47,508 research outputs found
A family of formulas with reversal of high avoidability index
We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting due to its size and the simple structure of its members. For each k ∈ {4,5}, there are several previously known avoidable formulas (without reversal) of avoidability index k, but they are small in number and they all have rather complex structure.http://dx.doi.org/10.1142/S021819671750024
Theory for nucleation at an interface and magnetization reversal of a two-layer nanowire
Nucleation at the interface between two adjoining regions with dissimilar physical properties is investigated using a model for magnetization reversal of a two-layer ferromagnetic nanowire. Each layer of the nanowire is considered to have a different degree of magnetic anisotropy, representing a hard magnetic layer exchange-coupled to a softer layer. A magnetic field applied along the easy axis causes the softer layer to reverse, forming a domain wall close to the interface. For small applied fields this state is metastable and complete reversal of the nanowire takes place via activation over a barrier. A reversal mechanism involving nucleation at an interface is proposed, whereby a domain wall changes in width as it passes from the soft layer to the hard layer during activation. Langer’s statistical theory for the decay of a metastable state is used to derive rates of magnetization reversal, and simple formulas are found in limiting cases for the activation energy, rate of reversal, and critical field at which the metastable state becomes unstable. These formulas depend on the anisotropy difference between each layer, and the behavior of the reversal rate prefactor is interpreted in terms of activation entropy and domain-wall dynamics
Induced vs Spontaneous Breakdown of S-matrix Unitarity: Probability of No Return in Quantum Chaotic and Disordered Systems
We investigate systematically sample-to sample fluctuations of the
probability of no return into a given entrance channel for wave
scattering from disordered systems. For zero-dimensional ("quantum chaotic")
and quasi one-dimensional systems with broken time-reversal invariance we
derive explicit formulas for the distribution of , and investigate
particular cases. Finally, relating to violation of S-matrix unitarity
induced by internal dissipation, we use the same quantity to identify the
Anderson delocalisation transition as the phenomenon of spontaneous breakdown
of S-matrix unitarity.Comment: This is the published version, with a few modifications added to the
last par
On avoidability of formulas with reversal
While a characterization of unavoidable formulas (without reversal) is well-known, little
is known about the avoidability of formulas with reversal in general. In this article, we characterize the unavoidable formulas with reversal that have at most two one-way variables (x is a one-way variable in formula with reversal φ if exactly one of x and x^R appears in φ)."This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), grant numbers 418646-2012 and 42410-2010.
Systematic Design of Antireflection Coating for Semi-infinite One-dimensional Photonic Crystals Using Bloch Wave Expansion
We present a systematic method for designing a perfect antireflection coating
(ARC) for a semi-infinite one-dimensional (1D) photonic crystal (PC) with an
arbitrary unit cell. We use Bloch wave expansion and time reversal symmetry,
which leads exactly to analytic formulas of structural parameters for the ARC
and renormalized Fresnel coefficients of the PC. Surface immittance (admittance
and impedance) matching plays an essential role in designing the ARC of 1D
PC's, which is shown together with a practical example.Comment: This article may be downloaded for personal use only. Any other use
requires prior permission of the author and the American Institute of Physic
The Entropy Production of Ornstein-Uhlenbeck Active Particles: a path integral method for correlations
By employing a path integral formulation, we obtain the entropy production
rate for a system of active Ornstein-Uhlenbeck particles (AOUP) both in the
presence and in the absence of thermal noise. The present treatment clarifies
some contraddictions concerning the definition of the entropy production rate
in the AOUP model, recently appeared in the literature. We derive explicit
formulas for three different cases: overdamped Brownian particle, AOUP with and
without thermal noise. In addition, we show that it is not necessary to
introduce additional hypotheses concerning the parity of auxiliary variables
under time reversal transformation. Our results agree with those based on a
previous mesoscopic approach
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