29,164 research outputs found
Average Continuous Control of Piecewise Deterministic Markov Processes
This paper deals with the long run average continuous control problem of
piecewise deterministic Markov processes (PDMP's) taking values in a general
Borel space and with compact action space depending on the state variable. The
control variable acts on the jump rate and transition measure of the PDMP, and
the running and boundary costs are assumed to be positive but not necessarily
bounded. Our first main result is to obtain an optimality equation for the long
run average cost in terms of a discrete-time optimality equation related to the
embedded Markov chain given by the post-jump location of the PDMP. Our second
main result guarantees the existence of a feedback measurable selector for the
discrete-time optimality equation by establishing a connection between this
equation and an integro-differential equation. Our final main result is to
obtain some sufficient conditions for the existence of a solution for a
discrete-time optimality inequality and an ordinary optimal feedback control
for the long run average cost using the so-called vanishing discount approach.Comment: 34 page
Mathisson's helical motions demystified
The motion of spinning test particles in general relativity is described by
Mathisson-Papapetrou-Dixon equations, which are undetermined up to a spin
supplementary condition, the latter being today still an open question. The
Mathisson-Pirani (MP) condition is known to lead to rather mysterious helical
motions which have been deemed unphysical, and for this reason discarded. We
show that these assessments are unfounded and originate from a subtle (but
crucial) misconception. We discuss the kinematical explanation of the helical
motions, and dynamically interpret them through the concept of hidden momentum,
which has an electromagnetic analogue. We also show that, contrary to previous
claims, the frequency of the helical motions coincides exactly with the
zitterbewegung frequency of the Dirac equation for the electron.Comment: To appear in the Proceedings of the Spanish Relativity Meeting 2011
(ERE2011), "Towards new paradigms", Madrid 29 August - 2 September 201
Reference Frames and the Physical Gravito-Electromagnetic Analogy
The similarities between linearized gravity and electromagnetism are known
since the early days of General Relativity. Using an exact approach based on
tidal tensors, we show that such analogy holds only on very special conditions
and depends crucially on the reference frame. This places restrictions on the
validity of the "gravito-electromagnetic" equations commonly found in the
literature.Comment: 9 Pages, 1 figure. To appear in the Proceedings of the IAU Symposium
261 "Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and
Data Analysis", Virginia Beach, USA, 27 April - 1 May 200
Electromagnetic and Gravitational Invariants
The curvature invariants have been subject of recent interest in the context of the experimental detection of the gravitomagnetic field, namely due to the debate concerning the notions of "extrinsic" and "intrinsic" gravitomagnetism. In this work we explore the physical meaning of the curvature invariants, dissecting their relationship with the gravitomagnetic effects
Electromagnetic and Gravitational Invariants
The curvature invariants have been subject of recent interest in the context of the experimental detection of the gravitomagnetic field, namely due to the debate concerning the notions of "extrinsic" and "intrinsic" gravitomagnetism. In this work we explore the physical meaning of the curvature invariants, dissecting their relationship with the gravitomagnetic effects
Electromagnetic and Gravitational Invariants
The curvature invariants have been subject of recent interest in the context of the experimental detection of the gravitomagnetic field, namely due to the debate concerning the notions of "extrinsic" and "intrinsic" gravitomagnetism. In this work we explore the physical meaning of the curvature invariants, dissecting their relationship with the gravitomagnetic effects
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