant effect on Si diffusivity within the range of parameters studied in this work. Nevertheless, with increasing temperature, the magnetic disorder increases and its effect on the Si diffusivity also increases. In the case of vacancy diffusion, with increasing Si concentration, its diffusion prefactor decreases while the migration barrier more or less remained constant and the effect of magnetic disorder increases with Si concentration. Important vacancy-Si/Fe atom exchange processes and their activation barriers were identified, and the effect of energetics on ordered phase formation in Fe-Si alloys are discussed.

Nonlocal electrical diffusion equation

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

Magnetic Dissipation in Asymmetric Strong Guide 3D Simulations: Examples of Magnetic Diffusion and Reconnection

NASA Astrophysics Data System (ADS)

Scudder, J. D.; Karimabadi, H.; Daughton, W. S.

2013-12-01

Interpretations of 2D simulations of magnetic reconnection are greatly simplified by using the flux function, usually the out of plane component of the vector potential. This theoretical device is no longer available when simulations are analyzed in 3-D. We illustrate the results of determining the locale rates of flux slippage in simulations by a technique based on Maxwell's equations. The technique recovers the usual results obtained for the flux function in 2D simulations, but remains viable in 3D simulations where there is no flux function. The method has also been successfully tested for full PIC simulations where reconnection is geometrically forbiddden. While such layers possess measurable flux slippages (diffusion) their level is not as strong as recorded in known 2D PIC reconnection sites using the same methodology. This approach will be used to explore the spatial incidence and strength of flux slippages across a 3D, asymmetric, strong guide field run discussed previously in the literature. Regions of diffusive behavior are illustrated where LHDI has been previously identified out on the separatrices, while much stronger flux slippages, typical of the X-regions of 2D simulations, are shown to occur elsewhere throughout the simulation. These results suggest that reconnection requires sufficiently vigorous flux slippage to be self sustaining, while non-zero flux slippage can and does occur without being at the reconnection site. A cross check of this approach is provided by the mixing ratio of tagged simulation particles of known spatial origin discussed by Daughton et al., 2013 (this meeting); they provide an integral measure of flux slippage up to the present point in the simulation. We will discuss the correlations between our Maxwell based flux slippage rates and the inferred rates of change of this mixing ratio (as recorded in the local fluid frame).

Control of Meridional Flow by a Non-Uniform Rotational Magnetic Field

NASA Technical Reports Server (NTRS)

Mazuruk, Konstantin; Ramachandran, Narayanan

1999-01-01

The diffusive mass transfer of species during crystal growth in vertical ampoules is significantly affected by fluid flow in the liquid mother phase (melt). For electrically conductive melts, an elegant way of remotely inducing and controlling this flow is by utilizing a uniform rotational magnetic field (RMF) in the transverse direction. It induces an azimuthal flow which tends to homogenize the thermal and solutal fields. The rotating field also reduces the diffusion boundary layer, stabilizes temperature fluctuations, and promotes better overall crystal growth. For moderate strengths of the applied magnetic field (2-20 m Tesla) with frequencies of up to 400 Hz, the induced secondary meridional flow becomes significant. It typically consists of one roll at the bottom of the liquid column and a second roll (vortex) at the top. The flow along the centerline (ampoule axis) is directed from the growing solid (interface) towards the liquid (melt). In case of convex interfaces (e.g. in floating zone crystal growth) such flow behavior is beneficial since it suppresses diffusion at the center. However, for concave interfaces (e.g. vertical Bridgman crystal growth) such a flow tends to exacerbate the situation in making the interface shape more concave. It would be beneficial to have some control of this meridional flow- for example, a single recirculating cell with controllable direction and flow magnitude will make this technique even more attractive for crystal growth. Such flow control is a possibility if a non-uniform PNE field is utilized for this purpose. Although this idea has been proposed earlier, it has not been conclusively demonstrated so far. In this work, we derive the governing equations for the fluid dynamics for such a system and obtain solutions for a few important cases. Results from parallel experimental measurements of fluid flow in a mercury column subjected to non-uniform RMF will also be presented.

