Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. I. Theory

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Rogachevskii, Igor; Kleeorin, Nathan [Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105 (Israel); Ruchayskiy, Oleg [Discovery Center, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Boyarsky, Alexey [Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden (Netherlands); Fröhlich, Jürg [Institute of Theoretical Physics, ETH Hönggerberg, CH-8093 Zurich (Switzerland); Brandenburg, Axel; Schober, Jennifer, E-mail: gary@bgu.ac.il [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm (Sweden)

2017-09-10

The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right- and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma ( chiral magnetic effect ). We present a self-consistent treatment of the chiral MHD equations , which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfvén wave for incompressible flows, increases the frequencies of the Alfvén wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark–gluon plasma.

Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. I. Theory

International Nuclear Information System (INIS)

Rogachevskii, Igor; Kleeorin, Nathan; Ruchayskiy, Oleg; Boyarsky, Alexey; Fröhlich, Jürg; Brandenburg, Axel; Schober, Jennifer

2017-01-01

The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right- and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma ( chiral magnetic effect ). We present a self-consistent treatment of the chiral MHD equations , which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfvén wave for incompressible flows, increases the frequencies of the Alfvén wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark–gluon plasma.

Non-linear dynamo waves in an incompressible medium when the turbulence dissipative coefficients depend on temperature

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A. D. Pataraya

1997-01-01

Full Text Available Non-linear α-ω; dynamo waves existing in an incompressible medium with the turbulence dissipative coefficients depending on temperature are studied in this paper. We investigate of α-ω solar non-linear dynamo waves when only the first harmonics of magnetic induction components are included. If we ignore the second harmonics in the non-linear equation, the turbulent magnetic diffusion coefficient increases together with the temperature, the coefficient of turbulent viscosity decreases, and for an interval of time the value of dynamo number is greater than 1. In these conditions a stationary solution of the non-linear equation for the dynamo wave's amplitude exists; meaning that the magnetic field is sufficiently excited. The amplitude of the dynamo waves oscillates and becomes stationary. Using these results we can explain the existence of Maunder's minimum.

Time-resolved observation of discrete and continuous MHD dynamo in the reversed-field pinch edge

International Nuclear Information System (INIS)

Ji, H.; Almagri, A.F.; Prager, S.C.; Sarff, J.S.

1994-01-01

We report the first experimental verification of the MHD dynamo in the RFP. A burst of magnetohydrodynamic (MHD) dynamo electric field is observed during the sawtooth crash, followed by an increase in the local parallel current in the MST RFP edge. By measuring each term, the parallel MHD mean-field Ohm's law is observed to hold within experimental error bars both between and during sawtooth crashes

Present state of the theory of a MHD-dynamo

Energy Technology Data Exchange (ETDEWEB)

Soward, A M; Roberts, P H

1976-01-01

A review is given of the state of the theory of a MHD-dynamo, that is, the theory of self-excited magnetic fields in homogeneous moving liquids. A description is given of two basic approaches-the turbulent dynamos of Steinbeck, Krause and Redler and the high-conductivity dynamo of Braginski, and a look is also taken at the relation between these dynamos. Finally a look is taken at the results of recent studies of the total problem of a MHD-dynamo, that is, at the results of recent attempts to solve the electro- and hydrodynamic equations and to obtain self-excited fields. 6 figs., 122 ref. (SJR)

MHD turbulent dynamo in astrophysics: Theory and numerical simulation

Science.gov (United States)

Chou, Hongsong

2001-10-01

This thesis treats the physics of dynamo effects through theoretical modeling of magnetohydrodynamic (MHD) systems and direct numerical simulations of MHD turbulence. After a brief introduction to astrophysical dynamo research in Chapter 1, the following issues in developing dynamic models of dynamo theory are addressed: In Chapter 2, nonlinearity that arises from the back reaction of magnetic field on velocity field is considered in a new model for the dynamo α-effect. The dependence of α-coefficient on magnetic Reynolds number, kinetic Reynolds number, magnetic Prandtl number and statistical properties of MHD turbulence is studied. In Chapter 3, the time-dependence of magnetic helicity dynamics and its influence on dynamo effects are studied with a theoretical model and 3D direct numerical simulations. The applicability of and the connection between different dynamo models are also discussed. In Chapter 4, processes of magnetic field amplification by turbulence are numerically simulated with a 3D Fourier spectral method. The initial seed magnetic field can be a large-scale field, a small-scale magnetic impulse, and a combination of these two. Other issues, such as dynamo processes due to helical Alfvénic waves and the implication and validity of the Zeldovich relation, are also addressed in Appendix B and Chapters 4 & 5, respectively. Main conclusions and future work are presented in Chapter 5. Applications of these studies are intended for astrophysical magnetic field generation through turbulent dynamo processes, especially when nonlinearity plays central role. In studying the physics of MHD turbulent dynamo processes, the following tools are developed: (1)A double Fourier transform in both space and time for the linearized MHD equations (Chapter 2 and Appendices A & B). (2)A Fourier spectral numerical method for direct simulation of 3D incompressible MHD equations (Appendix C).

Magnetic field saturation in the Riga dynamo experiment.

Science.gov (United States)

Gailitis, A; Lielausis, O; Platacis, E; Dement'ev, S; Cifersons, A; Gerbeth, G; Gundrum, T; Stefani, F; Christen, M; Will, G

2001-04-02

After the dynamo experiment in November 1999 [A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000)] had shown magnetic field self-excitation in a spiraling liquid metal flow, in a second series of experiments emphasis was placed on the magnetic field saturation regime as the next principal step in the dynamo process. The dependence of the strength of the magnetic field on the rotation rate is studied. Various features of the saturated magnetic field are outlined and possible saturation mechanisms are discussed.

GRAND MINIMA AND EQUATORWARD PROPAGATION IN A CYCLING STELLAR CONVECTIVE DYNAMO

Energy Technology Data Exchange (ETDEWEB)

Augustson, Kyle; Miesch, Mark [High Altitude Observatory, Center Green 1, Boulder, CO 80301 (United States); Brun, Allan Sacha [Laboratoire AIM Paris-Saclay, CEA/DSM–CNRS–Université Paris Diderot, IRFU/SAp, Gif-sur-Yvette (France); Toomre, Juri [JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309 (United States)

2015-08-20

The 3D MHD Anelastic Spherical Harmonic code, using slope-limited diffusion, is employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate. The dynamo-generated magnetic fields possesses many timescales, with a prominent polarity cycle occurring roughly every 6.2 years. The magnetic field forms large-scale toroidal wreaths, whose formation is tied to the low Rossby number of the convection in this simulation. The polarity reversals are linked to the weakened differential rotation and a resistive collapse of the large-scale magnetic field. An equatorial migration of the magnetic field is seen, which is due to the strong modulation of the differential rotation rather than a dynamo wave. A poleward migration of magnetic flux from the equator eventually leads to the reversal of the polarity of the high-latitude magnetic field. This simulation also enters an interval with reduced magnetic energy at low latitudes lasting roughly 16 years (about 2.5 polarity cycles), during which the polarity cycles are disrupted and after which the dynamo recovers its regular polarity cycles. An analysis of this grand minimum reveals that it likely arises through the interplay of symmetric and antisymmetric dynamo families. This intermittent dynamo state potentially results from the simulation’s relatively low magnetic Prandtl number. A mean-field-based analysis of this dynamo simulation demonstrates that it is of the α-Ω type. The timescales that appear to be relevant to the magnetic polarity reversal are also identified.

Differential rotation and the solar dynamo

International Nuclear Information System (INIS)

Stix, M.

1976-01-01

A number of numerical models for the generation of mean magnetic fields is examined and the fields are compared with the mean field of the Sun. In particular, αω-dynamos, which are based on differential rotation and cyclonic turbulence, are studied in the case of cylindrical surfaces of isorotation. Such dynamos have an oscillatory antisymmetric field as the most easily excited mode. Only models with an angular velocity which increases with increasing depth appear to be compatible with observations. A search for oscillatory ω x j-dynamos, where the α-effect is replaced by a different mean electric field perpendicular to the rotation vector ω and the mean current density j is also made. Oscillatory modes do exist for models with radial shear. Their migration is equatorwards for inwards increasing angular velocity. (orig./BJ) [de

Large-scale dynamo action due to α fluctuations in a linear shear flow

Science.gov (United States)

Sridhar, S.; Singh, Nishant K.

2014-12-01

We present a model of large-scale dynamo action in a shear flow that has stochastic, zero-mean fluctuations of the α parameter. This is based on a minimal extension of the Kraichnan-Moffatt model, to include a background linear shear and Galilean-invariant α-statistics. Using the first-order smoothing approximation we derive a linear integro-differential equation for the large-scale magnetic field, which is non-perturbative in the shearing rate S , and the α-correlation time τα . The white-noise case, τα = 0 , is solved exactly, and it is concluded that the necessary condition for dynamo action is identical to the Kraichnan-Moffatt model without shear; this is because white-noise does not allow for memory effects, whereas shear needs time to act. To explore memory effects we reduce the integro-differential equation to a partial differential equation, valid for slowly varying fields when τα is small but non-zero. Seeking exponential modal solutions, we solve the modal dispersion relation and obtain an explicit expression for the growth rate as a function of the six independent parameters of the problem. A non-zero τα gives rise to new physical scales, and dynamo action is completely different from the white-noise case; e.g. even weak α fluctuations can give rise to a dynamo. We argue that, at any wavenumber, both Moffatt drift and Shear always contribute to increasing the growth rate. Two examples are presented: (a) a Moffatt drift dynamo in the absence of shear and (b) a Shear dynamo in the absence of Moffatt drift.

Simulation study of dynamo structure in reversed field pinch

International Nuclear Information System (INIS)

Nagata, A.; Sato, K.I.; Ashida, H.; Amano, T.

1992-10-01

The dynamo structure in the reversed field pinch (RFP) is studied through the nonlinear dynamics of single-helicity mode. Simulation is concentrated upon the physical structure of nonlinear interactions of the plasma flow and magnetic fluctuation. The result indicates that when the initial equilibrium profile is deformed by resistive diffusion, the radial flow is driven near the core of the plasma. As this flow forms a vortex structure and magnetic fluctuation grows radially, the dynamo electric field is spirally induced just inside the reversal surface and then the toroidal flux is increased. This dynamo electric field correlates to nonlinear evolution of the kinetic energy of m=1 mode, and the increase of the toroidal flux is originated in the growth process of the magnetic energy of this mode. Consequently, the RFP configuration can be sustained by the single-helicity evolution of m=1 mode alone, and the electric field induced by the interactions of the toroidal velocity and the radial magnetic field is the most dominant source on the dynamo action. (author)

An MHD Dynamo Experiment.

Science.gov (United States)

O'Connell, R.; Forest, C. B.; Plard, F.; Kendrick, R.; Lovell, T.; Thomas, M.; Bonazza, R.; Jensen, T.; Politzer, P.; Gerritsen, W.; McDowell, M.

1997-11-01

A MHD experiment is being constructed which will have the possibility of showing dynamo action: the self--generation of currents from fluid motion. The design allows sufficient experimental flexibility and diagnostic access to study a variety of issues central to dynamo theory, including mean--field electrodynamics and saturation (backreaction physics). Initially, helical flows required for dynamo action will be driven by propellers embedded in liquid sodium. The flow fields will first be measured using laser doppler velocimetry in a water experiment with an identical fluid Reynolds number. The magnetic field evolution will then be predicted using a MHD code, replacing the water with sodium; if growing magnetic fields are found, the experiment will be repeated with sodium.

Helicity, Reconnection, and Dynamo Effects

International Nuclear Information System (INIS)

Ji, Hantao

1998-01-01

The inter-relationships between magnetic helicity, magnetic reconnection, and dynamo effects are discussed. In laboratory experiments, where two plasmas are driven to merge, the helicity content of each plasma strongly affects the reconnection rate, as well as the shape of the diffusion region. Conversely, magnetic reconnection events also strongly affect the global helicity, resulting in efficient helicity cancellation (but not dissipation) during counter-helicity reconnection and a finite helicity increase or decrease (but less efficiently than dissipation of magnetic energy) during co-helicity reconnection. Close relationships also exist between magnetic helicity and dynamo effects. The turbulent electromotive force along the mean magnetic field (alpha-effect), due to either electrostatic turbulence or the electron diamagnetic effect, transports mean-field helicity across space without dissipation. This has been supported by direct measurements of helicity flux in a laboratory plasma. When the dynamo effect is driven by electromagnetic turbulence, helicity in the turbulent field is converted to mean-field helicity. In all cases, however, dynamo processes conserve total helicity except for a small battery effect, consistent with the observation that the helicity is approximately conserved during magnetic relaxation

3-dimensional simulation of dynamo effect of reversed field pinch

International Nuclear Information System (INIS)

Koide, Shinji.

1990-09-01

A non-linear numerical simulation of the dynamo effect of a reversed field pinch (RFP) with finite beta is presented. It is shown that the m=-1, n=(9,10,11,....,19) modes cause the dynamo effect and sustain the field reversed configuration. The role of the m=0 modes on the dynamo effect is carefully examined. Our simulation shows that the magnetic field fluctuation level scales as S -0.2 or S -0.3 in the range of 10 3 5 , while Nebel, Caramana and Schnack obtained the fluctuation level is independent of S for a pressureless RFP plasma. (author)

Many-Body Mean-Field Equations: Parallel implementation

International Nuclear Information System (INIS)

Vallieres, M.; Umar, S.; Chinn, C.; Strayer, M.

1993-01-01

We describe the implementation of Hartree-Fock Many-Body Mean-Field Equations on a Parallel Intel iPSC/860 hypercube. We first discuss the Nuclear Mean-Field approach in physical terms. Then we describe our parallel implementation of this approach on the Intel iPSC/860 hypercube. We discuss and compare the advantages and disadvantages of the domain partition versus the Hilbert space partition for this problem. We conclude by discussing some timing experiments on various computing platforms

Derivation and precision of mean field electrodynamics with mesoscale fluctuations

Science.gov (United States)

Zhou, Hongzhe; Blackman, Eric G.

2018-06-01

Mean field electrodynamics (MFE) facilitates practical modelling of secular, large scale properties of astrophysical or laboratory systems with fluctuations. Practitioners commonly assume wide scale separation between mean and fluctuating quantities, to justify equality of ensemble and spatial or temporal averages. Often however, real systems do not exhibit such scale separation. This raises two questions: (I) What are the appropriate generalized equations of MFE in the presence of mesoscale fluctuations? (II) How precise are theoretical predictions from MFE? We address both by first deriving the equations of MFE for different types of averaging, along with mesoscale correction terms that depend on the ratio of averaging scale to variation scale of the mean. We then show that even if these terms are small, predictions of MFE can still have a significant precision error. This error has an intrinsic contribution from the dynamo input parameters and a filtering contribution from differences in the way observations and theory are projected through the measurement kernel. Minimizing the sum of these contributions can produce an optimal scale of averaging that makes the theory maximally precise. The precision error is important to quantify when comparing to observations because it quantifies the resolution of predictive power. We exemplify these principles for galactic dynamos, comment on broader implications, and identify possibilities for further work.

Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. II. Simulations

Science.gov (United States)

Schober, Jennifer; Rogachevskii, Igor; Brandenburg, Axel; Boyarsky, Alexey; Fröhlich, Jürg; Ruchayskiy, Oleg; Kleeorin, Nathan

2018-05-01

Using direct numerical simulations (DNS), we study laminar and turbulent dynamos in chiral magnetohydrodynamics with an extended set of equations that accounts for an additional contribution to the electric current due to the chiral magnetic effect (CME). This quantum phenomenon originates from an asymmetry between left- and right-handed relativistic fermions in the presence of a magnetic field and gives rise to a chiral dynamo. We show that the magnetic field evolution proceeds in three stages: (1) a small-scale chiral dynamo instability, (2) production of chiral magnetically driven turbulence and excitation of a large-scale dynamo instability due to a new chiral effect (α μ effect), and (3) saturation of magnetic helicity and magnetic field growth controlled by a conservation law for the total chirality. The α μ effect becomes dominant at large fluid and magnetic Reynolds numbers and is not related to kinetic helicity. The growth rate of the large-scale magnetic field and its characteristic scale measured in the numerical simulations agree well with theoretical predictions based on mean-field theory. The previously discussed two-stage chiral magnetic scenario did not include stage (2), during which the characteristic scale of magnetic field variations can increase by many orders of magnitude. Based on the findings from numerical simulations, the relevance of the CME and the chiral effects revealed in the relativistic plasma of the early universe and of proto-neutron stars are discussed.

The nonlinear differential equations governing a hierarchy of self-exciting coupled Faraday-disk homopolar dynamos

Science.gov (United States)

Hide, Raymond

1997-02-01

This paper discusses the derivation of the autonomous sets of dimensionless nonlinear ordinary differential equations (ODE's) that govern the behaviour of a hierarchy of related electro-mechanical self-exciting Faraday-disk homopolar dynamo systems driven by steady mechanical couples. Each system comprises N interacting units which could be arranged in a ring or lattice. Within each unit and connected in parallel or in series with the coil are electric motors driven into motion by the dynamo, all having linear characteristics, so that nonlinearity arises entirely through the coupling between components. By introducing simple extra terms into the equations it is possible to represent biasing effects arising from impressed electromotive forces due to thermoelectric or chemical processes and from the presence of ambient magnetic fields. Dissipation in the system is due not only to ohmic heating but also to mechanical friction in the disk and the motors, with the latter agency, no matter how weak, playing an unexpectedly crucial rôle in the production of régimes of chaotic behaviour. This has already been demonstrated in recent work on a case of a single unit incorporating just one series motor, which is governed by a novel autonomous set of nonlinear ODE's with three time-dependent variables and four control parameters. It will be of mathematical as well as geophysical and astrophysical interest to investigate systematically phase and amplitude locking and other types of behaviour in the more complicated cases that arise when N > 1, which can typically involve up to 6 N dependent variables and 19 N-5 control parameters. Even the simplest members of the hierarchy, with N as low as 1, 2 or 3, could prove useful as physically-realistic low-dimensional models in theoretical studies of fluctuating stellar and planetary magnetic fields. Geomagnetic polarity reversals could be affected by the presence of the Earth's solid metallic inner core, driven like an electric motor

The Global Solar Dynamo

Science.gov (United States)

Cameron, R. H.; Dikpati, M.; Brandenburg, A.

2017-09-01

A brief summary of the various observations and constraints that underlie solar dynamo research are presented. The arguments that indicate that the solar dynamo is an alpha-omega dynamo of the Babcock-Leighton type are then shortly reviewed. The main open questions that remain are concerned with the subsurface dynamics, including why sunspots emerge at preferred latitudes as seen in the familiar butterfly wings, why the cycle is about 11 years long, and why the sunspot groups emerge tilted with respect to the equator (Joy's law). Next, we turn to magnetic helicity, whose conservation property has been identified with the decline of large-scale magnetic fields found in direct numerical simulations at large magnetic Reynolds numbers. However, magnetic helicity fluxes through the solar surface can alleviate this problem and connect theory with observations, as will be discussed.

New results on an equipartition dynamo

DEFF Research Database (Denmark)

Dorch, S. B. F.; Archontis, V.

2006-01-01

This contribution presents results from numerical computer experiments with a 3-d steady sine flow (with zero mean helicity) that drives fast dynamo action. The mode of operation of this so-called ``no-cosines" dynamo (recently dubbed ``the Archontis dynamo"" by David Galloway) was studied during...... significantly higher that intermittent turbulent dynamos: Namely very close to energy equipartition for high Reynolds numbers. The equipartition solution however is not turbulent but a laminar solution that acts as an attractor to other modes. Similarities and differences, in the way the magnetic field...

Ionospheric disturbance dynamo

International Nuclear Information System (INIS)

Blanc, M.; Richmond, A.D.

1980-01-01

A numerical simulation study of the thermospheric winds produced by auroral heating during magnetic storms, and of their global dynamo effects, establishes the main features of the ionospheric disturbanc dynamo. Driven by auroral heating, a Hadley cell is created with equatorward winds blowing above about 120 km at mid-latitudes. The transport of angular momentum by these winds produces a subrotation of the midlatitude thermosphere, or westward motion with respect to the earth. The westward winds in turn drive equatorward Pedersen currents which accumulate charge toward the equator, resulting in the generation of a poleward electric field, a westward E x B drift, and an eastward current. When realistic local time conductivity variations are simulated, the eastward mid-latitude current is found to close partly via lower latitudes, resulting in an 'anti-Sq' type of current vortex. Both electric field and current at low latitudes thus vary in opposition to their normal quiet-day behavior. This total pattern of distrubance winds, electric fields, and currents is superimposed upon the background quiet-day pattern. When the neutral winds are artificially confined on the nightside, the basic pattern of predominantly westward E x B plasma drifts still prevails on the nightside but no longer extends into the dayside. Considerable observational evidence exists, suggesting that the ionospheric disturbance dynamo has an appreciable influence on storm-time ionospheric electric fields at middle and low latitudes

A basal magma ocean dynamo to explain the early lunar magnetic field

Science.gov (United States)

Scheinberg, Aaron L.; Soderlund, Krista M.; Elkins-Tanton, Linda T.

2018-06-01

The source of the ancient lunar magnetic field is an unsolved problem in the Moon's evolution. Theoretical work invoking a core dynamo has been unable to explain the magnitude of the observed field, falling instead one to two orders of magnitude below it. Since surface magnetic field strength is highly sensitive to the depth and size of the dynamo region, we instead hypothesize that the early lunar dynamo was driven by convection in a basal magma ocean formed from the final stages of an early lunar magma ocean; this material is expected to be dense, radioactive, and metalliferous. Here we use numerical convection models to predict the longevity and heat flow of such a basal magma ocean and use scaling laws to estimate the resulting magnetic field strength. We show that, if sufficiently electrically conducting, a magma ocean could have produced an early dynamo with surface fields consistent with the paleomagnetic observations.

Dynamos and MHD theory of turbulence suppression

International Nuclear Information System (INIS)

Yoshizawa, Akira; Yokoi, Nobumitsu; Itoh, Sanae-I; Itoh, Kimitaka

2003-12-01

Characteristics of electrically-conducting media are reviewed from the macroscopic viewpoint based on the mean-field magnetohydrodynamics, while being compared with the methodology and knowledge in fluid mechanics. The themes covered in this review range from the generation mechanism of stellar magnetic fields (dynamo) to transport properties in fusion. The primary concern here is to see the characteristics common to these apparently different phenomena, within the framework of the mean-field theory. Owing to the intrinsic limitation of the approach, the present discussions are limited more or less to specific aspects of phenomena. They are supplemented with the reference to theoretical, numerical, and observational approaches intrinsic to each theme. In the description of dynamo phenomena, an emphasis is put on the cross-helicity dynamo. Features common to the stellar magnetic-field generation and the rotational-motion drive in toroidal plasmas are illustrated on this basis. (author)

Spectroscopic measurement of the MHD dynamo in the MST reversed field pinch

International Nuclear Information System (INIS)

Chapman, J.T.

1998-09-01

The author has directly observed the coupling of ion velocity fluctuations and magnetic field fluctuations to produce an MHD dynamo electric field in the interior of the MST reversed field pinch. Chord averaged ion velocity fluctuations were measured with a fast spectroscopic diagnostic which collects line radiation from intrinsic carbon impurities simultaneously along two lines of sight. The chords employed for the measurements resolved long wavelength velocity fluctuations of several km/s at 8--20 kHz as tiny, fast Doppler shifts in the emitted line profile. During discrete dynamo events the velocity fluctuations, like the magnetic fluctuations, increase dramatically. The toroidal and poloidal chords with impact parameters of 0.3 a and 0.6 a respectively, resolved fluctuation wavenumbers with resonance surfaces near or along the lines of sight indicating a radial velocity fluctuation width for each mode which spans only a fraction of the plasma radius. The phase between the measured toroidal velocity fluctuations and the magnetic fluctuations matches the predictions of resistive MHD while the poloidal velocity fluctuations exhibit a phase consistent with the superposition of MHD effects and the advection of a mean flow gradient past the poloidal line of sight. Radial velocity fluctuations resolved by a chord through the center of the plasma were small compared to the poloidal and toroidal fluctuations and exhibited low coherence with the magnetic fluctuations. The ensembled nonlinear product of the ion velocity fluctuations and fluctuations in the magnetic field indicates a substantial dynamo electric field which peaks during the periods of spontaneous flux generation

Spectroscopic measurement of the MHD dynamo in the MST reversed field pinch

Energy Technology Data Exchange (ETDEWEB)

Chapman, James Tharp [Univ. of Wisconsin, Madison, WI (United States)

1998-09-01

The author has directly observed the coupling of ion velocity fluctuations and magnetic field fluctuations to produce an MHD dynamo electric field in the interior of the MST reversed field pinch. Chord averaged ion velocity fluctuations were measured with a fast spectroscopic diagnostic which collects line radiation from intrinsic carbon impurities simultaneously along two lines of sight. The chords employed for the measurements resolved long wavelength velocity fluctuations of several km/s at 8-20 kHz as tiny, fast Doppler shifts in the emitted line profile. During discrete dynamo events the velocity fluctuations, like the magnetic fluctuations, increase dramatically. The toroidal and poloidal chords with impact parameters of 0.3 a and 0.6 a respectively, resolved fluctuation wavenumbers with resonance surfaces near or along the lines of sight indicating a radial velocity fluctuation width for each mode which spans only a fraction of the plasma radius. The phase between the measured toroidal velocity fluctuations and the magnetic fluctuations matches the predictions of resistive MHD while the poloidal velocity fluctuations exhibit a phase consistent with the superposition of MHD effects and the advection of a mean flow gradient past the poloidal line of sight. Radial velocity fluctuations resolved by a chord through the center of the plasma were small compared to the poloidal and toroidal fluctuations and exhibited low coherence with the magnetic fluctuations. The ensembled nonlinear product of the ion velocity fluctuations and fluctuations in the magnetic field indicates a substantial dynamo electric field which peaks during the periods of spontaneous flux generation.

EFFECTS OF FOSSIL MAGNETIC FIELDS ON CONVECTIVE CORE DYNAMOS IN A-TYPE STARS

International Nuclear Information System (INIS)

Featherstone, Nicholas A.; Toomre, Juri; Browning, Matthew K.; Brun, Allan Sacha

2009-01-01

The vigorous magnetic dynamo action achieved within the convective cores of A-type stars may be influenced by fossil magnetic fields within their radiative envelopes. We study such effects through three-dimensional simulations that model the inner 30% by radius of a 2 M sun A-type star, capturing the convective core and a portion of the overlying radiative envelope within our computational domain. We employ the three-dimensional anelastic spherical harmonic code to model turbulent dynamics within a deep rotating spherical shell. The interaction between a fossil field and the core dynamo is examined by introducing a large-scale magnetic field into the radiative envelope of a mature A star dynamo simulation. We find that the inclusion of a twisted toroidal fossil field can lead to a remarkable transition in the core dynamo behavior. Namely, a super-equipartition state can be realized in which the magnetic energy built by dynamo action is 10-fold greater than the kinetic energy of the convection itself. Such strong-field states may suggest that the resulting Lorentz forces should seek to quench the flows, yet we have achieved super-equipartition dynamo action that persists for multiple diffusion times. This is achieved by the relative co-alignment of the flows and magnetic fields in much of the domain, along with some lateral displacements of the fastest flows from the strongest fields. Convection in the presence of such strong magnetic fields typically manifests as 4-6 cylindrical rolls aligned with the rotation axis, each possessing central axial flows that imbue the rolls with a helical nature. The roll system also possesses core-crossing flows that couple distant regions of the core. We find that the magnetic fields exhibit a comparable global topology with broad, continuous swathes of magnetic field linking opposite sides of the convective core. We have explored several poloidal and toroidal fossil field geometries, finding that a poloidal component is essential

Turbulent transport coefficients in spherical wedge dynamo simulations of solar-like stars

Science.gov (United States)

Warnecke, J.; Rheinhardt, M.; Tuomisto, S.; Käpylä, P. J.; Käpylä, M. J.; Brandenburg, A.

2018-01-01

Aims: We investigate dynamo action in global compressible solar-like convective dynamos in the framework of mean-field theory. Methods: We simulate a solar-type star in a wedge-shaped spherical shell, where the interplay between convection and rotation self-consistently drives a large-scale dynamo. To analyze the dynamo mechanism we apply the test-field method for azimuthally (φ) averaged fields to determine the 27 turbulent transport coefficients of the electromotive force, of which six are related to the α tensor. This method has previously been used either in simulations in Cartesian coordinates or in the geodynamo context and is applied here for the first time to fully compressible simulations of solar-like dynamos. Results: We find that the φφ-component of the α tensor does not follow the profile expected from that of kinetic helicity. The turbulent pumping velocities significantly alter the effective mean flows acting on the magnetic field and therefore challenge the flux transport dynamo concept. All coefficients are significantly affected by dynamically important magnetic fields. Quenching as well as enhancement are being observed. This leads to a modulation of the coefficients with the activity cycle. The temporal variations are found to be comparable to the time-averaged values and seem to be responsible for a nonlinear feedback on the magnetic field generation. Furthermore, we quantify the validity of the Parker-Yoshimura rule for the equatorward propagation of the mean magnetic field in the present case.

Stellar convection and dynamo theory

Energy Technology Data Exchange (ETDEWEB)

Jennings, R L

1989-10-01

In considering the large scale stellar convection problem the outer layers of a star are modelled as two co-rotating plane layers coupled at a fluid/fluid interface. Heating from below causes only the upper fluid to convect, although this convection can penetrate into the lower fluid. Stability analysis is then used to find the most unstable mode of convection. With parameters appropriate to the Sun the most unstable mode is steady convection in thin cells (aspect ratio {approx equal} 0.2) filling the convection zone. There is negligible vertical motion in the lower fluid, but considerable thermal penetration, and a large jump in helicity at the interface, which has implications for dynamo theory. An {alpha}{omega} dynamo is investigated in isolation from the convection problem. Complexity is included by allowing both latitudinal and time dependence in the magnetic fields. The nonlinear dynamics of the resulting partial differential equations are analysed in considerable detail. On varying the main control parameter D (the dynamo number), many transitions of behaviour are found involving many forms of time dependence, but not chaos. Further, solutions which break equatorial symmetry are common and provide a theoretical explanation of solar observations which have this symmetry. Overall the behaviour was more complicated than expected. In particular, there were multiple stable solutions at fixed D, meaning that similar stars can have very different magnetic patterns, depending upon their history. (author).

Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence

Science.gov (United States)

Bartolucci, Daniele; Jevnikar, Aleks; Lee, Youngae; Yang, Wen

2018-04-01

The understanding of some large energy, negative specific heat states in the Onsager description of 2D turbulence seem to require the analysis of a subtle open problem about bubbling solutions of the mean field equation. Motivated by this application we prove that, under suitable non-degeneracy assumptions on the associated m-vortex Hamiltonian, the m-point bubbling solutions of the mean field equation are non-degenerate as well. Then we deduce that the Onsager mean field equilibrium entropy is smooth and strictly convex in the high energy regime on domains of second kind.

Magnetic field dynamos and magnetically triggered flow instabilities

Science.gov (United States)

Stefani, F.; Albrecht, T.; Arlt, R.; Christen, M.; Gailitis, A.; Gellert, M.; Giesecke, A.; Goepfert, O.; Herault, J.; Kirillov, O. N.; Mamatsashvili, G.; Priede, J.; Rüdiger, G.; Seilmayer, M.; Tilgner, A.; Vogt, T.

2017-07-01

The project A2 of the LIMTECH Alliance aimed at a better understanding of those magnetohydrodynamic instabilities that are relevant for the generation and the action of cosmic magnetic fields. These comprise the hydromagnetic dynamo effect and various magnetically triggered flow instabilities, such as the magnetorotational instability and the Tayler instability. The project was intended to support the experimental capabilities to become available in the framework of the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN). An associated starting grant was focused on the dimensioning of a liquid metal experiment on the newly found magnetic destabilization of rotating flows with positive shear. In this survey paper, the main results of these two projects are summarized.

Ion heating and MHD dynamo fluctuations in the reversed field pinch

International Nuclear Information System (INIS)

Scime, E.; Hokin, S.; Watts, C.; Mattor, N.

1992-01-01

Ion temperature measurements, time resolved to 10 μs, have been made in the Madison Symmetric Torus reversed-field pinch with a five channel charge exchange analyzer. The ion temperature, T i ∼ 200 eV for I = 350 kA, increases by as much as 100% during discrete dynamo bursts in MST discharges. Magnetic field fluctuations in the range 0.5--5 MHz were also measured. Structure in the fluctuation frequency spectrum at the ion cyclotron frequency appears as the bursts terminate, suggesting that the mechanism of ion heating involves the dissipation of dynamo fluctuations at ion gyro-orbit scales

Small-scale dynamo at low magnetic Prandtl numbers

Science.gov (United States)

Schober, Jennifer; Schleicher, Dominik; Bovino, Stefano; Klessen, Ralf S.

2012-12-01

The present-day Universe is highly magnetized, even though the first magnetic seed fields were most probably extremely weak. To explain the growth of the magnetic field strength over many orders of magnitude, fast amplification processes need to operate. The most efficient mechanism known today is the small-scale dynamo, which converts turbulent kinetic energy into magnetic energy leading to an exponential growth of the magnetic field. The efficiency of the dynamo depends on the type of turbulence indicated by the slope of the turbulence spectrum v(ℓ)∝ℓϑ, where v(ℓ) is the eddy velocity at a scale ℓ. We explore turbulent spectra ranging from incompressible Kolmogorov turbulence with ϑ=1/3 to highly compressible Burgers turbulence with ϑ=1/2. In this work, we analyze the properties of the small-scale dynamo for low magnetic Prandtl numbers Pm, which denotes the ratio of the magnetic Reynolds number, Rm, to the hydrodynamical one, Re. We solve the Kazantsev equation, which describes the evolution of the small-scale magnetic field, using the WKB approximation. In the limit of low magnetic Prandtl numbers, the growth rate is proportional to Rm(1-ϑ)/(1+ϑ). We furthermore discuss the critical magnetic Reynolds number Rmcrit, which is required for small-scale dynamo action. The value of Rmcrit is roughly 100 for Kolmogorov turbulence and 2700 for Burgers. Furthermore, we discuss that Rmcrit provides a stronger constraint in the limit of low Pm than it does for large Pm. We conclude that the small-scale dynamo can operate in the regime of low magnetic Prandtl numbers if the magnetic Reynolds number is large enough. Thus, the magnetic field amplification on small scales can take place in a broad range of physical environments and amplify week magnetic seed fields on short time scales.

Small-scale dynamo at low magnetic Prandtl numbers.

Science.gov (United States)

Schober, Jennifer; Schleicher, Dominik; Bovino, Stefano; Klessen, Ralf S

2012-12-01

The present-day Universe is highly magnetized, even though the first magnetic seed fields were most probably extremely weak. To explain the growth of the magnetic field strength over many orders of magnitude, fast amplification processes need to operate. The most efficient mechanism known today is the small-scale dynamo, which converts turbulent kinetic energy into magnetic energy leading to an exponential growth of the magnetic field. The efficiency of the dynamo depends on the type of turbulence indicated by the slope of the turbulence spectrum v(ℓ)∝ℓ^{ϑ}, where v(ℓ) is the eddy velocity at a scale ℓ. We explore turbulent spectra ranging from incompressible Kolmogorov turbulence with ϑ=1/3 to highly compressible Burgers turbulence with ϑ=1/2. In this work, we analyze the properties of the small-scale dynamo for low magnetic Prandtl numbers Pm, which denotes the ratio of the magnetic Reynolds number, Rm, to the hydrodynamical one, Re. We solve the Kazantsev equation, which describes the evolution of the small-scale magnetic field, using the WKB approximation. In the limit of low magnetic Prandtl numbers, the growth rate is proportional to Rm^{(1-ϑ)/(1+ϑ)}. We furthermore discuss the critical magnetic Reynolds number Rm_{crit}, which is required for small-scale dynamo action. The value of Rm_{crit} is roughly 100 for Kolmogorov turbulence and 2700 for Burgers. Furthermore, we discuss that Rm_{crit} provides a stronger constraint in the limit of low Pm than it does for large Pm. We conclude that the small-scale dynamo can operate in the regime of low magnetic Prandtl numbers if the magnetic Reynolds number is large enough. Thus, the magnetic field amplification on small scales can take place in a broad range of physical environments and amplify week magnetic seed fields on short time scales.

Linear astrophysical dynamos in rotating spheres: Differential rotation, anisotropic turbulent magnetic diffusivity, and solar-stellar cycle magnetic parity

International Nuclear Information System (INIS)

Yoshimura, H.; Wang, Z.; Wu, F.

1984-01-01

Differential rotation dependence of the selection mechanism for magnetic parity of solar and stellar cycles is studied by assuming various differential rotation profiles inn the dynamo equation. The parity selection depends on propagation direction of oscillating magnetic fields in the form of dynamo waves which propagate along isorotation surfaces. When there is any radial gradient in the differential rotation, dynamo waves propagate either equatorward or poleward. In the former case, field systems of the two hemispheres approach each other and collide at the equator. Then, odd parity is selected. In the latter case, field systems of the two hemispheres recede from each other and do not collide at the equator, an even parity is selected. Thus the equatorial migration of wings of the butterfly iagram of the solar cycle and its odd parity are intrinsically related. In the case of purely latitudibnal differential rotation, dynamo waves propagate purely radially and growth rates of odd and even modes are nearly the same even when dynamo strength is weak when the parity selection mechanism should work most efficiently. In this case, anisotropy of turbulent diffusivity is a decisive factor to separate odd and even modes. Unlike in the case of radial-gradient-dominated differential rotation in which any difference between diffusivities for poloidal and toroidal fields enhancess the parity selection without changing the parity, the parity selection in the case of latitudinal-gradient-dominated differential rotation depends on the difference of diffusivities for poloidal and toroidal fields. When diffusivity for poloidal fields iss larger than that for toroidal fields, odd parity is selected; and when diffusivity for toroidal fields is larger, even parity is selected

On the saturation of astrophysical dynamos

DEFF Research Database (Denmark)

Dorch, Bertil; Archontis, Vasilis

2004-01-01

In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and we study the dynamo's mode of operation during both the linear and non-linear saturation regimes. It turns out that in addition to a high growth rate in the li......In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and we study the dynamo's mode of operation during both the linear and non-linear saturation regimes. It turns out that in addition to a high growth rate...

Functional differential equation approach to the large N expansion and mean field perturbation theory

International Nuclear Information System (INIS)

Bender, C.M.; Cooper, F.

1985-01-01

An apparent difference between formulating mean field perturbation theory for lambdaphi 4 field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi 4 field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equations for the fields phi and chi (equivalent1/2lambda/Nphi/sub α/phi/sup α/-μ 2 ) in the presence of two external sources j = -deltaGAMMA/deltaphi, S = -deltaGAMMA/deltachi

Transitions in rapidly rotating convection dynamos

Science.gov (United States)

Tilgner, A.

