The principal aim of this work is the evidence on empirical way that catastrophic bifurcation breakdowns or transitions, proceeded by flickering phenomenon, are present on notoriously significant and unpredictable financial markets. Overall, in this
work we developed various metrics associated with catastrophic bifurcation transitions, in particular, the catastrophic slowing down (analogous to the critical slowing down). All these things were considered on a well-defined example of financial markets of small and middle to large capitalization. The catastrophic bifurcation transition seems to be connected with the question of whether the early-warning signals are present in financial markets. This question continues to fascinate both the research community and the general public. Interestingly, such early-warning signals have recently been identified and explained to be a consequence of a catastrophic bifurcation transition phenomenon observed in multiple physical systems, e.g. in ecosystems, climate dynamics and in medicine (epileptic seizure and asthma attack). In the present work we provide an analogical, positive identification of such phenomenon by examining its several different indicators in the context of a well-defined daily bubble; this bubble was induced by the recent worldwide financial crisis on typical financial markets of small and middle to large capitalization.
The Crab Nebula was formed after the collapse of a massive star about a thousand years ago, leaving behind a pulsar that inflates a bubble of ultra-relativistic electron-positron pairs permeated with magnetic field. The observation of brief but brigh
t flares of energetic gamma rays suggests that pairs are accelerated to PeV energies within a few days; such rapid acceleration cannot be driven by shocks. Here, it is argued that the flares may be the smoking gun of magnetic dissipation in the Nebula. Using 2D and 3D particle-in-cell simulations, it is shown that the observations are consistent with relativistic magnetic reconnection, where pairs are subject to strong radiative cooling. The Crab flares may highlight the importance of relativistic magnetic reconnection in astrophysical sources.
The discovery of rapid synchrotron gamma-ray flares above 100 MeV from the Crab Nebula has attracted new interest in alternative particle acceleration mechanisms in pulsar wind nebulae. Diffuse shock-acceleration fails to explain the flares because p
article acceleration and emission occur during a single or even sub-Larmor timescale. In this regime, the synchrotron energy losses induce a drag force on the particle motion that balances the electric acceleration and prevents the emission of synchrotron radiation above 160 MeV. Previous analytical studies and 2D particle-in-cell (PIC) simulations indicate that relativistic reconnection is a viable mechanism to circumvent the above difficulties. The reconnection electric field localized at X-points linearly accelerates particles with little radiative energy losses. In this paper, we check whether this mechanism survives in 3D, using a set of large PIC simulations with radiation reaction force and with a guide field. In agreement with earlier works, we find that the relativistic drift kink instability deforms and then disrupts the layer, resulting in significant plasma heating but few non-thermal particles. A moderate guide field stabilizes the layer and enables particle acceleration. We report that 3D magnetic reconnection can accelerate particles above the standard radiation reaction limit, although the effect is less pronounced than in 2D with no guide field. We confirm that the highest energy particles form compact bunches within magnetic flux ropes, and a beam tightly confined within the reconnection layer, which could result in the observed Crab flares when, by chance, the beam crosses our line of sight.
Photonic crystal (PhC) defect cavities that support an accelerating mode tend to trap unwanted higher-order modes (HOMs) corresponding to zero-group-velocity PhC lattice modes at the top of the bandgap. The effect is explained quite generally from ph
otonic band and perturbation theoretical arguments. Transverse wakefields resulting from this effect are observed in a hybrid dielectric PhC accelerating cavity based on a triangular lattice of sapphire rods. These wakefields are, on average, an order of magnitude higher than those in the waveguide-damped Compact Linear Collider (CLIC) copper cavities. The avoidance of translational symmetry (and, thus, the bandgap concept) can dramatically improve HOM damping in PhC-based structures.
It is generally accepted that astrophysical sources cannot emit synchrotron radiation above 160 MeV in their rest frame. This limit is given by the balance between the accelerating electric force and the radiation reaction force acting on the electro
ns. The discovery of synchrotron gamma-ray flares in the Crab Nebula, well above this limit, challenges this classical picture of particle acceleration. To overcome this limit, particles must accelerate in a region of high electric field and low magnetic field. This is possible only with a non-ideal magnetohydrodynamic process, like magnetic reconnection. We present the first numerical evidence of particle acceleration beyond the synchrotron burnoff limit, using a set of 2D particle-in-cell simulations of ultra-relativistic pair plasma reconnection. We use a new code, Zeltron, that includes self-consistently the radiation reaction force in the equation of motion of the particles. We demonstrate that the most energetic particles move back and forth across the reconnection layer, following relativistic Speiser orbits. These particles then radiate >160 MeV synchrotron radiation rapidly, within a fraction of a full gyration, after they exit the layer. Our analysis shows that the high-energy synchrotron flux is highly variable in time because of the strong anisotropy and inhomogeneity of the energetic particles. We discover a robust positive correlation between the flux and the cut-off energy of the emitted radiation, mimicking the effect of relativistic Doppler amplification. A strong guide field quenches the emission of >160 MeV synchrotron radiation. Our results are consistent with the observed properties of the Crab flares, supporting the reconnection scenario.
For embedded boundary electromagnetics using the Dey-Mittra algorithm, a special grad-div matrix constructed in this work allows use of multigrid methods for efficient inversion of Maxwells curl-curl matrix. Efficient curl-curl
A more accurate, stable, finite-difference time-domain (FDTD) algorithm is developed for simulating Maxwells equations with isotropic or anisotropic dielectric materials. This algorithm is in many cases more accurate than previous algorithms (G. R. W
erner et. al., 2007; A. F. Oskooi et. al., 2009), and it remedies a defect that causes instability with high dielectric contrast (usually for epsilon{} significantly greater than 10) with either isotropic or anisotropic dielectrics. Ultimately this algorithm has first-order error (in the grid cell size) when the dielectric boundaries are sharp, due to field discontinuities at the dielectric interface. Accurate treatment of the discontinuities, in the limit of infinite wavelength, leads to an asymmetric, unstable update (C. A. Bauer et. al., 2011), but the symmetrized version of the latter is stable and more accurate than other FDTD methods. The convergence of field values supports the hypothesis that global first-order error can be achieved by second-order error in bulk material with zero-order error on the surface. This latter point is extremely important for any applications measuring surface fields.
The resistance $R$ vs perpendicular external magnetic field $H$ was measured for superconducting Nb thin--film microbridges with and without microholes [antidots (ADs)]. Well below the transition temperature, integral $R(H)$ measurements of the resis
tive transition to the normal state on the plain bridge show two distinct regions, which can be identified as bulk and edge superconductivity, respectively. The latter case appears when bulk superconductivity becomes suppressed at the upper critical field $H_{c2}$ and below the critical field of edge superconductivity $H_{c3}approx 1.7, H_{c2}$. The presence of additional edges in the AD bridge leads to a different shape of the $R(H)$ curves. We used low-temperature scanning laser microscopy (LTSLM) to visualize the current distribution in the plain and AD bridge upon sweeping $H$. While the plain bridge shows a dominant LTSLM signal at its edges for $H > H_{c2}$ the AD bridge also gives a signal from the inner parts of the bridge due to the additional edge states around the ADs. LTSLM reveals an asymmetry in the current distribution between left and right edges, which confirms theoretical predictions. Furthermore, the experimental results are in good agreement with our numerical simulations (based on the time-dependent Ginzburg--Landau model) yielding the spatial distribution of the order parameter and current density for different bias currents and $H$ values.
We studied experimentally the effect of a stripe-like domain structure in a ferromagnetic BaFe_{12}O_{19} substrate on the magnetoresistance of a superconducting Pb microbridge. The system was designed in such a way that the bridge is oriented perpen
dicular to the domain walls. It is demonstrated that depending on the ratio between the amplitude of the nonuniform magnetic field B_0, induced by the ferromagnet, and the upper critical field H_{c2} of the superconducting material, the regions of the reverse-domain superconductivity in the H-T plane can be isolated or can overlap (H is the external magnetic field, T is temperature). The latter case corresponds to the condition B_0/H_{c2}<1 and results in the formation of superconductivity above the magnetic domains of both polarities. We discovered the regime of edge-assisted reverse-domain superconductivity, corresponding to localized superconductivity near the edges of the bridge above the compensated magnetic domains. Direct verification of the formation of inhomogeneous superconducting states and external-field-controlled switching between normal state and inhomogeneous superconductivity were obtained by low-temperature scanning laser microscopy.
Two utmost cases of super-extreme events influence on the velocity autocorrelation function (VAF) were considered. The VAF itself was derived within the hierarchical Weierstrass-Mandelbrot Continuous-Time Random Walk (WM-CTRW) formalism, which is abl
e to cover a broad spectrum of continuous-time random walks. Firstly, we studied a super-extreme event in a form of a sustained drift, whose duration time is much longer than that of any other event. Secondly, we considered a super-extreme event in the form of a shock with the size and velocity much larger than those corresponding to any other event. We found that the appearance of these super-extreme events substantially changes the results determined by extreme events (the so called black swans) that are endogenous to the WM-CTRW process. For example, changes of the VAF in the latter case are in the form of some instability and distinctly differ from those caused in the former case. In each case these changes are quite different compared to the situation without super-extreme events suggesting the possibility to detect them in natural system if they occur.