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

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

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

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

PubMed

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

2011-08-01

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

The diffusion approximation. An application to radiative transfer in clouds

NASA Technical Reports Server (NTRS)

Arduini, R. F.; Barkstrom, B. R.

1976-01-01

It is shown how the radiative transfer equation reduces to the diffusion equation. To keep the mathematics as simple as possible, the approximation is applied to a cylindrical cloud of radius R and height h. The diffusion equation separates in cylindrical coordinates and, in a sample calculation, the solution is evaluated for a range of cloud radii with cloud heights of 0.5 km and 1.0 km. The simplicity of the method and the speed with which solutions are obtained give it potential as a tool with which to study the effects of finite-sized clouds on the albedo of the earth-atmosphere system.

Extended phase graphs with anisotropic diffusion

NASA Astrophysics Data System (ADS)

Weigel, M.; Schwenk, S.; Kiselev, V. G.; Scheffler, K.; Hennig, J.

2010-08-01

The extended phase graph (EPG) calculus gives an elegant pictorial description of magnetization response in multi-pulse MR sequences. The use of the EPG calculus enables a high computational efficiency for the quantitation of echo intensities even for complex sequences with multiple refocusing pulses with arbitrary flip angles. In this work, the EPG concept dealing with RF pulses with arbitrary flip angles and phases is extended to account for anisotropic diffusion in the presence of arbitrary varying gradients. The diffusion effect can be expressed by specific diffusion weightings of individual magnetization pathways. This can be represented as an action of a linear operator on the magnetization state. The algorithm allows easy integration of diffusion anisotropy effects. The formalism is validated on known examples from literature and used to calculate the effective diffusion weighting in multi-echo sequences with arbitrary refocusing flip angles.

Cavity equations for a positive- or negative-refraction-index material with electric and magnetic nonlinearities.

PubMed

Mártin, Daniel A; Hoyuelos, Miguel

2009-11-01

We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative-refraction-index material with third-order effective electric and magnetic nonlinearities. Two coupled nonlinear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato-Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors.

Breakdown of the Stokes-Einstein Relation for the Rotational Diffusivity of Polymer Grafted Nanoparticles in Polymer Melts.

PubMed

Maldonado-Camargo, Lorena; Rinaldi, Carlos

2016-11-09

We report observations of breakdown of the Stokes-Einstein relation for the rotational diffusivity of polymer-grafted spherical nanoparticles in polymer melts. The rotational diffusivity of magnetic nanoparticles coated with poly(ethylene glycol) dispersed in poly(ethylene glycol) melts was determined through dynamic magnetic susceptibility measurements of the collective rotation of the magnetic nanoparticles due to imposed time-varying magnetic torques. These measurements clearly demonstrate the existence of a critical molecular weight for the melt polymer, below which the Stokes-Einstein relation accurately describes the rotational diffusivity of the polymer-grafted nanoparticles and above which the Stokes-Einstein relation ceases to apply. This critical molecular weight was found to correspond to a chain contour length that approximates the hydrodynamic diameter of the nanoparticles.

Inside the Black Box: Magnetic Reconnection and the Magnetospheric Multiscale Mission

NASA Astrophysics Data System (ADS)

Cassak, P. A.

2016-03-01

The motivation for the recently launched Magnetospheric Multiscale mission is learning about the process of magnetic reconnection, especially the physics of what is called the diffusion region. The diffusion region is often treated as a black box but is the home of very important physics, which is of great significance to understanding space weather. This article is a brief review of what is known—and not known—about the diffusion region in magnetic reconnection, written for the broad space weather community and its stakeholders (with an appendix for readers interested in more technical matters). The focus is on the physics of magnetic reconnection and the diffusion region, why it has been challenging to study, how MMS will contribute, and how the community will benefit from its measurements.

A complete multifluid model for bipolar semiconductors, with interacting carriers, phonons, and photons

NASA Astrophysics Data System (ADS)

Rossani, A.