2013-12-01

It is commonly assumed that buoyancy in the fluid core powers the geodynamo. We study here the minimal model of a convection driven dynamo, which is a horizontal plane layer in a gravity field, filled with electrically conducting fluid, heated from below and cooled from above, and rotating about a vertical axis. Such a plane layer may be viewed as a local approximation to the geophysically more relevant spherical geometry. The numerical simulations have been run on graphics processing units with at least 960 cores. If the convection is driven stronger and stronger at fixed rotation rate, the flow behaves at some point as if it was not rotating. This transition shows in the scaling of the heat transport which can be used to distinguish slow from rapid rotation. One expects dynamos to behave differently in these two flow regimes. But even within the convection flows which are rapidly rotating according to this criterion, it will be shown that different types of dynamos exist. In one state, the magnetic field strength obeys a scaling indicative of a magnetostrophic balance, in which the Lorentz force is in equilibrium with the Coriolis force. The flow in this case is helical. A different state exists at higher magnetic Reynolds numbers, in which the magnetic energy obeys a different scaling law and the helicity of the flow is much reduced. As one increases the Rayleigh number, all other parameters kept constant, one may find both types of dynamos separated by an interval of Rayleigh numbers in which there are no dynamos at all. The effect of these transitions on energy dissipation and mean field generation have also been studied.

Magnetic and velocity fields in a dynamo operating at extremely small Ekman and magnetic Prandtl numbers

Science.gov (United States)

Šimkanin, Ján; Kyselica, Juraj

2017-12-01

Numerical simulations of the geodynamo are becoming more realistic because of advances in computer technology. Here, the geodynamo model is investigated numerically at the extremely low Ekman and magnetic Prandtl numbers using the PARODY dynamo code. These parameters are more realistic than those used in previous numerical studies of the geodynamo. Our model is based on the Boussinesq approximation and the temperature gradient between upper and lower boundaries is a source of convection. This study attempts to answer the question how realistic the geodynamo models are. Numerical results show that our dynamo belongs to the strong-field dynamos. The generated magnetic field is dipolar and large-scale while convection is small-scale and sheet-like flows (plumes) are preferred to a columnar convection. Scales of magnetic and velocity fields are separated, which enables hydromagnetic dynamos to maintain the magnetic field at the low magnetic Prandtl numbers. The inner core rotation rate is lower than that in previous geodynamo models. On the other hand, dimensional magnitudes of velocity and magnetic fields and those of the magnetic and viscous dissipation are larger than those expected in the Earth's core due to our parameter range chosen.

Turbulent Diffusion of the Geomagnetic Field and Dynamo Theories

OpenAIRE

Filippi, Enrico

2016-01-01

The thesis deals with the Dynamo Theories of the Earth’s Magnetic Field and mainly deepens the turbulence phenomena in the fluid Earth’s core. Indeed, we think that these phenomena are very important to understand the recent decay of the geomagnetic field. The thesis concerns also the dynamics of the outer core and some very rapid changes of the geomagnetic field observed in the Earth’s surface and some aspects regarding the (likely) isotropic turbulence in the Magnetohydrodynamics. These top...

Large-scale dynamo of accretion disks around supermassive nonrotating black holes

Directory of Open Access Journals (Sweden)

Poplavsky A.L.

2006-01-01

Full Text Available In this paper one presents an analytical model of accretion disk magnetosphere dynamics around supermassive nonrotating black holes in the centers of active galactic nuclei. Based on general relativistic equations of magneto hydrodynamics, the nonstationary solutions for time-dependent dynamo action in the accretion disks, spatial and temporal distribution of magnetic field are found. It is shown that there are two distinct stages of dynamo process: the transient and the steady-state regimes, the induction of magnetic field at t > 6:6665 x 1011GM/c3 s becomes stationary, magnetic field is located near the innermost stable circular orbit, and its value rises up to ~ 105 G. Applications of such systems with nonrotating black holes in real active galactic nuclei are discussed.

Helicity--vorticity turbulent pumping of magnetic fields in the solar dynamo

OpenAIRE

Pipin, V. V.

2012-01-01

The interaction of helical convective motions and differential rotation in the solar convection zone results in turbulent drift of a large-scale magnetic field. We discuss the pumping mechanism and its impact on the solar dynamo.

Numerical models of planetary dynamos

International Nuclear Information System (INIS)

Glatzmaier, G.A.; Roberts, P.H.

1992-01-01

We describe a nonlinear, axisymmetric, spherical-shell model of planetary dynamos. This intermediate-type dynamo model requires a prescribed helicity field (the alpha effect) and a prescribed buoyancy force or thermal wind (the omega effect) and solves for the axisymmetric time-dependent magnetic and velocity fields. Three very different time dependent solutions are obtained from different prescribed sets of alpha and omega fields

Nuclear structure information studied through Dirac equation with deformed mean fields

International Nuclear Information System (INIS)

Dudek, J.

2000-01-01

Complete text of publication follows. Relativistic mean-field theory provides a formal expression for the Dirac equation for the nucleonic motion in an atomic nucleus. The 'potentials' within such a formalism are given in terms of the meson fields, the latter obtained through a coupled system of equations of the Klein-Grodon type. Usually the whole system is being solved by using a Hartree approximation by employing an iterative selfonsistent algorithms. On a more phenomenological level one can parametrize the potentials that enter into a Dirac equation rather than obtain the selfconsistently; such a simplification was suggested some time ago by the Munich group. We introduce a Woods-Saxon type parametrisation and verify by a non-linear search routine what are the 'best fit potential parameters' that reproduce the single particle excitations in the double-magic spherical nuclei as well as the band-head properties in some hundreds of deformed nuclei. Next, by introducing a low-energy reduction of the Dirac equation, one may obtain in a natural way a Pauli Schrodinger type equation with a position dependent effective mass. The role of the corresponding term in a description of single particle energies of the nucleons is illustrated and the implications for the cranking equation are discussed in some detail. (author)

Nonlinear MHD dynamo operating at equipartition

DEFF Research Database (Denmark)

Archontis, V.; Dorch, Bertil; Nordlund, Åke

2007-01-01

Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy-equipartition a......Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy......, and that it can saturate at a level significantly higher than intermittent turbulent dynamos, namely at energy equipartition, for high values of the magnetic and fluid Reynolds numbers. The equipartition solution however does not remain time-independent during the simulation but exhibits a much more intricate...

A Model of the Turbulent Electric Dynamo in Multi-Phase Media

Science.gov (United States)

Dementyeva, Svetlana; Mareev, Evgeny

2016-04-01

Many terrestrial and astrophysical phenomena witness the conversion of kinetic energy into electric energy (the energy of the quasi-stationary electric field) in conducting media, which is natural to treat as manifestations of electric dynamo by analogy with well-known theory of magnetic dynamo. Such phenomena include thunderstorms and lightning in the Earth's atmosphere and atmospheres of other planets, electric activity caused by dust storms in terrestrial and Martian atmospheres, snow storms, electrical discharges occurring in technological setups, connected with intense mixing of aerosol particles like in the milling industry. We have developed a model of the large-scale turbulent electric dynamo in a weakly conducting medium, containing two heavy-particle components. We have distinguished two main classes of charging mechanisms (inductive and non-inductive) in accordance with the dependence or independence of the electric charge, transferred during a particle collision, on the electric field intensity and considered the simplified models which demonstrate the possibility of dynamo realization and its specific peculiarities for these mechanisms. Dynamo (the large-scale electric field growth) appears due to the charge separation between the colliding and rebounding particles. This process is may be greatly intensified by the turbulent mixing of particles with different masses and, consequently, different inertia. The particle charge fluctuations themselves (small-scale dynamo), however, do not automatically mean growth of the large-scale electric field without a large-scale asymmetry. Such an asymmetry arises due to the dependence of the transferred charge magnitude on the electric field intensity in the case of the inductive mechanism of charge separation, or due to the gravity and convection for non-inductive mechanisms. We have found that in the case of the inductive mechanism the large-scale dynamo occurs if the medium conductivity is small enough while the

A NEW SIMPLE DYNAMO MODEL FOR STELLAR ACTIVITY CYCLE

Energy Technology Data Exchange (ETDEWEB)

Yokoi, N.; Hamba, F. [Institute of Industrial Science, University of Tokyo, Tokyo 153-8505 (Japan); Schmitt, D. [Max-Planck Institut für Sonnensystemforschung, Göttingen D-37077 (Germany); Pipin, V., E-mail: nobyokoi@iis.u-tokyo.ac.jp [Institute of Solar–Terrestrial Physics, Russian Academy of Science, Irkutsk 664033 (Russian Federation)

2016-06-20

A new simple dynamo model for stellar activity cycle is proposed. By considering an inhomogeneous flow effect on turbulence, it is shown that turbulent cross helicity (velocity–magnetic-field correlation) enters the expression of turbulent electromotive force as the coupling coefficient for the mean absolute vorticity. This makes the present model different from the current α –Ω-type models in two main ways. First, in addition to the usual helicity ( α ) and turbulent magnetic diffusivity ( β ) effects, we consider the cross-helicity effect as a key ingredient of the dynamo process. Second, the spatiotemporal evolution of cross helicity is solved simultaneously with the mean magnetic fields. The basic scenario is as follows. In the presence of turbulent cross helicity, the toroidal field is induced by the toroidal rotation. Then, as in usual models, the α effect generates the poloidal field from the toroidal one. This induced poloidal field produces a turbulent cross helicity whose sign is opposite to the original one (negative production). With this cross helicity of the reversed sign, a reversal in field configuration starts. Eigenvalue analyses of the simplest possible model give a butterfly diagram, which confirms the above scenario and the equatorward migrations, the phase relationship between the cross helicity and magnetic fields. These results suggest that the oscillation of the turbulent cross helicity is a key for the activity cycle. The reversal of the cross helicity is not the result of the magnetic-field reversal, but the cause of the latter. This new model is expected to open up the possibility of the mean-field or turbulence closure dynamo approaches.

A simple stochastic model for dipole moment fluctuations in numerical dynamo simulations

Directory of Open Access Journals (Sweden)

Domenico G. eMeduri

2016-04-01

Full Text Available Earth's axial dipole field changes in a complex fashion on many differenttime scales ranging from less than a year to tens of million years.Documenting, analysing, and replicating this intricate signalis a challenge for data acquisition, theoretical interpretation,and dynamo modelling alike. Here we explore whether axial dipole variationscan be described by the superposition of a slow deterministic driftand fast stochastic fluctuations, i.e. by a Langevin-type system.The drift term describes the time averaged behaviour of the axial dipole variations,whereas the stochastic part mimics complex flow interactions over convective time scales.The statistical behaviour of the system is described by a Fokker-Planck equation whichallows useful predictions, including the average rates of dipole reversals and excursions.We analyse several numerical dynamo simulations, most of which havebeen integrated particularly long in time, and also the palaeomagneticmodel PADM2M which covers the past 2 Myr.The results show that the Langevin description provides a viable statistical modelof the axial dipole variations on time scales longer than about 1 kyr.For example, the axial dipole probability distribution and the average reversalrate are successfully predicted.The exception is PADM2M where the stochastic model reversal rate seems too low.The dependence of the drift on the axial dipolemoment reveals the nonlinear interactions that establish thedynamo balance. A separate analysis of inductive and diffusive magnetic effectsin three dynamo simulations suggests that the classical quadraticquenching of induction predicted by mean-field theory seems at work.

Risk-sensitive mean-field games

KAUST Repository

Tembine, Hamidou

2014-04-01

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.

Risk-sensitive mean-field games

KAUST Repository

Tembine, Hamidou; Zhu, Quanyan; Başar, Tamer

2014-01-01

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.

Planetary Dynamos: Investigations of Saturn and Ancient Mars

Energy Technology Data Exchange (ETDEWEB)

Stanley, Sabine [University of Toronto

2012-04-18

Magnetic field observations by spacecraft missions have provided vital information on planetary dynamos. The four giant planets as well as Earth, Mercury and Ganymede have observable magnetic fields generated by active dynamos. In contrast, Moon and Mars only have remanent crustal fields from dynamo action in their early histories. A variety of magnetic field morphologies and intensities can be found in the solar system. We have found that some of the differences between planetary magnetic fields can be explained as the result of the presence of boundary thermal variations or stably-stratified layers. In this talk, I will discuss how dynamos are affected by these complications and discuss the implications for Mars’ magnetic dichotomy and Saturn’s extremely axisymmetric magnetic field.

Convection and Dynamo Action in Ice Giant Dynamo Models with Electrical Conductivity Stratification

Science.gov (United States)

Soderlund, K. M.; Featherstone, N. A.; Heimpel, M. H.; Aurnou, J. M.

2017-12-01

Uranus and Neptune are relatively unexplored, yet critical for understanding the physical and chemical processes that control the behavior and evolution of giant planets. Because their multipolar magnetic fields, three-jet zonal winds, and extreme energy balances are distinct from other planets in our Solar System, the ice giants provide a unique opportunity to test hypotheses for internal dynamics and magnetic field generation. While it is generally agreed that dynamo action in the ionic ocean generates their magnetic fields, the mechanisms that control the morphology, strength, and evolution of the dynamos - which are likely distinct from those in the gas giants and terrestrial planets - are not well understood. We hypothesize that the dynamos and zonal winds are dynamically coupled and argue that their characteristics are a consequence of quasi-three-dimensional turbulence in their interiors. Here, we will present new dynamo simulations with an inner electrically conducting region and outer electrically insulating layer to self-consistently couple the ionic oceans and molecular envelopes of these planets. For each simulation, the magnetic field morphology and amplitude, zonal flow profile, and internal heat flux pattern will be compared against corresponding observations of Uranus and Neptune. We will also highlight how these simulations will both contribute to and benefit from a future ice giant mission.

Persistence and origin of the lunar core dynamo

Science.gov (United States)

Suavet, Clément; Weiss, Benjamin P.; Cassata, William S.; Shuster, David L.; Gattacceca, Jérôme; Chan, Lindsey; Garrick-Bethell, Ian; Head, James W.; Grove, Timothy L.; Fuller, Michael D.

2013-01-01

The lifetime of the ancient lunar core dynamo has implications for its power source and the mechanism of field generation. Here, we report analyses of two 3.56-Gy-old mare basalts demonstrating that they were magnetized in a stable and surprisingly intense dynamo magnetic field of at least ∼13 μT. These data extend the known lifetime of the lunar dynamo by ∼160 My and indicate that the field was likely continuously active until well after the final large basin-forming impact. This likely excludes impact-driven changes in rotation rate as the source of the dynamo at this time in lunar history. Rather, our results require a persistent power source like precession of the lunar mantle or a compositional convection dynamo. PMID:23650386

Small-scale kinematic dynamo and non-dynamo in inertial-range turbulence

International Nuclear Information System (INIS)

Eyink, Gregory L; Neto, Antonio F

2010-01-01

We investigate the Lagrangian mechanism of the kinematic 'fluctuation' magnetic dynamo in a turbulent plasma flow at small magnetic Prandtl numbers. The combined effect of turbulent advection and plasma resistivity is to carry infinitely many field lines to each space point, with the resultant magnetic field at that point given by the average over all the individual line vectors. As a consequence of the roughness of the advecting velocity, this remains true even in the limit of zero resistivity. We show that the presence of the dynamo effect requires sufficient angular correlation of the passive line vectors that arrive simultaneously at the same space point. We illustrate this in detail for the Kazantsev-Kraichnan model of the kinematic dynamo with a Gaussian advecting velocity that is spatially rough and white noise in time. In the regime where dynamo action fails, we also obtain the precise rate of decay of the magnetic energy. These exact results for the model are obtained by a generalization of the 'slow-mode expansion' of Bernard, Gawedzki and Kupiainen to non-Hermitian evolution. Much of our analysis applies also to magnetohydrodynamic turbulence.

Magnetic reversals from planetary dynamo waves

DEFF Research Database (Denmark)

Sheyko, Andrey; Finlay, Chris; Jackson, Andrew

2016-01-01

A striking feature of many natural dynamos is their ability to undergo polarity reversals. The best documented example is Earth's magnetic field, which has reversed hundreds of times during its history. The origin of geomagnetic polarity reversals lies in a magnetohydrodynamic process that takes ...... to kinematic dynamo waves. Because our results are relevant in a regime of low viscosity and high magnetic diffusivity, and with geophysically appropriate boundary conditions, this form of dynamo wave may also be involved in geomagnetic reversals.......A striking feature of many natural dynamos is their ability to undergo polarity reversals. The best documented example is Earth's magnetic field, which has reversed hundreds of times during its history. The origin of geomagnetic polarity reversals lies in a magnetohydrodynamic process that takes...... place in Earth's core, but the precise mechanism is debated. The majority of numerical geodynamo simulations that exhibit reversals operate in a regime in which the viscosity of the fluid remains important, and in which the dynamo mechanism primarily involves stretching and twisting of field lines...

Dynamo generated by the centrifugal instability

Science.gov (United States)

Marcotte, Florence; Gissinger, Christophe

2016-10-01

We present a scenario for magnetic field amplification where an electrically conducting fluid is confined in a differentially rotating, spherical shell with thin aspect ratio. When the angular momentum sufficiently decreases outwards, a hydrodynamic instability develops in the equatorial region, characterized by pairs of counter-rotating toroidal vortices similar to those observed in cylindrical Couette flow. These spherical Taylor-Couette vortices generate a subcritical dynamo magnetic field dominated by nonaxisymmetric components. We show that the critical magnetic Reynolds number seems to reach a constant value at large Reynolds number and that the global rotation can strongly decrease the dynamo onset. Our numerical results are understood within the framework of a simple dynamical system, and we propose a low-dimensional model for subcritical dynamo bifurcations. Implications for both laboratory dynamos and astrophysical magnetic fields are finally discussed.

Waldmeier's Rules in the Solar and Stellar Dynamos

Science.gov (United States)

Pipin, Valery; Kosovichev, Alexander

2015-08-01

The Waldmeier's rules [1] establish important empirical relations between the general parameters of magnetic cycles (such as the amplitude, period, growth rate and time profile) on the Sun and solar-type stars [2]. Variations of the magnetic cycle parameters depend on properties of the global dynamo processes operating in the stellar convection zones. We employ nonlinear mean-field axisymmetric dynamo models [3] and calculate of the magnetic cycle parameters, such as the dynamo cycle period, total magnetic and Poynting fluxes for the Sun and solar-type stars with rotational periods from 15 to 30 days. We consider two types of the dynamo models: 1) distributed (D-type) models employing the standard α - effect distributed in the whole convection zone, and 2) Babcock-Leighton (BL-type) models with a non-local α - effect. The dynamo models take into account the principal mechanisms of the nonlinear dynamo generation and saturation, including the magnetic helicity conservation, magnetic buoyancy effects, and the feedback on the angular momentum balance inside the convection zones. Both types of models show that the dynamo generated magnetic flux increases with the increase of the rotation rate. This corresponds to stronger brightness variations. The distributed dynamo model reproduces the observed dependence of the cycle period on the rotation rate for the Sun analogs better than the BL-type model. For the solar-type stars rotating more rapidly than the Sun we find dynamo regimes with multiple periods. Such stars with multiple cycles form a separate branch in the variability-rotation diagram.1. Waldmeier, M., Prognose für das nächste Sonnenfleckenmaximum, 1936, Astron. Nachrichten, 259,262. Soon,W.H., Baliunas,S.L., Zhang,Q.,An interpretation of cycle periods of stellar chromospheric activity, 1993, ApJ, 414,333. Pipin,V.V., Dependence of magnetic cycle parameters on period of rotation in nonlinear solar-type dynamos, 2015, astro-ph: 14125284

UNDERSTANDING SOLAR TORSIONAL OSCILLATIONS FROM GLOBAL DYNAMO MODELS

International Nuclear Information System (INIS)

Guerrero, G.; Smolarkiewicz, P. K.; Pino, E. M. de Gouveia Dal; Kosovichev, A. G.; Mansour, N. N.

2016-01-01

The phenomenon of solar “torsional oscillations” (TO) represents migratory zonal flows associated with the solar cycle. These flows are observed on the solar surface and, according to helioseismology, extend through the convection zone. We study the origin of the TO using results from a global MHD simulation of the solar interior that reproduces several of the observed characteristics of the mean-flows and magnetic fields. Our results indicate that the magnetic tension (MT) in the tachocline region is a key factor for the periodic changes in the angular momentum transport that causes the TO. The torque induced by the MT at the base of the convection zone is positive at the poles and negative at the equator. A rising MT torque at higher latitudes causes the poles to speed up, whereas a declining negative MT torque at the lower latitudes causes the equator to slow-down. These changes in the zonal flows propagate through the convection zone up to the surface. Additionally, our results suggest that it is the magnetic field at the tachocline that modulates the amplitude of the surface meridional flow rather than the opposite as assumed by flux-transport dynamo models of the solar cycle.

New computation results for the solar dynamo

International Nuclear Information System (INIS)

Csada, I.K.

1983-01-01

The analytical solution to the solar dynamo equation leads to a relatively simple algorythm for the computation in terms of kinematic models. The internal and external velocities taken to be in the form of axisymmetric meridional circulation and differential rotation, respectively. Pure radial expanding motions in the corona are also taken into consideration. Numerical results are presented in terms of the velocity parameters for the period of field reversal, decay time, magnitudes and phases of the first four multipoles. (author)

Ion heating and MHD dynamo fluctuations in the reversed field pinch

International Nuclear Information System (INIS)

Scime, E.E.

1992-05-01

Ion temperature measurements, time resolved to 10 μs, have been made in the Madison Symmetric Torus (MST) reversed field pinch (RFP) with a five channel charge exchange analyzer. The characteristic anomalously high ion temperature of RFP discharges has been observed in the MST. The evolution of the ion and electron temperature, as well as density and charge exchange power loss, were measured for a series of reproducible discharges. The ion heating expected from collisional processes with the electrons is calculated and shown too small to explain the measured ion temperatures. The charge exchange determined ion temperature is also compared to measurements of the thermally broadened CV 227.1 nm line. The ion temperature, T i ∼ 250 eV for I = 360 kA, increases by more than 100% during discrete dynamo bursts in MST discharges. Magnetic field fluctuations in the range 0.5 endash 5 MHz were also measured during the dynamo bursts. Structure in the fluctuation frequency spectrum at the ion cyclotron frequency appears as the bursts terminate, suggesting that the mechanism of ion heating involves the dissipation of dynamo fluctuations at ion cyclotron frequencies. Theoretical models for ion heating are reviewed and discussed in light of the experimental results. Similar electron heating mechanisms may be responsible for the discrepancy between measured and expected loop voltages in the RFP. The electrons, as well as the ions, may be heated by turbulent mechanisms, and a RFP energy budget including such phenomena is described

A two-billion-year history for the lunar dynamo.

Science.gov (United States)

Tikoo, Sonia M; Weiss, Benjamin P; Shuster, David L; Suavet, Clément; Wang, Huapei; Grove, Timothy L

2017-08-01

Magnetic studies of lunar rocks indicate that the Moon generated a core dynamo with surface field intensities of ~20 to 110 μT between at least 4.25 and 3.56 billion years ago (Ga). The field subsequently declined to lunar dynamo by at least 1 billion years. Such a protracted history requires an extraordinarily long-lived power source like core crystallization or precession. No single dynamo mechanism proposed thus far can explain the strong fields inferred for the period before 3.56 Ga while also allowing the dynamo to persist in such a weakened state beyond ~2.5 Ga. Therefore, our results suggest that the dynamo was powered by at least two distinct mechanisms operating during early and late lunar history.

Solar Internal Rotation and Dynamo Waves: A Two Dimensional ...

Indian Academy of Sciences (India)

tribpo

Solar Internal Rotation and Dynamo Waves: A Two Dimensional. Asymptotic Solution in the Convection Zone ... We calculate here a spatial 2 D structure of the mean magnetic field, adopting real profiles of the solar internal ... of the asymptotic solution in low (middle) and high (right panel) latitudes. field is shifted towards the ...

Solar Dynamo Driven by Periodic Flow Oscillation

Science.gov (United States)

Mayr, Hans G.; Hartle, Richard E.; Einaudi, Franco (Technical Monitor)

2001-01-01

We have proposed that the periodicity of the solar magnetic cycle is determined by wave mean flow interactions analogous to those driving the Quasi Biennial Oscillation in the Earth's atmosphere. Upward propagating gravity waves would produce oscillating flows near the top of the radiation zone that in turn would drive a kinematic dynamo to generate the 22-year solar magnetic cycle. The dynamo we propose is built on a given time independent magnetic field B, which allows us to estimate the time dependent, oscillating components of the magnetic field, (Delta)B. The toroidal magnetic field (Delta)B(sub phi) is directly driven by zonal flow and is relatively large in the source region, (Delta)(sub phi)/B(sub Theta) much greater than 1. Consistent with observations, this field peaks at low latitudes and has opposite polarities in both hemispheres. The oscillating poloidal magnetic field component, (Delta)B(sub Theta), is driven by the meridional circulation, which is difficult to assess without a numerical model that properly accounts for the solar atmosphere dynamics. Scale-analysis suggests that (Delta)B(sub Theta) is small compared to B(sub Theta) in the dynamo region. Relative to B(sub Theta), however, the oscillating magnetic field perturbations are expected to be transported more rapidly upwards in the convection zone to the solar surface. As a result, (Delta)B(sub Theta) (and (Delta)B(sub phi)) should grow relative to B(sub Theta), so that the magnetic fields reverse at the surface as observed. Since the meridional and zonai flow oscillations are out of phase, the poloidal magnetic field peaks during times when the toroidal field reverses direction, which is observed. With the proposed wave driven flow oscillation, the magnitude of the oscillating poloidal magnetic field increases with the mean rotation rate of the fluid. This is consistent with the Bode-Blackett empirical scaling law, which reveals that in massive astrophysical bodies the magnetic moment tends

The Hottest Hot Jupiters May Host Atmospheric Dynamos

Energy Technology Data Exchange (ETDEWEB)

Rogers, T. M. [Department of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne (United Kingdom); McElwaine, J. N. [Planetary Science Institute, Tucson, AZ 85721 (United States)

2017-06-01

Hot Jupiters have proven themselves to be a rich class of exoplanets that test our theories of planetary evolution and atmospheric dynamics under extreme conditions. Here, we present three-dimensional magnetohydrodynamic simulations and analytic results that demonstrate that a dynamo can be maintained in the thin, stably stratified atmosphere of a hot Jupiter, independent of the presumed deep-seated dynamo. This dynamo is maintained by conductivity variations arising from strong asymmetric heating from the planets’ host star. The presence of a dynamo significantly increases the surface magnetic field strength and alters the overall planetary magnetic field geometry, possibly affecting star–planet magnetic interactions.

Turbulent Liquid Metal Dynamo Experiments

International Nuclear Information System (INIS)

Forest, Cary

2007-01-01

The self-generation of magnetic fields in planets and stars--the dynamo effect--is a long-standing problem of magnetohydrodynamics and plasma physics. Until recently, research on the self-excitation process has been primarily theoretical. In this talk, I will begin with a tutorial on how magnetic fields are generated in planets and stars, describing the 'Standard Model' of self-excitation known as the alpha-omega dynamo. In this model, axisymmetric differential rotation can produce the majority of the magnetic field, but some non-axisymmetric, turbulence driven currents are also necessary. Understanding the conversion of turbulent kinetic energy in the fluid motion into electrical currents and thus magnetic fields, is a major challenge for both experiments and theory at this time. I will then report on recent results from a 1 meter diameter, spherical, liquid sodium dynamo experiment at the University of Wisconsin, in which the first clear evidence for these turbulence driven currents has been observed.

Turbulent Dynamo Amplification of Magnetic Fields in Laser-Produced Plasmas: Simulations and Experiments

Science.gov (United States)

Tzeferacos, P.; Rigby, A.; Bott, A.; Bell, A.; Bingham, R.; Casner, A.; Cattaneo, F.; Churazov, E.; Forest, C.; Katz, J.; Koenig, M.; Li, C.-K.; Meinecke, J.; Petrasso, R.; Park, H.-S.; Remington, B.; Ross, J.; Ryutov, D.; Ryu, D.; Reville, B.; Miniati, F.; Schekochihin, A.; Froula, D.; Lamb, D.; Gregori, G.

2017-10-01

The universe is permeated by magnetic fields, with strengths ranging from a femtogauss in the voids between the filaments of galaxy clusters to several teragauss in black holes and neutron stars. The standard model for cosmological magnetic fields is the nonlinear amplification of seed fields via turbulent dynamo. We have conceived experiments to demonstrate and study the turbulent dynamo mechanism in the laboratory. Here, we describe the design of these experiments through large-scale 3D FLASH simulations on the Mira supercomputer at ANL, and the laser-driven experiments we conducted with the OMEGA laser at LLE. Our results indicate that turbulence is capable of rapidly amplifying seed fields to near equipartition with the turbulent fluid motions. This work was supported in part from the ERC (FP7/2007-2013, No. 256973 and 247039), and the U.S. DOE, Contract No. B591485 to LLNL, FWP 57789 to ANL, Grant No. DE-NA0002724 and DE-SC0016566 to the University of Chicago, and DE-AC02-06CH11357 to ANL.

The solar dynamo

International Nuclear Information System (INIS)

Brandenburg, A.; Helsinki Univ.; Tuominen, I.

1991-01-01

The traditional αΩ-dynamo as a model for the solar cycle has been successful in explaining the butterfly diagram, phase relations between poloidal and toroidal field, and polar branch migration features. Observational and theoretical achievements in recent years have however shaken this picture. The current trend is towards dynamos operating in the overshoot region of the convection zone. Nevertheless, there are many open questions and a consistent picture has not been established. In this paper we compare recent approaches and discuss remaining problems. (orig.)

Physical conditions for Jupiter-like dynamo models

Science.gov (United States)

Duarte, Lúcia D. V.; Wicht, Johannes; Gastine, Thomas

2018-01-01

The Juno mission will measure Jupiter's magnetic field with unprecedented precision and provide a wealth of additional data that will allow us to constrain the planet's interior structure and dynamics. Here we analyse 66 different numerical simulations in order to explore the sensitivity of the dynamo-generated magnetic field to the planets interior properties. Jupiter field models based on pre-Juno data and up-to-date interior models based on ab initio simulations serve as benchmarks. Our results suggest that Jupiter-like magnetic fields can be found for a number of different models. These complement the steep density gradients in the outer part of the simulated shell with an electrical conductivity profile that mimics the low conductivity in the molecular hydrogen layer and thus renders the dynamo action in this region largely unimportant. We find that whether we assume an ideal gas or use the more realistic interior model based on ab initio simulations makes no difference. However, two other factors are important. A low Rayleigh number leads to a too strong axial dipole contribution while the axial dipole dominance is lost altogether when the convective driving is too strong. The required intermediate range that yields Jupiter-like magnetic fields depends on the other system properties. The second important factor is the convective magnetic Reynolds number radial profile Rmc(r), basically a product of the non-axisymmetric flow velocity and electrical conductivity. We find that the depth where Rmc exceeds about 50 is a good proxy for the top of the dynamo region. When the dynamo region sits too deep, the axial dipole is once more too dominant due to geometric reasons. Extrapolating our results to Jupiter and the result suggests that the Jovian dynamo extends to 95% of the planetary radius. The zonal flow system in our simulations is dominated by an equatorial jet which remains largely confined to the molecular layer. Where the jet reaches down to higher

TURBULENCE AND DYNAMO IN GALAXY CLUSTER MEDIUM: IMPLICATIONS ON THE ORIGIN OF CLUSTER MAGNETIC FIELDS

International Nuclear Information System (INIS)

Xu Hao; Collins, David C.; Norman, Michael L.; Li Hui; Li Shengtai

2009-01-01

We present self-consistent cosmological magnetohydrodynamic (MHD) simulations that simultaneously follow the formation of a galaxy cluster and the magnetic field ejection by an active galactic nucleus (AGN). We find that the magnetic fields ejected by the AGNs, though initially distributed in relatively small volumes, can be transported throughout the cluster and be further amplified by the intracluster medium (ICM) turbulence during the cluster formation process. The ICM turbulence is shown to be generated and sustained by the frequent mergers of smaller halos. Furthermore, a cluster-wide dynamo process is shown to exist in the ICM and amplify the magnetic field energy and flux. The total magnetic energy in the cluster can reach ∼10 61 erg while micro Gauss (μG) fields can distribute over ∼ Mpc scales throughout the whole cluster. This finding shows that magnetic fields from AGNs, being further amplified by the ICM turbulence through small-scale dynamo processes, can be the origin of cluster-wide magnetic fields.

Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

Energy Technology Data Exchange (ETDEWEB)

Kelly, Aaron; Markland, Thomas E., E-mail: tmarkland@stanford.edu [Department of Chemistry, Stanford University, Stanford, California 94305 (United States); Brackbill, Nora [Department of Physics, Stanford University, Stanford, California 94305 (United States)

2015-03-07

In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations.

Science.gov (United States)

Kelly, Aaron; Brackbill, Nora; Markland, Thomas E

2015-03-07

In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

Measurement of the dynamo effect in a plasma

International Nuclear Information System (INIS)

Ji, H.; Prager, S.C.; Almagri, A.F.; Sarff, J.S.; Hirano, Y.; Toyama, H.

1995-11-01

A series of the detailed experiments has been conducted in three laboratory plasma devices to measure the dynamo electric field along the equilibrium field line (the α effect) arising from the correlation between the fluctuating flow velocity and magnetic field. The fluctuating flow velocity is obtained from probe measurement of the fluctuating E x B drift and electron diamagnetic drift. The three major findings are (1) the α effect accounts for the dynamo current generation, even in the time dependence through a ''sawtooth'' cycle; (2) at low collisionality the dynamo is explained primarily by the widely studied pressureless Magnetohydrodynamic (MHD) model, i.e., the fluctuating velocity is dominated by the E x B drift; (3) at high collisionality, a new ''electron diamagnetic dynamo'' is observed, in which the fluctuating velocity is dominated by the diamagnetic drift. In addition, direct measurements of the helicity flux indicate that the dynamo activity transports magnetic helicity from one part of the plasma to another, but the total helicity is roughly conserved, verifying J.B. Taylor's conjecture

Systematic parameter study of dynamo bifurcations in geodynamo simulations

Science.gov (United States)

Petitdemange, Ludovic

2018-04-01

We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions with no-slip boundaries. Unlike in previous studies on dynamo bifurcations, the control parameters have been varied significantly in order to deduce general tendencies. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition disappears and is replaced by a region of bistability for which dipolar and multipolar dynamos coexist. Such a result was also observed in models with free-slip boundaries in which the geostrophic zonal flow can develop and participate to the dynamo mechanism for non-dipolar fields. We show that a similar process develops in no-slip models when viscous effects are reduced sufficiently. The following three regimes are distinguished: (i) Close to the onset of convection (Rac) with only the most critical convective mode (wave number) being present, dynamos set in supercritically in the Ekman number regime explored here and are dipole-dominated. Larger critical magnetic Reynolds numbers indicate that they are particularly inefficient. (ii) in the range 3 10) , the relative importance of zonal flows increases with Ra in non-magnetic models. The field topology depends on the magnitude of the initial magnetic field. The dipolar branch has a subcritical behavior whereas the multipolar branch has a supercritical behavior. By approaching more realistic parameters, the extension of this bistable regime increases. A hysteretic behavior questions the common interpretation for geomagnetic reversals. Far above the dynamo threshold (by increasing the magnetic Prandtl number), Lorentz forces contribute to the first order force balance, as predicted for planetary dynamos. When

Energy transfers in dynamos with small magnetic Prandtl numbers

KAUST Repository

Kumar, Rohit

2015-06-25

We perform numerical simulation of dynamo with magnetic Prandtl number Pm = 0.2 on 10243 grid, and compute the energy fluxes and the shell-to-shell energy transfers. These computations indicate that the magnetic energy growth takes place mainly due to the energy transfers from large-scale velocity field to large-scale magnetic field and that the magnetic energy flux is forward. The steady-state magnetic energy is much smaller than the kinetic energy, rather than equipartition; this is because the magnetic Reynolds number is near the dynamo transition regime. We also contrast our results with those for dynamo with Pm = 20 and decaying dynamo. © 2015 Taylor & Francis.

Mean field games

KAUST Repository

Gomes, Diogo A.

2014-01-06

In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.

Mean field games

KAUST Repository

Gomes, Diogo A.

2014-01-01

In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.

TIDALLY DRIVEN DYNAMOS IN A ROTATING SPHERE

International Nuclear Information System (INIS)

Cébron, D.; Hollerbach, R.

2014-01-01

Large-scale planetary or stellar magnetic fields generated by a dynamo effect are mostly attributed to flows forced by buoyancy forces in electrically conducting fluid layers. However, these large-scale fields may also be controlled by tides, as previously suggested for the star τ-boo, Mars, or the early Moon. By simulating a small local patch of a rotating fluid, Barker and Lithwick have recently shown that tides can drive small-scale dynamos by exciting a hydrodynamic instability, the so-called elliptical (or tidal) instability. By performing global magnetohydrodynamic simulations of a rotating spherical fluid body, we investigate if this instability can also drive the observed large-scale magnetic fields. We are thus interested in the dynamo threshold and the generated magnetic field in order to test if such a mechanism is relevant for planets and stars. Rather than solving the problem in a geometry deformed by tides, we consider a spherical fluid body and add a body force to mimic the tidal deformation in the bulk of the fluid. This allows us to use an efficient spectral code to solve the magnetohydrodynamic problem. We first compare the hydrodynamic results with theoretical asymptotic results and numerical results obtained in a truly deformed ellipsoid, which confirms the presence of elliptical instability. We then perform magnetohydrodynamic simulations and investigate the dynamo capability of the flow. Kinematic and self-consistent dynamos are finally simulated, showing that the elliptical instability is capable of generating a dipole-dominated large-scale magnetic field in global simulations of a fluid rotating sphere

A THREE-DIMENSIONAL BABCOCK-LEIGHTON SOLAR DYNAMO MODEL

International Nuclear Information System (INIS)

Miesch, Mark S.; Dikpati, Mausumi

2014-01-01

We present a three-dimensional (3D) kinematic solar dynamo model in which poloidal field is generated by the emergence and dispersal of tilted sunspot pairs (more generally bipolar magnetic regions, or BMRs). The axisymmetric component of this model functions similarly to previous 2.5 dimensional (2.5D, axisymmetric) Babcock-Leighton (BL) dynamo models that employ a double-ring prescription for poloidal field generation but we generalize this prescription into a 3D flux emergence algorithm that places BMRs on the surface in response to the dynamo-generated toroidal field. In this way, the model can be regarded as a unification of BL dynamo models (2.5D in radius/latitude) and surface flux transport models (2.5D in latitude/longitude) into a more self-consistent framework that builds on the successes of each while capturing the full 3D structure of the evolving magnetic field. The model reproduces some basic features of the solar cycle including an 11 yr periodicity, equatorward migration of toroidal flux in the deep convection zone, and poleward propagation of poloidal flux at the surface. The poleward-propagating surface flux originates as trailing flux in BMRs, migrates poleward in multiple non-axisymmetric streams (made axisymmetric by differential rotation and turbulent diffusion), and eventually reverses the polar field, thus sustaining the dynamo. In this Letter we briefly describe the model, initial results, and future plans

On the initial conditions of time-dependent mean-field equations of evolution. Pt. 2

International Nuclear Information System (INIS)

Troudet, T.; Paris-11 Univ., 91 - Orsay

1986-01-01

We analyze the problem so far untouched of determining the initial mean-field wavefunction in the context of zero-temperature mean-field descriptions of time-dependent expectation values and quantum fluctuations of nuclear observables. The nucleus, at zero temperature, is taken to be in a low-lying excited many-body eigenstate and is approximated by the corresponding RPA wavefunction as a continuous superposition of coherent states (i.e. Slater determinants). A generating function Gsub(A)(lambda) for time-dependent expectation values and quantum fluctuations is constructed within the formalism of functional integration. By applying the saddle-point method to the functional action of Gsub(A)(lambda) and then taking its lambda-derivatives, we recover the well-known TDHF theory and propose a simple determination of the initial Slater determinant for an appropriate mean-field description of time-dependent expectation values. The analog mean-field description of quadratic-quantum fluctuations proceeds similarly and in addition includes the contribution of the uncorrelated TDHF-RPA phonons coupled to collective excitations of the initial (static) mean-field configuration. When the collective TDHF-RPA excitations are solely taken into account, we obtain an improved version of the Balian-Veneroni dispersion formula by showing how to determine the initial mean-field wavefunction. By first taking the lambda-derivatives of Gsub(A)(lambda) before applying the saddle-point method, the initial mean-field wavefunction is found to be non-linearly coupled to the mean-field dynamics themselves. In return, and in contrast to the first quantization scheme, these both depend non-trivially upon the observable A being measured so that approximations must be proposed to simplify the resulting mean-field equations. (orig.)

