Pattern formation in a ring cavity with temporally incoherent feedback

We present a theoretical and experimental study of modulation instability and pattern formation in a passive nonlinear optical cavity that is longer than the coherence length of the light circulating in it. Pattern formation in this cavity exhibits various features of a second-order phase transition, closely resembling laser action

The biological and mathematical basis of L systems

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Two-color quantum memory in double-Λ media

We propose a quantum memory for a single-photon wave packet in a superposition of two different colors, i.e., two different frequency components, using the electromagnetically induced transparency technique in a double-Λ system. We examine a specific configuration in which the two frequency components are able to exchange energy through a four-wave mixing process as they propagate, so the state of the incident photon is recovered periodically at certain positions in the medium. We investigate the propagation dynamics as a function of the relative phase between the coupling beams and the input single-photon frequency components. Moreover, by considering time-dependent coupling beams, we numerically simulate the storage and retrieval of a two-frequency-component single-photon qubit

Analogue models of classical and semiclassical gravity

Formal analogies between gravitational and acoustic or optical phenomena have been a subject of study for over a century, leading to interesting scenarios for testing kinematic aspects of general relativity in terrestrial laboratories. Here, some aspects about analog models of gravity obtained from the description of these two different kind of systems are analysed. First, light propagation in linear magnetoeletric media is examined. In particular, it is shown that this effect produces mixed time-space terms in the effective metric that depend only on the antisymmetric part of the generally non-symmetric magnetoelectric coefficient. Furthermore, the dispersion relation related to the linear effect motivates the analysis of an idealised exact model presenting an analog event horizon. Then, a short discussion comparing different ways of constructing analog models is provided. Subsequently, motivated by the results obtained in the optical context, we make a bibliographic review about those analog models obtained from moving media, establishing an equivalence between the propagation of acoustic perturbations in such a background and the propagation of free scalar fields near a Schwarschild black hole. This last aspect drives us to analyse the particle production in this scenario, a result that was first addressed by Stephen Hawking [1, 2], which yields to the the description of the so called Hawking radiation. When treating a non-stationary spacetime, particularly those presenting a gravitational collapse, we can extend the description of quantum fields to curved spacetimes by splitting the metric into two asymptotically stationary regions, with that we show that the presence of the horizon is fundamental for the creation of particles. Finally, it is also shown that the thermal distribution of this particle emission is identical to the Planck distribution for bosons, and because of that the Hawking temperature appears to be very small when we consider astrophysical scenarios

Forward modeling of standing slow modes in flaring coronal loops

Standing slow-mode waves in hot flaring loops are exclusively observed in spectrometers and are used to diagnose the magnetic field strength and temperature of the loop structure. Owing to the lack of spatial information, the longitudinal mode cannot be effectively identified. In this study, we simulate standing slow-mode waves in flaring loops and compare the synthesized line emission properties with Solar Ultraviolet Measurements of Emitted Radiation spectrographic and Solar Dynamics Observatory/Atmospheric Imaging Assembly imaging observations. We find that the emission intensity and line width oscillations are a quarter period out of phase with Doppler shift velocity in both time and spatial domain, which can be used to identify a standing slow-mode wave from spectroscopic observations. However, the longitudinal overtones could only be measured with the assistance of imagers. We find emission intensity asymmetry in the positive and negative modulations; this is because the contribution function pertaining to the atomic emission process responds differently to positive and negative temperature variations. One may detect half periodicity close to the loop apex, where emission intensity modulation is relatively small. The line-of-sight projection affects the observation of Doppler shift significantly. A more accurate estimate of the amplitude of velocity perturbation is obtained by de-projecting the Doppler shift by a factor of 1–2θ/π rather than the traditionally used cosθ. If a loop is heated to the hotter wing, the intensity modulation could be overwhelmed by background emission, while the Doppler shift velocity could still be detected to a certain extent

Forward modeling of standing slow modes in flaring coronal loops

Standing slow-mode waves in hot flaring loops are exclusively observed in spectrometers and are used to diagnose the magnetic field strength and temperature of the loop structure. Owing to the lack of spatial information, the longitudinal mode cannot be effectively identified. In this study, we simulate standing slow-mode waves in flaring loops and compare the synthesized line emission properties with Solar Ultraviolet Measurements of Emitted Radiation spectrographic and Solar Dynamics Observatory/Atmospheric Imaging Assembly imaging observations. We find that the emission intensity and line width oscillations are a quarter period out of phase with Doppler shift velocity in both time and spatial domain, which can be used to identify a standing slow-mode wave from spectroscopic observations. However, the longitudinal overtones could only be measured with the assistance of imagers. We find emission intensity asymmetry in the positive and negative modulations; this is because the contribution function pertaining to the atomic emission process responds differently to positive and negative temperature variations. One may detect half periodicity close to the loop apex, where emission intensity modulation is relatively small. The line-of-sight projection affects the observation of Doppler shift significantly. A more accurate estimate of the amplitude of velocity perturbation is obtained by de-projecting the Doppler shift by a factor of 1–2θ/π rather than the traditionally used cosθ. If a loop is heated to the hotter wing, the intensity modulation could be overwhelmed by background emission, while the Doppler shift velocity could still be detected to a certain extent.Publisher PDFPeer reviewe

Accepting grammars and systems

We investigate several kinds of regulated rewriting (programmed, matrix, with regular control, ordered, and variants thereof) and of parallel rewriting mechanisms (Lindenmayer systems, uniformly limited Lindenmayer systems, limited Lindenmayer systems and scattered context grammars) as accepting devices, in contrast with the usual generating mode. In some cases, accepting mode turns out to be just as powerful as generating mode, e.g. within the grammars of the Chomsky hierarchy, within random context, regular control, L systems, uniformly limited L systems, scattered context. Most of these equivalences can be proved using a metatheorem on so-called context condition grammars. In case of matrix grammars and programmed grammars without appearance checking, a straightforward construction leads to the desired equivalence result. Interestingly, accepting devices are (strictly) more powerful than their generating counterparts in case of ordered grammars, programmed and matrix grammars with appearance checking (even programmed grammarsm with unconditional transfer), and 1lET0L systems. More precisely, if we admit erasing productions, we arrive at new characterizations of the recursivley enumerable languages, and if we do not admit them, we get new characterizations of the context-sensitive languages. Moreover, we supplement the published literature showing: - The emptiness and membership problems are recursivley solvable for generating ordered grammars, even if we admit erasing productions. - Uniformly limited propagating systems can be simulated by programmed grammars without erasing and without appearance checking, hence the emptiness and membership problems are recursively solvable for such systems. - We briefly discuss the degree of nondeterminism and the degree of synchronization for devices with limited parallelism

On the Asymmetry Between Upward and Downward Field-Aligned Currents Interacting With the Ionosphere

The paper presents results from the numerical study of the magnetosphere-ionosphere interactions driven by the large-scale electric field in the magnetically conjugate, high-latitude regions of northern and southern hemispheres. Simulations of the two-fluid MHD model demonstrate that these interactions can lead to a generation of a system of small-scale, intense field-aligned currents with a significant difference in size and amplitude between the upward and downward currents. In particular, in both hemispheres, the downward currents (where the electrons are flowing from the ionosphere) become more narrow and intense than the adjacent upward currents. At high latitudes, the field-aligned currents are closely related to the discrete auroral arcs. The fact that this mechanism produces very narrow and intense downward currents embedded into the broader upward current regions makes it relevant to the explanation of the “black” auroral arcs appearing as narrow, dark strips embedded in the broad luminous background