2017-12-01

If electrons (e) and holes (h) in metals or semiconductors are heated to the temperatures T_e and T_h greater than the lattice temperature, the electron-phonon interaction causes energy relaxation. In the non-uniform case a momentum relaxation occurs as well. In view of such an application, a new model, based on an asymptotic procedure for solving the kinetic equations of carriers, phonons, and photons, is proposed, which gives naturally the displaced Maxwellian at the leading order. Several generation-recombination (GR) events occur in bipolar semiconductors. In the presence of photons the most important ones are the radiative GR events, direct, indirect, and exciton-catalyzed. Phonons and photons are treated here as a participating species, with their own equation. All the phonon-photon interactions are accounted for. Moreover, carrier-photon (Compton) interactions are introduced, which make complete the model. After that, balance equations for the electron number, hole number, energy densities, and momentum densities are constructed, which constitute now a system of macroscopic equations for the chemical potentials (carriers), the temperatures (carriers and bosons), and the drift velocities (carriers and bosons). In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered, even in the presence of an external magnetic field.

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

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

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Berk, Herbert

2016-10-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Diffusion thermo effects on unsteady MHD free convection flow of a Kuvshinski fluid past a vertical porous plate in slip flow regime

NASA Astrophysics Data System (ADS)

Narsu, Sivakumar; Rushi Kumar, B.

2017-11-01

The main purpose of this work is to investigate the diffusion-thermo effects on unsteady combined convection magneto-hydromagnetic boundary layer flow of viscous electrically conducting and chemically reacting fluid over a vertical permeable radiated plate embedded in a highly porous medium. The slip flow regime is applied at the porous interface a uniform magnetic field is applied normal to the fluid flow direction which absorbs the fluid with suction that varies with time. The dimensionless governing equations are solved analytically using two terms harmonic and non-harmonic functions. The expressions for the fields of velocity, temperature and concentration are obtained. For engineering interest we also calculated the physical quantities the skin friction coefficient, Nusselt and Sherwood number are derived. The effects of various physical parameters on the flow quantities are studied through graphs and tables. For the validity, we have checked our results with previously published work and found good agreement with already existing studies.

Ab initio modeling of CW-ESR spectra of the double spin labeled peptide Fmoc-(Aib-Aib-TOAC)2-Aib-OMe in acetonitrile.

PubMed

Zerbetto, Mirco; Carlotto, Silvia; Polimeno, Antonino; Corvaja, Carlo; Franco, Lorenzo; Toniolo, Claudio; Formaggio, Fernando; Barone, Vincenzo; Cimino, Paola

2007-03-15

In this work we address the interpretation, via an ab initio integrated computational approach, of the CW-ESR spectra of the double spin labeled, 310-helical, peptide Fmoc-(Aib-Aib-TOAC)2-Aib-OMe dissolved in acetonitrile. Our approach is based on the determination of geometric and local magnetic parameters of the heptapeptide by quantum mechanical density functional calculations taking into account solvent and, when needed, vibrational averaging contributions. The system is then described by a stochastic Liouville equation for the two electron spins interacting with each other and with two 14N nuclear spins, in the presence of diffusive rotational dynamics. Parametrization of the diffusion rotational tensor is provided by a hydrodynamic model. CW-ESR spectra are simulated with minimal resorting to fitting procedures, proving that the combination of sensitive ESR spectroscopy and sophisticated modeling can be highly helpful in providing 3D structural and dynamic information on molecular systems.

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

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

Diffusion Processes Satisfying a Conservation Law Constraint

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

Bakosi, J.; Ristorcelli, J. R.