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

Energy Technology Data Exchange (ETDEWEB)

Ichimura, Chiaki; Yokoyama, Takaaki [Department of Earth and Planetary Science, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan)

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 Lorentz 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.

Gravitational dynamos and the low-frequency geomagnetic secular variation.

Science.gov (United States)

Olson, P

2007-12-18

Self-sustaining numerical dynamos are used to infer the sources of low-frequency secular variation of the geomagnetic field. Gravitational dynamo models powered by compositional convection in an electrically conducting, rotating fluid shell exhibit several regimes of magnetic field behavior with an increasing Rayleigh number of the convection, including nearly steady dipoles, chaotic nonreversing dipoles, and chaotic reversing dipoles. The time average dipole strength and dipolarity of the magnetic field decrease, whereas the dipole variability, average dipole tilt angle, and frequency of polarity reversals increase with Rayleigh number. Chaotic gravitational dynamos have large-amplitude dipole secular variation with maximum power at frequencies corresponding to a few cycles per million years on Earth. Their external magnetic field structure, dipole statistics, low-frequency power spectra, and polarity reversal frequency are comparable to the geomagnetic field. The magnetic variability is driven by the Lorentz force and is characterized by an inverse correlation between dynamo magnetic and kinetic energy fluctuations. A constant energy dissipation theory accounts for this inverse energy correlation, which is shown to produce conditions favorable for dipole drift, polarity reversals, and excursions.

An Experimental MHD Dynamo

International Nuclear Information System (INIS)

Forest, C. B.

2002-01-01

The project is designed to understand current and magnetic field generation in plasmas and other magnetohydrodynamic systems. The experiments will investigate the generation of a dynamo using liquid Na

A long-lived lunar dynamo driven by continuous mechanical stirring.

Science.gov (United States)

Dwyer, C A; Stevenson, D J; Nimmo, F

2011-11-09

Lunar rocks contain a record of an ancient magnetic field that seems to have persisted for more than 400 million years and which has been attributed to a lunar dynamo. Models of conventional dynamos driven by thermal or compositional convection have had difficulty reproducing the existence and apparently long duration of the lunar dynamo. Here we investigate an alternative mechanism of dynamo generation: continuous mechanical stirring arising from the differential motion, due to Earth-driven precession of the lunar spin axis, between the solid silicate mantle and the liquid core beneath. We show that the fluid motions and the power required to drive a dynamo operating continuously for more than one billion years and generating a magnetic field that had an intensity of more than one microtesla 4.2 billion years ago are readily obtained by mechanical stirring. The magnetic field is predicted to decrease with time and to shut off naturally when the Moon recedes far enough from Earth that the dissipated power is insufficient to drive a dynamo; in our nominal model, this occurred at about 48 Earth radii (2.7 billion years ago). Thus, lunar palaeomagnetic measurements may be able to constrain the poorly known early orbital evolution of the Moon. This mechanism may also be applicable to dynamos in other bodies, such as large asteroids.

DIPOLE COLLAPSE AND DYNAMO WAVES IN GLOBAL DIRECT NUMERICAL SIMULATIONS

Energy Technology Data Exchange (ETDEWEB)

Schrinner, Martin; Dormy, Emmanuel [MAG (ENS/IPGP), LRA, Ecole Normale Superieure, 24 Rue Lhomond, 75252 Paris Cedex 05 (France); Petitdemange, Ludovic, E-mail: martin@schrinner.eu [Previously at Max-Planck-Institut fuer Astronomie, Koenigstuhl 17, 69117 Heidelberg, Germany. (Germany)

2012-06-20

Magnetic fields of low-mass stars and planets are thought to originate from self-excited dynamo action in their convective interiors. Observations reveal a variety of field topologies ranging from large-scale, axial dipoles to more structured magnetic fields. In this article, we investigate more than 70 three-dimensional, self-consistent dynamo models in the Boussinesq approximation obtained by direct numerical simulations. The control parameters, the aspect ratio, and the mechanical boundary conditions have been varied to build up this sample of models. Both strongly dipolar and multipolar models have been obtained. We show that these dynamo regimes in general can be distinguished by the ratio of a typical convective length scale to the Rossby radius. Models with a predominantly dipolar magnetic field were obtained, if the convective length scale is at least an order of magnitude larger than the Rossby radius. Moreover, we highlight the role of the strong shear associated with the geostrophic zonal flow for models with stress-free boundary conditions. In this case the above transition disappears and is replaced by a region of bistability for which dipolar and multipolar dynamos coexist. We interpret our results in terms of dynamo eigenmodes using the so-called test-field method. We can thus show that models in the dipolar regime are characterized by an isolated 'single mode'. Competing overtones become significant as the boundary to multipolar dynamos is approached. We discuss how these findings relate to previous models and to observations.

Nonlinear dynamo in the intracluster medium

Science.gov (United States)

Beresnyak, Andrey; Miniati, Francesco

2018-05-01

Hot plasma in galaxy clusters, the intracluster medium is observed to be magnetized with magnetic fields of around a μG and the correlation scales of tens of kiloparsecs, the largest scales of the magnetic field so far observed in the Universe. Can this magnetic field be used as a test of the primordial magnetic field in the early Universe? In this paper, we argue that if the cluster field was created by the nonlinear dynamo, the process would be insensitive to the value of the initial field. Our model combines state of the art hydrodynamic simulations of galaxy cluster formation in a fully cosmological context with nonlinear dynamo theory. Initial field is not a parameter in this model, yet it predicts magnetic scale and strength compatible with observations.

Magnetic reversals from planetary dynamo waves.

Science.gov (United States)

Sheyko, Andrey; Finlay, Christopher C; Jackson, Andrew

2016-11-24

A striking feature of many natural dynamos is their ability to undergo polarity reversals. The best documented example is Earth's magnetic field, which has reversed hundreds of times during its history. The origin of geomagnetic polarity reversals lies in a magnetohydrodynamic process that takes place in Earth's core, but the precise mechanism is debated. The majority of numerical geodynamo simulations that exhibit reversals operate in a regime in which the viscosity of the fluid remains important, and in which the dynamo mechanism primarily involves stretching and twisting of field lines by columnar convection. Here we present an example of another class of reversing-geodynamo model, which operates in a regime of comparatively low viscosity and high magnetic diffusivity. This class does not fit into the paradigm of reversal regimes that are dictated by the value of the local Rossby number (the ratio of advection to Coriolis force). Instead, stretching of the magnetic field by a strong shear in the east-west flow near the imaginary cylinder just touching the inner core and parallel to the axis of rotation is crucial to the reversal mechanism in our models, which involves a process akin to kinematic dynamo waves. Because our results are relevant in a regime of low viscosity and high magnetic diffusivity, and with geophysically appropriate boundary conditions, this form of dynamo wave may also be involved in geomagnetic reversals.

The effect of collisionality and diamagnetism on the plasma dynamo

International Nuclear Information System (INIS)

Ji, H.; Yagi, Y.; Hattori, K.; Hirano, Y.; Shimada, T.; Maejima, Y.; Hayase, K.; Almagri, A.F.; Prager, S.C.; Sarff, J.S.

1995-01-01

Fluctuation-induced dynamo forces are measured over a wide range of electron collisionality in the edge of TPE-1RM20 Reversed-Field Pinch (RFP). In the collisionless region the Magnetohydrodynamic (MHD) dynamo alone can sustain the parallel current, while in the collisional region a new dynamo mechanism resulting from the fluctuations in the electron diamagnetic drift becomes dominant. A comprehensive picture of the RFP dynamo emerges by combining with earlier results from MST and REPUTE RFPs

Effects due to induced azimuthal eddy currents in a self-exciting Faraday disk homopolar dynamo with a nonlinear series motor. I.. Two special cases

Science.gov (United States)

Hide, Raymond; Moroz, Irene M.

1999-10-01

The elucidation of the behaviour of physically realistic self-exciting Faraday-disk dynamos bears inter alia on attempts by theoretical geophysicists to interpret observations of geomagnetic polarity reversals. Hide [The nonlinear differential equations governing a hierarchy of self-exciting coupled Faraday-disk homopolar dynamos, Phys. Earth Planet. Interiors 103 (1997) 281-291; Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo, Nonlinear Processes in Geophysics 4 (1998) 201-205] has introduced a novel 4-mode set of nonlinear ordinary differential equations to describe such a dynamo in which a nonlinear electric motor is connected in series with the coil. The applied couple, α, driving the disk is steady and the Lorentz couple driving the motor is a quadratic function, x(1-ɛ)+ɛσx 2, of the dynamo-generated current x, with 0≤ɛ≤1. When there are no additional biasing effects due to background magnetic fields etc., the behaviour of the dynamo is determined by eight independent non-negative control parameters. These include ρ, proportional to the resistance of the disk to azimuthal eddy currents, and β, an inverse measure of the moment of inertia of the armature of the motor. When β=0 (the case when the motor is absent and ɛ and σ are redundant) and ρ -1≠0 , the 4-mode dynamo equations reduce to the 3-mode Lorenz equations, which can behave chaotically [E. Knobloch, Chaos in the segmented disc dynamo, Phys. Lett. A 82 (1981) 439-440]. When β≠0 but ρ -1=0 , the 4-mode set of equations reduces to a 3-mode dynamo [R. Hide (1997), see above], which can also behave chaotically when ɛ=0 [R. Hide, A.C. Skeldon, D.J. Acheson, A study of two novel self-exciting single-disk homopolar dynamos: theory, Proc. R. Soc. Lond. A 452 (1996) 1369-1395] but not when ɛ=1 [R. Hide (1998), see above]. In the latter case, however, all persistent fluctuations are completely quenched [R. Hide (1998), see above]. In this paper we investigate

Lorentz violation bounds from torsion trace fermion sector and galaxy M51 data and chiral dynamos

Energy Technology Data Exchange (ETDEWEB)

Garcia de Andrade, L.C. [IF-UERJ, Departamento de Fisica Teorica, Rio de Janeiro, RJ (Brazil)

2017-06-15

Earlier we have computed a Lorentz violation (LV) bound for torsion terms via galactic dynamos and found bounds similar to the one obtained by Kostelecky et al. (Phys Rev Lett 100:111102, 2008) which is of the order of 10{sup -31} GeV. Their result was found making use of the axial torsion vector in terms of Dirac spinors and minimal torsion coupling in flat space-time of fermions. In this paper, a torsion dynamo equation obtained using the variation of the torsion trace and galaxy M51 data of 500 pc are used to place an upper bound of 10{sup -26} GeV in LV, which agrees with the one by Kostelecky and his group using an astrophysical framework background. Their lowest bound was obtained in earth laboratory using dual masers. One of the purposes of this paper is to apply the Faraday self-induction magnetic equation, recently extended to torsioned space-time, by the author to show that it lends support to physics in Riemann-Cartan space-time, in several distinct physical backgrounds. Backreaction magnetic effects are used to obtain the LV bounds. Previously Bamba et al. (JCAP 10:058, 2012) have used the torsion trace in their teleparallel investigation of the IGMF, with the argument that the torsion trace leads to less weaker effects than the other irreducible components of the torsion tensor. LV is computed in terms of a chiral-torsion-like current in the new dynamo equation analogous to the Dvornikov and Semikoz dynamo equation with chiral magnetic currents. Making use of the chiral-torsion dynamo equation we estimate the LV bounds in the early universe to be of the order of 10{sup -24} GeV, which was the order of the charged-lepton sector. Our main result is that it is possible to obtain more stringent bounds than the ones found in the fermion sector of astrophysics in the new revised 2017 data table for CPT and Lorentz violation by Kostelecky and Mewes. They found in several astrophysical backgrounds, orders of magnitude such as 10{sup -24} and 10{sup -23} Ge

The two-wave X-ray field calculated by means of integral-equation methods

International Nuclear Information System (INIS)

Bremer, J.

1984-01-01

The problem of calculating the two-wave X-ray field on the basis of the Takagi-Taupin equations is discussed for the general case of curved lattice planes. A two-dimensional integral equation which incorporates the nature of the incoming radiation, the form of the crystal/vacuum boundary, and the curvature of the structure, is deduced. Analytical solutions for the symmetrical Laue case with incoming plane waves are obtained directly for perfect crystals by means of iteration. The same method permits a simple derivation of the narrow-wave Laue and Bragg cases. Modulated wave fronts are discussed, and it is shown that a cut-off in the width of an incoming plane wave leads to lateral oscillations which are superimposed on the Pendelloesung fringes. Bragg and Laue shadow fields are obtained. The influence of a non-zero kernel is discussed and a numerical procedure for calculating wave amplitudes in curved crystals is presented. (Auth.)

Faraday's first dynamo: A retrospective

Science.gov (United States)

Smith, Glenn S.

2013-12-01

In the early 1830s, Michael Faraday performed his seminal experimental research on electromagnetic induction, in which he created the first electric dynamo—a machine for continuously converting rotational mechanical energy into electrical energy. His machine was a conducting disc, rotating between the poles of a permanent magnet, with the voltage/current obtained from brushes contacting the disc. In his first dynamo, the magnetic field was asymmetric with respect to the axis of the disc. This is to be contrasted with some of his later symmetric designs, which are the ones almost invariably discussed in textbooks on electromagnetism. In this paper, a theoretical analysis is developed for Faraday's first dynamo. From this analysis, the eddy currents in the disc and the open-circuit voltage for arbitrary positioning of the brushes are determined. The approximate analysis is verified by comparing theoretical results with measurements made on an experimental recreation of the dynamo. Quantitative results from the analysis are used to elucidate Faraday's qualitative observations, from which he learned so much about electromagnetic induction. For the asymmetric design, the eddy currents in the disc dissipate energy that makes the dynamo inefficient, prohibiting its use as a practical generator of electric power. Faraday's experiments with his first dynamo provided valuable insight into electromagnetic induction, and this insight was quickly used by others to design practical generators.

Solar activity simulation and forecast with a flux-transport dynamo

Science.gov (United States)

Macario-Rojas, Alejandro; Smith, Katharine L.; Roberts, Peter C. E.

2018-06-01

We present the assessment of a diffusion-dominated mean field axisymmetric dynamo model in reproducing historical solar activity and forecast for solar cycle 25. Previous studies point to the Sun's polar magnetic field as an important proxy for solar activity prediction. Extended research using this proxy has been impeded by reduced observational data record only available from 1976. However, there is a recognised need for a solar dynamo model with ample verification over various activity scenarios to improve theoretical standards. The present study aims to explore the use of helioseismology data and reconstructed solar polar magnetic field, to foster the development of robust solar activity forecasts. The research is based on observationally inferred differential rotation morphology, as well as observed and reconstructed polar field using artificial neural network methods via the hemispheric sunspot areas record. Results show consistent reproduction of historical solar activity trends with enhanced results by introducing a precursor rise time coefficient. A weak solar cycle 25, with slow rise time and maximum activity -14.4% (±19.5%) with respect to the current cycle 24 is predicted.

Faraday rotation signatures of fluctuation dynamos in young galaxies

Science.gov (United States)

Sur, Sharanya; Bhat, Pallavi; Subramanian, Kandaswamy

2018-03-01

Observations of Faraday rotation through high-redshift galaxies have revealed that they host coherent magnetic fields that are of comparable strengths to those observed in nearby galaxies. These fields could be generated by fluctuation dynamos. We use idealized numerical simulations of such dynamos in forced compressible turbulence up to rms Mach number of 2.4 to probe the resulting rotation measure (RM) and the degree of coherence of the magnetic field. We obtain rms values of RM at dynamo saturation of the order of 45-55 per cent of the value expected in a model where fields are assumed to be coherent on the forcing scale of turbulence. We show that the dominant contribution to the RM in subsonic and transonic cases comes from the general sea of volume filling fields, rather than from the rarer structures. However, in the supersonic case, strong field regions as well as moderately overdense regions contribute significantly. Our results can account for the observed RMs in young galaxies.

A DOUBLE-RING ALGORITHM FOR MODELING SOLAR ACTIVE REGIONS: UNIFYING KINEMATIC DYNAMO MODELS AND SURFACE FLUX-TRANSPORT SIMULATIONS

International Nuclear Information System (INIS)

Munoz-Jaramillo, Andres; Martens, Petrus C. H.; Nandy, Dibyendu; Yeates, Anthony R.

2010-01-01

The emergence of tilted bipolar active regions (ARs) and the dispersal of their flux, mediated via processes such as diffusion, differential rotation, and meridional circulation, is believed to be responsible for the reversal of the Sun's polar field. This process (commonly known as the Babcock-Leighton mechanism) is usually modeled as a near-surface, spatially distributed α-effect in kinematic mean-field dynamo models. However, this formulation leads to a relationship between polar field strength and meridional flow speed which is opposite to that suggested by physical insight and predicted by surface flux-transport simulations. With this in mind, we present an improved double-ring algorithm for modeling the Babcock-Leighton mechanism based on AR eruption, within the framework of an axisymmetric dynamo model. Using surface flux-transport simulations, we first show that an axisymmetric formulation-which is usually invoked in kinematic dynamo models-can reasonably approximate the surface flux dynamics. Finally, we demonstrate that our treatment of the Babcock-Leighton mechanism through double-ring eruption leads to an inverse relationship between polar field strength and meridional flow speed as expected, reconciling the discrepancy between surface flux-transport simulations and kinematic dynamo models.

THE TURBULENT DYNAMO IN HIGHLY COMPRESSIBLE SUPERSONIC PLASMAS

Energy Technology Data Exchange (ETDEWEB)

Federrath, Christoph [Research School of Astronomy and Astrophysics, The Australian National University, Canberra, ACT 2611 (Australia); Schober, Jennifer [Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Strasse 2, D-69120 Heidelberg (Germany); Bovino, Stefano; Schleicher, Dominik R. G., E-mail: christoph.federrath@anu.edu.au [Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen (Germany)

2014-12-20

The turbulent dynamo may explain the origin of cosmic magnetism. While the exponential amplification of magnetic fields has been studied for incompressible gases, little is known about dynamo action in highly compressible, supersonic plasmas, such as the interstellar medium of galaxies and the early universe. Here we perform the first quantitative comparison of theoretical models of the dynamo growth rate and saturation level with three-dimensional magnetohydrodynamical simulations of supersonic turbulence with grid resolutions of up to 1024{sup 3} cells. We obtain numerical convergence and find that dynamo action occurs for both low and high magnetic Prandtl numbers Pm = ν/η = 0.1-10 (the ratio of viscous to magnetic dissipation), which had so far only been seen for Pm ≥ 1 in supersonic turbulence. We measure the critical magnetic Reynolds number, Rm{sub crit}=129{sub −31}{sup +43}, showing that the compressible dynamo is almost as efficient as in incompressible gas. Considering the physical conditions of the present and early universe, we conclude that magnetic fields need to be taken into account during structure formation from the early to the present cosmic ages, because they suppress gas fragmentation and drive powerful jets and outflows, both greatly affecting the initial mass function of stars.

Energy transfers in large-scale and small-scale dynamos

Science.gov (United States)

Samtaney, Ravi; Kumar, Rohit; Verma, Mahendra

2015-11-01

We present the energy transfers, mainly energy fluxes and shell-to-shell energy transfers in small-scale dynamo (SSD) and large-scale dynamo (LSD) using numerical simulations of MHD turbulence for Pm = 20 (SSD) and for Pm = 0.2 on 10243 grid. For SSD, we demonstrate that the magnetic energy growth is caused by nonlocal energy transfers from the large-scale or forcing-scale velocity field to small-scale magnetic field. The peak of these energy transfers move towards lower wavenumbers as dynamo evolves, which is the reason for the growth of the magnetic fields at the large scales. The energy transfers U2U (velocity to velocity) and B2B (magnetic to magnetic) are forward and local. For LSD, we show that the magnetic energy growth takes place via energy transfers from large-scale velocity field to large-scale magnetic field. We observe forward U2U and B2B energy flux, similar to SSD.

Mean Field Games Models-A Brief Survey

KAUST Repository

Gomes, Diogo A.

2013-11-20

The mean-field framework was developed to study systems with an infinite number of rational agents in competition, which arise naturally in many applications. The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently around the same time in the engineering community by P. Caines, Minyi Huang, and Roland Malhamé. Since these seminal contributions, the research in mean-field games has grown exponentially, and in this paper we present a brief survey of mean-field models as well as recent results and techniques. In the first part of this paper, we study reduced mean-field games, that is, mean-field games, which are written as a system of a Hamilton-Jacobi equation and a transport or Fokker-Planck equation. We start by the derivation of the models and by describing some of the existence results available in the literature. Then we discuss the uniqueness of a solution and propose a definition of relaxed solution for mean-field games that allows to establish uniqueness under minimal regularity hypothesis. A special class of mean-field games that we discuss in some detail is equivalent to the Euler-Lagrange equation of suitable functionals. We present in detail various additional examples, including extensions to population dynamics models. This section ends with a brief overview of the random variables point of view as well as some applications to extended mean-field games models. These extended models arise in problems where the costs incurred by the agents depend not only on the distribution of the other agents, but also on their actions. The second part of the paper concerns mean-field games in master form. These mean-field games can be modeled as a partial differential equation in an infinite dimensional space. We discuss both deterministic models as well as problems where the agents are correlated. We end the paper with a mean-field model for price impact. © 2013 Springer Science+Business Media New York.

Mean Field Games Models-A Brief Survey

KAUST Repository

Gomes, Diogo A.; Saú de, Joã o

2013-01-01

The mean-field framework was developed to study systems with an infinite number of rational agents in competition, which arise naturally in many applications. The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently around the same time in the engineering community by P. Caines, Minyi Huang, and Roland Malhamé. Since these seminal contributions, the research in mean-field games has grown exponentially, and in this paper we present a brief survey of mean-field models as well as recent results and techniques. In the first part of this paper, we study reduced mean-field games, that is, mean-field games, which are written as a system of a Hamilton-Jacobi equation and a transport or Fokker-Planck equation. We start by the derivation of the models and by describing some of the existence results available in the literature. Then we discuss the uniqueness of a solution and propose a definition of relaxed solution for mean-field games that allows to establish uniqueness under minimal regularity hypothesis. A special class of mean-field games that we discuss in some detail is equivalent to the Euler-Lagrange equation of suitable functionals. We present in detail various additional examples, including extensions to population dynamics models. This section ends with a brief overview of the random variables point of view as well as some applications to extended mean-field games models. These extended models arise in problems where the costs incurred by the agents depend not only on the distribution of the other agents, but also on their actions. The second part of the paper concerns mean-field games in master form. These mean-field games can be modeled as a partial differential equation in an infinite dimensional space. We discuss both deterministic models as well as problems where the agents are correlated. We end the paper with a mean-field model for price impact. © 2013 Springer Science+Business Media New York.

Ab Initio Simulations of a Supernova-driven Galactic Dynamo in an Isolated Disk Galaxy

Energy Technology Data Exchange (ETDEWEB)

Butsky, Iryna [Astronomy Department, University of Washington, Seattle, WA 98195 (United States); Zrake, Jonathan; Kim, Ji-hoon; Yang, Hung-I; Abel, Tom [Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Menlo Park, CA 94025 (United States)

2017-07-10

We study the magnetic field evolution of an isolated spiral galaxy, using isolated Milky Way–mass galaxy formation simulations and a novel prescription for magnetohydrodynamic (MHD) supernova feedback. Our main result is that a galactic dynamo can be seeded and driven by supernova explosions, resulting in magnetic fields whose strength and morphology are consistent with observations. In our model, supernovae supply thermal energy and a low-level magnetic field along with their ejecta. The thermal expansion drives turbulence, which serves a dual role by efficiently mixing the magnetic field into the interstellar medium and amplifying it by means of a turbulent dynamo. The computational prescription for MHD supernova feedback has been implemented within the publicly available ENZO code and is fully described in this paper. This improves upon ENZO 's existing modules for hydrodynamic feedback from stars and active galaxies. We find that the field attains microgauss levels over gigayear timescales throughout the disk. The field also develops a large-scale structure, which appears to be correlated with the disk’s spiral arm density structure. We find that seeding of the galactic dynamo by supernova ejecta predicts a persistent correlation between gas metallicity and magnetic field strength. We also generate all-sky maps of the Faraday rotation measure from the simulation-predicted magnetic field, and we present a direct comparison with observations.

Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource

Energy Technology Data Exchange (ETDEWEB)

Graber, P. Jameson, E-mail: jameson-graber@baylor.edu [Baylor University, Department of Mathematics (United States)

2016-12-15

We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.

An impurity solver for nonequilibrium dynamical mean field theory based on hierarchical quantum master equations

Energy Technology Data Exchange (ETDEWEB)

Haertle, Rainer [Institut fuer Theoretische Physik, Georg-August-Universitaet Goettingen, Goettingen (Germany); Millis, Andrew J. [Department of Physics, Columbia University, New York (United States)

2016-07-01

We present a new impurity solver for real-time and nonequilibrium dynamical mean field theory applications, based on the recently developed hierarchical quantum master equation approach. Our method employs a hybridization expansion of the time evolution operator, including an advanced, systematic truncation scheme. Convergence to exact results for not too low temperatures has been demonstrated by a direct comparison to quantum Monte Carlo simulations. The approach is time-local, which gives us access to slow dynamics such as, e.g., in the presence of magnetic fields or exchange interactions and to nonequilibrium steady states. Here, we present first results of this new scheme for the description of strongly correlated materials in the framework of dynamical mean field theory, including benchmark and new results for the Hubbard and periodic Anderson model.

Dynamical Regimes and the Dynamo Bifurcation in Geodynamo Simulations

Science.gov (United States)

Petitdemange, L.

2017-12-01

We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core : in a rotating spherical shell with thermally driven motions with no-slip boundaries. Unlike previous studies on dynamo bifurcations, the control parameters have been varied significantly in order to deduce general tendencies. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition is replaced by a region of bistability for which dipolar and multipolar dynamos coexist. Such a result was also observed in models with free-slip boundaries in which the strong shear of geostrophic zonal flows can develop and gives rise to non-dipolar fields. We show that a similar process develops in no-slip models when viscous effects are reduced sufficiently.Close to the onset of convection (Rac), the axial dipole grows exponentially in the kinematic phase and saturation occurs by marginally changing the flow structure close to the dynamo threshold Rmc. The resulting bifurcation is then supercritical.In the range 3RacIf (Ra/Ra_c>10), important zonal flows develop in non-magnetic models with low viscosity. The field topology depends on the initial magnetic field. The dipolar branch has a subcritical behaviour whereas the multipolar branch is supercritical. By approaching more realistic parameters, the extension of this bistable regime increases (lower Rossby numbers). An hysteretic behaviour questions the common interpretation for geomagnetic reversals. Far above Rm_c$, the Lorentz force becomes dominant, as it is expected in planetary cores.

Energy transfers and magnetic energy growth in small-scale dynamo

KAUST Repository

Kumar, Rohit Raj

2013-12-01

In this letter we investigate the dynamics of magnetic energy growth in small-scale dynamo by studying energy transfers, mainly energy fluxes and shell-to-shell energy transfers. We perform dynamo simulations for the magnetic Prandtl number Pm = 20 on 10243 grid using the pseudospectral method. We demonstrate that the magnetic energy growth is caused by nonlocal energy transfers from the large-scale or forcing-scale velocity field to small-scale magnetic field. The peak of these energy transfers moves towards lower wave numbers as dynamo evolves, which is the reason why the integral scale of the magnetic field increases with time. The energy transfers U2U (velocity to velocity) and B2B (magnetic to magnetic) are forward and local. Copyright © EPLA, 2013.

Extended Deterministic Mean-Field Games

KAUST Repository

Gomes, Diogo A.

2016-04-21

In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.

Extended Deterministic Mean-Field Games

KAUST Repository

Gomes, Diogo A.; Voskanyan, Vardan K.

2016-01-01

In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.

Magnetorotational Dynamo Action in the Shearing Box

Science.gov (United States)

Walker, Justin; Boldyrev, Stanislav

2017-10-01

Magnetic dynamo action caused by the magnetorotational instability is studied in the shearing-box approximation with no imposed net magnetic flux. Consistent with recent studies, the dynamo action is found to be sensitive to the aspect ratio of the box: it is much easier to obtain in tall boxes (stretched in the direction normal to the disk plane) than in long boxes (stretched in the radial direction). Our direct numerical simulations indicate that the dynamo is possible in both cases, given a large enough magnetic Reynolds number. To explain the relatively larger effort required to obtain the dynamo action in a long box, we propose that the turbulent eddies caused by the instability most efficiently fold and mix the magnetic field lines in the radial direction. As a result, in the long box the scale of the generated strong azimuthal (stream-wise directed) magnetic field is always comparable to the scale of the turbulent eddies. In contrast, in the tall box the azimuthal magnetic flux spreads in the vertical direction over a distance exceeding the scale of the turbulent eddies. As a result, different vertical sections of the tall box are permeated by large-scale nonzero azimuthal magnetic fluxes, facilitating the instability. NSF AGS-1261659, Vilas Associates Award, NSF-Teragrid Project TG-PHY110016.

Out-of-equilibrium dynamical mean-field equations for the perceptron model

Science.gov (United States)

Agoritsas, Elisabeth; Biroli, Giulio; Urbani, Pierfrancesco; Zamponi, Francesco

2018-02-01

Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.

Dynamos driven by poloidal flows in untwisted, curved and flat Riemannian diffusive flux tubes

International Nuclear Information System (INIS)

De Andrade, L.C.G.

2010-01-01

Recently Vishik anti-fast dynamo theorem has been tested against non-stretching flux tubes (Phys. Plasmas, 15 (2008)). In this paper, another anti dynamo theorem, called Cowling's theorem, which states that axisymmetric magnetic fields cannot support dynamo action, is carefully tested against thick tubular and curved Riemannian untwisted flows, as well as thin flux tubes in diffusive and diffusion less media. In the non-diffusive media Cowling's theorem is not violated in thin Riemann-flat untwisted flux tubes, where the Frenet curvature is negative. Nevertheless the diffusion action in the thin flux tube leads to a dynamo action driven by poloidal flows as shown by Love and Gubbins (Geophysical Res., 23 (1996) 857) in the context of geo dynamos. Actually it is shown that a slow dynamo action is obtained. In this case the Frenet and Riemann curvature still vanishes. In the case of magnetic filaments in diffusive media dynamo action is obtained when the Frenet scalar curvature is negative. Since the Riemann curvature tensor can be expressed in terms of the Frenet curvature of the magnetic flux tube axis, this result can be analogous to a recent result obtained by Chicone, Latushkin and Smith, which states that geodesic curvature in compact Riemannian manifolds can drive dynamo action in the manifold. It is also shown that in the absence of diffusion, magnetic energy does not grow but magnetic toroidal magnetic field can be generated by the poloidal field, what is called a plasma dynamo.

A COUPLED 2 × 2D BABCOCK–LEIGHTON SOLAR DYNAMO MODEL. II. REFERENCE DYNAMO SOLUTIONS

International Nuclear Information System (INIS)

Lemerle, Alexandre; Charbonneau, Paul

2017-01-01

In this paper we complete the presentation of a new hybrid 2 × 2D flux transport dynamo (FTD) model of the solar cycle based on the Babcock–Leighton mechanism of poloidal magnetic field regeneration via the surface decay of bipolar magnetic regions (BMRs). This hybrid model is constructed by allowing the surface flux transport (SFT) simulation described in Lemerle et al. to provide the poloidal source term to an axisymmetric FTD simulation defined in a meridional plane, which in turn generates the BMRs required by the SFT. A key aspect of this coupling is the definition of an emergence function describing the probability of BMR emergence as a function of the spatial distribution of the internal axisymmetric magnetic field. We use a genetic algorithm to calibrate this function, together with other model parameters, against observed cycle 21 emergence data. We present a reference dynamo solution reproducing many solar cycle characteristics, including good hemispheric coupling, phase relationship between the surface dipole and the BMR-generating internal field, and correlation between dipole strength at cycle maximum and peak amplitude of the next cycle. The saturation of the cycle amplitude takes place through the quenching of the BMR tilt as a function of the internal field. The observed statistical scatter about the mean BMR tilt, built into the model, acts as a source of stochasticity which dominates amplitude fluctuations. The model thus can produce Dalton-like epochs of strongly suppressed cycle amplitude lasting a few cycles and can even shut off entirely following an unfavorable sequence of emergence events.

A COUPLED 2 × 2D BABCOCK–LEIGHTON SOLAR DYNAMO MODEL. II. REFERENCE DYNAMO SOLUTIONS

Energy Technology Data Exchange (ETDEWEB)

Lemerle, Alexandre; Charbonneau, Paul, E-mail: lemerle@astro.umontreal.ca, E-mail: paulchar@astro.umontreal.ca [Département de physique, Université de Montréal, 2900 Boulevard Édouard-Montpetit, Montréal, QC, H3T 1J4 (Canada)

2017-01-10

In this paper we complete the presentation of a new hybrid 2 × 2D flux transport dynamo (FTD) model of the solar cycle based on the Babcock–Leighton mechanism of poloidal magnetic field regeneration via the surface decay of bipolar magnetic regions (BMRs). This hybrid model is constructed by allowing the surface flux transport (SFT) simulation described in Lemerle et al. to provide the poloidal source term to an axisymmetric FTD simulation defined in a meridional plane, which in turn generates the BMRs required by the SFT. A key aspect of this coupling is the definition of an emergence function describing the probability of BMR emergence as a function of the spatial distribution of the internal axisymmetric magnetic field. We use a genetic algorithm to calibrate this function, together with other model parameters, against observed cycle 21 emergence data. We present a reference dynamo solution reproducing many solar cycle characteristics, including good hemispheric coupling, phase relationship between the surface dipole and the BMR-generating internal field, and correlation between dipole strength at cycle maximum and peak amplitude of the next cycle. The saturation of the cycle amplitude takes place through the quenching of the BMR tilt as a function of the internal field. The observed statistical scatter about the mean BMR tilt, built into the model, acts as a source of stochasticity which dominates amplitude fluctuations. The model thus can produce Dalton-like epochs of strongly suppressed cycle amplitude lasting a few cycles and can even shut off entirely following an unfavorable sequence of emergence events.

Latitudinal profile of the ionospheric disturbance dynamo magnetic signature: comparison with the DP2 magnetic disturbance

Directory of Open Access Journals (Sweden)

K. Z. Zaka

2009-09-01

Full Text Available During magnetic storms, the auroral electrojets intensification affects the thermospheric circulation on a global scale. This process which leads to electric field and current disturbance at middle and low latitudes, on the quiet day after the end of a storm, has been attributed to the ionospheric disturbance dynamo (Ddyn. The magnetic field disturbance observed as a result of this process is the reduction of the H component amplitude in the equatorial region which constitutes the main characteristic of the ionospheric disturbance dynamo process, associated with a westward electric current flow. The latitudinal profile of the Ddyn disturbance dynamo magnetic signature exhibits an eastward current at mid latitudes and a westward one at low latitudes with a substantial amplification at the magnetic equator. Such current flow reveals an "anti-Sq" system established between the mid latitudes and the equatorial region and opposes the normal Sq current vortex. However, the localization of the eastward current and consequently the position and the extent of the "anti-Sq" current vortex changes from one storm to another. Indeed, for a strong magnetic storm, the eastward current is well established at mid latitudes about 45° N and for a weak magnetic storm, the eastward current is established toward the high latitudes (about 60° N, near the Joule heating region, resulting in a large "anti-Sq" current cell. The latitudinal profile of the Ddyn disturbance as well as the magnetic disturbance DP2 generated by the mechanism of prompt penetration of the magnetospheric convection electric field in general, show a weak disturbance at the low latitudes with a substantial amplification at the magnetic equator. Due to the intensity of the storm, the magnitude of the DP2 appears higher than the Ddyn over the American and Asian sector contrary to the African sector.

Obstacle mean-field game problem

KAUST Repository

Gomes, Diogo A.; Patrizi, Stefania

2015-01-01

In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions. © European Mathematical Society 2015.

Ohm's law for mean magnetic fields

International Nuclear Information System (INIS)

Boozer, A.H.

1986-05-01

The magnetic fields associated with plasmas frequently exhibit small amplitude MHD fluctuations. It is useful to have equations for the magnetic field averaged over these fluctuations, the so-called mean field equations. Under very general assumptions it is shown that the effect of MHD fluctuations on a force-free plasma can be represented by one parameter in Ohm's law, which is effectively the coefficient of electric current viscosity

Ohm's law for mean magnetic fields

International Nuclear Information System (INIS)

Boozer, A.H.

1986-01-01

The magnetic fields associated with plasmas frequently exhibit small-amplitude MHD fluctuations. It is useful to have equations for the magnetic field averaged over these fluctuations, the so-called mean field equations. Under very general assumptions, it is shown that the effect of MHD fluctuations on a force-free plasma can be represented by one parameter in Ohm's law, which is effectively the coefficient of electric current viscosity. (author)

Simulations of Dynamo and Magnetorotational Instability in Madison Plasma Experiments and Astrophysical Disks

Energy Technology Data Exchange (ETDEWEB)

Ebrahimi, Fatima [Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences

2018-02-22

Magnetic fields are observed to exist on all scales in many astrophysical sources such as stars, galaxies, and accretion discs. Understanding the origin of large scale magnetic fields, whereby the field emerges on spatial scales large compared to the fluctuations, has been a particularly long standing challenge. Our physics objective are: 1) what are the minimum ingredients for large-scale dynamo growth? 2) could a large-scale magnetic field grow out of turbulence and sustained despite the presence of dissipation? These questions are fundamental for understanding the large-scale dynamo in both laboratory and astrophysical plasmas. Here, we report major new findings in the area of Large-Scale Dynamo (magnetic field generation).

Magnetic Helicities and Dynamo Action in Magneto-rotational Turbulence

Energy Technology Data Exchange (ETDEWEB)

Bodo, G.; Rossi, P. [INAF/Osservatorio Astrofisico di Torino, Strada Osservatorio 20, I-10025 Pino Torinese (Italy); Cattaneo, F. [Department of Astronomy and Astrophysics, The University of Chicago, 5640 S. Ellis Avenue, Chicago IL 60637 (United States); Mignone, A., E-mail: bodo@oato.inaf.it [Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino (Italy)

2017-07-10

We examine the relationship between magnetic flux generation, taken as an indicator of large-scale dynamo action, and magnetic helicity, computed as an integral over the dynamo volume, in a simple dynamo. We consider dynamo action driven by magneto-rotational turbulence (MRT) within the shearing-box approximation. We consider magnetically open boundary conditions that allow a flux of helicity in or out of the computational domain. We circumvent the problem of the lack of gauge invariance in open domains by choosing a particular gauge—the winding gauge—that provides a natural interpretation in terms of the average winding number of pairwise field lines. We use this gauge precisely to define and measure the helicity and the helicity flux for several realizations of dynamo action. We find in these cases that the system as a whole does not break reflectional symmetry and that the total helicity remains small even in cases when substantial magnetic flux is generated. We find no particular connection between the generation of magnetic flux and the helicity or the helicity flux through the boundaries. We suggest that this result may be due to the essentially nonlinear nature of the dynamo processes in MRT.

