16,081 research outputs found
Optimal Switching for Hybrid Semilinear Evolutions
We consider the optimization of a dynamical system by switching at discrete
time points between abstract evolution equations composed by nonlinearly
perturbed strongly continuous semigroups, nonlinear state reset maps at mode
transition times and Lagrange-type cost functions including switching costs. In
particular, for a fixed sequence of modes, we derive necessary optimality
conditions using an adjoint equation based representation for the gradient of
the costs with respect to the switching times. For optimization with respect to
the mode sequence, we discuss a mode-insertion gradient. The theory unifies and
generalizes similar approaches for evolutions governed by ordinary and delay
differential equations. More importantly, it also applies to systems governed
by semilinear partial differential equations including switching the principle
part. Examples from each of these system classes are discussed
A Theory of Ex Post Inefficient Renegotiation
We propose a theory of ex post inefficient renegotiation that is based on loss aversion. When two parties write a long-term contract that has to be renegotiated after the realization of the state of the world, they take the initial contract as a reference point to which they compare gains and losses of the renegotiated transaction. We show that loss aversion makes the renegotiated outcome sticky and materially inefficient. The theory has important implications for the optimal design of long-term contracts. First, it explains why parties often abstain from writing a beneficial long-term contract or why some contracts specify transactions that are never ex post efficient. Second, it shows under what conditions parties should rely on the allocation of ownership rights to protect relationship-specific investments rather than writing a specific performance contract. Third, it shows that employment contracts can be strictly optimal even if parties are free to renegotiate
ROSAT PSPC detection of soft X-ray absorption in GB 1428+4217: The most distant matter yet probed with X-ray spectroscopy
We report on a ROSAT PSPC observation of the highly-luminous z = 4.72
radio-loud quasar GB 1428+4217 obtained between 1998 December 11 and 17, the
final days of the ROSAT satellite. The low-energy sensitivity of the PSPC
detector was employed to constrain the intrinsic X-ray absorption of the
currently most distant X-ray detected object. Here we present the detection of
significant soft X-ray absorption towards GB 1428+4217, making the absorbing
material the most distant matter yet probed with X-ray spectroscopy. X-ray
variability by 25+-8 per cent is detected on a timescale of 6500 s in the rest
frame. The X-ray variation requires an unusually high radiative efficiency of
at least 4.2, further supporting the blazar nature of the source.Comment: 6 pages incl. 6 figures, accepted for publication in Monthly Notice
Spin edge helices in a perpendicular magnetic field
We present an exact solution to the problem of the spin edge states in the
presence of equal Bychkov-Rashba and Dresselhaus spin-orbit fields in a
two-dimensional electron system, restricted by a hard-wall confining potential
and exposed to a perpendicular magnetic field. We find that the spectrum of the
spin edge states depends critically on the orientation of the sample edges with
respect to the crystallographic axes. Such a strikingly different spectral
behavior generates new modes of the persistent spin helix-spin edge helices
with novel properties, which can be tuned by the applied electric and magnetic
fields.Comment: In press in Physical Review Letters; Revised arguments in the
introductory part; 3 figure
XMM-Newton observations of GB B1428+4217: confirmation of intrinsic soft X-ray absorption
We report the results of XMM-Newton observations of the X-ray bright,
radio-loud blazar GB B1428+4217 at a redshift of z=4.72. We confirm the
presence of soft X-ray spectral flattening at energies <0.7 keV as reported in
previous ROSAT and BeppoSAX observations. At hard X-ray energies the spectrum
is consistent with a power-law although we find the spectral slope varied
between both XMM-Newton observations and is also significantly different from
that reported previously. Whilst we cannot rule-out intrinsic cold absorption
to explain the spectral depression, we favour a dust-free warm absorber. Cold
absorption requires a column density ~1.4-1.6 x 10^22 cm^-2 whilst a warm
absorber could have up to ~10^23 cm^-2 and an ionization parameter ~10^2. The
spectrum of GB B1428+4217 shows remarkable parallels with that of the z=4.4
blazar PMN J0525-3343, in which the available evidence is also most consistent
with a warm absorber model.Comment: 5 pages, 5 figures, MNRAS accepted. Minor changes to sections 3.1 and
Upper limit on the critical strength of central potentials in relativistic quantum mechanics
In the context of relativistic quantum mechanics, where the Schr\"odinger
equation is replaced by the spinless Salpeter equation, we show how to
construct a large class of upper limits on the critical value,
, of the coupling constant, , of the central potential,
. This critical value is the value of for which a first
-wave bound state appears.Comment: 8 page
Electron spin relaxation in graphene: the role of the substrate
Theory of the electron spin relaxation in graphene on the SiO substrate
is developed. Charged impurities and polar optical surface phonons in the
substrate induce an effective random Bychkov-Rashba-like spin-orbit coupling
field which leads to spin relaxation by the D'yakonov-Perel' mechanism.
Analytical estimates and Monte Carlo simulations show that the corresponding
spin relaxation times are between micro- to milliseconds, being only weakly
temperature dependent. It is also argued that the presence of adatoms on
graphene can lead to spin lifetimes shorter than nanoseconds.Comment: 5 pages, 4 figure
Control of electron spin and orbital resonance in quantum dots through spin-orbit interactions
Influence of resonant oscillating electromagnetic field on a single electron
in coupled lateral quantum dots in the presence of phonon-induced relaxation
and decoherence is investigated. Using symmetry arguments it is shown that spin
and orbital resonance can be efficiently controlled by spin-orbit interactions.
The control is possible due to the strong sensitivity of Rabi frequency to the
dot configuration (orientation of the dot and a static magnetic field) as a
result of the anisotropy of the spin-orbit interactions. The so called easy
passage configuration is shown to be particularly suitable for magnetic
manipulation of spin qubits, ensuring long spin relaxation time and protecting
the spin qubit from electric field disturbances accompanying on-chip
manipulations.Comment: 11 pages, 5 figures; v2: introduction and conclusions broadened,
moderate structure and content change
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