13,757 research outputs found
The Role of the Magnetorotational Instability in the Sun
We calculate growth rates for nonaxisymmetric instabilities including the
magnetorotational instability (MRI) throughout the Sun. We first derive a
dispersion relation for nonaxisymmetric instability including the effects of
shear, convective buoyancy, and three diffusivities (thermal conductivity,
resistivity, and viscosity). We then use a solar model evolved with the stellar
evolution code MESA and angular velocity profiles determined by Global
Oscillations Network Group (GONG) helioseismology to determine the unstable
modes present at each location in the Sun and the associated growth rates. The
overall instability has unstable modes throughout the convection zone and also
slightly below it at middle and high latitudes. It contains three classes of
modes: large-scale hydrodynamic convective modes, large-scale hydrodynamic
shear modes, and small-scale magnetohydrodynamic (MHD) shear modes, which may
be properly called MRI modes. While large-scale convective modes are the most
rapidly growing modes in most of the convective zone, MRI modes are important
in both stably stratified and convectively unstable locations near the
tachocline at colatitudes theta less than 53 degrees. Nonaxisymmetric MRI modes
grow faster than the corresponding axisymmetric modes; for some poloidal
magnetic fields, the nonaxisymmetric MRI growth rates are similar to the
angular rotation frequency Omega, while axisymmetric modes are stabilized. We
briefly discuss the saturation of the field produced by MRI modes, finding that
the implied field at the base of the convective zone in the Sun is comparable
to that derived based on dynamos active in the tachocline and that the
saturation of field resulting from the MRI may be of importance even in the
upper convection zone.Comment: 20 pages, 11 figure
Calculation of the microcanonical temperature for the classical Bose field
The ergodic hypothesis asserts that a classical mechanical system will in
time visit every available configuration in phase space. Thus, for an ergodic
system, an ensemble average of a thermodynamic quantity can equally well be
calculated by a time average over a sufficiently long period of dynamical
evolution. In this paper we describe in detail how to calculate the temperature
and chemical potential from the dynamics of a microcanonical classical field,
using the particular example of the classical modes of a Bose-condensed gas.
The accurate determination of these thermodynamics quantities is essential in
measuring the shift of the critical temperature of a Bose gas due to
non-perturbative many-body effects.Comment: revtex4, 10 pages, 1 figure. v2: updated to published version. Fuller
discussion of numerical results, correction of some minor error
Apparent Clustering and Apparent Background Earthquakes Biased by Undetected Seismicity
In models of triggered seismicity and in their inversion with empirical data,
the detection threshold m_d is commonly equated to the magnitude m_0 of the
smallest triggering earthquake. This unjustified assumption neglects the
possibility of shocks below the detection threshold triggering observable
events. We introduce a formalism that distinguishes between the detection
threshold m_d and the minimum triggering earthquake m_0 < m_d. By considering
the branching structure of one complete cascade of triggered events, we derive
the apparent branching ratio n_a (which is the apparent fraction of aftershocks
in a given catalog) and the apparent background source S_a that are observed
when only the structure above the detection threshold m_d is known due to the
presence of smaller undetected events that are capable of triggering larger
events. If earthquake triggering is controlled in large part by the smallest
magnitudes as several recent analyses have shown, this implies that previous
estimates of the clustering parameters may significantly underestimate the true
values: for instance, an observed fraction of 55% of aftershocks is
renormalized into a true value of 75% of triggered events.Comment: 12 pages; incl. 6 Figures, AGU styl
Critical Dynamics of a Two-dimensional Superfluid near a Non-Thermal Fixed Point
Critical dynamics of an ultracold Bose gas far from equilibrium is studied in
two spatial dimensions. Superfluid turbulence is created by quenching the
equilibrium state close to zero temperature. Instead of immediately
re-thermalizing, the system approaches a meta-stable transient state,
characterized as a non-thermal fixed point. A focus is set on the vortex
density and vortex-antivortex correlations which characterize the evolution
towards the non-thermal fixed point and the departure to final
(quasi-)condensation. Two distinct power-law regimes in the vortex-density
decay are found and discussed in terms of a vortex binding-unbinding transition
and a kinetic description of vortex scattering. A possible relation to decaying
turbulence in classical fluids is pointed out. By comparing the results to
equilibrium studies of a two-dimensional Bose gas, an intuitive understanding
of the location of the non-thermal fixed point in a reduced phase space is
developed.Comment: 11 pages, 13 figures; PRA versio
FACTORS INFLUENCING CHANGES IN POTATO AND POTATO SUBSTITUTE DEMAND
Despite the rapid rise in complex carbohydrate consumption over the last twenty-five years, fresh potato consumption has fallen by over 50%. Fresh potato growers and retailers alike need to know whether these changes reflect consumer responses to changing relative prices or incomes, or whether they are due to changes in consumer tastes. This paper uses a linear approximation almost ideal demand system (LA/AIDS) to investigate the effect of relative prices, expenditures, and a set of socioeconomic variables on complex carbohydrate demand. Estimation results show that the socioeconomic variables explain some of the changes in demand, but a significant amount remains as evidence of a change in consumer tastes.Demand and Price Analysis,
Quantum Glassiness
Describing matter at near absolute zero temperature requires understanding a
system's quantum ground state and the low energy excitations around it, the
quasiparticles, which are thermally populated by the system's contact to a heat
bath. However, this paradigm breaks down if thermal equilibration is
obstructed. This paper presents solvable examples of quantum many-body
Hamiltonians of systems that are unable to reach their ground states as the
environment temperature is lowered to absolute zero. These examples, three
dimensional generalizations of quantum Hamiltonians proposed for topological
quantum computing, 1) have no quenched disorder, 2) have solely local
interactions, 3) have an exactly solvable spectrum, 4) have topologically
ordered ground states, and 5) have slow dynamical relaxation rates akin to
those of strong structural glasses.Comment: 4 page
- …