A theory of the Earth's magnetic field and of sunspots, based on a self-excited dynamo incorporating the Hall effect

Directory of Open Access Journals (Sweden)

A. de Paor

2001-01-01

Full Text Available A new viewpoint on the generation and maintenance of the Earth's magnetic field is put forward, which integrates self-exciting dynamo theory with the possibility of energy coupling along orthogonal axes provided by the Hall effect. A nonlinear third-order system is derived, with a fourth equation serving as an observer of unspecified geophysical processes which could result in field reversal. Lyapunov analysis proves that chaos is not intrinsic to this system. Relative constancy of one of the variables produces pseudo equilibrium in a second order subsystem and allows for self-excitation of the geomagnetic field. Electromagnetic analysis yields expressions for key parameters. Models for secular variations recorded at London, Palermo and at the Cape of Good Hope over the past four hundred years are offered. Offset of the Earth's magnetic axis from the geographic axis is central to time-varying declination, but its causes have not yet been established. Applicability of the model to the explanation of sunspot activity is outlined. A corroborating experiment published by Peter Barlow in 1831 is appended.

Back-reaction beyond the mean field approximation

International Nuclear Information System (INIS)

Kluger, Y.

1993-01-01

A method for solving an initial value problem of a closed system consisting of an electromagnetic mean field and its quantum fluctuations coupled to fermions is presented. By tailoring the large N f expansion method to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured, and a systematic energy conserving and gauge invariant expansion about the electromagnetic mean field in powers of 1/N f is developed. The resulting equations may be used to study the quantum nonequilibrium effects of pair creation in strong electric fields and the scattering and transport processes of a relativistic e + e - plasma. Using the Bjorken ansatz of boost invariance initial conditions in which the initial electric mean field depends on the proper time only, we show numerical results for the case in which the N f expansion is truncated in the lowest order, and compare them with those of a phenomenological transport equation

On self-exciting coupled Faraday disk homopolar dynamos driving series motors

Science.gov (United States)

Moroz, Irene M.; Hide, Raymond; Soward, Andrew M.

1998-06-01

We present the results of a preliminary analytical and numerical study of one of the simpler members of a hierarchy of N (where N ≥ 1) coupled self-exciting Faraday disk homopolar dynamos, incorporating motors as additional electrical elements driven by the dynamo-generated current, as proposed by Hide (1997). The hierarchy is a generalisation of a single disk dynamo ( N = 1) with just one electric motor in the system, and crucially, incorporating effects due to mechanical friction in both the disk and the motor, as investigated by Hide et al. (1996). This is describable by a set of three coupled autonomous nonlinear ordinary differential equations, which, due to the presence of the motor, has solutions corresponding to co-existing periodic states of increasing complexity, as well as to chaotic dynamics. We consider the case of two such homopolar dynamos ( N = 2) with generally dissimilar characteristics but coupled together magnetically, with the aim of determining the extent to which this coupled system differs in its behaviour from the single disk dynamo with a series motor (Hide et al. 1996). In the case when the units are identical, the behaviour of the double dynamo system (after initial transients have decayed away) is identical to that of the single dynamo system, with solutions (including “synchronised chaos”) locked in both amplitude and phase. When there is no motor in the system and the coefficient of mechanical friction in the disks is small, these transients resemble the well-known ‘non-synchronous’, but structurally unstable Rikitake solution.

When did the lunar core dynamo cease?

Science.gov (United States)

Tikoo, S. M.; Weiss, B. P.; Shuster, D. L.; Fuller, M.

2013-12-01

Remanent magnetization in the lunar crust and in returned Apollo samples has long suggested that the Moon formed a metallic core and an ancient dynamo magnetic field. Recent paleomagnetic investigations of lunar samples demonstrate that the Moon had a core dynamo which produced ~30-110 μT surface fields between at least 4.2 and 3.56 billion years ago (Ga). Tikoo et al. (1) recently found that the field declined to below several μT by 3.19 Ga. However, given that even values of a few μT are at the upper end of the intensities predicted by dynamo theory for this late in lunar history, it remains uncertain when the lunar dynamo actually ceased completely. Determining this requires a young lunar rock with extraordinarily high magnetic recording fidelity. With this goal, we are conducting a new analysis of young regolith breccia 15498. Although the breccia's age is currently uncertain, the presence of Apollo 15-type mare basalt clasts provides an upper limit constraint of ~3.3 Ga, while trapped Ar data suggest a lithification age of ~1.3 Ga. In stark contrast to the multidomain character of virtually all lunar crystalline rocks, the magnetic carriers in 15498 are on average pseudo-single domain to superparamagnetic, indicating that the sample should provide high-fidelity paleointensity records. A previous alternating field (AF) and thermal demagnetization study of 15498 by Gose et al. (2) observed that the sample carries stable remanent magnetization which persists to unblocking temperatures of at least 650°C. Using a modified Thellier technique, they reported a paleointensity of 2 μT. Although this value may have been influenced by spurious remanence acquired during pretreatment with AF demagnetization, our results confirm the presence of an extremely stable (blocked to coercivities >290 mT) magnetization in the glassy matrix. We also found that this magnetization is largely unidirectional across mutually oriented subsamples. The cooling timescale of this rock (~1

Derivation of mean-field dynamics for fermions

International Nuclear Information System (INIS)

Petrat, Soeren

2014-01-01

In this work, we derive the time-dependent Hartree(-Fock) equations as an effective dynamics for fermionic many-particle systems. Our main results are the first for a quantum mechanical mean-field dynamics for fermions; in previous works, the mean-field limit is usually either coupled to a semiclassical limit, or the interaction is scaled down so much, that the system behaves freely for large particle number N. We mainly consider systems with total kinetic energy bounded by const.N and long-range interaction potentials, e.g., Coulomb interaction. Examples for such systems are large molecules or certain solid states. Our analysis also applies to attractive interactions, as, e.g., in fermionic stars. The fermionic Hartree(-Fock) equations are a standard tool to describe, e.g., excited states or chemical reactions of large molecules (like proteins). A deeper understanding of these equations as an approximation to the time evolution of a many body quantum system is thus highly relevant. We consider the fermionic Hartree equations (i.e., the Hartree-Fock equations without exchange term) in this work, since the exchange term is subleading in our setting. The main result is that the fermionic Hartree dynamics approximates the Schroedinger dynamics well for large N. This statement becomes exact in the thermodynamic limit N→∞. We give explicit values for the rates of convergence. We prove two types of results. The first type is very general and concerns arbitrary free Hamiltonians (e.g., relativistic, non-relativistic, with external fields) and arbitrary interactions. The theorems give explicit conditions on the solutions to the fermionic Hartree equations under which a derivation of the mean-field dynamics succeeds. The second type of results scrutinizes situations where the conditions are fulfilled. These results are about non-relativistic free Hamiltonians with external fields, systems with total kinetic energy bounded by const.N and with long-range interactions of

Stellar rotation, dynamo, electromagnetic braking, age an lithium burning

International Nuclear Information System (INIS)

Schatzmann, E.

1989-01-01

After an introduction describing the problem and the observational tests of the theory a consistant model of the dynamo mechanism in rotating star is presented. This provides for the electromagnetic braking a law Ω ∼ (1.t/t c har) -3 / 4 , in good agreement with the observations. This rests on the hypothesis that the main contribution to the EM braking is due to the magnetic field present in bipolar magnetic spots at the surface of the stellar disk. The premain sequence EM braking provides an initial angular velocity on arrival on the main sequence which is slightly smaller than the angular velocity when the dynamo turns on. Starting the dynamo takes place when the level at which the (αΩ) dynamo number becomes larger than one drops below the ionization level of hydrogen. Before that time, the surface dynamo mechanism would take place in a region of low ionization, where the magnetic Reynods number is so small that dissipation overtakes the building of the magnetic field. Turbulent mixing with a turbulent diffusion coefficient proportional to Ω 2 provides a consistant picture of the time and mass dependance of the surface abundance of Lithium. When the level of Li-burning is sufficiently far from the bottom of the convective zone an asymptotic value of lithium abundance is reached. This can explain the anomalous Li abundance of pop.II stars. (author). 40 refs

Saturn Dynamo Model (Invited)

Science.gov (United States)

Glatzmaier, G. A.

2010-12-01

There has been considerable interest during the past few years about the banded zonal winds and global magnetic field on Saturn (and Jupiter). Questions regarding the depth to which the intense winds extend below the surface and the role they play in maintaining the dynamo continue to be debated. The types of computer models employed to address these questions fall into two main classes: general circulation models (GCMs) based on hydrostatic shallow-water assumptions from the atmospheric and ocean modeling communities and global non-hydrostatic deep convection models from the geodynamo and solar dynamo communities. The latter class can be further divided into Boussinesq models, which do not account for density stratification, and anelastic models, which do. Recent efforts to convert GCMs to deep circulation anelastic models have succeeded in producing fluid flows similar to those obtained from the original deep convection anelastic models. We describe results from one of the original anelastic convective dynamo simulations and compare them to a recent anelastic dynamo benchmark for giant gas planets. This benchmark is based on a polytropic reference state that spans five density scale heights with a radius and rotation rate similar to those of our solar system gas giants. The resulting magnetic Reynolds number is about 3000. Better spatial resolution will be required to produce more realistic predictions that capture the effects of both the density and electrical conductivity stratifications and include enough of the turbulent kinetic energy spectrum. Important additional physics may also be needed in the models. However, the basic models used in all simulation studies of the global dynamics of giant planets will hopefully first be validated by doing these simpler benchmarks.

A model of the solar cycle driven by the dynamo action of the global convection in the solar convection zone

International Nuclear Information System (INIS)

Yoshimura, H.

1976-01-01

Extensive numerical studies of the dynamo equations due to the global convection are presented to simulate the solar cycle and to open the way to study general stellar magnetic cycles. The dynamo equations which represent the longitudinally-averaged magnetohydrodynamical action (mean magnetohydrodynamics) of the global convection under the influence of the rotation in the solar convection zone are considered here as an initial boundary-value problem. The latitudinal and radial structure of the dynamo action consisting of a generation action due to the differential rotation and a regeneration action due to the global convection is parameterized in accordance with the structure of the rotation and of the global convection. This is done especially in such a way as to represent the presence of the two cells of the regeneration action in the radial direction in which the action has opposite signs, which is typical of the regeneration action of the global convection. The effects of the dynamics of the global convection (e.g., the effects of the stratification of the physical conditions in the solar convection zone) are presumed to be all included in those parameters used in the model and they are presumed not to alter the results drastically since these effects are only to change the structure of the regeneration action topologically. (Auth.)

Mean field approximation versus exact treatment of collisions in few-body systems

International Nuclear Information System (INIS)

Lemm, J.; Weiguny, A.; Giraud, B.G.

1990-01-01

A variational principle for calculating matrix elements of the full resolvent operator for a many-body system is studied. Its mean field approximation results in non-linear equations of Hartree (-Fock) type, with initial and final channel wave functions as driving terms. The mean field equations will in general have many solutions whereas the exact problem being linear, has a unique solution. In a schematic model with separable forces the mean field equations are analytically soluble, and for the exact problem the resulting integral equations are solved numerically. Comparing exact and mean field results over a wide range of system parameters, the mean field approach proves to be a very reliable approximation, which is not plagued by the notorious problem of defining asymptotic channels in the time-dependent mean field method. (orig.)

Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

OpenAIRE

A. M. de Paor

1998-01-01

International audience; Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ? has the value 1 is proved via ...

A study of the required Rayleigh number to sustain dynamo with various inner core radius

Science.gov (United States)

Nishida, Y.; Katoh, Y.; Matsui, H.; Kumamoto, A.

2017-12-01

It is widely accepted that the geomagnetic field is sustained by thermal and compositional driven convections of a liquid iron alloy in the outer core. The generation process of the geomagnetic field has been studied by a number of MHD dynamo simulations. Recent studies of the ratio of the Earth's core evolution suggest that the inner solid core radius ri to the outer liquid core radius ro changed from ri/ro = 0 to 0.35 during the last one billion years. There are some studies of dynamo in the early Earth with smaller inner core than the present. Heimpel et al. (2005) revealed the Rayleigh number Ra of the onset of dynamo process as a function of ri/ro from simulation, while paleomagnetic observation shows that the geomagnetic field has been sustained for 3.5 billion years. While Heimpel and Evans (2013) studied dynamo processes taking into account the thermal history of the Earth's interior, there were few cases corresponding to the early Earth. Driscoll (2016) performed a series of dynamo based on a thermal evolution model. Despite a number of dynamo simulations, dynamo process occurring in the interior of the early Earth has not been fully understood because the magnetic Prandtl numbers in these simulations are much larger than that for the actual outer core.In the present study, we performed thermally driven dynamo simulations with different aspect ratio ri/ro = 0.15, 0.25 and 0.35 to evaluate the critical Ra for the thermal convection and required Ra to maintain the dynamo. For this purpose, we performed simulations with various Ra and fixed the other control parameters such as the Ekman, Prandtl, and magnetic Prandtl numbers. For the initial condition and boundary conditions, we followed the dynamo benchmark case 1 by Christensen et al. (2001). The results show that the critical Ra increases with the smaller aspect ratio ri/ro. It is confirmed that larger amplitude of buoyancy is required in the smaller inner core to maintain dynamo.

Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes

Science.gov (United States)

Kyriakopoulos, Charalampos; Grossmann, Gerrit; Wolf, Verena; Bortolussi, Luca

2018-01-01

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree kmax of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large kmax. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.

MAGNETIC QUENCHING OF TURBULENT DIFFUSIVITY: RECONCILING MIXING-LENGTH THEORY ESTIMATES WITH KINEMATIC DYNAMO MODELS OF THE SOLAR CYCLE

International Nuclear Information System (INIS)

Munoz-Jaramillo, Andres; Martens, Petrus C. H.; Nandy, Dibyendu

2011-01-01

The turbulent magnetic diffusivity in the solar convection zone is one of the most poorly constrained ingredients of mean-field dynamo models. This lack of constraint has previously led to controversy regarding the most appropriate set of parameters, as different assumptions on the value of turbulent diffusivity lead to radically different solar cycle predictions. Typically, the dynamo community uses double-step diffusivity profiles characterized by low values of diffusivity in the bulk of the convection zone. However, these low diffusivity values are not consistent with theoretical estimates based on mixing-length theory, which suggest much higher values for turbulent diffusivity. To make matters worse, kinematic dynamo simulations cannot yield sustainable magnetic cycles using these theoretical estimates. In this work, we show that magnetic cycles become viable if we combine the theoretically estimated diffusivity profile with magnetic quenching of the diffusivity. Furthermore, we find that the main features of this solution can be reproduced by a dynamo simulation using a prescribed (kinematic) diffusivity profile that is based on the spatiotemporal geometric average of the dynamically quenched diffusivity. This bridges the gap between dynamically quenched and kinematic dynamo models, supporting their usage as viable tools for understanding the solar magnetic cycle.

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

Science.gov (United States)

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.

A Single Mode Study of a Quasi-Geostrophic Convection-Driven Dynamo Model

Science.gov (United States)

Plumley, M.; Calkins, M. A.; Julien, K. A.; Tobias, S.

2017-12-01

Planetary magnetic fields are thought to be the product of hydromagnetic dynamo action. For Earth, this process occurs within the convecting, turbulent and rapidly rotating outer core, where the dynamics are characterized by low Rossby, low magnetic Prandtl and high Rayleigh numbers. Progress in studying dynamos has been limited by current computing capabilities and the difficulties in replicating the extreme values that define this setting. Asymptotic models that embrace these extreme parameter values and enforce the dominant balance of geostrophy provide an option for the study of convective flows with actual relevance to geophysics. The quasi-geostrophic dynamo model (QGDM) is a multiscale, fully-nonlinear Cartesian dynamo model that is valid in the asymptotic limit of low Rossby number. We investigate the QGDM using a simplified class of solutions that consist of a single horizontal wavenumber which enforces a horizontal structure on the solutions. This single mode study is used to explore multiscale time stepping techniques and analyze the influence of the magnetic field on convection.

Measurement of core velocity fluctuations and the dynamo in a reversed-field pinch

International Nuclear Information System (INIS)

Den Hartog, D.J.; Craig, D.; Fiksel, G.; Fontana, P.W.; Prager, S.C.; Sarff, J.S.; Chapman, J.T.

1998-01-01

Plasma flow velocity fluctuations have been directly measured in the high temperature magnetically confined plasma in the Madison Symmetric Torus (MST) Reversed-Field Pinch (RFP). These measurements show that the flow velocity fluctuations are correlated with magnetic field fluctuations. This initial measurement is subject to limitations of spatial localization and other uncertainties, but is evidence for sustainment of the RFP magnetic field configuration by the magnetohydrodynamic (MHD) dynamo. Both the flow velocity and magnetic field fluctuations are the result of global resistive MHD modes of helicity m = 1, n = 5--10 in the core of MST. Chord-averaged flow velocity fluctuations are measured in the core of MST by recording the Doppler shift of impurity line emission with a specialized high resolution and throughput grating spectrometer. Magnetic field fluctuations are recorded with a large array of small edge pickup coils, which allows spectral decomposition into discrete modes and subsequent correlation with the velocity fluctuation data

GLOBAL GALACTIC DYNAMO DRIVEN BY COSMIC RAYS AND EXPLODING MAGNETIZED STARS

International Nuclear Information System (INIS)

Hanasz, Michal; Woltanski, Dominik; Kowalik, Kacper

2009-01-01

We report the first results of the first global galactic-scale cosmic ray (CR)-MHD simulations of CR-driven dynamo. We investigate the dynamics of magnetized interstellar medium (ISM), which is dynamically coupled with CR gas. We assume that exploding stars deposit small-scale, randomly oriented, dipolar magnetic fields into the differentially rotating ISM, together with a portion of CRs, accelerated in supernova shocks. We conduct numerical simulations with the aid of a new parallel MHD code PIERNIK. We find that the initial magnetization of galactic disks by exploding magnetized stars forms favorable conditions for the CR-driven dynamo. We demonstrate that dipolar magnetic fields supplied on small supernova remnant scales can be amplified exponentially by the CR-driven dynamo, to the present equipartition values, and transformed simultaneously to large galactic scales. The resulting magnetic field structure in an evolved galaxy appears spiral in the face-on view and reveals the so-called X-shaped structure in the edge-on view.

A Maximum Principle for SDEs of Mean-Field Type

Energy Technology Data Exchange (ETDEWEB)

Andersson, Daniel, E-mail: danieand@math.kth.se; Djehiche, Boualem, E-mail: boualem@math.kth.se [Royal Institute of Technology, Department of Mathematics (Sweden)

2011-06-15

We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.

A Maximum Principle for SDEs of Mean-Field Type

International Nuclear Information System (INIS)

Andersson, Daniel; Djehiche, Boualem

2011-01-01

We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.

Continuous Time Finite State Mean Field Games

International Nuclear Information System (INIS)

Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigão

2013-01-01

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games

Continuous Time Finite State Mean Field Games

Energy Technology Data Exchange (ETDEWEB)

Gomes, Diogo A., E-mail: dgomes@math.ist.utl.pt [Instituto Superior Tecnico, Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Matematica (Portugal); Mohr, Joana, E-mail: joana.mohr@ufrgs.br; Souza, Rafael Rigao, E-mail: rafars@mat.ufrgs.br [UFRGS, Instituto de Matematica (Brazil)

2013-08-01

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N{yields}{infinity} of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.

Towards the geophysical regime in numerical dynamo models: studies of rapidly-rotating convection driven dynamos with low Pm and constant heat flux boundary conditions

DEFF Research Database (Denmark)

Sheyko, A.A.; Finlay, Chris; Marti, P.

We present a set of numerical dynamo models with the convection strength varied by a factor of 30 and the ratio of magnetic to viscous diffusivities by a factor of 20 at rapid rotation rates (E =nu/(2 Omega d^2 ) = 10-6 and 10-7 ) using a heat flux outer BC. This regime has been little explored...... on the structure of the dynamos and how this changes in relation to the selection of control parameters, a comparison with the proposed rotating convection and dynamo scaling laws, energy spectra of steady solutions and inner core rotation rates. Magnetic field on the CMB. E=2.959*10-7, Ra=6591.0, Pm=0.05, Pr=1....

BABCOCK–LEIGHTON SOLAR DYNAMO: THE ROLE OF DOWNWARD PUMPING AND THE EQUATORWARD PROPAGATION OF ACTIVITY

International Nuclear Information System (INIS)

Karak, Bidya Binay; Cameron, Robert

2016-01-01

The key elements of the Babcock–Leighton dynamos are the generation of poloidal field through decay and the dispersal of tilted bipolar active regions and the generation of toroidal field through the observed differential rotation. These models are traditionally known as flux transport dynamo models as the equatorward propagations of the butterfly wings in these models are produced due to an equatorward flow at the bottom of the convection zone. Here we investigate the role of downward magnetic pumping near the surface using a kinematic Babcock–Leighton model. We find that the pumping causes the poloidal field to become predominately radial in the near-surface shear layer, which allows the negative radial shear to effectively act on the radial field to produce a toroidal field. We observe a clear equatorward migration of the toroidal field at low latitudes as a consequence of the dynamo wave even when there is no meridional flow in the deep convection zone. Both the dynamo wave and the flux transport type solutions are thus able to reproduce some of the observed features of the solar cycle including the 11-year periodicity. The main difference between the two types of solutions is the strength of the Babcock–Leighton source required to produce the dynamo action. A second consequence of the magnetic pumping is that it suppresses the diffusion of fields through the surface, which helps to allow an 11-year cycle at (moderately) larger values of magnetic diffusivity than have previously been used.

BABCOCK–LEIGHTON SOLAR DYNAMO: THE ROLE OF DOWNWARD PUMPING AND THE EQUATORWARD PROPAGATION OF ACTIVITY

Energy Technology Data Exchange (ETDEWEB)

Karak, Bidya Binay; Cameron, Robert, E-mail: bkarak@ucar.edu [Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Göttingen (Germany)

2016-11-20

The key elements of the Babcock–Leighton dynamos are the generation of poloidal field through decay and the dispersal of tilted bipolar active regions and the generation of toroidal field through the observed differential rotation. These models are traditionally known as flux transport dynamo models as the equatorward propagations of the butterfly wings in these models are produced due to an equatorward flow at the bottom of the convection zone. Here we investigate the role of downward magnetic pumping near the surface using a kinematic Babcock–Leighton model. We find that the pumping causes the poloidal field to become predominately radial in the near-surface shear layer, which allows the negative radial shear to effectively act on the radial field to produce a toroidal field. We observe a clear equatorward migration of the toroidal field at low latitudes as a consequence of the dynamo wave even when there is no meridional flow in the deep convection zone. Both the dynamo wave and the flux transport type solutions are thus able to reproduce some of the observed features of the solar cycle including the 11-year periodicity. The main difference between the two types of solutions is the strength of the Babcock–Leighton source required to produce the dynamo action. A second consequence of the magnetic pumping is that it suppresses the diffusion of fields through the surface, which helps to allow an 11-year cycle at (moderately) larger values of magnetic diffusivity than have previously been used.

Using dynamo theory to predict the sunspot number during solar cycle 21

Science.gov (United States)

Schatten, K. H.; Scherrer, P. H.; Svalgaard, L.; Wilcox, J. M.

1978-01-01

On physical grounds it is suggested that the polar field strength of the sun near a solar minimum is closely related to the solar activity of the following cycle. Four methods of estimating the polar magnetic field strength of the sun near solar minimum are employed to provide an estimate of the yearly mean sunspot number of cycle 21 at solar maximum of 140 + or - 20. This estimate may be considered a first-order attempt to predict the cycle activity using one parameter of physical importance based upon dynamo theory.

Mean Field Games for Stochastic Growth with Relative Utility

Energy Technology Data Exchange (ETDEWEB)

Huang, Minyi, E-mail: mhuang@math.carleton.ca [Carleton University, School of Mathematics and Statistics (Canada); Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu [University of Puerto Rico, Department of Mathematics (United States)

2016-12-15

This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.

Mean Field Games for Stochastic Growth with Relative Utility

International Nuclear Information System (INIS)

Huang, Minyi; Nguyen, Son Luu

2016-01-01

This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.

Spectral gaps, inertial manifolds and kinematic dynamos

Energy Technology Data Exchange (ETDEWEB)

Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)]. E-mail: mnjmhd@am.uva.es

2005-10-17

Inertial manifolds are desirable objects when ones wishes a dynamical process to behave asymptotically as a finite-dimensional ones. Recently [Physica D 194 (2004) 297] these manifolds are constructed for the kinematic dynamo problem with time-periodic velocity. It turns out, however, that the conditions imposed on the fluid velocity to guarantee the existence of inertial manifolds are too demanding, in the sense that they imply that all the solutions tend exponentially to zero. The inertial manifolds are meaningful because they represent different decay rates, but the classical dynamos where the magnetic field is maintained or grows are not covered by this approach, at least until more refined estimates are found.

Mean fields and self consistent normal ordering of lattice spin and gauge field theories

International Nuclear Information System (INIS)

Ruehl, W.

1986-01-01

Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived. (orig.)

Continuous time finite state mean field games

KAUST Repository

Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigã o

2013-01-01

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.

Continuous time finite state mean field games

KAUST Repository

Gomes, Diogo A.

2013-04-23

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.

Boundary effects on the MHD dynamo in laboratory plasmas

International Nuclear Information System (INIS)

Ho, Y.L.; Prager, S.C.

1989-07-01

In recent laboratory experiments, a dynamo-like mechanism has been demonstrated in which a portion of the axisymmetric component of the magnetic field is believed to be sustained by 3D spatial fluctuations in the field and flow. With a conducting shell at the plasma surface, past MHD computation shows that sustainment arises from fluctuations which cause magnetic reconnection. If the conducting wall is retracted from the plasma surface, the fluctuations are amplified and the dynamo sustainment is still active for the times studied, but an increased energy input to the plasma is required through the applied electric field. The retraction of the conducting wall enhances the helicity dissipation rate by the intersection of the fields with the resistive surface which bounds the plasma. This enhanced helicity dissipation is balanced by the helicity injection that accompanies the increased applied electric field. 17 refs., 7 figs., 1 tab

A spherical Taylor-Couette dynamo

Science.gov (United States)

Marcotte, Florence; Gissinger, Christophe

2016-04-01

We present a new scenario for magnetic field amplification in the planetary interiors where an electrically conducting fluid is confined in a differentially rotating, spherical shell (spherical Couette flow) with thin aspect-ratio. When the angular momentum sufficiently decreases outwards, a primary hydrodynamic instability is widely known to develop in the equatorial region, characterized by pairs of counter-rotating, axisymmetric toroidal vortices (Taylor vortices) similar to those observed in cylindrical Couette flow. We characterize the subcritical dynamo bifurcation due to this spherical Taylor-Couette flow and study its evolution as the flow successively breaks into wavy and turbulent Taylor vortices for increasing Reynolds number. We show that the critical magnetic Reynolds number seems to reach a constant value as the Reynolds number is gradually increased. The role of global rotation on the dynamo threshold and the implications for planetary interiors are finally discussed.

Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

Science.gov (United States)

de Paor, A. M.

Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ɛ has the value 1 is proved via the Popov theorem from feedback system stability theory.

Magnetism, dynamo action and the solar-stellar connection

Directory of Open Access Journals (Sweden)

Allan Sacha Brun

2017-09-01

Full Text Available Abstract The Sun and other stars are magnetic: magnetism pervades their interiors and affects their evolution in a variety of ways. In the Sun, both the fields themselves and their influence on other phenomena can be uncovered in exquisite detail, but these observations sample only a moment in a single star’s life. By turning to observations of other stars, and to theory and simulation, we may infer other aspects of the magnetism—e.g., its dependence on stellar age, mass, or rotation rate—that would be invisible from close study of the Sun alone. Here, we review observations and theory of magnetism in the Sun and other stars, with a partial focus on the “Solar-stellar connection”: i.e., ways in which studies of other stars have influenced our understanding of the Sun and vice versa. We briefly review techniques by which magnetic fields can be measured (or their presence otherwise inferred in stars, and then highlight some key observational findings uncovered by such measurements, focusing (in many cases on those that offer particularly direct constraints on theories of how the fields are built and maintained. We turn then to a discussion of how the fields arise in different objects: first, we summarize some essential elements of convection and dynamo theory, including a very brief discussion of mean-field theory and related concepts. Next we turn to simulations of convection and magnetism in stellar interiors, highlighting both some peculiarities of field generation in different types of stars and some unifying physical processes that likely influence dynamo action in general. We conclude with a brief summary of what we have learned, and a sampling of issues that remain uncertain or unsolved.

Anelastic spherical dynamos with radially variable electrical conductivity

Science.gov (United States)

Dietrich, W.; Jones, C. A.

2018-05-01

A series of numerical simulations of the dynamo process operating inside gas giant planets has been performed. We use an anelastic, fully nonlinear, three-dimensional, benchmarked MHD code to evolve the flow, entropy and magnetic field. Our models take into account the varying electrical conductivity, high in the ionised metallic hydrogen region, low in the molecular outer region. Our suite of electrical conductivity profiles ranges from Jupiter-like, where the outer hydrodynamic region is quite thin, to Saturn-like, where there is a thick non-conducting shell. The rapid rotation leads to the formation of two distinct dynamical regimes which are separated by a magnetic tangent cylinder - mTC. Outside the mTC there are strong zonal flows, where Reynolds stress balances turbulent viscosity, but inside the mTC Lorentz force reduces the zonal flow. The dynamic interaction between both regions induces meridional circulation. We find a rich diversity of magnetic field morphologies. There are Jupiter-like steady dipolar fields, and a belt of quadrupolar dominated dynamos spanning the range of models between Jupiter-like and Saturn-like conductivity profiles. This diversity may be linked to the appearance of reversed sign helicity in the metallic regions of our dynamos. With Saturn-like conductivity profiles we find models with dipolar magnetic fields, whose axisymmetric components resemble those of Saturn, and which oscillate on a very long time-scale. However, the non-axisymmetric field components of our models are at least ten times larger than those of Saturn, possibly due to the absence of any stably stratified layer.

Covariant field equations in supergravity

Energy Technology Data Exchange (ETDEWEB)

Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)

2017-12-15

Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Covariant field equations in supergravity

International Nuclear Information System (INIS)

Vanhecke, Bram; Proeyen, Antoine van

2017-01-01

Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Stochastic quantization and mean field approximation

International Nuclear Information System (INIS)

Jengo, R.; Parga, N.

1983-09-01

In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)

Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

Directory of Open Access Journals (Sweden)

A. M. de Paor

1998-01-01

Full Text Available Hide (Nonlinear Processes in Geophysics, 1998 has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ε has the value 1 is proved via the Popov theorem from feedback system stability theory.

Effect of metallic walls on dynamos generated by laminar boundary-driven flow in a spherical domain.

Science.gov (United States)

Guervilly, Céline; Wood, Toby S; Brummell, Nicholas H

2013-11-01

We present a numerical study of dynamo action in a conducting fluid encased in a metallic spherical shell. Motions in the fluid are driven by differential rotation of the outer metallic shell, which we refer to as "the wall." The two hemispheres of the wall are held in counter-rotation, producing a steady, axisymmetric interior flow consisting of differential rotation and a two-cell meridional circulation with radial inflow in the equatorial plane. From previous studies, this type of flow is known to maintain a stationary equatorial dipole by dynamo action if the magnetic Reynolds number is larger than about 300 and if the outer boundary is electrically insulating. We vary independently the thickness, electrical conductivity, and magnetic permeability of the wall to determine their effect on the dynamo action. The main results are the following: (a) Increasing the conductivity of the wall hinders the dynamo by allowing eddy currents within the wall, which are induced by the relative motion of the equatorial dipole field and the wall. This processes can be viewed as a skin effect or, equivalently, as the tearing apart of the dipole by the differential rotation of the wall, to which the field lines are anchored by high conductivity. (b) Increasing the magnetic permeability of the wall favors dynamo action by constraining the magnetic field lines in the fluid to be normal to the wall, thereby decoupling the fluid from any induction in the wall. (c) Decreasing the wall thickness limits the amplitude of the eddy currents, and is therefore favorable for dynamo action, provided that the wall is thinner than the skin depth. We explicitly demonstrate these effects of the wall properties on the dynamo field by deriving an effective boundary condition in the limit of vanishing wall thickness.

Energy fluxes in helical magnetohydrodynamics and dynamo action

Indian Academy of Sciences (India)

Kinetic and magnetic helicities do not affect the renormalized parameters, ... Generation of magnetic field in plasma, usually referred to as 'dynamo', is one of the ..... energy fluxes for the inertial-range wave numbers where the same power.

Equation of state of isospin-asymmetric nuclear matter in relativistic mean-field models with chiral limits

International Nuclear Information System (INIS)

Jiang Weizhou; Li Baozn; Chen Liewen

2007-01-01

Using in-medium hadron properties according to the Brown-Rho scaling due to the chiral symmetry restoration at high densities and considering naturalness of the coupling constants, we have newly constructed several relativistic mean-field Lagrangians with chiral limits. The model parameters are adjusted such that the symmetric part of the resulting equation of state at supra-normal densities is consistent with that required by the collective flow data from high energy heavy-ion reactions, while the resulting density dependence of the symmetry energy at sub-saturation densities agrees with that extracted from the recent isospin diffusion data from intermediate energy heavy-ion reactions. The resulting equations of state have the special feature of being soft at intermediate densities but stiff at high densities naturally. With these constrained equations of state, it is found that the radius of a 1.4M o canonical neutron star is in the range of 11.9 km≤R≤13.1 km, and the maximum neutron star mass is around 2.0M o close to the recent observations

Magnetic fluctuation induced transport and edge dynamo measurements in the MST reversed-field pinch

International Nuclear Information System (INIS)

Hokin, S.; Fiksel, G.; Ji, H.

1994-09-01

Probe measurements in MST indicate that RFP particle and energy loss is governed by magnetic fluctuations inside r/a = 0.8, with energy carried out convectively by superthermal electrons. The radial loss rate is lower than the Rechester-Rosenbluth level, presumably due to the establishment of a restraining ambipolar potential. Several aspects of these measurements contradict the Kinetic Dynamo Theory, while the MHD dynamo EMF is measured to be large enough to drive the edge current carried by these superthermal electrons

Instrumental Implementation of an Experiment to Demonstrate αω -dynamos in Accretion Disks

Science.gov (United States)

Si, Jiahe; Sonnenfeld, Richard; Colgate, Art; Li, Hui; Nornberg, Mark

2016-10-01

The New Mexico Liquid Metal αω -dynamo experiment is aimed to demonstrate a galactic dynamo. Our goal is to generate the ω-effect and α-effect by two semi-coherent flows in laboratory. Two coaxial cylinders are used to generate Taylor-Couette flows to simulate the differential rotation of accretion disks. Plumes induced by jets injected into the Couette flows are expected to produce helicities necessary for the α-effect. We have demonstrated an 8-fold poloidal-to-toroidal flux amplification from differential rotation (the ω-effect) by minimizing turbulence in our apparatus. To demonstrate the α-effect, the experimental apparatus is undergoing significant upgrade. We have constructed a helicity injection facility, and are also designing and testing a new data acquisition system capable of transmitting data in a high speed rotating frame. Additional magnetic field diagnostics will also be included. The upgrade is intended to answer the question of whether a self-sustaining αω -dynamo can be constructed with a realistic fluid flow field, as well as to obtain more details to understand dynamo action in highly turbulent Couette flow.

MHD dynamo action in space plasmas

International Nuclear Information System (INIS)

Faelthammar, C.G.

1984-05-01

Electric currents are now recognized to play a major role in the physical process of the Earths magnetosphere as well as in distant astrophysical plasmas. In driving these currents MHD dynamos as well as generators of a thermoelectric nature are important. The primary source of power for the Earths magnetospheric process is the solar wind, which supplies a voltage of the order of 200 kV across the magnetosphere. The direction of the large-scale solar wind electric field varies of many different time scales. The power input to the magnetosphere is closely correlated with the direction of the large-scale solar wind electric field in such a fashion as to mimick the response of a half-wave rectifier with a down-to-dusk conduction direction. Behind this apparently simple response there are complex plasma physical processes that are still very incompletely understood. They are intimately related to auroras, magnetic storms, radiation belts and changes in magnetospheric plasma populations. Similar dynamo actions should occur at other planets having magnetospheres. Recent observations seem to indicate that part of the power input to the Earths magnetosphere comes through MHD dynamo action of a forced plasma flow inside the flanks of the magnetopause and may play a role in other parts of the magnetosphere, too. An example of a cosmical MHD connected to a solid load is the corotating plasma of Jupiters inner magnetosphere, sweeping past the plants inner satelites. In particular the electric currents thereby driven to and from the satellite Io have attracted considerable interest.(author)

New Mexico Liquid Metal αω -dynamo experiment: Most Recent Progress

Science.gov (United States)

Si, Jiahe; Sonnenfeld, Richard; Colgate, Art; Li, Hui

2017-10-01

The goal of the New Mexico Liquid Metal αω -dynamo experiment is to demonstrate a galactic dynamo can be generated through two phases, the ω-phase and α-phase by two semi-coherent flows in laboratory. We have demonstrated an 8-fold poloidal-to-toroidal flux amplification from differential rotation (the ω-effect) by minimizing turbulence in our apparatus. To demonstrate the α-effect, major upgrades are needed. The upgrades include building a helicity injection facility, mounting new 100hp motors and new sensors, designing a new data acquisition system capable of transmitting data from about 80 sensors in a high speed rotating frame with an overall 200kS/sec sampling rate. We hope the upgrade can be utilized to answer the question of whether a self-sustaining αω -dynamo can be implemented with a realistic lab fluid flow field, as well as to obtain more details to understand dynamo action in highly turbulent Couette flow.

Evolution of pulsarmagnetism by virtue of a Faraday dynamo mechanism

International Nuclear Information System (INIS)

Heintzmann, H.; Novello, M.

1983-01-01

The evidence that radio-pulsars are slowed-down and Roentgen - pulsars accelerated predominantly by magnetic torques is now very strong. Angular momentum is transferred away from the neutron star to the velocity-of-light cylinder or from the Alfven - cylinder down to the neutron star by means of a magnetic spring the physical origin of which is an appropriate current flowing along the magnetic field lines. As this current must be closed at the neutron star's surface and no Hall-Field can be built-up a Faraday dynamo mechanism is set up. It is pointed out that this mechanism could switch -off a radio pulsar or turn-on a Roentgen pulsar. Many disconcerting pulsar observations could thus be explained, if radio pulsars can be reactivated in the galactic plane by means of accretion of matter in dense clouds and if Roentgenpulsars must first create a sufficiently strong magnetic field to function as a regularly pulsed emitter. (Author) [pt

Inertial effects on thermochemically driven convection and hydromagnetic dynamos in a spherical shell

Czech Academy of Sciences Publication Activity Database

Šimkanin, Ján; Kyselica, Juraj; Guba, P.

2018-01-01

Roč. 212, č. 3 (2018), s. 2194-2205 ISSN 0956-540X Institutional support: RVO:67985530 Keywords : composition and structure of the core * dynamo * nonlinear differential equations * numerical modelling Subject RIV: DE - Earth Magnetism, Geodesy, Geography Impact factor: 2.414, year: 2016

Vector solution for the mean electromagnetic fields in a layer of random particles

Science.gov (United States)

Lang, R. H.; Seker, S. S.; Levine, D. M.