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

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

PubMed

Petrovic, Ljubomir M; Atanackovic, Teodor M

2008-04-01

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

Nuclear magnetic resonance diffusion pore imaging: Experimental phase detection by double diffusion encoding

NASA Astrophysics Data System (ADS)

Demberg, Kerstin; Laun, Frederik Bernd; Windschuh, Johannes; Umathum, Reiner; Bachert, Peter; Kuder, Tristan Anselm

2017-02-01

Diffusion pore imaging is an extension of diffusion-weighted nuclear magnetic resonance imaging enabling the direct measurement of the shape of arbitrarily formed, closed pores by probing diffusion restrictions using the motion of spin-bearing particles. Examples of such pores comprise cells in biological tissue or oil containing cavities in porous rocks. All pores contained in the measurement volume contribute to one reconstructed image, which reduces the problem of vanishing signal at increasing resolution present in conventional magnetic resonance imaging. It has been previously experimentally demonstrated that pore imaging using a combination of a long and a narrow magnetic field gradient pulse is feasible. In this work, an experimental verification is presented showing that pores can be imaged using short gradient pulses only. Experiments were carried out using hyperpolarized xenon gas in well-defined pores. The phase required for pore image reconstruction was retrieved from double diffusion encoded (DDE) measurements, while the magnitude could either be obtained from DDE signals or classical diffusion measurements with single encoding. The occurring image artifacts caused by restrictions of the gradient system, insufficient diffusion time, and by the phase reconstruction approach were investigated. Employing short gradient pulses only is advantageous compared to the initial long-narrow approach due to a more flexible sequence design when omitting the long gradient and due to faster convergence to the diffusion long-time limit, which may enable application to larger pores.

The Role of Nongyrotropy in Balancing the Reconnection Diffusion Region

NASA Astrophysics Data System (ADS)

Hesse, M.; Liu, Y. H.; Chen, L. J.; Bessho, N.; Wang, S.; Burch, J. L.; Moretto, T.; Genestreti, K.; Phan, T.; Tenfjord, P.

2017-12-01

The structure of the reconnection diffusion region is, to a large degree, determined by the requirement to balance both the current flow and its dissipation processes, and the forces exerted onto the current layer by the inflow magnetic pressure. These balances are critical: without resupply processes, the transport of accelerated and current-carrying particles away from the diffusion region would generate a current density depletion, which, in principle, could lead to a mismatch with the curl of the magnetic field. Similarly, without heating processes, the convection of hot plasma away from the diffusion region would generate a force imbalance with the ambient magnetic field. The fact that neither of these imbalances occur is a consequence of the reconnection electric field, which is therefore not only required to facilitate magnetic flux transport, but also to provide the energization required to maintain balance in the diffusion region. In this presentation, we will use particle-in-cell simulations to analyze these balance conditions. We will furthermore show that nongyrotropic particle dynamics plays a key role both as current dissipation mechanism, and as overall heating mechanism in the diffusion region current layer.

Cross-field diffusion in Hall thrusters and other plasma thrusters

NASA Astrophysics Data System (ADS)

Boeuf, J. P.

2012-10-01

Understanding and quantifying electron transport perpendicular to the magnetic field is a challenge in many low temperature plasma applications. Hall effect thrusters (HETs) provide an excellent example of cross-field transport. The HET is a very successful concept that can be considered both as a gridless ion source and an electromagnetic thruster. In HETs, the electric field E accelerating the ions is a consequence of the Lorentz force due to an external magnetic field B acting on the ExB Hall electron current. An essential aspect of HETs is that the ExB drift is closed, i.e. is in the azimuthal direction of a cylindrical channel. In the first part of this presentation we will discuss the physics of cross-field electron transport in HETs, and the current understanding (or non-understanding) of the possible role of turbulence and wall collisions on cross-field diffusion. We will also briefly comment on alternative designs of ion sources based on the same principles as the conventional HET (Anode Layer Thruster, Diverging Cusp Field Thrusters, End-Hall ion sources). In a second part of the presentation we show that the Lorentz force acting on diamagnetic currents (associated with the ∇PexB term in the electron momentum equation) can also provide thrust. This is the case for example in helicon thrusters where the plasma expands in a magnetic nozzle. We will report and discuss recent work on helicon thrusters and other devices where the diamagnetic current is dominant (with some examples where the ∇PexB current is not closed and is directed toward a wall!).