On Some Ergodic Impulse Control Problems with Constraint

This paper studies the impulse control of a general Markov process under the average (or ergodic) cost when the impulse instants are restricted to be the arrival times of an exogenous process, and this restriction is referred to as a constraint. A detailed setting is described, a characterization of the optimal cost is obtained as a solution of an HJB equation, and an optimal impulse control is identified

Summary of sand waves and regimes of flow in alluvial channels

CER60MLA24.Includes bibliographical references

Recommended modifications to the Cheesman Outlet Works

Prepared for Denver Board of Water Commissioners.September 1969.CER69-70-JPT-MLA-47.Includes bibliographical references

Origin of type-2 thermal-ion upflows in the auroral ionosphere

International audienceThe origin of thermal ion outflows exceeding 1km/s in the high-latitude F-region has been a subject of considerable debate. For cases with strong convection electric fields, the "evaporation" of the ions due to frictional heating below 400-500km has been shown to provide some satisfactory answers. By contrast, in the more frequent subclass of outflow events observed over auroral arcs, called type-2, there is no observational evidence for ion frictional heating. Instead, an electron temperature increase of up to 6000° K is observed over the outflow region. In this case, field-aligned electric fields have long been suspected to be involved, but this explanation did not seem to agree with expectations from the ion momentum balance. In the present work we provide a consistent scenario for the type-2 ion upflows based on our case study of an event that occurred on 20 February 1990. We introduce, for the first time, the electron energy balance in the analysis. We couple this equation with the ion momentum balance to study the salient features of the observations and conclude that type-2 ion outflows and the accompanying electron heating events are indeed consistent with the existence of a field-aligned electric field. However, for our explanation to work, we have to require that an allowance be made for electron scattering by high frequency turbulence. This turbulence could be generated at first by the very fast response of the electrons themselves to a newly imposed electric field that would be partly aligned with the geomagnetic field. The high frequencies of the waves would make it impossible for the ions to react to the waves. We have found the electron collision frequency associated with scattering from the waves to be rather modest, i.e. comparable to the ambient electron-ion collision frequency. The field-aligned electric field inferred from the observations is likewise of the same order of magnitude as the normal ambipolar field, at least for the case that we have studied in detail. We propose that the field-aligned electric field is maintained by the north-south motion of an east-west arc. The magnetic perturbation associated with the arc itself converts a small fraction of the perpendicular electric field into a field parallel to the total magnetic field, while the north-south motion ensures that the conversion never stops

Further study of the T phase

New data are presented in support of the conclusion that the T phase is propagated across oceans as compressional waves in the water. T phases from many circumpacific-belt shocks were recorded at the Honolulu seismograph station and at the Kaneohe and Point Sur SOFAR Stations, permitting the determination of oceanic velocity by simple division of epicentral distance by travel time since correction for land travel was unnecessary. The signals were much sharper and less prolonged than those previously studied. Very little scatter in the velocity was observed. Divergent views on the nature of T reported by other investigators are due to complications in path, travel time, and land correction introduced by the relatively large proportion of land (or shallow water) paths involved in the shocks which they have studied

Entropic force in black hole binaries and its Newtonian limits

We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive from a new adiabatic variational principle for the Hilbert action in the presence of apparent horizon surfaces. In this approach, entropy is strictly monotonic such that gravity is attractive for all separations including mergers, and the Bekenstein entropy bound is satisfied also at arbitrarily large separations, where gravity reduces to Newton's law. The latter is generalized to point particles in the Newtonian limit by application of Gibbs' principle to world-lines crossing light cones.Comment: Accepted for publication in Phys. Rev.