1986-01-01

The mean electromagnetic fields are found in a layer of randomly oriented particles lying over a half space. A matrix-dyadic formulation of Maxwell's equations is employed in conjunction with the Foldy-Lax approximation to obtain equations for the mean fields. A two variable perturbation procedure, valid in the limit of small fractional volume, is then used to derive uncoupled equations for the slowly varying amplitudes of the mean wave. These equations are solved to obtain explicit expressions for the mean electromagnetic fields in the slab region in the general case of arbitrarily oriented particles and arbitrary polarization of the incident radiation. Numerical examples are given for the application to remote sensing of vegetation.

Time-Dependent Mean-Field Games in the Subquadratic Case

KAUST Repository

Gomes, Diogo A.; Pimentel, Edgard A.; Sá nchez-Morgado, Hé ector

2014-01-01

In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.

Time-Dependent Mean-Field Games in the Subquadratic Case

KAUST Repository

Gomes, Diogo A.

2014-10-14

In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.

Momentum and density dependence of the nuclear mean field

International Nuclear Information System (INIS)

Behera, B.; Routray, T.R.

1999-01-01

The purpose of this is to analyse the momentum, density and temperature dependence of the mean field in nuclear matter derived from finite range effective interactions and to examine the influence of the functional form of the interaction on the high momentum behaviour of the mean field. Emphasis will be given to use very simple parametrizations of the effective interaction with a minimum number of adjustable parameters and yet capable of giving a good description of the mean field in nuclear matter over a wide range of momentum, density and temperature. As an application of the calculated equation of state of nuclear matter, phase transitions to quark-gluon plasma is studied where the quark phase is described by a zeroth order bag model equation of state

Pedestrian Flow in the Mean Field Limit

KAUST Repository

Haji Ali, Abdul Lateef

2012-11-01

We study the mean-field limit of a particle-based system modeling the behavior of many indistinguishable pedestrians as their number increases. The base model is a modified version of Helbing\\'s social force model. In the mean-field limit, the time-dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank-Nicholson method. The advection part is solved using a Lax-Wendroff-Leveque method or an upwind Backward Euler method depending on the advection speed. Moreover, we use multilevel Monte Carlo to estimate observables from the particle-based system. We discuss these numerical methods, and present numerical results showing the convergence of observables that were calculated using the particle-based model as the number of pedestrians increases to those calculated using the probability density function satisfying the Fokker-Planck equation.

Steady-state dynamo and current drive in a nonuniform bounded plasma

International Nuclear Information System (INIS)

Mett, R.R.; Taylor, J.B.

1991-03-01

Current drive due to helicity injection and dynamo effect are examined in an inhomogeneous bounded plasma. Averaged over a magnetic surface, there is in general no dynamo effect independent of resistivity -- contrary to the results found previously for an unbounded plasma. The dynamo field is calculated explicitly for an incompressible visco-resistive fluid in the plane-slab model. In accord with our general conclusion, outside the Alfven resonant layer it is proportional to the resistivity. Within the resonant layer there is a contribution which is enhanced, relative to its value outside the layer, by a factor (ωa 2 /(η + ν)), where ω is the wave frequency, a the plasma radius, η the magnetic diffusivity, and ν the kinematic viscosity. However, this contribution vanishes when integrated across the layer. The average field in the layer is enhanced by factor (ωa 2 /(η + ν)) 2/3 and is proportional to the shear in the magnetic field and the cube root of the gradient of the Alfven speed. These results are interpreted in terms of helicity balance, and reconciled with the infinite medium calculations. 15 refs

Dynamo Scaling Laws for Uranus and Neptune: The Role of Convective Shell Thickness on Dipolarity

Science.gov (United States)

Stanley, Sabine; Yunsheng Tian, Bob

2017-10-01

Previous dynamo scaling law studies (Christensen and Aubert, 2006) have demonstrated that the morphology of a planet’s magnetic field is determined by the local Rossby number (Ro_l): a non-dimensional diagnostic variable that quantifies the ratio of inertial forces to Coriolis forces on the average length scale of the flow. Dynamos with Ro_l ~ 0.1 produce multipolar magnetic fields. Scaling studies have also determined the dependence of the local Rossby number on non-dimensional parameters governing the system - specifically the Ekman, Prandtl, magnetic Prandtl and flux-based Rayleigh numbers (Olson and Christensen, 2006). When these scaling laws are applied to the planets, it appears that Uranus and Neptune should have dipole-dominated fields, contrary to observations. However, those scaling laws were derived using the specific convective shell thickness of the Earth’s core. Here we investigate the role of convective shell thickness on dynamo scaling laws. We find that the local Rossby number depends exponentially on the convective shell thickness. Including this new dependence on convective shell thickness, we find that the dynamo scaling laws now predict that Uranus and Neptune reside deeply in the multipolar regime, thereby resolving the previous contradiction with observations.

Identification of vortexes obstructing the dynamo mechanism in laboratory experiments

Science.gov (United States)

Limone, A.; Hatch, D. R.; Forest, C. B.; Jenko, F.

2013-06-01

The magnetohydrodynamic dynamo effect explains the generation of self-sustained magnetic fields in electrically conducting flows, especially in geo- and astrophysical environments. Yet the details of this mechanism are still unknown, e.g., how and to which extent the geometry, the fluid topology, the forcing mechanism, and the turbulence can have a negative effect on this process. We report on numerical simulations carried out in spherical geometry, analyzing the predicted velocity flow with the so-called singular value decomposition, a powerful technique that allows us to precisely identify vortexes in the flow which would be difficult to characterize with conventional spectral methods. We then quantify the contribution of these vortexes to the growth rate of the magnetic energy in the system. We identify an axisymmetric vortex, whose rotational direction changes periodically in time, and whose dynamics are decoupled from those of the large scale background flow, that is detrimental for the dynamo effect. A comparison with experiments is carried out, showing that similar dynamics were observed in cylindrical geometry. These previously unexpected eddies, which impede the dynamo effect, offer an explanation for the experimental difficulties in attaining a dynamo in spherical geometry.

Linear–Quadratic Mean-Field-Type Games: A Direct Method

Directory of Open Access Journals (Sweden)

Tyrone E. Duncan

2018-02-01

Full Text Available In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control actions of all decision-makers. We propose a direct method to solve the game, team, and bargaining problems. This solution approach does not require solving the Bellman–Kolmogorov equations or backward–forward stochastic differential equations of Pontryagin’s type. The proposed method can be easily implemented by beginners and engineers who are new to the emerging field of mean-field-type game theory. The optimal strategies for decision-makers are shown to be in a state-and-mean-field feedback form. The optimal strategies are given explicitly as a sum of the well-known linear state-feedback strategy for the associated deterministic linear–quadratic game problem and a mean-field feedback term. The equilibrium cost of the decision-makers are explicitly derived using a simple direct method. Moreover, the equilibrium cost is a weighted sum of the initial variance and an integral of a weighted variance of the diffusion and the jump process. Finally, the method is used to compute global optimum strategies as well as saddle point strategies and Nash bargaining solution in state-and-mean-field feedback form.

Ensemble averaged coherent state path integral for disordered bosons with a repulsive interaction (Derivation of mean field equations)

International Nuclear Information System (INIS)

Mieck, B.

2007-01-01

We consider bosonic atoms with a repulsive contact interaction in a trap potential for a Bose-Einstein condensation (BEC) and additionally include a random potential. The ensemble averages for two models of static (I) and dynamic (II) disorder are performed and investigated in parallel. The bosonic many body systems of the two disorder models are represented by coherent state path integrals on the Keldysh time contour which allow exact ensemble averages for zero and finite temperatures. These ensemble averages of coherent state path integrals therefore present alternatives to replica field theories or super-symmetric averaging techniques. Hubbard-Stratonovich transformations (HST) lead to two corresponding self-energies for the hermitian repulsive interaction and for the non-hermitian disorder-interaction. The self-energy of the repulsive interaction is absorbed by a shift into the disorder-self-energy which comprises as an element of a larger symplectic Lie algebra sp(4M) the self-energy of the repulsive interaction as a subalgebra (which is equivalent to the direct product of M x sp(2); 'M' is the number of discrete time intervals of the disorder-self-energy in the generating function). After removal of the remaining Gaussian integral for the self-energy of the repulsive interaction, the first order variations of the coherent state path integrals result in the exact mean field or saddle point equations, solely depending on the disorder-self-energy matrix. These equations can be solved by continued fractions and are reminiscent to the 'Nambu-Gorkov' Green function formalism in superconductivity because anomalous terms or pair condensates of the bosonic atoms are also included into the selfenergies. The derived mean field equations of the models with static (I) and dynamic (II) disorder are particularly applicable for BEC in d=3 spatial dimensions because of the singularity of the density of states at vanishing wavevector. However, one usually starts out from

Functional equations and Green's functions for augmented scalar fields

International Nuclear Information System (INIS)

Klauder, J.R.

1977-01-01

Certain noncanonical self-coupled scalar quantum field theories, previously formulated by means of functional integration, are herein recast into the form of functional differential equations for the Green's functional. From these expressions the set of coupled equations relating the Green's functions is obtained. The new equations are compared with those of the conventional formulation, and are proposed as alternatives, especially for nonrenormalizable models when the conventional equations fail

A wet, heterogeneous lunar interior: Lower mantle and core dynamo evolution

Science.gov (United States)

Evans, A. J.; Zuber, M. T.; Weiss, B. P.; Tikoo, S. M.

2014-05-01

While recent analyses of lunar samples indicate the Moon had a core dynamo from at least 4.2-3.56 Ga, mantle convection models of the Moon yield inadequate heat flux at the core-mantle boundary to sustain thermal core convection for such a long time. Past investigations of lunar dynamos have focused on a generally homogeneous, relatively dry Moon, while an initial compositionally stratified mantle is the expected consequence of a postaccretionary lunar magma ocean. Furthermore, recent re-examination of Apollo samples and geophysical data suggests that the Moon contains at least some regions with high water content. Using a finite element model, we investigate the possible consequences of a heterogeneously wet, compositionally stratified interior for the evolution of the Moon. We find that a postoverturn model of mantle cumulates could result in a core heat flux sufficiently high to sustain a dynamo through 2.5 Ga and a maximum surface, dipolar magnetic field strength of less than 1 μT for a 350-km core and near ˜2 μT for a 450-km core. We find that if water was transported or retained preferentially in the deep interior, it would have played a significant role in transporting heat out of the deep interior and reducing the lower mantle temperature. Thus, water, if enriched in the lower mantle, could have influenced core dynamo timing by over 1.0 Gyr and enhanced the vigor of a lunar core dynamo. Our results demonstrate the plausibility of a convective lunar core dynamo even beyond the period currently indicated by the Apollo samples.

Equations of motion for a (non-linear) scalar field model as derived from the field equations

International Nuclear Information System (INIS)

Kaniel, S.; Itin, Y.

2006-01-01

The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

Second relativistic mean field and virial equation of state for astrophysical simulations

International Nuclear Information System (INIS)

Shen, G.; Horowitz, C. J.; O'Connor, E.

2011-01-01

We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron star mergers, and black hole formation simulations. We employ full relativistic mean field (RMF) calculations for matter at intermediate density and high density, and the virial expansion of a nonideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. We calculate the resulting EOS at over 100 000 grid points in the temperature range T=0 to 80 MeV, the density range n B =10 -8 to 1.6 fm -3 , and the proton fraction range Y p =0 to 0.56. We then interpolate these data points using a suitable scheme to generate a thermodynamically consistent equation of state table on a finer grid. We discuss differences between this EOS, our NL3-based EOS, and previous EOSs by Lattimer-Swesty and H. Shen et al. for the thermodynamic properties, composition, and neutron star structure. The original FSUGold interaction produces an EOS, which we call FSU1.7, that has a maximum neutron star mass of 1.7 solar masses. A modification in the high-density EOS is introduced to increase the maximum neutron star mass to 2.1 solar masses and results in a slightly different EOS that we call FSU2.1. The EOS tables for FSU1.7 and FSU2.1 are available for download.

An update of Leighton's solar dynamo model

Science.gov (United States)

Cameron, R. H.; Schüssler, M.

2017-03-01

In 1969, Leighton developed a quasi-1D mathematical model of the solar dynamo, building upon the phenomenological scenario of Babcock published in 1961. Here we present a modification and extension of Leighton's model. Using the axisymmetric component (longitudinal average) of the magnetic field, we consider the radial field component at the solar surface and the radially integrated toroidal magnetic flux in the convection zone, both as functions of latitude. No assumptions are made with regard to the radial location of the toroidal flux. The model includes the effects of (I) turbulent diffusion at the surface and in the convection zone; (II) poleward meridional flow at the surface and an equatorward return flow affecting the toroidal flux; (III) latitudinal differential rotation and the near-surface layer of radial rotational shear; (iv) downward convective pumping of magnetic flux in the shear layer; and (v) flux emergence in the form of tilted bipolar magnetic regions treated as a source term for the radial surface field. While the parameters relevant for the transport of the surface field are taken from observations, the model condenses the unknown properties of magnetic field and flow in the convection zone into a few free parameters (turbulent diffusivity, effective return flow, amplitude of the source term, and a parameter describing the effective radial shear). Comparison with the results of 2D flux transport dynamo codes shows that the model captures the essential features of these simulations. We make use of the computational efficiency of the model to carry out an extended parameter study. We cover an extended domain of the 4D parameter space and identify the parameter ranges that provide solar-like solutions. Dipole parity is always preferred and solutions with periods around 22 yr and a correct phase difference between flux emergence in low latitudes and the strength of the polar fields are found for a return flow speed around 2 m s-1, turbulent

Mean Field Type Control with Congestion

Energy Technology Data Exchange (ETDEWEB)

Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Laurière, Mathieu [Univ. Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS (France)

2016-06-15

We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality.

Mean-field theory of nuclear structure and dynamics

International Nuclear Information System (INIS)

Negele, J.W.

1982-01-01

The physical and theoretical foundations are presented for the mean-field theory of nuclear structure and dynamics. Salient features of the many-body theory of stationary states are reviewed to motivate the time-dependent mean-field approximation. The time-dependent Hartree-Fock approximation and its limitations are discussed and general theoretical formulations are presented which yield time-dependent mean-field equations in lowest approximation and provide suitable frameworks for overcoming various conceptual and practical limitations of the mean-field theory. Particular emphasis is placed on recent developments utilizing functional integral techniques to obtain a quantum mean-field theory applicable to quantized eigenstates, spontaneous fission, the nuclear partition function, and scattering problems. Applications to a number of simple, idealized systems are presented to verify the approximations for solvable problems and to elucidate the essential features of mean-field dynamics. Finally, calculations utilizing moderately realistic geometries and interactions are reviewed which address heavy-ion collisions, fusion, strongly damped collisions, and fission

A General Stochastic Maximum Principle for SDEs of Mean-field Type

International Nuclear Information System (INIS)

Buckdahn, Rainer; Djehiche, Boualem; Li Juan

2011-01-01

We study the optimal control for stochastic differential equations (SDEs) of mean-field type, in which the coefficients depend on the state of the solution process as well as of its expected value. Moreover, the cost functional is also of mean-field type. This makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. For a general action space a Peng’s-type stochastic maximum principle (Peng, S.: SIAM J. Control Optim. 2(4), 966–979, 1990) is derived, specifying the necessary conditions for optimality. This maximum principle differs from the classical one in the sense that here the first order adjoint equation turns out to be a linear mean-field backward SDE, while the second order adjoint equation remains the same as in Peng’s stochastic maximum principle.

Tracing control of chaos for the coupled dynamos dynamical system

International Nuclear Information System (INIS)

Wang Xuedi; Tian Lixin

2004-01-01

This paper introduces a new method for the coupled dynamos dynamical system, which can be applied to the decision of the chaotic behavior of the system. And research the tracing control of the chaos for the coupled dynamos dynamical system by gradually changing the driving parameter for the chaos. With the different design of controllers, the numerical simulation results show the relation between the chaotic behavior and the changes of the parameter value. Furthermore, the result shows the difference of the controllers. In the mean time, it reveals the process of the orbit's gradual changing with the parameter value

A Study of Stochastic Resonance in the Periodically Forced Rikitake Dynamo

Directory of Open Access Journals (Sweden)

Chien-Chih Chen Chih-Yuan Tseng

2007-01-01

Full Text Available The geodynamo has widely been thought to be an intuitive and selfsustained model of the Earth¡¦s magnetic field. In this paper, we elucidate how a periodic signal could be embedded in the geomagnetic filed via the mechanism of stochastic resonance in a forced Rikitake dynamo. Based on the stochastic resonance observed in the periodically forced Rikitake dynamo, we thus suggest a common triggering for geomagnetic reversal and glacial events. Both kinds of catastrophes may result from the cyclic variation of the Earth¡¦s orbital eccentricity.

Mean Field Games with a Dominating Player

Energy Technology Data Exchange (ETDEWEB)

Bensoussan, A., E-mail: axb046100@utdallas.edu [The University of Texas at Dallas, International Center for Decision and Risk Analysis, Jindal School of Management (United States); Chau, M. H. M., E-mail: michaelchaumanho@gmail.com; Yam, S. C. P., E-mail: scpyam@sta.cuhk.edu.hk [The Chinese University of Hong Kong, Department of Statistics (Hong Kong, People’s Republic of China) (China)

2016-08-15

In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and equilibrium condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.

Measurements of the large-scale direct-current Earth potential and possible implications for the geomagnetic dynamo.

Science.gov (United States)

1985-07-05

The magnitude of the large-scale direct-current earth potential was measured on a section of a recently laid transatlantic telecommunications cable. Analysis of the data acquired on the 4476-kilometer cable yielded a mean direct-current potential drop of less than about 0.072 +/- 0.050 millivolts per kilometer. Interpreted in terms of a generation of the potential by the earth's geodynamo, such a small value of the mean potential implies that the toroidal and poloidal magnetic fields of the dynamo are approximately equal at the core-mantle boundary.

Large-scale vortices in compressible turbulent medium with the magnetic field

Science.gov (United States)

Gvaramadze, V. V.; Dimitrov, B. G.

1990-08-01

An averaged equation which describes the large scale vortices and Alfven waves generation in a compressible helical turbulent medium with a constant magnetic field is presented. The presence of the magnetic field leads to anisotropization of the vortex generation. Possible applications of the anisotropic vortex dynamo effect are accretion disks of compact objects.

Dynamo Tests for Stratification Below the Core-Mantle Boundary

Science.gov (United States)

Olson, P.; Landeau, M.

2017-12-01

Evidence from seismology, mineral physics, and core dynamics points to a layer with an overall stable stratification in the Earth's outer core, possibly thermal in origin, extending below the core-mantle boundary (CMB) for several hundred kilometers. In contrast, energetic deep mantle convection with elevated heat flux implies locally unstable thermal stratification below the CMB in places, consistent with interpretations of non-dipole geomagnetic field behavior that favor upwelling flows below the CMB. Here, we model the structure of convection and magnetic fields in the core using numerical dynamos with laterally heterogeneous boundary heat flux in order to rationalize this conflicting evidence. Strongly heterogeneous boundary heat flux generates localized convection beneath the CMB that coexists with an overall stable stratification there. Partially stratified dynamos have distinctive time average magnetic field structures. Without stratification or with stratification confined to a thin layer, the octupole component is small and the CMB magnetic field structure includes polar intensity minima. With more extensive stratification, the octupole component is large and the magnetic field structure includes intense patches or high intensity lobes in the polar regions. Comparisons with the time-averaged geomagnetic field are generally favorable for partial stratification in a thin layer but unfavorable for stratification in a thick layer beneath the CMB.

Energy coupling function and solar wind-magnetosphere dynamo

International Nuclear Information System (INIS)

Kan, J.R.; Lee, L.C.

1979-01-01

The power delivered by the solar wind dynamo to the open magnetosphere is calculated based on the concept of field line reconnection, independent of the MHD steady reconnection theories. By recognizing a previously overlooked geometrical relationship between the reconnection electric field and the magnetic field, the calculated power is shown to be approximately proportional to the Akasofu-Perreault energy coupling function for the magnetospheric substorm. In addition to the polar cap potential, field line reconnection also gives rise to parallel electric fields on open field lines in the high-latitude cusp and the polar cap reions

MAGNETIC CYCLES IN A DYNAMO SIMULATION OF FULLY CONVECTIVE M-STAR PROXIMA CENTAURI

Energy Technology Data Exchange (ETDEWEB)

Yadav, Rakesh K.; Wolk, Scott J. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Christensen, Ulrich R. [Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Göttingen (Germany); Poppenhaeger, Katja, E-mail: rakesh.yadav@cfa.harvard.edu [Astrophysics Research Center, Queen’s University Belfast, Belfast BT7 1NN (United Kingdom)

2016-12-20

The recent discovery of an Earth-like exoplanet around Proxima Centauri has shined a spot light on slowly rotating fully convective M-stars. When such stars rotate rapidly (period ≲20 days), they are known to generate very high levels of activity that is powered by a magnetic field much stronger than the solar magnetic field. Recent theoretical efforts are beginning to understand the dynamo process that generates such strong magnetic fields. However, the observational and theoretical landscape remains relatively uncharted for fully convective M-stars that rotate slowly. Here, we present an anelastic dynamo simulation designed to mimic some of the physical characteristics of Proxima Centauri, a representative case for slowly rotating fully convective M-stars. The rotating convection spontaneously generates differential rotation in the convection zone that drives coherent magnetic cycles where the axisymmetric magnetic field repeatedly changes polarity at all latitudes as time progress. The typical length of the “activity” cycle in the simulation is about nine years, in good agreement with the recently proposed activity cycle length of about seven years for Proxima Centauri. Comparing our results with earlier work, we hypothesis that the dynamo mechanism undergoes a fundamental change in nature as fully convective stars spin down with age.

Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods

KAUST Repository

Machado Velho, Roberto

2017-09-10

In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).

Dynamo action and magnetic buoyancy in convection simulations with vertical shear

Science.gov (United States)

Guerrero, G.; Käpylä, P.

2011-10-01

A hypothesis for sunspot formation is the buoyant emergence of magnetic flux tubes created by the strong radial shear at the tachocline. In this scenario, the magnetic field has to exceed a threshold value before it becomes buoyant and emerges through the whole convection zone. In this work we present the results of direct numerical simulations of compressible turbulent convection that include a vertical shear layer. Like the solar tachocline, the shear is located at the interface between convective and stable layers. We follow the evolution of a random seed magnetic field with the aim of study under what conditions it is possible to excite the dynamo instability and whether the dynamo generated magnetic field becomes buoyantly unstable and emerges to the surface as expected in the flux-tube context. We find that shear and convection are able to amplify the initial magnetic field and form large-scale elongated magnetic structures. The magnetic field strength depends on several parameters such as the shear amplitude, the thickness and location of the shear layer, and the magnetic Reynolds number (Rm). Models with deeper and thicker shear layers allow longer storage and are more favorable for generating a mean magnetic field. Models with higher Rm grow faster but saturate at slightly lower levels. Whenever the toroidal magnetic field reaches amplitudes greater a threshold value which is close to the equipartition value, it becomes buoyant and rises into the convection zone where it expands and forms mushroom shape structures. Some events of emergence, i.e., those with the largest amplitudes of the amplified field, are able to reach the very uppermost layers of the domain. These episodes are able to modify the convective pattern forming either broader convection cells or convective eddies elongated in the direction of the field. However, in none of these events the field preserves its initial structure. The back-reaction of the magnetic field on the fluid is also

Regularity theory for mean-field game systems

CERN Document Server

Gomes, Diogo A; Voskanyan, Vardan

2016-01-01

Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

Regularity Theory for Mean-Field Game Systems

KAUST Repository

Gomes, Diogo A.

2016-09-14

Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

Regularity Theory for Mean-Field Game Systems

KAUST Repository

Gomes, Diogo A.; Pimentel, Edgard A.; Voskanyan, Vardan K.

2016-01-01

Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

RED DWARF DYNAMO RAISES PUZZLE OVER INTERIORS OF LOWEST-MASS STARS

Science.gov (United States)

2002-01-01

-years away in the constellation Aquila. Gliese 752A is a red dwarf that is one-third the mass of the Sun and slightly more than half its diameter. By contrast, VB10 is physically smaller than the planet Jupiter and only about nine percent the mass of our Sun. This very faint star is near the threshold of the lowest possible mass for a true star (.08 solar masses), below which nuclear fusion processes cannot take place according to current models. A team led by Linsky used Hubble's Goddard High Resolution Spectrograph (GHRS) to make a one-hour long exposure of VB10 on October 12, 1994. No detectable ultraviolet emission was seen until the last five minutes, when bright emission was detected in a flare. Though the star's normal surface temperature is 4,500 degrees Fahrenheit, Hubble's GHRS detected a sudden burst of 270,000 degrees Fahrenheit in the star's outer atmosphere. Linsky attributes this rapid heating to the presence of an intense, but unstable, magnetic field. THE INTERIOR WORKINGS OF A STELLAR DYNAMO Before the Hubble observation, astronomers thought magnetic fields in stars required the same dynamo process which creates magnetic fields on the Sun. In the classic solar model, heat generated by nuclear fusion reactions at the star's center escapes through a radiative zone just outside the core. The heat travels from the radiative core to the star's surface through a convection zone. In this region, heat bubbles to the surface by motions similar to boiling in a pot of water. Dynamos, which accelerate electrons to create magnetic forces, operate when the interior of a star rotates faster than the surface. Recent studies of the Sun indicate its convective zone rotates at nearly the same rate at all depths. This means the solar dynamo must operate in the more rapidly rotating radiative core just below the convective zone. The puzzle is that stars below 20 percent the mass of our Sun do not have radiative cores, but instead transport heat from their core through

Analysis of wave equation in electromagnetic field by Proca equation

International Nuclear Information System (INIS)

Pamungkas, Oky Rio; Soeparmi; Cari

2017-01-01

This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

General Relativistic Mean Field Theory for rotating nuclei

Energy Technology Data Exchange (ETDEWEB)

Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki

1998-03-01

The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)

Dynamos in asymptotic-giant-branch stars as the origin of magnetic fields shaping planetary nebulae.

Science.gov (United States)

Blackman, E G; Frank, A; Markiel, J A; Thomas, J H; Van Horn, H M

2001-01-25

Planetary nebulae are thought to be formed when a slow wind from the progenitor giant star is overtaken by a subsequent fast wind generated as the star enters its white dwarf stage. A shock forms near the boundary between the winds, creating the relatively dense shell characteristic of a planetary nebula. A spherically symmetric wind will produce a spherically symmetric shell, yet over half of known planetary nebulae are not spherical; rather, they are elliptical or bipolar in shape. A magnetic field could launch and collimate a bipolar outflow, but the origin of such a field has hitherto been unclear, and some previous work has even suggested that a field could not be generated. Here we show that an asymptotic-giant-branch (AGB) star can indeed generate a strong magnetic field, having as its origin a dynamo at the interface between the rapidly rotating core and the more slowly rotating envelope of the star. The fields are strong enough to shape the bipolar outflows that produce the observed bipolar planetary nebulae. Magnetic braking of the stellar core during this process may also explain the puzzlingly slow rotation of most white dwarf stars.

Feasible homopolar dynamo with sliding liquid-metal contacts

International Nuclear Information System (INIS)

Priede, Jānis; Avalos-Zúñiga, Raúl

2013-01-01

We present a feasible homopolar dynamo design consisting of a flat, multi-arm spiral coil, which is placed above a fast-spinning metal ring and connected to the latter by sliding liquid-metal electrical contacts. Using a simple, analytically solvable axisymmetric model, we determine the optimal design of such a setup. For small contact resistance, the lowest magnetic Reynolds number, Rm≈34.6, at which the dynamo can work, is attained at the optimal ratio of the outer and inner radii of the rings R i /R o ≈0.36 and the spiral pitch angle 54.7°. In a setup of two copper rings with the thickness of 3 cm, R i =10 cm and R o =30 cm, self-excitation of the magnetic field is expected at a critical rotation frequency around 10 Hz

Mean field games for cognitive radio networks

KAUST Repository

Tembine, Hamidou

2012-06-01

In this paper we study mobility effect and power saving in cognitive radio networks using mean field games. We consider two types of users: primary and secondary users. When active, each secondary transmitter-receiver uses carrier sensing and is subject to long-term energy constraint. We formulate the interaction between primary user and large number of secondary users as an hierarchical mean field game. In contrast to the classical large-scale approaches based on stochastic geometry, percolation theory and large random matrices, the proposed mean field framework allows one to describe the evolution of the density distribution and the associated performance metrics using coupled partial differential equations. We provide explicit formulas and algorithmic power management for both primary and secondary users. A complete characterization of the optimal distribution of energy and probability of success is given.

Equations of motion for massive spin 2 field coupled to gravity

International Nuclear Information System (INIS)

Buchbinder, I.L.; Gitman, D.M.; Krykhtin, V.A.; Pershin, V.D.

2000-01-01

We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in α' we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory

Equations of motion for massive spin 2 field coupled to gravity

Energy Technology Data Exchange (ETDEWEB)

Buchbinder, I.L. E-mail: ilb@mail.tomsknet.ru; Gitman, D.M. E-mail: gitman@fma.if.usp.br; Krykhtin, V.A. E-mail: krykhtin@phys.dfe.tpu.edu.ru; Pershin, V.D. E-mail: pershin@ic.tsu.ru

2000-09-18

We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in {alpha}' we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory.

Particle Production and Effective Thermalization in Inhomogeneous Mean Field Theory

NARCIS (Netherlands)

Aarts, G.; Smit, J.

2000-01-01

As a toy model for dynamics in nonequilibrium quantum field theory we consider the abelian Higgs model in 1+1 dimensions with fermions. In the approximate dynamical equations, inhomogeneous classical (mean) Bose fields are coupled to quantized fermion fields, which are treated with a mode function

RIEGER-TYPE PERIODICITY DURING SOLAR CYCLES 14–24: ESTIMATION OF DYNAMO MAGNETIC FIELD STRENGTH IN THE SOLAR INTERIOR

Energy Technology Data Exchange (ETDEWEB)

Gurgenashvili, Eka; Zaqarashvili, Teimuraz V.; Kukhianidze, Vasil; Ramishvili, Giorgi; Shergelashvili, Bidzina [Abastumani Astrophysical Observatory at Ilia State University, Tbilisi, Georgia (United States); Oliver, Ramon; Ballester, Jose Luis [Departament de Física, Universitat de les Illes Balears, E-07122, Palma de Mallorca (Spain); Hanslmeier, Arnold [IGAM, Institute of Physics, University of Graz, Universitätsplatz 5, A-8010 Graz (Austria); Poedts, Stefaan, E-mail: teimuraz.zaqarashvili@uni-graz.at [Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, B-3001, Leuven (Belgium)

2016-07-20

Solar activity undergoes a variation over timescales of several months known as Rieger-type periodicity, which usually occurs near maxima of sunspot cycles. An early analysis showed that the periodicity appears only in some cycles and is absent in other cycles. But the appearance/absence during different cycles has not been explained. We performed a wavelet analysis of sunspot data from the Greenwich Royal Observatory and the Royal Observatory of Belgium during cycles 14–24. We found that the Rieger-type periods occur in all cycles, but they are cycle dependent: shorter periods occur during stronger cycles. Our analysis revealed a periodicity of 185–195 days during the weak cycles 14–15 and 24 and a periodicity of 155–165 days during the stronger cycles 16–23. We derived the dispersion relation of the spherical harmonics of the magnetic Rossby waves in the presence of differential rotation and a toroidal magnetic field in the dynamo layer near the base of the convection zone. This showed that the harmonics of fast Rossby waves with m = 1 and n = 4, where m ( n ) indicates the toroidal (poloidal) wavenumbers, perfectly fit with the observed periodicity. The variation of the toroidal field strength from weaker to stronger cycles may lead to the different periods found in those cycles, which explains the observed enigmatic feature of the Rieger-type periodicity. Finally, we used the observed periodicity to estimate the dynamo field strength during cycles 14–24. Our estimations suggest a field strength of ∼40 kG for the stronger cycles and ∼20 kG for the weaker cycles.

Accretion disc dynamo activity in local simulations spanning weak-to-strong net vertical magnetic flux regimes

Science.gov (United States)

Salvesen, Greg; Simon, Jacob B.; Armitage, Philip J.; Begelman, Mitchell C.

2016-03-01

Strongly magnetized accretion discs around black holes have attractive features that may explain enigmatic aspects of X-ray binary behaviour. The structure and evolution of these discs are governed by a dynamo-like mechanism, which channels part of the accretion power liberated by the magnetorotational instability (MRI) into an ordered toroidal magnetic field. To study dynamo activity, we performed three-dimensional, stratified, isothermal, ideal magnetohydrodynamic shearing box simulations. The strength of the self-sustained toroidal magnetic field depends on the net vertical magnetic flux, which we vary across almost the entire range over which the MRI is linearly unstable. We quantify disc structure and dynamo properties as a function of the initial ratio of mid-plane gas pressure to vertical magnetic field pressure, β _0^mid = p_gas / p_B. For 10^5 ≥ β _0^mid ≥ 10 the effective α-viscosity parameter scales as a power law. Dynamo activity persists up to and including β _0^mid = 10^2, at which point the entire vertical column of the disc is magnetic pressure dominated. Still stronger fields result in a highly inhomogeneous disc structure, with large density fluctuations. We show that the turbulent steady state βmid in our simulations is well matched by the analytic model of Begelman et al. describing the creation and buoyant escape of toroidal field, while the vertical structure of the disc can be broadly reproduced using this model. Finally, we discuss the implications of our results for observed properties of X-ray binaries.

Neutron fraction and neutrino mean free path predictions in relativistic mean field models

International Nuclear Information System (INIS)

Hutauruk, P.T.P.; Williams, C.K.; Sulaksono, A.; Mart, T.

2004-01-01

The equation of state (EOS) of dense matter and neutrino mean free path (NMFP) in a neutron star have been studied by using relativistic mean field models motivated by effective field theory. It is found that the models predict too large proton fractions, although one of the models (G2) predicts an acceptable EOS. This is caused by the isovector terms. Except G2, the other two models predict anomalous NMFP's. In order to minimize the anomaly, besides an acceptable EOS, a large M* is favorable. A model with large M* retains the regularity in the NMFP even for a small neutron fraction

A Dynamic BI–Orthogonal Field Equation Approach to Efficient Bayesian Inversion

Directory of Open Access Journals (Sweden)

Tagade Piyush M.

2017-06-01

Full Text Available This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen-Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.

Low-latitude plasma drifts from a simulation of the global atmospheric dynamo

International Nuclear Information System (INIS)

Crain, D.J.; Heelis, R.A.; Bailey, G.J.; Richmond, A.D.

1993-01-01

The authors work with a dynamo model to address questions about plasma drifts in the E region, primarily at low latitudes. Tidal winds have been known to have a big influence on electric fields in the E region, and magnetic fields and ion drifts in the equatorial F region. Recent work has centered on self consistency in simulations, using realistic wind distributions, 3-D current distributions, and more accurate measures of the currents and conductivities. The wind dynamo in the ionosphere is well accepted as the main source of electric fields in the low and mid latitudes. The authors present a self consistent model of the plasma distribution and the dynamo driven electric potential distribution. Their results are compared with other simulations. A major concern in their model was reproducing ion drift observations in the equatorial region. Their conclusion is that the F region plays a significant role in the low latitude dyanamo effects, much larger than was previously assumed. When they build into their model realistic ionospheric conditions, allow for appropriate wind distributions, and allow a self consistent redistribution of plasma in the night, they find the model simulates measured ion drifts more closely. Their model is normalized against observations at Jicamarca. By allowing E x B drifts in the ionosphere, and F region zonal winds they can reproduce many of the night changes in the ion drifts at Jicamarca

DYNAMO: a Mars upper atmosphere package for investigating solar wind interaction and escape processes, and mapping Martian fields

DEFF Research Database (Denmark)

Chassefiere, E.; Nagy, A.; Mandea, M.

2004-01-01

DYNAMO is a small multi-instrument payload aimed at characterizing current atmospheric escape, which is still poorly constrained, and improving gravity and magnetic field representations, in order to better understand the magnetic, geologic and thermal history of Mars. The internal structure...... of periapsis 170 km), and in a lesser extent 2a, offers an unprecedented opportunity to investigate by in situ probing the chemical and dynamical properties of the deep ionosphere, thermosphere, and the interaction between the atmosphere and the solar wind, and therefore the present atmospheric escape rate...

Short-time existence of solutions for mean-field games with congestion

KAUST Repository

Gomes, Diogo A.; Voskanyan, Vardan K.

2015-01-01

We consider time-dependent mean-field games with congestion that are given by a Hamilton–Jacobi equation coupled with a Fokker–Planck equation. These models are motivated by crowd dynamics in which agents have difficulty moving in high-density areas

Generation of large-scale vorticity in rotating stratified turbulence with inhomogeneous helicity: mean-field theory

Science.gov (United States)

Kleeorin, N.

2018-06-01

We discuss a mean-field theory of the generation of large-scale vorticity in a rotating density stratified developed turbulence with inhomogeneous kinetic helicity. We show that the large-scale non-uniform flow is produced due to either a combined action of a density stratified rotating turbulence and uniform kinetic helicity or a combined effect of a rotating incompressible turbulence and inhomogeneous kinetic helicity. These effects result in the formation of a large-scale shear, and in turn its interaction with the small-scale turbulence causes an excitation of the large-scale instability (known as a vorticity dynamo) due to a combined effect of the large-scale shear and Reynolds stress-induced generation of the mean vorticity. The latter is due to the effect of large-scale shear on the Reynolds stress. A fast rotation suppresses this large-scale instability.

Analytic equation of state for FCC C60 solid based on analytic mean-field potential approach

International Nuclear Information System (INIS)

Sun Jiuxun

2006-01-01

The analytic mean-field approach (AMFP) was applied to the FCC C60 solid. For the intermolecular forces the Girifalco potential has been utilized. The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The numerical results of thermodynamic quantities are compared with the molecular dynamic (MD) simulations and the unsymmetrized self-consistent field approach (CUSF) in the literature. It is shown that our AMFP results are in good agreement with the MD data both at low and high temperatures. The results of CUSF are in accordance with the AMFP at low temperature, but at high temperature the difference becomes prominent. Especially the AMFP predicted that the FCC C60 solid is stable upto 2202 K, the spinodal temperature, in good agreement with 2320 K from the MD simulation. However, the CUST just gives 1916 K, a temperature evidently lower than the MD data. The AMFP qualifies as a useful approach that can reasonably consider the anharmonic effects at high temperature

Reduction of the Poincare gauge field equations by means of a duality rotation

International Nuclear Information System (INIS)

Mielke, E.W.

1981-10-01

A rather general procedure is developed in order to reduce the two field equations of the Poincare gauge theory of gravity by a modified ansatz for the curvature tensor involving double duality. In the case of quasi-linear Lagrangians of the Yang-Mills type it is shown that non-trivial torsion solutions with duality properties necessarily ''live'' on an Einstein space as metrical background. (author)

Saturation of the turbulent dynamo.

Science.gov (United States)

Schober, J; Schleicher, D R G; Federrath, C; Bovino, S; Klessen, R S

2015-08-01

The origin of strong magnetic fields in the Universe can be explained by amplifying weak seed fields via turbulent motions on small spatial scales and subsequently transporting the magnetic energy to larger scales. This process is known as the turbulent dynamo and depends on the properties of turbulence, i.e., on the hydrodynamical Reynolds number and the compressibility of the gas, and on the magnetic diffusivity. While we know the growth rate of the magnetic energy in the linear regime, the saturation level, i.e., the ratio of magnetic energy to turbulent kinetic energy that can be reached, is not known from analytical calculations. In this paper we present a scale-dependent saturation model based on an effective turbulent resistivity which is determined by the turnover time scale of turbulent eddies and the magnetic energy density. The magnetic resistivity increases compared to the Spitzer value and the effective scale on which the magnetic energy spectrum is at its maximum moves to larger spatial scales. This process ends when the peak reaches a characteristic wave number k☆ which is determined by the critical magnetic Reynolds number. The saturation level of the dynamo also depends on the type of turbulence and differs for the limits of large and small magnetic Prandtl numbers Pm. With our model we find saturation levels between 43.8% and 1.3% for Pm≫1 and between 2.43% and 0.135% for Pm≪1, where the higher values refer to incompressible turbulence and the lower ones to highly compressible turbulence.

Mean-field approximation for spacing distribution functions in classical systems

Science.gov (United States)

González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

2012-01-01

We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

Uncertainty quantification for mean field games in social interactions

KAUST Repository

Dia, Ben Mansour

2016-01-09

We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.

Uncertainty quantification for mean field games in social interactions

KAUST Repository

Dia, Ben Mansour

2016-01-01

We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.

Chaotic Dynamos Generated by a Turbulent Flow of Liquid Sodium

International Nuclear Information System (INIS)

Ravelet, F.; Monchaux, R.; Aumaitre, S.; Chiffaudel, A.; Daviaud, F.; Dubrulle, B.; Berhanu, M.; Fauve, S.; Mordant, N.; Petrelis, F.; Bourgoin, M.; Odier, Ph.; Plihon, N.; Pinton, J.-F.; Volk, R.

2008-01-01

We report the observation of several dynamical regimes of the magnetic field generated by a turbulent flow of liquid sodium (VKS experiment). Stationary dynamos, transitions to relaxation cycles or to intermittent bursts, and random field reversals occur in a fairly small range of parameters. Large scale dynamics of the magnetic field result from the interactions of a few modes. The low dimensional nature of these dynamics is not smeared out by the very strong turbulent fluctuations of the flow

Solution of the hyperon puzzle within a relativistic mean-field model

Energy Technology Data Exchange (ETDEWEB)

Maslov, K.A. [National Research Nuclear University (MEPhI), 115409 Moscow (Russian Federation); Kolomeitsev, E.E., E-mail: E.Kolomeitsev@gsi.de [Matej Bel University, SK-97401 Banska Bystrica (Slovakia); Voskresensky, D.N. [National Research Nuclear University (MEPhI), 115409 Moscow (Russian Federation)

2015-09-02

The equation of state of cold baryonic matter is studied within a relativistic mean-field model with hadron masses and coupling constants depending on the scalar field. All hadron masses undergo a universal scaling, whereas the couplings are scaled differently. The appearance of hyperons in dense neutron star interiors is accounted for, however the equation of state remains sufficiently stiff if the reduction of the ϕ meson mass is included. Our equation of state matches well the constraints known from analyses of the astrophysical data and particle production in heavy-ion collisions.

Solution of the hyperon puzzle within a relativistic mean-field model

Directory of Open Access Journals (Sweden)

K.A. Maslov

2015-09-01

Full Text Available The equation of state of cold baryonic matter is studied within a relativistic mean-field model with hadron masses and coupling constants depending on the scalar field. All hadron masses undergo a universal scaling, whereas the couplings are scaled differently. The appearance of hyperons in dense neutron star interiors is accounted for, however the equation of state remains sufficiently stiff if the reduction of the ϕ meson mass is included. Our equation of state matches well the constraints known from analyses of the astrophysical data and particle production in heavy-ion collisions.

Large-scale flows, sheet plumes and strong magnetic fields in a rapidly rotating spherical dynamo

Science.gov (United States)

Takahashi, F.

2011-12-01

Mechanisms of magnetic field intensification by flows of an electrically conducting fluid in a rapidly rotating spherical shell is investigated. Bearing dynamos of the Eartn and planets in mind, the Ekman number is set at 10-5. A strong dipolar solution with magnetic energy 55 times larger than the kinetic energy of thermal convection is obtained. In a regime of small viscosity and inertia with the strong magnetic field, convection structure consists of a few large-scale retrograde flows in the azimuthal direction and sporadic thin sheet-like plumes. The magnetic field is amplified through stretching of magnetic lines, which occurs typically through three types of flow: the retrograde azimuthal flow near the outer boundary, the downwelling flow of the sheet plume, and the prograde azimuthal flow near the rim of the tangent cylinder induced by the downwelling flow. It is found that either structure of current loops or current sheets is accompanied in each flow structure. Current loops emerge as a result of stretching the magnetic lines along the magnetic field, wheres the current sheets are formed to counterbalance the Coriolis force. Convection structure and processes of magnetic field generation found in the present model are distinct from those in models at larger/smaller Ekman number.

Mean-field games with logistic population dynamics

KAUST Repository

Gomes, Diogo A.; De Lima Ribeiro, Ricardo

2013-01-01

In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.

Mean-field games with logistic population dynamics

KAUST Repository

Gomes, Diogo A.

2013-12-01

In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.

The magnetic universe geophysical and astrophysical dynamo theory

CERN Document Server

Rüdiger, Günther

2004-01-01

Magnetism is one of the most pervasive features of the Universe, with planets, stars and entire galaxies all having associated magnetic fields. All of these fields are generated by the motion of electrically conducting fluids, the so-called dynamo effect. The precise details of what drives the motion, and indeed what the fluid consists of, differ widely though. In this work the authors draw upon their expertise in geophysical and astrophysical MHD to explore some of these phenomena, and describe the similarities and differences between different magnetized objects. They also explain why magn

First Numerical Simulations of Turbulent Dynamos Driven by Libration, Precession and Tides in Triaxial Ellipsoids - An Alternative Route for Planetary Magnetism

Science.gov (United States)

Le Bars, M.; Kanuganti, S. R.; Favier, B.

2017-12-01

Most of the time, planetary dynamos are - tacitly or not - associated with thermo-solutal convection. The convective dynamo model has indeed proven successful to explain the current Earth's magnetic field. However, its results are sometimes difficult to reconcile with observational data and its validity can be questioned for several celestial bodies. For instance, the small size of the Moon and Ganymede makes it difficult to maintain a sufficient temperature gradient to sustain convection and to explain their past and present magnetic fields, respectively. The same caveat applies to the growing number of planetesimals shown to have generated magnetic fields in their early history. Finally, the energy budget of the early Earth is difficult to reconcile with a convective dynamo before the onset of inner core growth. Significant effort has thus been put into finding new routes for planetary dynamo. In particular, the rotational dynamics of planets, moons and small bodies, where their average spinning motion is periodically perturbed by the small mechanical forcings of libration, precession and/or tides, is now widely accepted as an efficient source of core turbulence. The underlying mechanism relies on a parametric instability where the inertial waves of the rotating fluid core are resonantly excited by the small forcing, leading to exponential growth and bulk filling intense motions, pumping their energy from the orbital dynamics. Dynamos driven by mechanical forcing have been suggested for the Moon, Mars, Io, the early Earth, etc. However, the real dynamo capacity of the corresponding flows has up-to-now been studied only in very limited cases, with simplified spherical/spheroidal geometries and/or overly viscous fluids. We will present here the first numerical simulations of dynamos driven by libration, precession and tides, in the triaxial ellipsoidal geometry and in the turbulent regime relevant for planetary cores. We will describe the numerical techniques

Non-equilibrium mean-field theories on scale-free networks

International Nuclear Information System (INIS)

Caccioli, Fabio; Dall'Asta, Luca

2009-01-01

Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters that implicitly account for the degree heterogeneity. The method is used to correctly predict the dynamical critical behavior of some binary spin models and reaction–diffusion processes. The validity of our non-equilibrium theory is further supported by showing its relation with the generalized Landau theory of equilibrium critical phenomena on networks

A homopolar disc dynamo experiment with liquid metal contacts

OpenAIRE

Avalos-Zúñiga, R. A.; Priede, J.; Bello-Morales, C. E.

2017-01-01

We present experimental results of a homopolar disc dynamo constructed at CICATA-Quer\\'etaro in Mexico. The device consists of a flat, multi-arm spiral coil which is placed above a fast-spinning metal disc and connected to the latter by sliding liquid-metal electrical contacts. Theoretically, self-excitation of the magnetic field is expected at the critical magnetic Reynolds number Rm~45, which corresponds to a critical rotation rate of about 10 Hz. We measured the magnetic field above the di...

An alternative to the TEM (Transformed Eulerian Mean) equations

Science.gov (United States)

Gaßmann, Almut

2013-04-01

The TEM equations constitute a powerful means to get access to the residual circulation. However, due to their foundation on the wave perspective, they deliver only a zonally averaged picture without access to the three-dimensional structure or the local origins of the residual circulation. Therefore it is worth to investigate whether there are alternatives. The pathway followed here is to perform a transformation of the momentum and the potential temperature equation before taking the zonal mean. This is done by removing the steady state ideal wind solution vid = ?×?B-(?±P) from the equations (? - potential temperature, B - Bernoulli function, P - Ertel's potential vorticity EPV, ?± - density). The advantage of that approach is that the total EPV-flux does no longer contain an explicitly visible 'do-nothing-flux'. This flux, ?? ×?B, does only vanish when averaging on isentropic surfaces, but not on other isosurfaces. Here we find the reason why the conventional zonal mean on isentropes delivers a direct overturning cell on each hemisphere, whereas on other isosurfaces we obtain the typical three-cell structure with Headley, Ferrel, and polar cells. It will be demonstrated and made visible through idealized climate experiments with the ICON-IAP model that the zonal averages of the nonideal wind components vnid = v - vid and wnid = w - wid constitute similar direct overturning cells on non-isentropic surfaces as obtained with the TEM-generated v* and w*. It is also interesting to inspect fields of local nonideal wind components, the very origin of the residual circulation.

Conformally covariant massless spin-two field equations

International Nuclear Information System (INIS)

Drew, M.S.; Gegenberg, J.D.

1980-01-01

An explicit proof is constructed to show that the field equations for a symmetric tensor field hsub(ab) describing massless spin-2 particles in Minkowski space-time are not covariant under the 15-parameter group SOsub(4,2); this group is usually associated with conformal transformations on flat space, and here it will be considered as a global gauge group which acts upon matter fields defined on space-time. Notwithstanding the above noncovariance, the equations governing the rank-4 tensor Ssub(abcd) constructed from hsub(ab) are shown to be covariant provided the contraction Ssub(ab) vanishes. Conformal covariance is proved by demonstrating the covariance of the equations for the equivalent 5-component complex field; in fact, covariance is proved for a general field equation applicable to massless particles of any spin >0. It is shown that the noncovariance of the hsub(ab) equations may be ascribed to the fact that the transformation behaviour of hsub(ab) is not the same as that of a field consisting of a gauge only. Since this is in contradistinction to the situation for the electromagnetic-field equations, the vector form of the electromagnetic equations is cast into a form which can be duplicated for the hsub(ab)-field. This procedure results in an alternative, covariant, field equation for hsub(ab). (author)

Applicability of self-consistent mean-field theory

International Nuclear Information System (INIS)

Guo Lu; Sakata, Fumihiko; Zhao Enguang

2005-01-01

Within the constrained Hartree-Fock (CHF) theory, an analytic condition is derived to estimate whether a concept of the self-consistent mean field is realized in the level repulsive region. The derived condition states that an iterative calculation of the CHF equation does not converge when the quantum fluctuations coming from two-body residual interaction and quadrupole deformation become larger than a single-particle energy difference between two avoided crossing orbits. By means of numerical calculation, it is shown that the analytic condition works well for a realistic case

Socio-economic applications of finite state mean field games

KAUST Repository

Gomes, Diogo A.

2014-10-06

In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments,which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.

Magnetic spiral arms in galaxy haloes

Science.gov (United States)

Henriksen, R. N.

2017-08-01

We seek the conditions for a steady mean field galactic dynamo. The parameter set is reduced to those appearing in the α2 and α/ω dynamo, namely velocity amplitudes, and the ratio of sub-scale helicity to diffusivity. The parameters can be allowed to vary on conical spirals. We analyse the mean field dynamo equations in terms of scale invariant logarithmic spiral modes and special exact solutions. Compatible scale invariant gravitational spiral arms are introduced and illustrated in an appendix, but the detailed dynamical interaction with the magnetic field is left for another work. As a result of planar magnetic spirals `lifting' into the halo, multiple sign changes in average rotation measures forming a regular pattern on each side of the galactic minor axis, are predicted. Such changes have recently been detected in the Continuum Halos in Nearby Galaxies-an EVLA Survey (CHANG-ES) survey.

Static Einstein--Maxwell field equations

International Nuclear Information System (INIS)

Das, A.

1979-01-01

The static Einstein--Maxwell field equations are investigated in the presence of both electric and magnetic fields. The sources or bodies are assumed to be of finite size and to not affect the connectivity of the associated space. Furthermore, electromagnetic and metric fields are assumed to have reasonable differentiabilities. It is then proved that the electric and magnetic field vectors are constant multiples of one another. Moreover, the static Einstein--Maxwell equations reduce to the static magnetovac case. If, furthermore, the variational derivation of the Einstein--Maxwell equations is assumed, then both the total electric and magnetic charge of each body must vanish. As a physical consequence it is pointed out that if a suspended magnet be electrically charged then it must experience a purely general relativistic torque

Efficiency Measurement Using a Motor-Dynamo Module

Science.gov (United States)

Ng, Pun-hon; Wong, Siu-ling; Mak, Se-yuen

2009-01-01

In this article, we describe a simple method which can be used to measure the efficiency of a low power dc motor, a motor-converted dynamo and a coupled motor-dynamo module as a function of the speed of rotation. The result can also be used to verify Faraday's law of electromagnetic induction. (Contains 1 table and 8 figures.)

Paleomagnetic evidence for dynamo activity driven by inward crystallisation of a metallic asteroid

Science.gov (United States)

Bryson, James F. J.; Weiss, Benjamin P.; Harrison, Richard J.; Herrero-Albillos, Julia; Kronast, Florian

2017-08-01

The direction in which a planetary core solidifies has fundamental implications for the feasibility and nature of dynamo generation. Although Earth's core is outwardly solidifying, the cores of certain smaller planetary bodies have been proposed to inwardly solidify due to their lower central pressures. However, there have been no unambiguous observations of inwardly solidified cores or the relationship between this solidification regime and planetary magnetic activity. To address this gap, we present the results of complimentary paleomagnetic techniques applied to the matrix metal and silicate inclusions within the IVA iron meteorites. This family of meteorites has been suggested to originate from a planetary core that had its overlaying silicate mantle removed by collisions during the early solar system. This process is thought to have produced a molten ball of metal that cooled rapidly and has been proposed to have inwardly solidified. Recent thermal evolution models of such a body predict that it should have generated an intense, multipolar and time-varying dynamo field. This field could have been recorded as a remanent magnetisation in the outer, cool layers of a solid crust on the IVA parent core. We find that the different components in the IVA iron meteorites display a range of paleomagnetic fidelities, depending crucially on the cooling rate of the meteorite. In particular, silicate inclusions in the quickly cooled São João Nepomuceno meteorite are poor paleomagnetic recorders. On the other hand, the matrix metal and some silicate subsamples from the relatively slowly cooled Steinbach meteorite are far better paleomagnetic recorders and provide evidence of an intense (≳100 μT) and directionally varying (exhibiting significant changes on a timescale ≲200 kyr) magnetic field. This is the first demonstration that some iron meteorites record ancient planetary magnetic fields. Furthermore, the observed field intensity, temporal variability and dynamo

On integrability conditions of the equations of nonsymmetrical chiral field on SO(4)

International Nuclear Information System (INIS)

Tskhakaya, D.D.

1990-01-01

Possibility of integrating the equations of nonsymmetrical chiral field on SO(4) by means of the inverse scattering method is investigated. Maximal number of the motion integrals is found for the corresponding system of ordinary differential equations

NONLINEAR DYNAMO IN A ROTATING ELECTRICALLY CONDUCTING FLUID

Directory of Open Access Journals (Sweden)

M. I. Kopp

2017-05-01

Full Text Available We found a new large-scale instability, which arises in the rotating conductive fluid with small-scale turbulence. Turbulence is generated by small-scale external force with a low Reynolds number. The theory is built simply by the method of multiscale asymptotic expansions. Nonlinear equations for vortex and magnetic perturbations obtained in the third order for small Reynolds number. It is shown that the combined effects of the Coriolis force and the small external forces in a rotating conducting fluid possible large-scale instability. The large-scale increments of the instability, correspond to generation as the vortex and magnetic disturbances. This type of instability is classified as hydrodynamic and MHD alpha-effect. We studied the stationary regimes of nonlinear equations of magneto-vortex dynamo. In the limit of weakly conducting fluid found stationary solutions in the form of helical kinks. In the limit of high conductivity fluid was obtained stationary solutions in the form of nonlinear periodic waves and kinks.

One-Dimensional Stationary Mean-Field Games with Local Coupling

KAUST Repository

Gomes, Diogo A.; Nurbekyan, Levon; Prazeres, Mariana

2017-01-01

A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton–Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption implies the existence and uniqueness of solutions. Here, we drop that assumption and construct explicit solutions for one-dimensional MFGs. These solutions exhibit phenomena not present in monotonically increasing MFGs: low-regularity, non-uniqueness, and the formation of regions with no agents.

One-Dimensional Stationary Mean-Field Games with Local Coupling

KAUST Repository

Gomes, Diogo A.

2017-05-25

A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton–Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption implies the existence and uniqueness of solutions. Here, we drop that assumption and construct explicit solutions for one-dimensional MFGs. These solutions exhibit phenomena not present in monotonically increasing MFGs: low-regularity, non-uniqueness, and the formation of regions with no agents.

Time dependent mean-field games

KAUST Repository

Gomes, Diogo A.

2014-01-06

We consider time dependent mean-field games (MFG) with a local power-like dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension. In the subquadratic case this is done by combining a Gagliardo-Nirenberg type of argument with a new class of polynomial estimates for solutions of the Fokker-Planck equation in terms of LrLp- norms of DpH. These techniques do not apply to the superquadratic case. In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.

Solar Field Mapping and Dynamo Behavior

Directory of Open Access Journals (Sweden)

Kenneth H. Schatten

2012-01-01

Full Text Available We discuss the importance of the Sun’s large-scale magnetic field to the Sun-Planetary environment. This paper narrows its focus down to the motion and evolution of the photospheric large-scale magnetic field which affects many environments throughout this region. For this purpose we utilize a newly developed Netlogo cellular automata model. The domain of this algorithmic model is the Sun’s photosphere. Within this computational space are placed two types of entities or agents; one may refer to them as bluebirds and cardinals; the former carries outward magnetic flux and the latter carries out inward magnetic flux. One may simply call them blue and red agents. The agents provide a granularity with discrete changes not present in smooth MHD models; they undergo three processes: birth, motion, and death within the photospheric domain. We discuss these processes, as well as how we are able to develop a model that restricts its domain to the photosphere and allows the deeper layers to be considered only through boundary conditions. We show the model’s ability to mimic a number of photospheric magnetic phenomena: the solar cycle (11-year oscillations, the Waldmeier effect, unipolar magnetic regions (e.g. sectors and coronal holes, Maunder minima, and the march/rush to the poles involving the geometry of magnetic field reversals. We also discuss why the Sun sometimes appears as a magnetic monopole, which of course requires no alteration of Maxwell’s equations.

Solving differential–algebraic equation systems by means of index reduction methodology

DEFF Research Database (Denmark)

Sørensen, Kim; Houbak, Niels; Condra, Thomas

2006-01-01

of a number of differential equations and algebraic equations — a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately...... stiff ODEs and index 1 DAEs by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of ordinary differential equations — ODEs....

Evidence favoring an internally generated dynamo in the H chondrite parent planetesimal from the Forest Vale meteorite

Science.gov (United States)

Getzin, B. L.; Bryson, J. F. J.; Weiss, B. P.; Gattacceca, J.

2016-12-01

Chondritic meteorites are traditionally assumed to originate from undifferentiated asteroids due to their unmelted texture and composition. This implies that their parent bodies should not have formed a core or generated a dynamo. However, recent measurements of the H chondrite Portales Valley (Bryson et al., this meeting) observed post-accretional remanent magnetization interpreted as a record of a core dynamo, indicating that some chondrite parent bodies were partially differentiated. However, it has been proposed that the H chondrites may have been magnetized instead by a crustal remanent field. If this crustal magnetization was imparted by an early external source, such as nebular fields or even the solar wind, then the magnetization of H chondrites may not require a core dynamo. To test this hypothesis, we measured the magnetic properties of the Forest Vale H4 ordinary chondrite. Forest Vale cooled quickly (10000 K/My) and so would have acquired magnetization that represents the bulk of the H chondrite parent body's crust during the first 10 My of the solar system. Based on alternating field and pressure demagnetization experiments of natural remanent magnetization (NRM) and anhysteretic remanent magnetization, we conclude that Forest Vale contains no ancient magnetization and, due to its poor intrinsic magnetic recording properties, is unable to acquire a magnetization that is stable against even weak shocks (0.2 GPa). Furthermore, we show that a crust composed of Forest-Vale-like material magnetized by the upper limit field intensities expected for the nebula and solar wind fields (50 μT and 1 μT, respectively) produces an insufficient crustal remanent field (<2.5 μT and <0.045 μT, respectively) to explain the paleointensity recorded by Portales Valley ( 10 μT). Thus, we conclude that the field that magnetization Portales Valley is unlikely to be from a crustal remanence magnetized by early external fields, favoring a partially differentiated asteroid

Derivation of the Finslerian gauge field equations

International Nuclear Information System (INIS)

Asanov, G.S.

1984-01-01

As is well known the simplest way of formulating the equations for the Yang-Mills gauge fields consists in taking the Lagrangian to be quadratic in the gauge tensor, whereas the application of such an approach to the gravitational field yields equations which are of essentially more complicated structure than the Einstein equations. On the other hand, in the gravitational field theory the Lagrangian can be constructed to be of forms which may be both quadratic and linear in the curvature tensor, whereas the latter possibility is absent in the current gauge field theories. In previous work it has been shown that the Finslerian structure of the space-time gives rise to certain gauge fields provided that the internal symmetries may be regarded as symmetries of a three-dimensional Riemannian space. Continuing this work we show that appropriate equations for these gauge fields can be formulated in both ways, namely on the basis of the quadratic Lagrangian or, if a relevant generalization of the Palatini method is applied, on the basis of a Lagrangian linear in the gauge field strength tensor. The latter possibility proves to result in equations which are similar to the Einstein equations, a distinction being that the Finslerian Cartan curvature tensor rather then the Riemann curvature tensor enters the equations. (author)

Emergence of Magnetic Flux Generated in a Solar Convective Dynamo. I. The Formation of Sunspots and Active Regions, and The Origin of Their Asymmetries

Energy Technology Data Exchange (ETDEWEB)

Chen, Feng; Rempel, Matthias; Fan, Yuhong, E-mail: chenfeng@ucar.edu [High Altitude Observatory, NCAR, P.O. Box 3000, Boulder, CO, 80307 (United States)

2017-09-10

We present a realistic numerical model of sunspot and active region formation based on the emergence of flux bundles generated in a solar convective dynamo. To this end, we use the magnetic and velocity fields in a horizontal layer near the top boundary of the solar convective dynamo simulation to drive realistic radiative-magnetohydrodynamic simulations of the uppermost layers of the convection zone. The main results are as follows. (1) The emerging flux bundles rise with the mean speed of convective upflows and fragment into small-scale magnetic elements that further rise to the photosphere, where bipolar sunspot pairs are formed through the coalescence of the small-scale magnetic elements. (2) Filamentary penumbral structures form when the sunspot is still growing through ongoing flux emergence. In contrast to the classical Evershed effect, the inflow seems to prevail over the outflow in a large part of the penumbra. (3) A well-formed sunspot is a mostly monolithic magnetic structure that is anchored in a persistent deep-seated downdraft lane. The flow field outside the spot shows a giant vortex ring that comprises an inflow below 15 Mm depth and an outflow above 15 Mm depth. (4) The sunspots successfully reproduce the fundamental properties of the observed solar active regions, including the more coherent leading spots with a stronger field strength, and the correct tilts of bipolar sunspot pairs. These asymmetries can be linked to the intrinsic asymmetries in the magnetic and flow fields adapted from the convective dynamo simulation.

A model of the solar cycle driven by the dynamo action of the global convection in the solar convection zone

International Nuclear Information System (INIS)

Yoshimura, H.

1975-01-01

The dynamo equation which represents the longitudinally averaged magnetohydrodynamical action of the global convection influenced by the rotation in the solar convection zone is solved numerically to simulate the solar cycle as an initial boundary-value problem. The radial and latitudinal structure of the dynamo action is parametrized in accordance with the structure of the rotation, and of the global convection especially in such a way as to represent the presence of the two cells of the regeneration action in the radial direction in which the action has opposite signs, which is typical of the regeneration action of the global convection. A nonlinear process is included by assuming that part of the magnetic field energy is dissipated when the magnetic field strength exceeds some critical value; the formation of active regions and subsequent dissipations are thus simulated. By adjusting the parameters within a reasonable range, oscillatory solutions are obtained to simulate the solar cycle with the period of the right order of magnitude and with the patterns of evolution of the latitudinal distribution of the toroidal component of the magnetic field similar to the observed Butterfly Diagram of sunspots. The evolution of the latitudinal distribution of the radial component of the magnetic field shows patterns similar to the Butterfly Diagram, but having two branches of different polarity in each hemisphere. The development of the radial structure of the magnetic field associated with the solar cycle is presented. The importance of the poleward migrating branch of the Butterfly Diagram is emphasized in relation to the relative importance of the role of the latitudinal and radial shears of the differential rotation

Quantum mean-field theory of collective dynamics and tunneling

International Nuclear Information System (INIS)

Negele, J.W.

1981-01-01

A fundamental problem in quantum many-body theory is formulation of a microscopic theory of collective motion. For self-bound, saturating systems like finite nuclei described in the context of nonrelativistic quantum mechanics with static interactions, the essential problem is how to formulate a systematic quantal theory in which the relevant collective variables and their dynamics arise directly and naturally from the Hamiltonian and the system under consideration. Significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples are summarized. An exact expression for an observable of interest is written using a functional integral representation for the evolution operator, and tractable time-dependent mean field equations are obtained by application of the stationary-phase approximation (SPA) to the functional integral. Corrections to the lowest-order theory may be systematically enumerated. 6 figures

Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo

Science.gov (United States)

Hide, R.

In the interpretation of geomagnetic polarity reversals with their highly variable frequency over geological time it is necessary, as with other irregularly fluctuating geophysical phenomena, to consider the relative importance of forced contributions associated with changing boundary conditions and of free contributions characteristic of the behaviour of nonlinear systems operating under fixed boundary conditions. New evidence -albeit indirect- in favour of the likely predominance of forced contributions is provided by the discovery reported here of the possibility of complete quenching by nonlineax effects of current fluctuations in a self-exciting homopolar dynamo with its single Faraday disk driven into rotation with angular speed y(τ) (where τ denotes time) by a steady applied couple. The armature of an electric motor connected in series with the coil of the dynamo is driven into rotation' with angular speed z(τ) by a torque xf (x) due to Lorentz forces associated with the electric current x(τ) in the system (just as certain parts of the spectrum of eddies within the liquid outer core are generated largely by Lorentz forces associated with currents generated by the self-exciting magnetohydrodynamic (MHD) geodynamo). The discovery is based on bifurcation analysis supported by computational studies of the following (mathematically novel) autonomous set of nonlinear ordinary differential equations: dx/dt = x(y - 1) - βzf(x), dy/dt = α(1 - x²) - κy, dz/dt = xf (x) -λz, where f (x) = 1 - ɛ + ɛσx, in cases when the dimensionless parameters (α, β, κ, λ, σ) are all positive and 0 ≤ ɛ ≤ 1. Within those regions of (α, β, κ, λ, σ) parameter space where the applied couple, as measured by α, is strong enough for persistent dynamo action (i.e. x ≠ 0) to occur at all, there are in general extensive regions where x(τ) exhibits large amplitude regular or irregular (chaotic) fluctuations. But these fluctuating régimes shrink in size as increases

Solving differential-algebraic equation systems by means of index reduction methodology

DEFF Research Database (Denmark)

Sørensen, Kim; Houbak, Niels; Condra, Thomas Joseph

2006-01-01

of a number of differential equations and algebraic equations - a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately...... stiff ODE’s and index 1 DAE’s by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of Ordinary- Differential-Equations - ODE’s....

Probabilistic theory of mean field games with applications

CERN Document Server

Carmona, René

2018-01-01

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic...

Merging Belief Propagation and the Mean Field Approximation

DEFF Research Database (Denmark)

Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro

2010-01-01

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence......) as a starting point. In this method message passing fixed point equations (which correspond to the update rules in a message passing algorithm) are then obtained by imposing different region-based approximations and constraints on the mean field and belief propagation parts of the corresponding factor graph....... Our results can be applied, for example, to algorithms that perform joint channel estimation and decoding in iterative receivers. This is demonstrated in a simple example....

IMPACT OF A REALISTIC DENSITY STRATIFICATION ON A SIMPLE SOLAR DYNAMO CALCULATION

Energy Technology Data Exchange (ETDEWEB)

Cardoso, Elisa; Lopes, Ilidio, E-mail: ilidio.lopes@ist.utl.pt [Centro Multidisciplinar de Astrofisica, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal)

2012-09-20

In our Sun, the magnetic cycle is driven by the dynamo action occurring inside the convection zone, beneath the surface. Rotation couples with plasma turbulent motions to produce organized magnetic fields that erupt at the surface and undergo relatively regular cycles of polarity reversal. Among others, the axisymmetric dynamo models have been proved to be a quite useful tool to understand the dynamical processes responsible for the evolution of the solar magnetic cycle and the formation of the sunspots. Here, we discuss the role played by the radial density stratification on the critical layers of the Sun on the solar dynamo. The current view is that a polytropic description of the density stratification from beneath the tachocline region up to the Sun's surface is sufficient for the current precision of axisymmetric dynamo models. In this work, by using an up-to-date density profile obtained from a standard solar model, which is itself consistent with helioseismic data, we show that the detailed peculiarities of the density in critical regions of the Sun's interior, such as the tachocline, the base of the convection zone, the layers of partial ionization of hydrogen and helium, and the super-adiabatic layer, play a non-negligible role on the evolution of the solar magnetic cycle. Furthermore, we found that the chemical composition of the solar model plays a minor role in the formation and evolution of the solar magnetic cycle.

IMPACT OF A REALISTIC DENSITY STRATIFICATION ON A SIMPLE SOLAR DYNAMO CALCULATION

International Nuclear Information System (INIS)

Cardoso, Elisa; Lopes, Ilídio

2012-01-01

In our Sun, the magnetic cycle is driven by the dynamo action occurring inside the convection zone, beneath the surface. Rotation couples with plasma turbulent motions to produce organized magnetic fields that erupt at the surface and undergo relatively regular cycles of polarity reversal. Among others, the axisymmetric dynamo models have been proved to be a quite useful tool to understand the dynamical processes responsible for the evolution of the solar magnetic cycle and the formation of the sunspots. Here, we discuss the role played by the radial density stratification on the critical layers of the Sun on the solar dynamo. The current view is that a polytropic description of the density stratification from beneath the tachocline region up to the Sun's surface is sufficient for the current precision of axisymmetric dynamo models. In this work, by using an up-to-date density profile obtained from a standard solar model, which is itself consistent with helioseismic data, we show that the detailed peculiarities of the density in critical regions of the Sun's interior, such as the tachocline, the base of the convection zone, the layers of partial ionization of hydrogen and helium, and the super-adiabatic layer, play a non-negligible role on the evolution of the solar magnetic cycle. Furthermore, we found that the chemical composition of the solar model plays a minor role in the formation and evolution of the solar magnetic cycle.

Quantum mean-field theory of collective dynamics and tunneling

International Nuclear Information System (INIS)

Negele, J.W.; Massachusetts Inst. of Tech., Cambridge

1981-01-01

In collaboration with Shimon Levit and Zvi Paltiel, significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples will be summarized here. (orig./HSI)

Multivector field formulation of Hamiltonian field theories: equations and symmetries

Energy Technology Data Exchange (ETDEWEB)

Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)

1999-12-03

We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)

Invariant gauge families inherent in Abelian-gauge field theory. [Scalar dipole ghost field, free-field equations

Energy Technology Data Exchange (ETDEWEB)

Yokoyama, Kan-ichi; Kubo, Reijiro

1974-12-01

The framework of the Nakanishi-Lautrup formalism should be enlarged by introducing a scalar dipole ghost field B(x), which is called gauge on field, together with its pair field. By taking free Lagrangian density, Free-field equations can be described. The vacuum is defined by using a neutral vector field U..mu..(x). The state-vector space is generated by the adjoining conjugates of U..mu..sup((+))(x), and auxiliary fields B(x), B/sub 1/(x) and B/sub 2/(x), which were introduced in the form of the Lagrangian density. The physical states can be defined by the supplementary conditions of the form B/sub 1/sup((+))(x) 1 phys>=B/sub 2/sup((+))(x) 1 phys>=0. It is seen that all the field equations and all the commutators are kept form-invariant, and that the gauge parameter ..cap alpha.. is transformed into ..cap alpha..' given by ..cap alpha..'=..cap alpha..+lambda, with epsilon unchanged. The Lagrangian density is specified only by the gauge invariant parameter epsilon. The gauge structure of theory has universal meaning over whole Abelian-gauge field. C-number gauge transformation and the gauge structure in the presence of interaction are also discussed.

Introduction to Plasma Dynamo, Reconnection and Shocks

Energy Technology Data Exchange (ETDEWEB)

Intrator, Thomas P. [Los Alamos National Laboratory

2012-08-30

In our plasma universe, most of what we can observe is composed of ionized gas, or plasma. This plasma is a conducting fluid, which advects magnetic fields when it flows. Magnetic structure occurs from the smallest planetary to the largest cosmic scales. We introduce at a basic level some interesting features of non linear magnetohydrodynamics (MHD). For example, in our plasma universe, dynamo creates magnetic fields from gravitationally driven flow energy in an electrically conducting medium, and conversely magnetic reconnection annihilates magnetic field and accelerates particles. Shocks occur when flows move faster than the local velocity (sonic or Alfven speed) for the propagation of information. Both reconnection and shocks can accelerate particles, perhaps to gigantic energies, for example as observed with 10{sup 20} eV cosmic rays.

Generalized equations of gravitational field

International Nuclear Information System (INIS)

Stanyukovich, K.P.; Borisova, L.B.

1985-01-01

Equations for gravitational fields are obtained on the basis of a generalized Lagrangian Z=f(R) (R is the scalar curvature). Such an approach permits to take into account the evolution of a gravitation ''constant''. An expression for the force Fsub(i) versus the field variability is obtained. Conservation laws are formulated differing from the standard ones by the fact that in the right part of new equations the value Fsub(i) is present that goes to zero at an ultimate passage to the standard Einstein theory. An equation of state is derived for cosmological metrics for a particular case, f=bRsup(1+α) (b=const, α=const)

Generalized quantum mean-field systems and their application to ultracold atoms

International Nuclear Information System (INIS)

Trimborn-Witthaut, Friederike Annemarie

2011-01-01

-symmetric states and discuss their representation by quantum phase space distributions in terms of generalized coherent states. In particular, this allows for an explicit calculation of the evolution equations and bounds for the ground state energy. In the second part of this thesis we analyse the dynamics of ultracold atoms in optical lattices described by the Bose-Hubbard Hamiltonian, which provide an important example of the generalized quantum mean-field systems treated in the first part. In the mean-field limit the dynamics is described by the (discrete) Gross-Pitaevskii equation. We give a detailed analysis of the interplay between dissipation and strong interactions in different dynamical settings, where we especially focus on the relation between the mean-field description and the full many-particle dynamics given by a master equation. (orig.)

The aurora and the magnetosphere - The Chapman Memorial Lecture. [dynamo theory development, 1600-present

Science.gov (United States)

Akasofu, S.-I.

1974-01-01

Review of recent progress in magnetospheric physics, in particular, in understanding the magnetospheric substorm. It is shown that a number of magnetospheric phenomena can now be understood by viewing the solar wind-magnetosphere interaction as an MHD dynamo; auroral phenomena are powered by the dynamo. Also, magnetospheric responses to variations of the north-south and east-west components of the interplanetary magnetic field have been identified. The magnetospheric substorm is entirely different from the responses of the magnetosphere to the southward component of the interplanetary magnetic field. It may be associated with the formation of a neutral line within the plasma sheet and with an enhanced reconnection along the line. A number of substorm-associated phenomena can be understood by noting that the new neutral line formation is caused by a short-circuiting of a part of the magnetotail current.

The magnetic field experiment onboard Equator-S and its scientific possibilities

Directory of Open Access Journals (Sweden)

K.-H. Fornacon

1999-12-01

Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

The magnetic field experiment onboard Equator-S and its scientific possibilities

Directory of Open Access Journals (Sweden)

K.-H. Fornacon

Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.

Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

Energy fluxes in helical magnetohydrodynamics and dynamo action

Indian Academy of Sciences (India)

... large-scale magnetic field arising due to non-helical interactions and (2) inverse energy flux of magnetic energy caused by helical interactions. Based on our flux results, a primitive model for galactic dynamo has been constructed. Our calculations yield dynamo time-scale for a typical galaxy to be of the order of 108 years.

Three-dimensional dynamo-thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers by DQ-FD coupled

International Nuclear Information System (INIS)

Akbari Alashti, R.; Khorsand, M.

2012-01-01

Three-dimensional elastic analysis is carried out for functionally graded cylindrical shells bonded with piezoelectric layers subjected to dynamic and thermal loads. Material properties are assumed to be graded in the radial direction obeying a simple power law with constant Poisson's ratio. Two versions of differential quadrature (DQ) method coupled with the finite difference (FD) method are employed to discretize the governing differential equations in space and time domains. The convergence is studied and results of the axisymmetric loadings are verified with reported results. Effects of the grading index of material properties, thermal gradient, boundary conditions, thickness of piezoelectric layers and electric excitation on stress, displacement, electric and temperature fields are presented. Highlights: ► Dynamo-thermo-elastic analysis of an FGM shell with piezoelectric layer is carried out. ► Governing equations are solved by DQ-FD coupled. ► Effects of grading index, temperature difference and piezoelectric thickness are presented.

Heavy-ion interactions in relativistic mean-field models

International Nuclear Information System (INIS)

Rashdan, M.

1996-01-01

The interaction potential between spherical nuclei and the elastic scattering cross section are calculated within relativistic mean-field (linear and non-linear) models, using a generalized relativistic local density approximation. The nuclear densities are calculated self-consistently from the solution of the relativistic mean-field equations. It is found that both the linear and non-linear models predict the characteristic switching-over phenomenon of the heavy-ion nuclear potential, where the potential gets attraction with increasing energy up to some value where it reverses this behaviour. The non-linear NLC model predicts a deeper potential than the linear LW model. The elastic scattering cross section calculated within the non-linear NLC model is in better agreement with experiments than that calculated within the linear LW model. (orig.)

Effective field equations for expectation values

International Nuclear Information System (INIS)

Jordan, R.D.

