Structural Invariance of Sunspot Umbrae Over the Solar Cycle: 1993-2004

Measurements of maximum magnetic flux, minimum intensity, and size are presented for 12 967 sunspot umbrae detected on the NASA/NSO spectromagnetograms between 1993 and 2004 to study umbral structure and strength during the solar cycle. The umbrae are selected using an automated thresholding technique. Measured umbral intensities are first corrected for a confirming observation of umbral limb-darkening. Log-normal fits to the observed size distribution confirm that the size spectrum shape does not vary with time. The intensity-magnetic flux relationship is found to be steady over the solar cycle. The dependence of umbral size on the magnetic flux and minimum intensity are also independent of cycle phase and give linear and quadratic relations, respectively. While the large sample size does show a low amplitude oscillation in the mean minimum intensity and maximum magnetic flux correlated with the solar cycle, this can be explained in terms of variations in the mean umbral size. These size variations, however, are small and do not substantiate a meaningful change in the size spectrum of the umbrae generated by the Sun. Thus, in contrast to previous reports, the observations suggest the equilibrium structure, as testified by the invariant size-magnetic field relationship, as well as the mean size (i.e. strength) of sunspot umbrae do not significantly depend on solar cycle phase.Comment: 17 pages, 6 figures. Published in Solar Physic

Constitutive modeling of deformation behavior of high-entropy alloys with face-centered cubic crystal structure

A constitutive model based on the dislocation glide and deformation twinning is adapted to face-centered cubic high-entropy alloys (HEAs) as exemplified by the CrMnFeCoNi system. In this model, the total dislocation density is considered as the only internal variable, while the evolution equation describing its variation during plastic deformation is governed by the volume fraction of twinned material. The suitability of the model for describing the strain hardening behavior of HEAs was verified experimentally through compression tests on alloy CrMnFeCoNi and its microstructure characterization by electron backscatter diffraction and X-ray diffraction using synchrotron radiation. ? 2017 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.1111Ysciescopu

Dynamic transition in driven vortices across the peak effect in superconductors

We study the zero-temperature dynamic transition from the disordered flow to an ordered flow state in driven vortices in type-II superconductors. The transition current $I_{p}$ is marked by a sharp kink in the $V(I)$ characteristic with a concomitant large increase in the defect concentration. On increasing magnetic field $B$, the $I_{p}(B)$ follows the behaviour of the critical current $I_{c}(B)$. Specifically, in the peak effect regime $I_{p}(B)$ increases rapidly along with $I_{c}$. We also discuss the effect of varying disorder strength on $I_{p}$.Comment: 4 pages, 4 figure

Critical depinning force and vortex lattice order in disordered superconductors

We simulate the ordering of vortices and its effects on the critical current in superconductors with varied vortex-vortex interaction strength and varied pinning strengths for a two-dimensional system. For strong pinning the vortex lattice is always disordered and the critical depinning force only weakly increases with decreasing vortex-vortex interactions. For weak pinning the vortex lattice is defect free until the vortex-vortex interactions have been reduced to a low value, when defects begin to appear with a simultaneous rapid increase in the critical depinning force. In each case the depinning force shows a maximum for non-interacting vortices. The relative height of the peak increases and the peak width decreases for decreasing pinning strength in excellent agreement with experimental trends associated with the peak effect. We show that scaling relations exist between the distance between defects in the vortex lattice and the critical depinning force.Comment: 5 pages, 6 figure

Time-dependent Stochastic Modeling of Solar Active Region Energy

A time-dependent model for the energy of a flaring solar active region is presented based on a stochastic jump-transition model (Wheatland and Glukhov 1998; Wheatland 2008; Wheatland 2009). The magnetic free energy of the model active region varies in time due to a prescribed (deterministic) rate of energy input and prescribed (random) flare jumps downwards in energy. The model has been shown to reproduce observed flare statistics, for specific time-independent choices for the energy input and flare transition rates. However, many solar active regions exhibit time variation in flare productivity, as exemplified by NOAA active region AR 11029 (Wheatland 2010). In this case a time-dependent model is needed. Time variation is incorporated for two cases: 1. a step change in the rates of flare jumps; and 2. a step change in the rate of energy supply to the system. Analytic arguments are presented describing the qualitative behavior of the system in the two cases. In each case the system adjusts by shifting to a new stationary state over a relaxation time which is estimated analytically. The new model retains flare-like event statistics. In each case the frequency-energy distribution is a power law for flare energies less than a time-dependent rollover set by the largest energy the system is likely to attain at a given time. For Case 1, the model exhibits a double exponential waiting-time distribution, corresponding to flaring at a constant mean rate during two intervals (before and after the step change), if the average energy of the system is large. For Case 2 the waiting-time distribution is a simple exponential, again provided the average energy of the system is large. Monte Carlo simulations of Case~1 are presented which confirm the analytic estimates. The simulation results provide a qualitative model for observed flare statistics in active region AR 11029.Comment: 25 pages, 9 figure

Transverse depinning in strongly driven vortex lattices with disorder

Using numerical simulations we investigate the transverse depinning of moving vortex lattices interacting with random disorder. We observe a finite transverse depinning barrier for vortex lattices that are driven with high longitudinal drives, when the vortex lattice is defect free and moving in correlated 1D channels. The transverse barrier is reduced as the longitudinal drive is decreased and defects appear in the vortex lattice, and the barrier disappears in the plastic flow regime. At the transverse depinning transition, the vortex lattice moves in a staircase pattern with a clear transverse narrow-band voltage noise signature.Comment: 4 pages, 4 figure

A Statistical Study on Photospheric Magnetic Nonpotentiality of Active Regions and Its Relationship with Flares during Solar Cycles 22-23

A statistical study is carried out on the photospheric magnetic nonpotentiality in solar active regions and its relationship with associated flares. We select 2173 photospheric vector magnetograms from 1106 active regions observed by the Solar Magnetic Field Telescope at Huairou Solar Observing Station, National Astronomical Observatories of China, in the period of 1988-2008, which covers most of the 22nd and 23rd solar cycles. We have computed the mean planar magnetic shear angle (\bar{\Delta\phi}), mean shear angle of the vector magnetic field (\bar{\Delta\psi}), mean absolute vertical current density (\bar{|J_{z}|}), mean absolute current helicity density (\bar{|h_{c}|}), absolute twist parameter (|\alpha_{av}|), mean free magnetic energy density (\bar{\rho_{free}}), effective distance of the longitudinal magnetic field (d_{E}), and modified effective distance (d_{Em}) of each photospheric vector magnetogram. Parameters \bar{|h_{c}|}, \bar{\rho_{free}}, and d_{Em} show higher correlation with the evolution of the solar cycle. The Pearson linear correlation coefficients between these three parameters and the yearly mean sunspot number are all larger than 0.59. Parameters \bar{\Delta\phi}, \bar{\Delta\psi}, \bar{|J_{z}|}, |\alpha_{av}|, and d_{E} show only weak correlations with the solar cycle, though the nonpotentiality and the complexity of active regions are greater in the activity maximum periods than in the minimum periods. All of the eight parameters show positive correlations with the flare productivity of active regions, and the combination of different nonpotentiality parameters may be effective in predicting the flaring probability of active regions.Comment: 20 pages, 5 figures, 4 tables, accepted for publication in Solar Physic

Exotic trees

We discuss the scaling properties of free branched polymers. The scaling behaviour of the model is classified by the Hausdorff dimensions for the internal geometry: d_L and d_H, and for the external one: D_L and D_H. The dimensions d_H and D_H characterize the behaviour for long distances while d_L and D_L for short distances. We show that the internal Hausdorff dimension is d_L=2 for generic and scale-free trees, contrary to d_H which is known be equal two for generic trees and to vary between two and infinity for scale-free trees. We show that the external Hausdorff dimension D_H is directly related to the internal one as D_H = \alpha d_H, where \alpha is the stability index of the embedding weights for the nearest-vertex interactions. The index is \alpha=2 for weights from the gaussian domain of attraction and 0<\alpha <2 for those from the L\'evy domain of attraction. If the dimension D of the target space is larger than D_H one finds D_L=D_H, or otherwise D_L=D. The latter result means that the fractal structure cannot develop in a target space which has too low dimension.Comment: 33 pages, 6 eps figure

Dynamic ordering and frustration of confined vortex rows studied by mode-locking experiments

The flow properties of confined vortex matter driven through disordered mesoscopic channels are investigated by mode locking (ML) experiments. The observed ML effects allow to trace the evolution of both the structure and the number of confined rows and their match to the channel width as function of magnetic field. From a detailed analysis of the ML behavior for the case of 3-rows we obtain ({\it i}) the pinning frequency $f_p$, ({\it ii}) the onset frequency $f_c$ for ML ($\propto$ ordering velocity) and ({\it iii}) the fraction $L_{ML}/L$ of coherently moving 3-row regions in the channel. The field dependence of these quantities shows that, at matching, where $L_{ML}$ is maximum, the pinning strength is small and the ordering velocity is low, while at mismatch, where $L_{ML}$ is small, both the pinning force and the ordering velocity are enhanced. