17,784 research outputs found
The Parker Magnetostatic Theorem
We demonstrate the Parker Magnetostatic Theorem in terms of a small
neighborhood in solution space containing continuous force-free magnetic fields
in small deviations from the uniform field. These fields are embedded in a
perfectly conducting fluid bounded by a pair of rigid plates where each field
is anchored, taking the plates perpendicular to the uniform field. Those
force-free fields obtainable from the uniform field by continuous magnetic
footpoint displacements at the plates have field topologies that are shown to
be a restricted subset of the field topologies similarly created without
imposing the force-free equilibirum condition. The theorem then follows from
the deduction that a continuous nonequilibrum field with a topology not in that
subset must find a force-free state containing tangential discontinuities.Comment: 13 pages, no figur
Digital computer control of a 30-cm mercury ion thruster
The major objective was to define the exact role of an onboard spacecraft computer in the control of ion thrusters. An initial computer control system with accurate high speed capability was designed, programmed, and tested with the computer as the sole control element for an operating ion thruster. The command functions and a code format for a spacecraft digital control system were established. A second computer control system was constructed to operate with these functions and format. A throttle program sequence was established and tested. A two thruster array was tested with these computer control systems and the results reported
Static current-sheet models of quiescent prominences
A particular class of theoretical models idealize the prominence to be a discrete flat electric-current sheet suspended vertically in a potential magnetic field. The weight of the prominence is supported by the Lorentz force in the current sheet. These models can be extended to have curved electric-current sheets and to vary three-dimensionally. The equation for force balance is 1 over 4 pi (del times B) times Bdel p- p9 z=zero. Using Cartesian coordinates we take, for simplicity, a uniform gravity with constant acceleration g in the direction -z. If we are interested not in the detailed internal structure of the prominence, but in the global magnetic configuration around the prominence, we may take prominence plasma to be cold. Consideration is given to how such equilibrium states can be constructed. To simplify the mathematical problem, suppose there is no electric current in the atmosphere except for the discrete currents in the cold prominence sheet. Let us take the plane z =0 to be the base of the atmosphere and restrict our attention to the domain z greater than 0. The task we have is to solve for a magnetic field which is everywhere potential except on some free surface S, subject to suit able to boundary conditions. The surface S is determined by requiring that it possesses a discrete electric current density such that the Lorentz force on it is everywhere vertically upward to balance the weight of the material m(S). Since the magnetic field is potential in the external atmosphere, the latter is decoupled from the magnetic field and its plane parallel hydrostatic pressure and density can be prescribed
Electrostatic propulsion system with a direct nuclear electrogenerator Patent
Nuclear electric generator for accelerating charged propellant particles in electrostatic propulsion syste
Reciprocal relativity of noninertial frames: quantum mechanics
Noninertial transformations on time-position-momentum-energy space {t,q,p,e}
with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and
the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of
transformations contains the Lorentz group as the inertial special case. In the
limit of small forces and velocities, it reduces to the expected Hamilton
transformations leaving invariant the symplectic metric and the nonrelativistic
line element ds^2=dt^2. The U(1,3) transformations bound relative velocities by
c and relative forces by b. Spacetime is no longer an invariant subspace but is
relative to noninertial observer frames. Born was lead to the metric by a
concept of reciprocity between position and momentum degrees of freedom and for
this reason we call this reciprocal relativity.
For large b, such effects will almost certainly only manifest in a quantum
regime. Wigner showed that special relativistic quantum mechanics follows from
the projective representations of the inhomogeneous Lorentz group. Projective
representations of a Lie group are equivalent to the unitary reprentations of
its central extension. The same method of projective representations of the
inhomogeneous U(1,3) group is used to define the quantum theory in the
noninertial case. The central extension of the inhomogeneous U(1,3) group is
the cover of the quaplectic group Q(1,3)=U(1,3)*s H(4). H(4) is the
Weyl-Heisenberg group. A set of second order wave equations results from the
representations of the Casimir operators
On Asymptotic Optimality of Dual Scheduling Algorithm In A Generalized Switch
Generalized switch is a model of a queueing system where parallel servers are interdependent and have time-varying service capabilities. This paper considers the dual scheduling algorithm that uses rate control and queue-length based scheduling to allocate resources for a generalized switch. We consider a saturated system in which each user has infinite amount of data to be served. We prove the asymptotic optimality of the dual scheduling algorithm for such a system, which says that the vector of average service rates of the scheduling algorithm maximizes some aggregate concave utility functions. As the fairness objectives can be achieved by appropriately choosing utility functions, the asymptotic optimality establishes the fairness properties of the dual scheduling algorithm.
The dual scheduling algorithm motivates a new architecture for scheduling, in which an additional queue is introduced to interface the user data queue and the time-varying server and to modulate the scheduling process, so as to achieve different performance objectives. Further research would include scheduling with Quality of Service guarantees with the dual scheduler, and its application and implementation in various versions of the generalized switch model
Random Access Game and Medium Access Control Design
Motivated partially by a control-theoretic viewpoint, we propose a game-theoretic model, called random access game, for contention control. We characterize Nash equilibria of random access games, study their dynamics, and propose distributed algorithms (strategy evolutions) to achieve Nash equilibria. This provides a general analytical framework that is capable of modeling a large class of system-wide quality-of-service (QoS) models via the specification of per-node utility functions, in which system-wide fairness or service differentiation can be achieved in a distributed manner as long as each node executes a contention resolution algorithm that is designed to achieve the Nash equilibrium. We thus propose a novel medium access method derived from carrier sense multiple access/collision avoidance (CSMA/CA) according to distributed strategy update mechanism achieving the Nash equilibrium of random access game. We present a concrete medium access method that adapts to a continuous contention measure called conditional collision probability, stabilizes the network into a steady state that achieves optimal throughput with targeted fairness (or service differentiation), and can decouple contention control from handling failed transmissions. In addition to guiding medium access control design, the random access game model also provides an analytical framework to understand equilibrium and dynamic properties of different medium access protocols
The Abundance of Molecular Hydrogen and its Correlation with Midplane Pressure in Galaxies: Non-Equilibrium, Turbulent, Chemical Models
Observations of spiral galaxies show a strong linear correlation between the
ratio of molecular to atomic hydrogen surface density R_mol and midplane
pressure. To explain this, we simulate three-dimensional, magnetized
turbulence, including simplified treatments of non-equilibrium chemistry and
the propagation of dissociating radiation, to follow the formation of H_2 from
cold atomic gas. The formation time scale for H_2 is sufficiently long that
equilibrium is not reached within the 20-30 Myr lifetimes of molecular clouds.
The equilibrium balance between radiative dissociation and H_2 formation on
dust grains fails to predict the time-dependent molecular fractions we find. A
simple, time-dependent model of H_2 formation can reproduce the gross behavior,
although turbulent density perturbations increase molecular fractions by a
factor of few above it. In contradiction to equilibrium models, radiative
dissociation of molecules plays little role in our model for diffuse radiation
fields with strengths less than ten times that of the solar neighborhood,
because of the effective self-shielding of H_2. The observed correlation of
R_mol with pressure corresponds to a correlation with local gas density if the
effective temperature in the cold neutral medium of galactic disks is roughly
constant. We indeed find such a correlation of R_mol with density. If we
examine the value of R_mol in our local models after a free-fall time at their
average density, as expected for models of molecular cloud formation by
large-scale gravitational instability, our models reproduce the observed
correlation over more than an order of magnitude range in density.Comment: 24 pages, 4 figures, accepted for publication in Astrophys. J,
changes include addition of models with higher radiation fields and
substantial clarification of the narrativ
Three-dimensional magnetostatic models of the large-scale corona
A special class of magnetostatic equilibria is described, which are mathematically simple and yet sufficiently versatile so as to fit any arbitrary normal magnetic flux prescribed at the photosphere. With these solutions, the corona can be modeled with precisely the same mathematically simple procedure as has previously been done with potential fields. The magnetostatic model predicts, in addition to the coronal magnetic field, the three dimensional coronal density which can be compared with coronagraph observations
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