1986-01-01

We discuss functional methods which allow calculation of expectation values, rather than the usual in-out amplitudes, from a path integral. The technique, based on Schwinger's idea of summing over paths which go from the past to the future and then back to the past, provides effective field equations satisfied by the expectation value of the field. These equations are shown to be real and causal for a general theory up to two-loop order, and unitarity is checked to this order. These methods are applied to a simple quantum-mechanical example to illustrate the differences between the new formalism and the standard theory. When applied to the gravitational field, the new effective field equations should be useful for studies of quantum cosmology

Socio-economic applications of finite state mean field games.

Science.gov (United States)

Gomes, Diogo; Velho, Roberto M; Wolfram, Marie-Therese

2014-11-13

In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Time-Dependent Mean-Field Games with Logarithmic Nonlinearities

KAUST Repository

Gomes, Diogo A.

2015-10-06

In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.

Time-Dependent Mean-Field Games with Logarithmic Nonlinearities

KAUST Repository

Gomes, Diogo A.; Pimentel, Edgard

2015-01-01

In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.

Gravitational closure of matter field equations

Science.gov (United States)

Düll, Maximilian; Schuller, Frederic P.; Stritzelberger, Nadine; Wolz, Florian

2018-04-01

The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for diffeomorphism-invariant gravitational dynamics that can equip the coefficients of a given system of matter field equations with causally compatible canonical dynamics. Concretely, we show how starting from any linear local matter field equations whose principal polynomial satisfies three physicality conditions, one may calculate coefficient functions which then enter an otherwise immutable set of countably many linear homogeneous partial differential equations. Any solution of these so-called gravitational closure equations then provides a Lagrangian density for any type of tensorial geometry that features ultralocally in the initially specified matter Lagrangian density. Thus the given system of matter field equations is indeed closed by the so obtained gravitational equations. In contrast to previous work, we build the theory on a suitable associated bundle encoding the canonical configuration degrees of freedom, which allows one to include necessary constraints on the geometry in practically tractable fashion. By virtue of the presented mechanism, one thus can practically calculate, rather than having to postulate, the gravitational theory that is required by specific matter field dynamics. For the special case of standard model matter one obtains general relativity.

Role of asymmetric meridional circulation in producing north-south asymmetry in a solar cycle dynamo model

Energy Technology Data Exchange (ETDEWEB)

Belucz, Bernadett [Eötvös University, Department of Astronomy, 1518 Budapest, Pf. 32 (Hungary); Dikpati, Mausumi [High Altitude Observatory, National Center for Atmospheric Research, 3080 Center Green, Boulder, CO 80307-3000 (United States)

2013-12-10

Solar cycles in the north and south hemispheres differ in cycle length, amplitude, profile, polar fields, and coronal structure. To show what role differences in meridional flow could play in producing these differences, we present the results of three sets of numerical simulations from a flux transport dynamo in which one property of meridional circulation has been changed in the south only. The changes are in amplitude and the presence of a second cell in latitude or in depth. An ascending phase speedup causes weakening of polar and toroidal fields; a speed decrease in a late descending phase does not change amplitudes. A long-duration speed increase leads to lower toroidal field peaks but unchanged polar field peaks. A second high-latitude circulation cell in an ascending phase weakens the next polar and toroidal field peaks, and the ascending phase is lengthened. A second cell in a late descending phase speeds up the cycle. A long-duration second cell leads to a poleward branch of the butterfly diagram and weaker polar fields. A second cell in depth reverses the tilt of the butterfly wing, decreasing polar fields when added during an ascending phase and increasing them during a late descending phase. A long-duration presence of a second cell in radius evolves the butterfly diagram far away from the observed one, with different dynamo periods in low and high latitudes. Thus, a second cell in depth is unlikely to persist more than a few years if the solar dynamo is advection-dominated. Our results show the importance of time variation and north-south asymmetry in meridional circulation in producing differing cycles in the north and south.

Role of asymmetric meridional circulation in producing north-south asymmetry in a solar cycle dynamo model

International Nuclear Information System (INIS)

Belucz, Bernadett; Dikpati, Mausumi

2013-01-01

Solar cycles in the north and south hemispheres differ in cycle length, amplitude, profile, polar fields, and coronal structure. To show what role differences in meridional flow could play in producing these differences, we present the results of three sets of numerical simulations from a flux transport dynamo in which one property of meridional circulation has been changed in the south only. The changes are in amplitude and the presence of a second cell in latitude or in depth. An ascending phase speedup causes weakening of polar and toroidal fields; a speed decrease in a late descending phase does not change amplitudes. A long-duration speed increase leads to lower toroidal field peaks but unchanged polar field peaks. A second high-latitude circulation cell in an ascending phase weakens the next polar and toroidal field peaks, and the ascending phase is lengthened. A second cell in a late descending phase speeds up the cycle. A long-duration second cell leads to a poleward branch of the butterfly diagram and weaker polar fields. A second cell in depth reverses the tilt of the butterfly wing, decreasing polar fields when added during an ascending phase and increasing them during a late descending phase. A long-duration presence of a second cell in radius evolves the butterfly diagram far away from the observed one, with different dynamo periods in low and high latitudes. Thus, a second cell in depth is unlikely to persist more than a few years if the solar dynamo is advection-dominated. Our results show the importance of time variation and north-south asymmetry in meridional circulation in producing differing cycles in the north and south.

Nonlinear evolution equations having a physical meaning

International Nuclear Information System (INIS)

Nakach, R.

1976-06-01

The non stationary self-similar solutions of the nonlinear evolution equations which can be solved by the inverse scattering method are studied. It turns out, as shown by means of several examples, that when the L linear operator associated with these equations, is of second order and only then, the self-similar solutions can be expressed in terms of the various Painleve's transcendents [fr

The electromagnetic field equations for moving media

International Nuclear Information System (INIS)

Ivezić, T

2017-01-01

In this paper a formulation of the field equation for moving media is developed by the generalization of an axiomatic geometric formulation of the electromagnetism in vacuum (Ivezić T 2005 Found. Phys. Lett. 18 401). First, the field equations with bivectors F ( x ) and ℳ ( x ) are presented and then these equations are written with the 4D vectors E ( x ), B ( x ), P ( x ) and M ( x ). The latter contain both the 4D velocity vector u of a moving medium and the 4D velocity vector v of the observers who measure E and B fields. They do not appear in previous literature. All these equations are also written in the standard basis and compared with Maxwell’s equations with 3D vectors. In this approach the Ampère-Maxwell law and Gauss’s law are inseparably connected in one law and the same happens with Faraday’s law and the law that expresses the absence of magnetic charge. It is shown that Maxwell’s equations with 3D vectors and the field equations with 4D geometric quantities are not equivalent in 4D spacetime (paper)

Generalization of Einstein's gravitational field equations

Science.gov (United States)

Moulin, Frédéric

2017-12-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

Sudden transitions and grand variations in the solar dynamo, past and future

NARCIS (Netherlands)

de Jager, C.; Duhau, S.

2012-01-01

The solar dynamo is the exotic dance of the sun's two major magnetic field components, the poloidal and the toroidal, interacting in anti-phase. On the basis of new data on the geomagnetic aa index, we improve our previous forecast of the properties of the current Schwabe cycle #24. Its maximum will

Estimates on the mean current in a sphere of plasma

International Nuclear Information System (INIS)

Nunez, Manuel

2003-01-01

Several turbulent dynamo models predict the concentration of the magnetic field in chaotic plasmas in sheets with the field vector pointing alternatively in opposite directions, which should produce strong current sheets. It is proved that if the plasma is contained in a rigid sphere with perfectly conducting boundary the geometry of these sheets must be balanced so that the mean current remains essentially bounded by the Coulomb gauged mean vector potential of the field. This magnitude remains regular even for the sharp field variations expected in a chaotic flow. For resistive plasmas the same arguments imply that the contribution to the total current of the regions near the boundary compensates the current of the central part of the sphere

Superconductivity a new approach based on the Bethe-Salpeter equation in the mean-field approximation

CERN Document Server

Malik, G P

2016-01-01

Given the Debye temperature of an elemental superconductor (SC) and its Tc, BCS theory enables one to predict the value of its gap 0 at T = 0, or vice versa. This monograph shows that non-elemental SCs can be similarly dealt with via the generalized BCS equations (GBCSEs) which, given any two parameters of the set {Tc, 10, 20 > 10}, enable one to predict the third. Also given herein are new equations for the critical magnetic field and critical current density of an elemental and a non-elemental SC — equations that are derived directly from those that govern pairing in them. The monograph includes topics that are usually not covered in any one text on superconductivity, e.g., BCS-BEC crossover physics, the long-standing puzzle posed by SrTiO3, and heavy-fermion superconductors — all of which are still imperfectly understood and therefore continue to avidly engage theoreticians. It suggests that addressing the Tcs, s and other properties (e.g., number densities of charge carriers) of high-Tc SCs via GBCSE...

Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates

Energy Technology Data Exchange (ETDEWEB)

Lakatos, Greg; O' Brien, John; Chou, Tom [Department of Biomathematics and Institute for Pure and Applied Mathematics, UCLA, Los Angeles, CA 90095 (United States)

2006-03-10

We analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean-field limit. The mean-field equations for particle densities are written in terms of Ricatti equations with the steady-state current J as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents J are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for J from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean-field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.

Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates

International Nuclear Information System (INIS)

Lakatos, Greg; O'Brien, John; Chou, Tom

2006-01-01

We analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean-field limit. The mean-field equations for particle densities are written in terms of Ricatti equations with the steady-state current J as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents J are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for J from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean-field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions

A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control

KAUST Repository

Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul

2015-01-01

In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng's type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.

A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control

KAUST Repository

Djehiche, Boualem

2015-02-24

In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng\\'s type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.

Evolution equations for Killing fields

International Nuclear Information System (INIS)

Coll, B.

1977-01-01

The problem of finding necessary and sufficient conditions on the Cauchy data for Einstein equations which insure the existence of Killing fields in a neighborhood of an initial hypersurface has been considered recently by Berezdivin, Coll, and Moncrief. Nevertheless, it can be shown that the evolution equations obtained in all these cases are of nonstrictly hyperbolic type, and, thus, the Cauchy data must belong to a special class of functions. We prove here that, for the vacuum and Einstein--Maxwell space--times and in a coordinate independent way, one can always choose, as evolution equations for the Killing fields, a strictly hyperbolic system: The above theorems can be thus extended to all Cauchy data for which the Einstein evolution problem has been proved to be well set

A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

Energy Technology Data Exchange (ETDEWEB)

Hosking, John Joseph Absalom, E-mail: j.j.a.hosking@cma.uio.no [University of Oslo, Centre of Mathematics for Applications (CMA) (Norway)

2012-12-15

We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

International Nuclear Information System (INIS)

Hosking, John Joseph Absalom

2012-01-01

We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966–979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197–216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

Energy transfers and magnetic energy growth in small-scale dynamo

KAUST Repository

Kumar, Rohit Raj; Verma, Mahendra K.; Samtaney, Ravi

2013-01-01

In this letter we investigate the dynamics of magnetic energy growth in small-scale dynamo by studying energy transfers, mainly energy fluxes and shell-to-shell energy transfers. We perform dynamo simulations for the magnetic Prandtl number Pm = 20

Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo

Directory of Open Access Journals (Sweden)

R. Hide

1997-01-01

Full Text Available In the interpretation of geomagnetic polarity reversals with their highly variable frequency over geological time it is necessary, as with other irregularly fluctuating geophysical phenomena, to consider the relative importance of forced contributions associated with changing boundary conditions and of free contributions characteristic of the behaviour of nonlinear systems operating under fixed boundary conditions.  New evidence -albeit indirect- in favour of the likely predominance of forced contributions is provided by the discovery reported here of the possibility of complete quenching by nonlineax effects of current fluctuations in a self-exciting homopolar dynamo with its single Faraday disk driven into rotation with angular speed y(τ (where τ denotes time by a steady applied couple.  The armature of an electric motor connected in series with the coil of the dynamo is driven into rotation' with angular speed z(τ by a torque xf (x due to Lorentz forces associated with the electric current x(τ in the system (just as certain parts of the spectrum of eddies within the liquid outer core are generated largely by Lorentz forces associated with currents generated by the self-exciting magnetohydrodynamic (MHD geodynamo.   The discovery is based on bifurcation analysis supported by computational studies of the following (mathematically novel autonomous set of nonlinear ordinary differential equations: dx/dt = x(y - 1 - βzf(x, dy/dt = α(1 - x² - κy, dz/dt = xf (x -λz,          where f (x = 1 - ε + εσx, in cases when the dimensionless parameters (α, β, κ, λ, σ are all positive and 0 ≤ ε ≤ 1. Within those regions of (α, β, κ, λ, σ parameter space where the applied couple, as measured by α, is strong enough for persistent dynamo action (i.e. x ≠ 0 to occur at all, there are in general extensive regions where x(τ exhibits large amplitude regular or irregular (chaotic fluctuations.  But these fluctuating r

Some consequences of shear on galactic dynamos with helicity fluxes

Science.gov (United States)

Zhou, Hongzhe; Blackman, Eric G.

2017-08-01

Galactic dynamo models sustained by supernova (SN) driven turbulence and differential rotation have revealed that the sustenance of large-scale fields requires a flux of small-scale magnetic helicity to be viable. Here we generalize a minimalist analytic version of such galactic dynamos to explore some heretofore unincluded contributions from shear on the total turbulent energy and turbulent correlation time, with the helicity fluxes maintained by either winds, diffusion or magnetic buoyancy. We construct an analytic framework for modelling the turbulent energy and correlation time as a function of SN rate and shear. We compare our prescription with previous approaches that include only rotation. The solutions depend separately on the rotation period and the eddy turnover time and not just on their ratio (the Rossby number). We consider models in which these two time-scales are allowed to be independent and also a case in which they are mutually dependent on radius when a radial-dependent SN rate model is invoked. For the case of a fixed rotation period (or a fixed radius), we show that the influence of shear is dramatic for low Rossby numbers, reducing the correlation time of the turbulence, which, in turn, strongly reduces the saturation value of the dynamo compared to the case when the shear is ignored. We also show that even in the absence of winds or diffusive fluxes, magnetic buoyancy may be able to sustain sufficient helicity fluxes to avoid quenching.

Mean field theory for a balanced hypercolumn model of orientation selectivity in primary visual cortex

DEFF Research Database (Denmark)

Lerchner, Alexander; Sterner, G.; Hertz, J.

2006-01-01

We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn, with a numerical procedure for solving the mean-field equations quantitatively. With our treatment, one can determine self-consistently both the firing rates and the firing correlations...

Effect of non-uniform mean flow field on acoustic propagation problems in computational aeroacoustics

DEFF Research Database (Denmark)

Si, Haiqing; Shen, Wen Zhong; Zhu, Wei Jun

2013-01-01

Acoustic propagation in the presence of a non-uniform mean flow is studied numerically by using two different acoustic propagating models, which solve linearized Euler equations (LEE) and acoustic perturbation equations (APE). As noise induced by turbulent flows often propagates from near field t...

Mean-field Ohm's law and coaxial helicity injection in force-free plasmas

International Nuclear Information System (INIS)

Weening, R. H.

2011-01-01

A theoretical analysis of steady-state coaxial helicity injection (CHI) in force-free plasmas is presented using a parallel mean-field Ohm's law that includes resistivity η and hyper-resistivity Λ terms. Using Boozer coordinates, a partial differential equation is derived for the time evolution of the mean-field poloidal magnetic flux, or magnetic Hamiltonian function, from the parallel mean-field Ohm's law. A general expression is obtained from the mean-field theory for the efficiency of CHI current drive in force-free plasmas. Inductances of internal energy, magnetic helicity, and poloidal magnetic flux are used to characterize axisymmetric plasma equilibria that have a model current profile. Using the model current profile, a method is suggested to determine the level of magnetohydrodynamic activity at the magnetic axis and the consequent deviation from the completely relaxed Taylor state. The mean-field Ohm's law model suggests that steady-state CHI can be viewed most simply as a boundary layer problem.

Dirac equation in magnetic-solenoid field

Energy Technology Data Exchange (ETDEWEB)

Gavrilov, S.P. [Dept. Fisica e Quimica, UNESP, Campus de Guaratingueta (Brazil); Gitman, D.M.; Smirnov, A.A. [Instituto de Fisica, Universidade de Sao Paulo (Brazil)

2004-07-01

We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid. (orig.)

Short-time existence of solutions for mean-field games with congestion

KAUST Repository

Gomes, Diogo A.

2015-11-20

We consider time-dependent mean-field games with congestion that are given by a Hamilton–Jacobi equation coupled with a Fokker–Planck equation. These models are motivated by crowd dynamics in which agents have difficulty moving in high-density areas. The congestion effects make the Hamilton–Jacobi equation singular. The uniqueness of solutions for this problem is well understood; however, the existence of classical solutions was only known in very special cases, stationary problems with quadratic Hamiltonians and some time-dependent explicit examples. Here, we demonstrate the short-time existence of C∞ solutions for sub-quadratic Hamiltonians.

Conserving gapless mean-field theory for weakly interacting Bose gases

International Nuclear Information System (INIS)

Kita, Takafumi

2006-01-01

This paper presents a conserving gapless mean-field theory for weakly interacting Bose gases. We first construct a mean-field Luttinger-Ward thermodynamic functional in terms of the condensate wave function Ψ and the Nambu Green's function G for the quasiparticle field. Imposing its stationarity respect to Ψ and G yields a set of equations to determine the equilibrium for general non-uniform systems. They have a plausible property of satisfying the Hugenholtz-Pines theorem to provide a gapless excitation spectrum. Also, the corresponding dynamical equations of motion obey various conservation laws. Thus, the present mean-field theory shares two important properties with the exact theory: 'conserving' and 'gapless'. The theory is then applied to a homogeneous weakly interacting Bose gas with s-wave scattering length a and particle mass m to clarify its basic thermodynamic properties under two complementary conditions of constant density n and constant pressure p. The superfluid transition is predicted to be first-order because of the non-analytic nature of the order-parameter expansion near T c inherent in Bose systems, i.e., the Landau-Ginzburg expansion is not possible here. The transition temperature T c shows quite a different interaction dependence between the n-fixed and p-fixed cases. In the former case T c increases from the ideal gas value T 0 as T c /T 0 =1+2.33an 1/3 , whereas it decreases in the latter as T c /T 0 =1-3.84a(mp/2πℎ 2 ) 1/5 . Temperature dependences of basic thermodynamic quantities are clarified explicitly. (author)

Statistical thermodynamics and mean-field theory for the alloy under irradiation model

International Nuclear Information System (INIS)

Kamyshendo, V.

1993-01-01

A generalization of statistical thermodynamics to the open systems case, is discussed, using as an example the alloy-under-irradiation model. The statistical properties of stationary states are described with the use of generalized thermodynamic potentials and 'quasi-interactions' determined from the master equation for micro-configuration probabilities. Methods for resolving this equation are illustrated by the mean-field type calculations of correlators, thermodynamic potentials and phase diagrams for disordered alloys

On the hyperbolicity of Einstein's and other gauge field equations

International Nuclear Information System (INIS)

Friedrich, H.

1985-01-01

It is shown that Einstein's vacuum field equations (respectively the conformal vacuum field equations) in a frame formalism imply a symmetric hyperbolic system of ''reduce'' propagation equations for any choice of coordinate system and frame field (and conformal factor). Certain freely specifiable ''gauge source'' functions occurring in the reduced equations reflect the choice of gauge. Together with the initial data they determine the gauge uniquely. Their choice does not affect the isometry class (conformal class) of a solution of an initial value problem. By the same method symmetric hyperbolic propagation equations are obtained from other gauge field equations, irrespective of the gauge. Using the concept of source functions one finds that Einstein's field equation, considered as second order equations for the metric coefficients, are of wave equation type in any coordinate system. (orig.)

Time-dependent mean-field games in the superquadratic case

KAUST Repository

Gomes, Diogo A.

2016-04-06

We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as key techniques used in the subquadratic case, which was studied in a previous publication of the authors, do not extend to the superquadratic setting. The main objective of the present paper is to address these difficulties. Because of the superquadratic structure of the Hamiltonian, Lipschitz estimates for the solutions of the Hamilton−Jacobi equation are obtained here through a novel set of techniques. These explore the parabolic nature of the problem through the nonlinear adjoint method. Well-posedness is proven by combining Lipschitz regularity for the Hamilton−Jacobi equation with polynomial estimates for solutions of the Fokker−Planck equation. Existence of classical solutions is then established under conditions depending only on the growth of the Hamiltonian and the dimension. Our results also add to current understanding of superquadratic Hamilton−Jacobi equations.

Time-dependent mean-field games in the superquadratic case

KAUST Repository

Gomes, Diogo A.; Pimentel, Edgard; Sá nchez-Morgado, Hé ctor

2016-01-01

We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as key techniques used in the subquadratic case, which was studied in a previous publication of the authors, do not extend to the superquadratic setting. The main objective of the present paper is to address these difficulties. Because of the superquadratic structure of the Hamiltonian, Lipschitz estimates for the solutions of the Hamilton−Jacobi equation are obtained here through a novel set of techniques. These explore the parabolic nature of the problem through the nonlinear adjoint method. Well-posedness is proven by combining Lipschitz regularity for the Hamilton−Jacobi equation with polynomial estimates for solutions of the Fokker−Planck equation. Existence of classical solutions is then established under conditions depending only on the growth of the Hamiltonian and the dimension. Our results also add to current understanding of superquadratic Hamilton−Jacobi equations.

Relativistic mean-field mass models

Energy Technology Data Exchange (ETDEWEB)

Pena-Arteaga, D.; Goriely, S.; Chamel, N. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium)

2016-10-15

We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented. (orig.)

Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods

KAUST Repository

Machado Velho, Roberto

2017-01-01

-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose

A mechanism for the dynamo terms to sustain closed-flux current, including helicity balance, by driving current which crosses the magnetic field

Energy Technology Data Exchange (ETDEWEB)

Jarboe, T. R.; Nelson, B. A.; Sutherland, D. A. [University of Washington, Seattle, Washington 98195 (United States)

2015-07-15

An analysis of imposed dynamo current drive (IDCD) [T.R. Jarboe et al., Nucl. Fusion 52 083017 (2012)] reveals: (a) current drive on closed flux surfaces seems possible without relaxation, reconnection, or other flux-surface-breaking large events; (b) the scale size of the key physics may be smaller than is often computationally resolved; (c) helicity can be sustained across closed flux; and (d) IDCD current drive is parallel to the current which crosses the magnetic field to produce the current driving force. In addition to agreeing with spheromak data, IDCD agrees with selected tokamak data.

Derivation of the phase field equations from the thermodynamic extremal principle

International Nuclear Information System (INIS)

Svoboda, J.; Fischer, F.D.; McDowell, D.L.

2012-01-01

Thermodynamics employs quantities that characterize the state of the system and provides driving forces for system evolution. These quantities can be applied by means of the thermodynamic extremal principle to obtain models and consequently constitutive equations for the evolution of the thermodynamic systems. The phase field method is a promising tool for simulation of the microstructure evolution in complex systems but introduces several parameters that are not standard in thermodynamics. The purpose of this paper is to show how the phase field method equations can be derived from the thermodynamic extremal principle, allowing the common treatment of the phase field parameters together with standard thermodynamic parameters in future applications. Fixed values of the phase field parameters may, however, not guarantee fixed values of thermodynamic parameters. Conditions are determined, for which relatively stable values of the thermodynamic parameters are guaranteed during phase field method simulations of interface migration. Finally, analytical relations between the thermodynamic and phase field parameters are found and verified for these simulations. A slight dependence of the thermodynamic parameters on the driving force is determined for the cases examined.

On the convergence of finite state mean-field games through Γ-convergence

KAUST Repository

Ferreira, Rita C.; Gomes, Diogo A.

2014-01-01

In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.

On the convergence of finite state mean-field games through Γ-convergence

KAUST Repository

Ferreira, Rita C.

2014-10-01

In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.

Recovery from Maunder-like Grand Minima in a Babcock–Leighton Solar Dynamo Model

Science.gov (United States)

Karak, Bidya Binay; Miesch, Mark

2018-06-01

The Sun occasionally goes through Maunder-like extended grand minima when its magnetic activity drops considerably from the normal activity level for several decades. Many possible theories have been proposed to explain the origin of these minima. However, how the Sun managed to recover from such inactive phases every time is even more enigmatic. The Babcock–Leighton type dynamos, which are successful in explaining many features of the solar cycle remarkably well, are not expected to operate during grand minima due to the lack of a sufficient number of sunspots. In this Letter, we explore the question of how the Sun could recover from grand minima through the Babcock–Leighton dynamo. In our three-dimensional dynamo model, grand minima are produced spontaneously as a result of random variations in the tilt angle of emerging active regions. We find that the Babcock–Leighton process can still operate during grand minima with only a minimal number of sunspots, and that the model can emerge from such phases without the need for an additional generation mechanism for the poloidal field. The essential ingredient in our model is a downward magnetic pumping, which inhibits the diffusion of the magnetic flux across the solar surface.

Nonequilibrium dynamical mean-field theory

Energy Technology Data Exchange (ETDEWEB)

Eckstein, Martin

2009-12-21

The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)

Nonequilibrium dynamical mean-field theory

International Nuclear Information System (INIS)

Eckstein, Martin

2009-01-01

The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)

Finite correlation time effects in kinematic dynamo problem

International Nuclear Information System (INIS)

Schekochihin, A.A.; Kulsrud, R.M.

2000-01-01

One-point statistics of the magnetic fluctuations in kinematic regime with large Prandtl number and non delta-correlated in time advecting velocity field are studied. A perturbation expansion in the ratio of the velocity correlation time to the dynamo growth time is constructed in the spirit of the Kliatskin-Tatarskii functional method and carried out to first order. The convergence properties are improved compared to the commonly used van Kampen-Terwiel method. The zeroth-order growth rate of the magnetic energy is estimated to be reduced (in three dimensions) by approximately 40%. This reduction is quite close to existing numerical results

Stationary axisymmetric Einstein--Maxwell field equations

International Nuclear Information System (INIS)

Catenacci, R.; Diaz Alonso, J.

1976-01-01

We show the existence of a formal identity between Einstein's and Ernst's stationary axisymmetric gravitational field equations and the Einstein--Maxwell and the Ernst equations for the electrostatic and magnetostatic axisymmetric cases. Our equations are invariant under very simple internal symmetry groups, and one of them appears to be new. We also obtain a method for associating two stationary axisymmetric vacuum solutions with every electrostatic known

Generation of dynamo waves by spatially separated sources in the Earth and other celestial bodies

Science.gov (United States)

Popova, E.

2017-12-01

The amplitude and the spatial configuration of the planetary and stellar magnetic field can changing over the years. Celestial bodies can have cyclic, chaotic or unchanging in time magnetic activity which is connected with a dynamo mechanism. This mechanism is based on the consideration of the joint influence of the alpha-effect and differential rotation. Dynamo sources can be located at different depths (active layers) of the celestial body and can have different intensities. Application of this concept allows us to get different forms of solutions and some of which can include wave propagating inside the celestial body. We analytically showed that in the case of spatially separated sources of magnetic field each source generates a wave whose frequency depends on the physical parameters of its source. We estimated parameters of sources required for the generation nondecaying waves. We discus structure of such sources and matter motion (including meridional circulation) in the liquid outer core of the Earth and active layers of other celestial bodies.

Displacement Convexity for First-Order Mean-Field Games

KAUST Repository

Seneci, Tommaso

2018-05-01

In this thesis, we consider the planning problem for first-order mean-field games (MFG). These games degenerate into optimal transport when there is no coupling between players. Our aim is to extend the concept of displacement convexity from optimal transport to MFGs. This extension gives new estimates for solutions of MFGs. First, we introduce the Monge-Kantorovich problem and examine related results on rearrangement maps. Next, we present the concept of displacement convexity. Then, we derive first-order MFGs, which are given by a system of a Hamilton-Jacobi equation coupled with a transport equation. Finally, we identify a large class of functions, that depend on solutions of MFGs, which are convex in time. Among these, we find several norms. This convexity gives bounds for the density of solutions of the planning problem.

Feasible homopolar dynamo with sliding liquid-metal contacts

OpenAIRE

Priede, Jānis; Avalos-Zúñiga, Raúl

2013-01-01

We present a feasible homopolar dynamo design consisting of a flat, multi-arm spiral coil, which is placed above a fast-spinning metal ring and connected to the latter by sliding liquid-metal electrical contacts. Using a simple, analytically solvable axisymmetric model, we determine the optimal design of such a setup. For small contact resistance, the lowest magnetic Reynolds number, Rm~34.6, at which the dynamo can work, is attained at the optimal ratio of the outer and inner radii of the ri...

A PROPOSED PARADIGM FOR SOLAR CYCLE DYNAMICS MEDIATED VIA TURBULENT PUMPING OF MAGNETIC FLUX IN BABCOCK–LEIGHTON-TYPE SOLAR DYNAMOS

Energy Technology Data Exchange (ETDEWEB)

Hazra, Soumitra; Nandy, Dibyendu [Department of Physical Sciences, Indian Institute of Science Education and Research, Kolkata (India)

2016-11-20

At present, the Babcock–Leighton flux transport solar dynamo models appear to be the most promising models for explaining diverse observational aspects of the sunspot cycle. The success of these flux transport dynamo models is largely dependent upon a single-cell meridional circulation with a deep equatorward component at the base of the Sun’s convection zone. However, recent observations suggest that the meridional flow may in fact be very shallow (confined to the top 10% of the Sun) and more complex than previously thought. Taken together, these observations raise serious concerns on the validity of the flux transport paradigm. By accounting for the turbulent pumping of magnetic flux, as evidenced in magnetohydrodynamic simulations of solar convection, we demonstrate that flux transport dynamo models can generate solar-like magnetic cycles even if the meridional flow is shallow. Solar-like periodic reversals are recovered even when meridional circulation is altogether absent. However, in this case, the solar surface magnetic field dynamics does not extend all the way to the polar regions. Very importantly, our results demonstrate that the Parker–Yoshimura sign rule for dynamo wave propagation can be circumvented in Babcock–Leighton dynamo models by the latitudinal component of turbulent pumping, which can generate equatorward propagating sunspot belts in the absence of a deep, equatorward meridional flow. We also show that variations in turbulent pumping coefficients can modulate the solar cycle amplitude and periodicity. Our results suggest the viability of an alternate magnetic flux transport paradigm—mediated via turbulent pumping—for sustaining solar-stellar dynamo action.

A PROPOSED PARADIGM FOR SOLAR CYCLE DYNAMICS MEDIATED VIA TURBULENT PUMPING OF MAGNETIC FLUX IN BABCOCK–LEIGHTON-TYPE SOLAR DYNAMOS

International Nuclear Information System (INIS)

Hazra, Soumitra; Nandy, Dibyendu

2016-01-01

At present, the Babcock–Leighton flux transport solar dynamo models appear to be the most promising models for explaining diverse observational aspects of the sunspot cycle. The success of these flux transport dynamo models is largely dependent upon a single-cell meridional circulation with a deep equatorward component at the base of the Sun’s convection zone. However, recent observations suggest that the meridional flow may in fact be very shallow (confined to the top 10% of the Sun) and more complex than previously thought. Taken together, these observations raise serious concerns on the validity of the flux transport paradigm. By accounting for the turbulent pumping of magnetic flux, as evidenced in magnetohydrodynamic simulations of solar convection, we demonstrate that flux transport dynamo models can generate solar-like magnetic cycles even if the meridional flow is shallow. Solar-like periodic reversals are recovered even when meridional circulation is altogether absent. However, in this case, the solar surface magnetic field dynamics does not extend all the way to the polar regions. Very importantly, our results demonstrate that the Parker–Yoshimura sign rule for dynamo wave propagation can be circumvented in Babcock–Leighton dynamo models by the latitudinal component of turbulent pumping, which can generate equatorward propagating sunspot belts in the absence of a deep, equatorward meridional flow. We also show that variations in turbulent pumping coefficients can modulate the solar cycle amplitude and periodicity. Our results suggest the viability of an alternate magnetic flux transport paradigm—mediated via turbulent pumping—for sustaining solar-stellar dynamo action.

String field equation from renormalization group

International Nuclear Information System (INIS)

Sakai, Kenji.

1988-10-01

We derive an equation of motion for an open bosonic string field which is introduced as a background field in a sigma model. By using the method of Klebanov and Susskind, we obtain the β-function for this background field and investigate its properties. (author)

Skew differential fields, differential and difference equations

NARCIS (Netherlands)

van der Put, M

2004-01-01

The central question is: Let a differential or difference equation over a field K be isomorphic to all its Galois twists w.r.t. the group Gal(K/k). Does the equation descend to k? For a number of categories of equations an answer is given.

Nonlinear cloudy bag model in the meson mean-field approximation

International Nuclear Information System (INIS)

Bunatyan, G.G.

1989-01-01

We investigate the cloudy bag model for the nucleon, including the essentially nonlinear interaction of the quarks with the meson field. From the boundary conditions, which guarantee the stability of the bag, we obtain equations for the size R of the bag, for the momentum p of the quarks, and for the mean pion field var-phi. We obtain an expression for the total energy E of the bag nucleon. By taking the appropriate averages of all the relations the calculations reduce to the case of a spherically symmetric bag. We show that in the general nonlinear cloudy bag model in question the equations for R, p, and var-phi have a simultaneous solution which corresponds to the absolute minimum of the bag energy E and, consequently, that there exists a stable equilibrium state of the bag nucleon

Extension of Gibbs-Duhem equation including influences of external fields

Science.gov (United States)

Guangze, Han; Jianjia, Meng

2018-03-01

Gibbs-Duhem equation is one of the fundamental equations in thermodynamics, which describes the relation among changes in temperature, pressure and chemical potential. Thermodynamic system can be affected by external field, and this effect should be revealed by thermodynamic equations. Based on energy postulate and the first law of thermodynamics, the differential equation of internal energy is extended to include the properties of external fields. Then, with homogeneous function theorem and a redefinition of Gibbs energy, a generalized Gibbs-Duhem equation with influences of external fields is derived. As a demonstration of the application of this generalized equation, the influences of temperature and external electric field on surface tension, surface adsorption controlled by external electric field, and the derivation of a generalized chemical potential expression are discussed, which show that the extended Gibbs-Duhem equation developed in this paper is capable to capture the influences of external fields on a thermodynamic system.

Dyons in presence of gravitation and symmetrized field equations

International Nuclear Information System (INIS)

Rawat, A.S.; Negi, O.P.S.

1999-01-01

Combined theory of gravitation and electromagnetism associated with particles carrying electric and magnetic charges has been established from an invariant action principle. Corresponding field equations, equation of motion and Einstein Maxwell's equations are obtained in unique and consistent way. It is shown that weak field approximation of slowly moving particle in gravitational field leads the symmetry between electromagnetic and linear gravitational fields. Postulation of the existence of gravimagnetic monopole leads structural symmetry between generalized electromagnetic and gravielectromagnetic fields. Corresponding quantization conditions and angular momentum are also analysed. (author)

Lifetime, turnover time, and fast magnetic field regeneration in random flows

International Nuclear Information System (INIS)

Tanner, S. E. M.

2007-01-01

The fast dynamo is thought to be relevant in the regeneration of magnetic fields in astrophysics where the value of the magnetic Reynolds number (Rm) is immense. The fast dynamo picture is one in which chaotic flows provide a mechanism for the stretching of magnetic field lines. Furthermore, a cascade of energy down to small scales results in intermittent regions of a small-scale, intense magnetic field. Given this scenario it is natural to invoke the use of kinematic random flows in order to understand field regeneration mechanisms better. Here a family of random flows is used to study the effects that L, the lifetime of the cell, and τ, the turnover time of the cell, may have on magnetic field regeneration. Defining the parameter Γ=L/τ, it has been varied according to Γ>1, Γ<1, Γ∼O(1). In the kinematic regime, dynamo growth rates and Lyapunov exponents are examined at varying values of Rm. The possibility of fast dynamo action is considered. In the nonlinear regime, magnetic and kinetic energies are examined. Results indicate that there does appear to be a relationship between Γ and dynamo efficiency. In particular, the most efficient dynamos seem to operate at lower values of Γ

Magnetic field evolution in dwarf and Magellanic-type galaxies

Science.gov (United States)

Siejkowski, H.; Soida, M.; Chyży, K. T.

2018-03-01

Aims: Low-mass galaxies radio observations show in many cases surprisingly high levels of magnetic field. The mass and kinematics of such objects do not favour the development of effective large-scale dynamo action. We attempted to check if the cosmic-ray-driven dynamo can be responsible for measured magnetization in this class of poorly investigated objects. We investigated how starburst events on the whole, as well as when part of the galactic disk, influence the magnetic field evolution. Methods: We created a model of a dwarf/Magellanic-type galaxy described by gravitational potential constituted from two components: the stars and the dark-matter halo. The model is evolved by solving a three-dimensional (3D) magnetohydrodynamic equation with an additional cosmic-ray component, which is approximated as a fluid. The turbulence is generated in the system via supernova explosions manifested by the injection of cosmic-rays. Results: The cosmic-ray-driven dynamo works efficiently enough to amplify the magnetic field even in low-mass dwarf/Magellanic-type galaxies. The e-folding times of magnetic energy growth are 0.50 and 0.25 Gyr for the slow (50 km s-1) and fast (100 km s-1) rotators, respectively. The amplification is being suppressed as the system reaches the equipartition level between kinetic, magnetic, and cosmic-ray energies. An episode of star formation burst amplifies the magnetic field but only for a short time while increased star formation activity holds. We find that a substantial amount of gas is expelled from the galactic disk, and that the starburst events increase the efficiency of this process.

Beyond the relativistic mean-field approximation. II. Configuration mixing of mean-field wave functions projected on angular momentum and particle number

International Nuclear Information System (INIS)

Niksic, T.; Vretenar, D.; Ring, P.

2006-01-01

The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the relativistic mean-field+Lipkin-Nogami BCS equations, with a constraint on the mass quadrupole moment. The model employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a density-independent δ-interaction in the pairing channel. Illustrative calculations are performed for 24 Mg, 32 S, and 36 Ar, and compared with results obtained employing the model developed in the first part of this work, i.e., without particle-number projection, as well as with the corresponding nonrelativistic models based on Skyrme and Gogny effective interactions

Development of mean field theories in nuclear physics and in desordered media

International Nuclear Information System (INIS)

Orland, Henri.

1981-04-01

This work, in two parts, deals with the development of mean field theories in nuclear physics (nuclei in balance and collisions of heavy ions) as well as in disordered media. In the first part, two different ways of tackling the problem of developments around mean field theories are explained. Possessing an approach wave function for the system, the natural idea for including the correlations is to develop the exact wave function of the system around the mean field wave function. The first two chapters show two different ways of dealing with this problem: the perturbative approach - Hartree-Fock equations with two body collisions and functional methods. In the second part: mean field theory for spin glasses. The problem for spin glasses is to construct a physically acceptable mean field theory. The importance of this problem in statistical mechanics is linked to the fact that the mean field theory provides a qualitative description of the low temperature phase and is the starting point needed for using more sophisticated methods (renormalization group). Two approaches to this problem are presented, one based on the Sherrington-Kirkpatrick model and the other based on a model of spins with purely local disorder and competitive interaction between the spins [fr

A New Method and a New Scaling for Deriving Fermionic Mean-Field Dynamics

International Nuclear Information System (INIS)

Petrat, Sören; Pickl, Peter

2016-01-01

We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schrödinger equation for fermionic many-particle systems in quantum mechanics. The method is an adaption of the method used in Pickl (Lett. Math. Phys. 97 (2) 151–164 2011) for bosonic systems to fermionic systems. It is based on a Gronwall type estimate for a suitable measure of distance between the microscopic solution and an antisymmetrized product state. We use this method to treat a new mean-field limit for fermions with long-range interactions in a large volume. Some of our results hold for singular attractive or repulsive interactions. We can also treat Coulomb interaction assuming either a mild singularity cutoff or certain regularity conditions on the solutions to the Hartree(-Fock) equations. In the considered limit, the kinetic and interaction energy are of the same order, while the average force is subleading. For some interactions, we prove that the Hartree(-Fock) dynamics is a more accurate approximation than a simpler dynamics that one would expect from the subleading force. With our method we also treat the mean-field limit coupled to a semiclassical limit, which was discussed in the literature before, and we recover some of the previous results. All results hold for initial data close (but not necessarily equal) to antisymmetrized product states and we always provide explicit rates of convergence.

Mean field theory for a balanced hypercolumn model of orientation selectivity in primary visual cortex

CERN Document Server

Lerchner, A; Hertz, J; Ahmadi, M

2004-01-01

We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our treatment, we can determine self-consistently both the firing rates and the firing correlations, without being restricted to specific neuron models. Here, we solve the analytically derived mean-field equations numerically for integrate-and-fire neurons. Several known key properties of orientation selective cortical neurons emerge naturally from the description: Irregular firing with statistics close to -- but not restricted to -- Poisson statistics; an almost linear gain function (firing frequency as a function of stimulus contrast) of the neurons within the network; and a contrast-invariant tuning width of the neuronal firing. We find that the irregularity in firing depends sensitively on synaptic strengths. If Fano factors are bigger than 1, then they are so for all stim...

Field equations for gravity quadratic in the curvature

International Nuclear Information System (INIS)

Rose, B.

1992-01-01

Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian-namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type-is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differs from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built. 6 refs

Relativistic mean field calculations in neutron-rich nuclei

Energy Technology Data Exchange (ETDEWEB)

Gangopadhyay, G.; Bhattacharya, Madhubrata [Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Roy, Subinit [Saha Institute of Nuclear Physics, Block AF, Sector 1, Kolkata- 700 064 (India)

2014-08-14

Relativistic mean field calculations have been employed to study neutron rich nuclei. The Lagrange's equations have been solved in the co-ordinate space. The effect of the continuum has been effectively taken into account through the method of resonant continuum. It is found that BCS approximation performs as well as a more involved Relativistic Continuum Hartree Bogoliubov approach. Calculations reveal the possibility of modification of magic numbers in neutron rich nuclei. Calculation for low energy proton scattering cross sections shows that the present approach reproduces the density in very light neutron rich nuclei.

A Stochastic Maximum Principle for General Mean-Field Systems

International Nuclear Information System (INIS)

Buckdahn, Rainer; Li, Juan; Ma, Jin

2016-01-01

In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.

A Stochastic Maximum Principle for General Mean-Field Systems

Energy Technology Data Exchange (ETDEWEB)

Buckdahn, Rainer, E-mail: Rainer.Buckdahn@univ-brest.fr [Université de Bretagne-Occidentale, Département de Mathématiques (France); Li, Juan, E-mail: juanli@sdu.edu.cn [Shandong University, Weihai, School of Mathematics and Statistics (China); Ma, Jin, E-mail: jinma@usc.edu [University of Southern California, Department of Mathematics (United States)

2016-12-15

In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.

Field Method for Integrating the First Order Differential Equation

Institute of Scientific and Technical Information of China (English)

JIA Li-qun; ZHENG Shi-wang; ZHANG Yao-yu

2007-01-01

An important modern method in analytical mechanics for finding the integral, which is called the field-method, is used to research the solution of a differential equation of the first order. First, by introducing an intermediate variable, a more complicated differential equation of the first order can be expressed by two simple differential equations of the first order, then the field-method in analytical mechanics is introduced for solving the two differential equations of the first order. The conclusion shows that the field-method in analytical mechanics can be fully used to find the solutions of a differential equation of the first order, thus a new method for finding the solutions of the first order is provided.

Decadal variability in core surface flows deduced from geomagnetic observatory monthly means

DEFF Research Database (Denmark)

Whaler, K. A.; Olsen, Nils; Finlay, Chris

2016-01-01

. On the annual to decadal timescale, the SV is generated primarily by advection in the fluid outer core. We demonstrate the utility of the revised monthly means by calculating models of the core surface advective flow between 1997 and 2013 directly from the SV data. One set of models assumes flow......Monthly means of the magnetic field measurements at ground observatories are a key data source for studying temporal changes of the core magnetic field. However, when they are calculated in the usual way, contributions of external (magnetospheric and ionospheric) origin may remain, which make them...... less favourable for studying the field generated by dynamo action in the core. We remove external field predictions, including a new way of characterising the magnetospheric ring current, from the data and then calculate revised monthly means using robust methods. The geomagnetic secular variation (SV...

Neutron stars in relativistic mean field theory with isovector scalar meson

International Nuclear Information System (INIS)

Kubis, S.; Kutschera, M.; Stachniewicz, S.

1996-12-01

We study the equation of state (EOS) of neutron star matter in a relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the δ-meson [a 0 (980)]. A range of values of the δ-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E s ∼ 30 MeV. We find that proton fraction of neutron star matter is higher in the presence of the δ-field whereas the energy per particle is lower. The EOS becomes slightly stiffer and the maximum mass of the neutron star increased with increasing δmeson coupling. The effect is stronger for soft EOS. (author). 7 refs, 6 figs, 1 tab

Neutron stars in relativistic mean field theory with isovector scalar meson

International Nuclear Information System (INIS)

Kubis, S.; Kutschera, M.; Stachniewicz, S.

1998-01-01

We study the equation of state (EOS) of β-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the δ-meson (a 0 (980)). A range of values of the δ-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E s ∼30 MeV. We find that the quantity most sensitive to the δ-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the δ-field. The energy per baryon also increases but the effect is smaller. The EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger δ-meson coupling. (author)

Neutron stars in relativistic mean field theory with isovector scalar meson

Energy Technology Data Exchange (ETDEWEB)

Kubis, S.; Kutschera, M.; Stachniewicz, S. [Institute of Nuclear Physics, Cracow (Poland)

1996-12-01

We study the equation of state (EOS) of neutron star matter in a relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the {delta}-meson [a{sub 0}(980)]. A range of values of the {delta}-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E{sub s} {approx} 30 MeV. We find that proton fraction of neutron star matter is higher in the presence of the {delta}-field whereas the energy per particle is lower. The EOS becomes slightly stiffer and the maximum mass of the neutron star increased with increasing {delta}meson coupling. The effect is stronger for soft EOS. (author). 7 refs, 6 figs, 1 tab.

Ermakov-Pinney equation in scalar field cosmologies

International Nuclear Information System (INIS)

Hawkins, Rachael M.; Lidsey, James E.

2002-01-01

It is shown that the dynamics of cosmologies sourced by a mixture of perfect fluids and self-interacting scalar fields are described by the nonlinear, Ermakov-Pinney equation. The general solution of this equation can be expressed in terms of particular solutions to a related, linear differential equation. This characteristic is employed to derive exact cosmologies in the inflationary and quintessential scenarios. The relevance of the Ermakov-Pinney equation to the braneworld scenario is discussed

Pairing gaps from nuclear mean-field models

International Nuclear Information System (INIS)

Bender, M.; Rutz, K.; Maruhn, J.A.

2000-01-01

We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi-magic nuclei in the framework of self-consistent nuclear mean-field models. The equations for the conventional BCS model and the approximate projection-before-variation Lipkin-Nogami method are formulated in terms of local density functionals for the effective interaction. We calculate the Lipkin-Nogami corrections of both the mean-field energy and the pairing energy. Various definitions of the pairing gap are discussed as three-point, four-point and five-point mass-difference formulae, averaged matrix elements of the pairing potential, and single-quasiparticle energies. Experimental values for the pairing gap are compared with calculations employing both a delta pairing force and a density-dependent delta interaction in the BCS and Lipkin-Nogami model. Odd-mass nuclei are calculated in the spherical blocking approximation which neglects part of the the core polarization in the odd nucleus. We find that the five-point mass difference formula gives a very robust description of the odd-even staggering, other approximations for the gap may differ from that up to 30% for certain nuclei. (orig.)

DYNAMO-HIA--a Dynamic Modeling tool for generic Health Impact Assessments.

Directory of Open Access Journals (Sweden)

Stefan K Lhachimi

Full Text Available BACKGROUND: Currently, no standard tool is publicly available that allows researchers or policy-makers to quantify the impact of policies using epidemiological evidence within the causal framework of Health Impact Assessment (HIA. A standard tool should comply with three technical criteria (real-life population, dynamic projection, explicit risk-factor states and three usability criteria (modest data requirements, rich model output, generally accessible to be useful in the applied setting of HIA. With DYNAMO-HIA (Dynamic Modeling for Health Impact Assessment, we introduce such a generic software tool specifically designed to facilitate quantification in the assessment of the health impacts of policies. METHODS AND RESULTS: DYNAMO-HIA quantifies the impact of user-specified risk-factor changes on multiple diseases and in turn on overall population health, comparing one reference scenario with one or more intervention scenarios. The Markov-based modeling approach allows for explicit risk-factor states and simulation of a real-life population. A built-in parameter estimation module ensures that only standard population-level epidemiological evidence is required, i.e. data on incidence, prevalence, relative risks, and mortality. DYNAMO-HIA provides a rich output of summary measures--e.g. life expectancy and disease-free life expectancy--and detailed data--e.g. prevalences and mortality/survival rates--by age, sex, and risk-factor status over time. DYNAMO-HIA is controlled via a graphical user interface and is publicly available from the internet, ensuring general accessibility. We illustrate the use of DYNAMO-HIA with two example applications: a policy causing an overall increase in alcohol consumption and quantifying the disease-burden of smoking. CONCLUSION: By combining modest data needs with general accessibility and user friendliness within the causal framework of HIA, DYNAMO-HIA is a potential standard tool for health impact assessment based

The circle equation over finite fields

DEFF Research Database (Denmark)

Aabrandt, Andreas; Hansen, Vagn Lundsgaard

2017-01-01

Interesting patterns in the geometry of a plane algebraic curve C can be observed when the defining polynomial equation is solved over the family of finite fields. In this paper, we examine the case of C the classical unit circle defined by the circle equation x2 + y2 = 1. As a main result, we es...

Coagulation kinetics beyond mean field theory using an optimised Poisson representation

Energy Technology Data Exchange (ETDEWEB)

Burnett, James [Department of Mathematics, UCL, Gower Street, London WC1E 6BT (United Kingdom); Ford, Ian J. [Department of Physics and Astronomy, UCL, Gower Street, London WC1E 6BT (United Kingdom)

2015-05-21

Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable “gauge” transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.

Guiding-center equations for electrons in ultraintense laser fields

International Nuclear Information System (INIS)

Moore, J.E.; Fisch, N.J.

1994-01-01

The guiding-center equations are derived for electrons in arbitrarily intense laser fields also subject to external fields and ponderomotive forces. Exhibiting the relativistic mass increase of the oscillating electrons, a simple frame-invariant equation is shown to govern the behavior of the electrons for sufficiently weak background fields and ponderomotive forces. The parameter regime for which such a formulation is valid is made precise, and some predictions of the equation are checked by numerical simulation

Computer simulation of a magnetohydrodynamic dynamo II

International Nuclear Information System (INIS)

Kageyama, Akira; Sato, Tetsuya.

1994-11-01

We performed a computer simulation of a magnetohydrodynamic dynamo in a rapidly rotating spherical shell. Extensive parameter runs are carried out changing the electrical resistivity. It is found that the total magnetic energy can grow more than ten times larger than the total kinetic energy of the convection motion when the resistivity is sufficiently small. When the resistivity is relatively large and the magnetic energy is comparable or smaller than the kinetic energy, the convection motion maintains its well-organized structure. However, when the resistivity is small and the magnetic energy becomes larger than the kinetic energy, the well-organized convection motion is highly disturbed. The generated magnetic field is organized as a set of flux tubes which can be divided into two categories. The magnetic field component parallel to the rotation axis tends to be confined inside the anticyclonic columnar convection cells. On the other hand, the component perpendicular to the rotation axis is confined outside the convection cells. (author)

Parallel implementation of many-body mean-field equations

International Nuclear Information System (INIS)

Chinn, C.R.; Umar, A.S.; Vallieres, M.; Strayer, M.R.

1994-01-01

We describe the numerical methods used to solve the system of stiff, nonlinear partial differential equations resulting from the Hartree-Fock description of many-particle quantum systems, as applied to the structure of the nucleus. The solutions are performed on a three-dimensional Cartesian lattice. Discretization is achieved through the lattice basis-spline collocation method, in which quantum-state vectors and coordinate-space operators are expressed in terms of basis-spline functions on a spatial lattice. All numerical procedures reduce to a series of matrix-vector multiplications and other elementary operations, which we perform on a number of different computing architectures, including the Intel Paragon and the Intel iPSC/860 hypercube. Parallelization is achieved through a combination of mechanisms employing the Gram-Schmidt procedure, broadcasts, global operations, and domain decomposition of state vectors. We discuss the approach to the problems of limited node memory and node-to-node communication overhead inherent in using distributed-memory, multiple-instruction, multiple-data stream parallel computers. An algorithm was developed to reduce the communication overhead by pipelining some of the message passing procedures

Impact of Convection on Surface Fluxes Observed During LASP/DYNAMO 2011

Science.gov (United States)

2014-12-01

20  Figure 8.  FFM maneuver used in the LASP/DYNAMO experiment (from Wang et al. 2013...Atmosphere Response Experiment DYNAMO Dynamics of Madden-Julian Oscillation EM electro-magnetic EO electro-optical FFM flight-level flux mapping FVS...level flux mapping ( FFM ) modules. Convection modules consisted of dropsonde cloud survey or radar convective element maneuver. Dropsonde modules

Is a deep one-cell meridional circulation essential for the flux transport solar dynamo?

International Nuclear Information System (INIS)

Hazra, Gopal; Karak, Bidya Binay; Choudhuri, Arnab Rai

2014-01-01

The solar activity cycle is successfully modeled by the flux transport dynamo, in which the meridional circulation of the Sun plays an important role. Most of the kinematic dynamo simulations assume a one-cell structure of the meridional circulation within the convection zone, with the equatorward return flow at its bottom. In view of the recent claims that the return flow occurs at a much shallower depth, we explore whether a meridional circulation with such a shallow return flow can still retain the attractive features of the flux transport dynamo (such as a proper butterfly diagram, the proper phase relation between the toroidal and poloidal fields). We consider additional cells of the meridional circulation below the shallow return flow—both the case of multiple cells radially stacked above one another and the case of more complicated cell patterns. As long as there is an equatorward flow in low latitudes at the bottom of the convection zone, we find that the solar behavior is approximately reproduced. However, if there is either no flow or a poleward flow at the bottom of the convection zone, then we cannot reproduce solar behavior. On making the turbulent diffusivity low, we still find periodic behavior, although the period of the cycle becomes unrealistically large. In addition, with a low diffusivity, we do not get the observed correlation between the polar field at the sunspot minimum and the strength of the next cycle, which is reproduced when diffusivity is high. On introducing radially downward pumping, we get a more reasonable period and more solar-like behavior even with low diffusivity.

Is a deep one-cell meridional circulation essential for the flux transport solar dynamo?

Energy Technology Data Exchange (ETDEWEB)

Hazra, Gopal; Karak, Bidya Binay; Choudhuri, Arnab Rai, E-mail: ghazra@physics.iisc.ernet.in [Department of Physics, Indian Institute of Science, Bangalore 560012 (India)

2014-02-20

The solar activity cycle is successfully modeled by the flux transport dynamo, in which the meridional circulation of the Sun plays an important role. Most of the kinematic dynamo simulations assume a one-cell structure of the meridional circulation within the convection zone, with the equatorward return flow at its bottom. In view of the recent claims that the return flow occurs at a much shallower depth, we explore whether a meridional circulation with such a shallow return flow can still retain the attractive features of the flux transport dynamo (such as a proper butterfly diagram, the proper phase relation between the toroidal and poloidal fields). We consider additional cells of the meridional circulation below the shallow return flow—both the case of multiple cells radially stacked above one another and the case of more complicated cell patterns. As long as there is an equatorward flow in low latitudes at the bottom of the convection zone, we find that the solar behavior is approximately reproduced. However, if there is either no flow or a poleward flow at the bottom of the convection zone, then we cannot reproduce solar behavior. On making the turbulent diffusivity low, we still find periodic behavior, although the period of the cycle becomes unrealistically large. In addition, with a low diffusivity, we do not get the observed correlation between the polar field at the sunspot minimum and the strength of the next cycle, which is reproduced when diffusivity is high. On introducing radially downward pumping, we get a more reasonable period and more solar-like behavior even with low diffusivity.

Mean-field level analysis of epidemics in directed networks

Energy Technology Data Exchange (ETDEWEB)

Wang, Jiazeng [School of Mathematical Sciences, Peking University, Beijing 100871 (China); Liu, Zengrong [Mathematics Department, Shanghai University, Shanghai 200444 (China)], E-mail: wangjiazen@yahoo.com.cn, E-mail: zrongliu@online.sh.cn

2009-09-04

The susceptible-infected-removed spreading model in a directed graph is studied. The mean-field level rate equations are built with the degree-degree connectivity correlation element and the (in, out)-degree distribution. And the outbreak threshold is obtained analytically-it is determined by the combination of connectivity probability and the degree distribution. Furthermore, the methods of calculating the degree-degree correlations in directed networks are presented. The numerical results of the discrete epidemic processes in networks verify our analyses.

Mean-field level analysis of epidemics in directed networks

International Nuclear Information System (INIS)

Wang, Jiazeng; Liu, Zengrong

2009-01-01

The susceptible-infected-removed spreading model in a directed graph is studied. The mean-field level rate equations are built with the degree-degree connectivity correlation element and the (in, out)-degree distribution. And the outbreak threshold is obtained analytically-it is determined by the combination of connectivity probability and the degree distribution. Furthermore, the methods of calculating the degree-degree correlations in directed networks are presented. The numerical results of the discrete epidemic processes in networks verify our analyses.

Generalization of Einstein's gravitational field equations

International Nuclear Information System (INIS)

Moulin, Frederic

2017-01-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory. (orig.)

Generalization of Einstein's gravitational field equations

Energy Technology Data Exchange (ETDEWEB)

Moulin, Frederic [Ecole Normale Superieure Paris-Saclay, Departement de Physique, Cachan (France)

2017-12-15

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory. (orig.)

Core Processes: Earth's eccentric magnetic field

DEFF Research Database (Denmark)

Finlay, Chris

2012-01-01

Earth’s magnetic field is characterized by a puzzling hemispheric asymmetry. Calculations of core dynamo processes suggest that lopsided growth of the planet’s inner core may be part of the cause.......Earth’s magnetic field is characterized by a puzzling hemispheric asymmetry. Calculations of core dynamo processes suggest that lopsided growth of the planet’s inner core may be part of the cause....

Conservation laws arising in the study of forward-forward Mean-Field Games

KAUST Repository

Gomes, Diogo A.; Nurbekyan, Levon; Sedjro, Marc

2017-01-01

We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear wave equations. Second, we investigate existence and long-time behavior of solutions for such models.

Conservation laws arising in the study of forward-forward Mean-Field Games

KAUST Repository

Gomes, Diogo A.

2017-04-24

We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear wave equations. Second, we investigate existence and long-time behavior of solutions for such models.

Neutron stars in relativistic mean field theory with isovector scalar meson

Energy Technology Data Exchange (ETDEWEB)

Kubis, S.; Kutschera, M.; Stachniewicz, S. [H. Niewodniczanski Institute of Nuclear Physics, Cracow (Poland)

1998-03-01

We study the equation of state (EOS) of {beta}-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the {delta}-meson (a{sub 0}(980)). A range of values of the {delta}-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E{sub s}{approx}30 MeV. We find that the quantity most sensitive to the {delta}-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the {delta}-field. The energy per baryon also increases but the effect is smaller. The EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger {delta}-meson coupling. (author) 8 refs, 6 figs, 2 tabs

Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach

DEFF Research Database (Denmark)

Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro

2013-01-01

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination...... correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixed-point equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard...

The physics of reversed-field pinch profile sustainment

International Nuclear Information System (INIS)

Moses, R.W.

1985-01-01

A description of the Reversed-Field Pinch (RFP) is given. There is experimental evidence that indicates that an RFP dynamo effect sustains field reversal in steady state. Three sustainment mechanisms are reviewed: the MHD model, the tangled discharge model, and the kinetic dynamo model. The relationship of these models to each another is discussed briefly

Relativistic n-body wave equations in scalar quantum field theory

International Nuclear Information System (INIS)

Emami-Razavi, Mohsen

2006-01-01

The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields

Noisy mean field game model for malware propagation in opportunistic networks

KAUST Repository

Tembine, Hamidou

2012-01-01

In this paper we present analytical mean field techniques that can be used to better understand the behavior of malware propagation in opportunistic large networks. We develop a modeling methodology based on stochastic mean field optimal control that is able to capture many aspects of the problem, especially the impact of the control and heterogeneity of the system on the spreading characteristics of malware. The stochastic large process characterizing the evolution of the total number of infected nodes is examined with a noisy mean field limit and compared to a deterministic one. The stochastic nature of the wireless environment make stochastic approaches more realistic for such types of networks. By introducing control strategies, we show that the fraction of infected nodes can be maintained below some threshold. In contrast to most of the existing results on mean field propagation models which focus on deterministic equations, we show that the mean field limit is stochastic if the second moment of the number of object transitions per time slot is unbounded with the size of the system. This allows us to compare one path of the fraction of infected nodes with the stochastic trajectory of its mean field limit. In order to take into account the heterogeneity of opportunistic networks, the analysis is extended to multiple types of nodes. Our numerical results show that the heterogeneity can help to stabilize the system. We verify the results through simulation showing how to obtain useful approximations in the case of very large systems. © 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering.

Mean field theory for non-abelian gauge theories and fluid dynamics. A brief progress report

International Nuclear Information System (INIS)

Wadia, Spenta R.

2009-01-01

We review the long standing problem of 'mean field theory' for non-abelian gauge theories. As a consequence of the AdS/CFT correspondence, in the large N limit, at strong coupling, and high temperatures and density, the 'mean field theory' is described by the Navier-Stokes equations of fluid dynamics. We also discuss and present results on the non-conformal fluid dynamics of the D1 brane in 1+1 dim. (author)

Equations for effective nuclear fields taking account of 2p2h configurations

International Nuclear Information System (INIS)

Kamerdzhiev, S.P.

1977-01-01

Equations taking into account 1p1h and 2p2h configurations were obta+ned by means of effective fields in the nucleus. The consideration is restricted by the even-even Fermi system only with particle-hole interaction and by the first order with respect to an external field, which corresponds to the case of an even-even nucleus without pairing in a weak external field. The principal results of the investigation are as follows: a set of equations for effective fields V 2 and V 4 is obtained by the Green function method; the solutxon of the set makes it possible to consider 1p1h and 2p2h configurations consecutively and dispense with the Hartree-Fock self-consistence. The equations for V 2 and V 4 can be used to obtain quantum equations taking into account 2p2h configurations and their effect on 1p1h states. Allowance for integration regions far removed from the Fermi surface results in the appearance of the V 4 0 seed portion in the V 4 effective field. Taking into account 2p2h configurations at V 4 0 not equal to 0 changes the form of the seed multipole operator of a nucleus; a new term appears in the expression for transition probability. As a rule, the V 4 0 value was neglected in investigations dealing with the 2p2h configuration

Generation of exact solutions to the Einstein field equations for homogeneous space--time

International Nuclear Information System (INIS)

Hiromoto, R.E.

1978-01-01

A formalism is presented capable of finding all homogeneous solutions of the Einstein field equations with an arbitrary energy-stress tensor. Briefly the method involves the classification of the four-dimensional Lie algebra over the reals into nine different broad classes, using only the Lorentz group. Normally the classification of Lie algebras means that one finds all essentially different solutions of the Jacobi identities, i.e., there exists no nonsingular linear transformation which transforms two sets of structure constants into the other. This approach is to utilize the geometrical considerations of the homogeneous spacetime and field equations to be solved. Since the set of orthonormal basis vectors is not only endowed with a Minkowskian metric, but also constitutes the vector space of our four-dimensional Lie algebras, the Lie algebras are classified against the Lorentz group restricts the linear group of transformations, denoting the essentially different Lie algebras, into nine different broad classes. The classification of the four-dimensional Lie algebras represents the unification of various methods previously introduced by others. Where their methods found only specific solutions to the Einstein field equations, systematic application of the nine different classes of Lie algebras guarantees the extraction of all solutions. Therefore, the methods of others were extended, and their foundations of formalism which goes beyond the present literature of exact homogeneous solutions to the Einstein field equations is built upon

Field Equations for Lovelock Gravity: An Alternative Route

Directory of Open Access Journals (Sweden)

Sumanta Chakraborty

2018-01-01

Full Text Available We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from Newton’s law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that, projecting the Riemann curvature tensor appropriately and taking a cue from Poisson’s equation, Einstein’s equations immediately follow. The above derivation naturally generalizes to Lovelock gravity theories where an appropriate curvature tensor satisfying the symmetries as well as the Bianchi derivative properties of the Riemann tensor has to be used. Interestingly, in the above derivation, the thermodynamic route to gravitational field equations, suited for null hypersurfaces, emerges quiet naturally.

Covariant field equations, gauge fields and conservation laws from Yang-Mills matrix models

International Nuclear Information System (INIS)

Steinacker, Harold

2009-01-01

The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.

Mean field limit for bosons with compact kernels interactions by Wigner measures transportation

International Nuclear Information System (INIS)

Liard, Quentin; Pawilowski, Boris

2014-01-01

We consider a class of many-body Hamiltonians composed of a free (kinetic) part and a multi-particle (potential) interaction with a compactness assumption on the latter part. We investigate the mean field limit of such quantum systems following the Wigner measures approach. We prove in particular the propagation of these measures along the flow of a nonlinear (Hartree) field equation. This enhances and complements some previous results of the same type shown in Z. Ammari and F. Nier and Fröhlich et al. [“Mean field limit for bosons and propagation of Wigner measures,” J. Math. Phys. 50(4), 042107 (2009); Z. Ammari and F. Nier and Fröhlich et al., “Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states,” J. Math. Pures Appl. 95(6), 585–626 (2011); Z. Ammari and F. Nier and Fröhlich et al., “Mean-field- and classical limit of many-body Schrödinger dynamics for bosons,” Commun. Math. Phys. 271(3), 681–697 (2007)

Monotone numerical methods for finite-state mean-field games

KAUST Repository

Gomes, Diogo A.; Saude, Joao

2017-01-01

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.

Monotone numerical methods for finite-state mean-field games

KAUST Repository

Gomes, Diogo A.

2017-04-29

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.

Short-range correlations in an extended time-dependent mean-field theory

International Nuclear Information System (INIS)

Madler, P.

1982-01-01

A generalization is performed of the time-dependent mean-field theory by an explicit inclusion of strong short-range correlations on a level of microscopic reversibility relating them to realistic nucleon-nucleon forces. Invoking a least action principle for correlated trial wave functions, equations of motion for the correlation functions and the single-particle model wave function are derived in lowest order of the FAHT cluster expansion. Higher order effects as well as long-range correlations are consider only to the extent to which they contribute to the mean field via a readjusted phenomenological effective two-body interaction. The corresponding correlated stationary problem is investigated and appropriate initial conditions to describe a heavy ion reaction are proposed. The singleparticle density matrix is evaluated

Mean-field lattice trees

NARCIS (Netherlands)

Borgs, C.; Chayes, J.T.; Hofstad, van der R.W.; Slade, G.

1999-01-01

We introduce a mean-field model of lattice trees based on embeddings into d of abstract trees having a critical Poisson offspring distribution. This model provides a combinatorial interpretation for the self-consistent mean-field model introduced previously by Derbez and Slade [9], and provides an

Statistical Mechanics of Turbulent Dynamos

Science.gov (United States)

Shebalin, John V.

2014-01-01

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much

Exact mean-field theory of ionic solutions: non-Debye screening

International Nuclear Information System (INIS)

Varela, L.M.; Garcia, Manuel; Mosquera, Victor

2003-01-01

The main aim of this report is to analyze the equilibrium properties of primitive model (PM) ionic solutions in the formally exact mean-field formalism. Previously, we review the main theoretical and numerical results reported throughout the last century for homogeneous (electrolytes) and inhomogeneous (electric double layer, edl) ionic systems, starting with the classical mean-field theory of electrolytes due to Debye and Hueckel (DH). In this formalism, the effective potential is derived from the Poisson-Boltzmann (PB) equation and its asymptotic behavior analyzed in the classical Debye theory of screening. The thermodynamic properties of electrolyte solutions are briefly reviewed in the DH formalism. The main analytical and numerical extensions of DH formalism are revised, ranging from the earliest extensions that overcome the linearization of the PB equation to the more sophisticated integral equation techniques introduced after the late 1960s. Some Monte Carlo and molecular dynamic simulations are also reviewed. The potential distributions in an inhomogeneous ionic system are studied in the classical PB framework, presenting the classical Gouy-Chapman (GC) theory of the electric double layer (edl) in a brief manner. The mean-field theory is adequately contextualized using field theoretic (FT) results and it is proven that the classical PB theory is recovered at the Gaussian or one-loop level of the exact FT, and a systematic way to obtain the corrections to the DH theory is derived. Particularly, it is proven following Kholodenko and Beyerlein that corrections to DH theory effectively lead to a renormalization of charges and Debye screening length. The main analytical and numerical results for this non-Debye screening length are reviewed, ranging from asymptotic expansions, self-consistent theory, nonlinear DH results and hypernetted chain (HNC) calculations. Finally, we study the exact mean-field theory of ionic solutions, the so-called dressed-ion theory

A class of exact solutions to the Einstein field equations

International Nuclear Information System (INIS)

Goyal, Nisha; Gupta, R K

2012-01-01

The Einstein-Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein-Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of Einstein-Maxwell equations. (paper)

CSR Fields: Direct Numerical Solution of the Maxwell's Equation

International Nuclear Information System (INIS)

Novokhatski, Alexander

2011-01-01

We discuss the properties of the coherent electromagnetic fields of a very short, ultra-relativistic bunch in a rectangular vacuum chamber inside a bending magnet. The analysis is based on the results of a direct numerical solution of Maxwell's equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields including coherent edge radiation. This approach should be useful in the study of existing and future concepts of particle accelerators and ultrafast coherent light sources. The coherent synchrotron radiation (CSR) fields have a strong action on the beam dynamics of very short bunches, which are moving in the bends of all kinds of magnetic elements. They are responsible for additional energy loss and energy spread; micro bunching and beam emittance growth. These fields may bound the efficiency of damping rings, electron-positron colliders and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned. This is relevant to most high-brightness beam applications. On the other hand these fields together with transition radiation fields can be used for beam diagnostics or even as a powerful resource of THz radiation. A history of the study of CSR and a good collection of references can be found in (1). Electromagnetic theory suggests several methods on how to calculate CSR fields. The most popular method is to use Lienard-Wiechert potentials. Other approach is to solve numerically the approximate equations, which are a Schrodinger type equation. These numerical methods are described in (2). We suggest that a direct solution of Maxwell's equations together with Newton's equations can describe the detailed structure of the CSR fields (3).

A Hamiltonian structure for the linearized Einstein vacuum field equations

International Nuclear Information System (INIS)

Torres del Castillo, G.F.

1991-01-01

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained (Author)

Reduction of static field equation of Faddeev model to first order PDE

International Nuclear Information System (INIS)

Hirayama, Minoru; Shi Changguang

2007-01-01

A method to solve the static field equation of the Faddeev model is presented. For a special combination of the concerned field, we adopt a form which is compatible with the field equation and involves two arbitrary complex functions. As a result, the static field equation is reduced to a set of first order partial differential equations

A THEORETICAL STUDY OF THE BUILD-UP OF THE SUN’S POLAR MAGNETIC FIELD BY USING A 3D KINEMATIC DYNAMO MODEL

Energy Technology Data Exchange (ETDEWEB)

Hazra, Gopal; Choudhuri, Arnab Rai [Department of Physics, Indian Institute of Science, Bangalore, 560012 (India); Miesch, Mark S., E-mail: ghazra@physics.iisc.ernet.in, E-mail: arnab@physics.iisc.ernet.in, E-mail: miesch@ucar.edu [High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO 80301 (United States)

2017-01-20

We develop a three-dimensional kinematic self-sustaining model of the solar dynamo in which the poloidal field generation is from tilted bipolar sunspot pairs placed on the solar surface above regions of strong toroidal field by using the SpotMaker algorithm, and then the transport of this poloidal field to the tachocline is primarily caused by turbulent diffusion. We obtain a dipolar solution within a certain range of parameters. We use this model to study the build-up of the polar magnetic field and show that some insights obtained from surface flux transport models have to be revised. We present results obtained by putting a single bipolar sunspot pair in a hemisphere and two symmetrical sunspot pairs in two hemispheres. We find that the polar fields produced by them disappear due to the upward advection of poloidal flux at low latitudes, which emerges as oppositely signed radial flux and which is then advected poleward by the meridional flow. We also study the effect that a large sunspot pair, violating Hale’s polarity law, would have on the polar field. We find that there would be some effect—especially if the anti-Hale pair appears at high latitudes in the mid-phase of the cycle—though the effect is not very dramatic.

Mean field theories and dual variation mathematical structures of the mesoscopic model

CERN Document Server

Suzuki, Takashi

2015-01-01

Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics.  spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature.  The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.

Large time asymptotics of solutions of the equations of principal chiral field

International Nuclear Information System (INIS)

Sukhanov, V.V.

1990-01-01

Asymptotic behaviour of solutions of the equations of principal chiral field when one of the arguments tends to infinity is investigated. Asymptotics of solutions of the corresponding spectral problem is investigated as well. explicit formulas are constructed which connect the coefficients of the asymptotic decomposition of the potential with the data of the corresponding inverse problem by means of a birational transformation

Mean-Field Games for Marriage

Science.gov (United States)

Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul

2014-01-01

This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple’s network on their feeling states and their well-being. PMID:24804835

Mean-field games for marriage.

Directory of Open Access Journals (Sweden)

Dario Bauso

Full Text Available This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being.

Mean-field theory of differential rotation in density stratified turbulent convection

Science.gov (United States)

Rogachevskii, I.

2018-04-01

A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on the combined effects of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral approach, which is valid for large Reynolds and Péclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.

Solution of radial spin-1 field equation in Robertson-Walker space-time via Heun's equation

International Nuclear Information System (INIS)

Zecca, A.

2010-01-01

The spin-1 field equation is considered in Robertson-Walker spacetime. The problem of the solution of the separated radial equations, previously discussed in the flat space-time case, is solved also for both the closed and open curvature case. The radial equation is reduced to Heun's differential equation that recently has been widely reconsidered. It is shown that the solution of the present Heun equation does not fall into the class of polynomial-like or hypergeometric functions. Heun's operator results also non-factorisable. The properties follow from application of general theorems and power series expansion. In the positive curvature case of the universe a discrete energy spectrum of the system is found. The result follows by requiring a polynomial-like behaviour of at least one component of the spinor field. Developments and applications of the theory suggest further study of the solution of Heun's equation.

Construction of alternative Hamiltonian structures for field equations

Energy Technology Data Exchange (ETDEWEB)

Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)

2001-08-10

We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)

Rarita-Schwinger field and multicomponent wave equation

International Nuclear Information System (INIS)

Kaloshin, A.E.; Lomov, V.P.

2011-01-01

We suggest a simple method to solve a wave equation for Rarita-Schwinger field without additional constraints. This method based on the use of off-shell projection operators allows one to diagonalize spin-1/2 sector of the field

Solutions of Einstein's field equations

Energy Technology Data Exchange (ETDEWEB)

Tomonaga, Y [Utsunomiya Univ. (Japan). Faculty of Education

1978-12-01

In this paper the author investigates the Einstein's field equations of the non-vacuum case and generalizes the solution of Robertson-Walker by the three dimensional Einstein spaces. In Section 2 the author shortly generalizes the dynamic space-time of G. Lemetre and A. Friedmann by a simple transformation.

Trapped Bose gas. Mean-field approximation and beyond

International Nuclear Information System (INIS)

Pitaevskii, L.P.

1998-01-01

The recent realization of Bose-Einstein condensation in atomic gases opens new possibilities for observation of macroscopic quantum phenomena. There are two important features of the system - weak interaction and significant spatial inhomogeneity. Because of this inhomogeneity a non-trivial 'zeroth-order' theory exists, compared to the 'first-order' Bogoliubov theory. This theory is based on the mean-field Gross-Pitaevskii equation for the condensate ψ -function. The equation is classical in its essence but contains the ℎ constant explicitly. Phenomena such as collective modes, interference, tunneling, Josephson-like current and quantized vortex lines can be described using this equation. The study of deviations from the zeroth-order theory arising from zero-point and thermal fluctuations is also of great interest. Thermal fluctuations are described by elementary excitations which define the thermodynamic behaviour of the system and result in Landau-type damping of collective modes. Fluctuations of the phase of the condensate wave function restrict the monochromaticity of the Josephson current. Fluctuations of the numbers of quanta result in the quantum collapse-revival of the collective oscillations. This phenomenon is considered in some details. Collapse time for the JILA experimental conditions turns out to be of the order of seconds. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)

Mean-field games for marriage

KAUST Repository

Bauso, Dario

2014-05-07

This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple\\'s network on their feeling states and their well-being. © 2014 Bauso et al.

Mean-field games for marriage

KAUST Repository

Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul

2014-01-01

This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being. © 2014 Bauso et al.

Self-consistent mean field theory studies of the thermodynamics and quantum spin dynamics of magnetic Skyrmions.

Science.gov (United States)

Wieser, R

2017-05-04

A self-consistent mean field theory is introduced and used to investigate the thermodynamics and spin dynamics of an S  =  1 quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. In addition, the spin dynamics of a magnetic Skyrmion is described by solving the time dependent Schrödinger equation with additional damping term. The Skyrmion annihilation process driven by an electric field is used to compare the trajectories of the quantum mechanical simulation with a semi-classical description for the spin expectation values using a differential equation similar to the classical Landau-Lifshitz-Gilbert equation.

Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations

Science.gov (United States)

Müller, Ingo

2008-12-01

Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. This presentation is based upon the book [1] of which the author of this paper is a co-author. For more details about the motivation and exploitation of the basic principles the interested reader is referred to that reference. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation. Physicists may prefer to appreciate the success of extended thermodynamics in light scattering and to work on the open problems concerning the modification of the Navier-Stokes-Fourier theory in rarefied gases as predicted by extended thermodynamics of 13, 14, and more moments.

Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model

KAUST Repository

Erban, Radek

2009-01-01

A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example, in the modeling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) are studied. Our approach is based on the chemical Fokker-Planck equation. To gain some insight into the advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, and then the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size. © 2009 Society for Industrial and Applied Mathematics.

Equations of motion derived from a generalization of Einstein's equation for the gravitational field

International Nuclear Information System (INIS)

Mociutchi, C.

1980-01-01

The extended Einstein's equation, combined with a vectorial theory of maxwellian type of the gravitational field, leads to: a) the equation of motion; b) the equation of the trajectory for the static case of spherical symmetry, the test particle having a rest mass other than zero, and c) the propagation of light on null geodesics. All the basic tests of the theory given by Einstein's extended equation. Thus, the new theory of gravitation suggested by us is competitive. (author)