263 research outputs found
Collisionless reconnection: The sub-microscale mechanism of magnetic field line interaction
Magnetic field lines are quantum objects carrying one quantum
of magnetic flux and have finite radius . Here
we argue that they possess a very specific dynamical interaction. Parallel
field lines reject each other. When confined to a certain area they form
two-dimensional lattices of hexagonal structure. We estimate the filling factor
of such an area. Antiparallel field lines, on the other hand, attract each
other. We identify the physical mechanism as being due to the action of the
gauge potential field which we determine quantum mechanically for two parallel
and two antiparallel field lines. The distortion of the quantum electrodynamic
vacuum causes a cloud of virtual pairs. We calculate the virtual pair
production rate from quantum electrodynamics and estimate the virtual pair
cloud density, pair current and Lorentz force density acting on the field lines
via the pair cloud. These properties of field line dynamics become important in
collisionless reconnection, consistently explaining why and how reconnection
can spontaneously set on in the field-free centre of a current sheet below the
electron-inertial scale.Comment: 13 journal pages, 6 figures, submitted to Ann. Geophy
Violent Relaxation of Indistinguishable Objects and Neutrino Hot Dark Matter in Clusters of Galaxies
The statistical mechanical investigation of violent relaxation (Lynden-Bell
1967) is extended to indistinguishable objects. It is found that,
coincidentally, the equilibrium distribution is the same as that obtained for
classical objects. For massive neutrinos, the Tremaine \& Gunn (1979) phase
space bound is revisited and reinterpretated as the limit indicating the onset
of degeneracy related to the coarse-grained phase space distribution. In the
context of one of the currently most popular cosmological models, the Cold and
Hot Dark Matter (CHDM) model (Primack et al. 1995), the onset of degeneracy may
be of importance in the core region of clusters of galaxies. Degeneracy allows
the neutrino HDM density to exceed the limit imposed by the Tremaine \& Gunn
(1979) bound while accounting for the phase space bound.Comment: AASTeX, 16 pages, 2 EPS figures, uses aas2pp4.sty. Accepted by ApJ
Letter
Ribbon graphs and mirror symmetry
Given a ribbon graph \u393 with some extra structure, we define, using constructible sheaves, a dg category CPM(\u393) meant to model the Fukaya category of a Riemann surface in the cell of Teichm\ufcller space described by \u393. When \u393 is appropriately decorated and admits a combinatorial \u201ctorus fibration with section,\u201d we construct from \u393 a one-dimensional algebraic stack X\u393 with toric components. We prove that our model is equivalent to Perf(X\u393), the dg category of perfect complexes on X\u393
Generalised-Lorentzian Thermodynamics
We extend the recently developed non-gaussian thermodynamic formalism
\cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its
most general form that allows for the formulation of a consistent thermodynamic
theory. All thermodynamic functions, including the definition of the
temperature, are shown to be meaningful. The thermodynamic potential from which
all relevant physical information in equilibrium can be extracted, is defined
consistently. The most important findings are the following two: (1) The
temperature is defined exactly in the same way as in classical statistical
mechanics as the derivative of the energy with respect to the entropy at
constant volume. (2) Observables are defined in the same way as in Boltzmannian
statistics as the linear averages of the new equilibrium distribution function.
This lets us conclude that the new state is a real thermodynamic equilibrium in
systems capable of strong turbulence with the new distribution function
replacing the Boltzmann distribution in such systems. We discuss the ideal gas,
find the equation of state, and derive the specific heat and adiabatic exponent
for such a gas. We also derive the new Gibbsian distribution of states. Finally
we discuss the physical reasons for the development of such states and the
observable properties of the new distribution function.Comment: 13 pages, 1 figur
Gibbsian theory of power law distributions
It is shown that power law phase space distributions describe marginally
stable Gibbsian equilibria far from thermal equilibrium which are expected to
occur in collisionless plasmas containing fully developed quasi-stationary
turbulence. Gibbsian theory is extended on the fundamental level to
statistically dependent subsystems introducing an `ordering parameter'
. Particular forms for the entropy and partition functions are derived
with super-additive (non-extensive) entropy, and a redefinition of temperature
in such systems is given.Comment: Physical Review Letters revised second revision (and shortened
because of overlength) co-author adde
Collisionless reconnection: magnetic field line interaction
Magneticfieldlinesarequantumobjectscarrying onequantum0=2πh ̄/eofmagneticfluxandhavefinite radius λm. Here we argue that they possess a very specific dynamicalinteraction.Parallelfieldlinesrejecteachother. When confined to a certain area they form two-dimensional lattices of hexagonal structure. We estimate the filling factor of such an area. Anti-parallel field lines, on the other hand, at- tract each other. We identify the physical mechanism as being due to the action of the gauge potential field, which we de- termine quantum mechanically for two parallel and two anti- parallel field lines. The distortion of the quantum electrody- namic vacuum causes a cloud of virtual pairs. We calculate the virtual pair production rate from quantum electrodynam- ics and estimate the virtual pair cloud density, pair current and Lorentz force density acting on the field lines via the pair cloud. These properties of field line dynamics become im- portant in collisionless reconnection, consistently explaining why and how reconnection can spontaneously set on in the field-free centre of a current sheet below the electron-inertial scale
Generic model for magnetic explosions applied to solar flares
An accepted model for magnetospheric substorms is proposed as the basis for a
generic model for magnetic explosions, and is applied to solar flares. The
model involves widely separated energy-release and particle-acceleration
regions, with energy transported Alfv\'enically between them. On a global
scale, these regions are coupled by a large-scale current that is set up during
the explosion by redirection of pre-existing current associated with the stored
magnetic energy. The explosion-related current is driven by an electromotive
force (EMF) due to the changing magnetic flux enclosed by this current. The
current path and the EMF are identified for an idealized quadrupolar model for
a flare
Kinetic description of avalanching systems
Avalanching systems are treated analytically using the renormalization group
(in the self-organized-criticality regime) or mean-field approximation,
respectively. The latter describes the state in terms of the mean number of
active and passive sites, without addressing the inhomogeneity in their
distribution. This paper goes one step further by proposing a kinetic
description of avalanching systems making use of the distribution function for
clusters of active sites. We illustrate application of the kinetic formalism to
a model proposed for the description of the avalanching processes in the
reconnecting current sheet of the Earth magnetosphere.Comment: 9 page
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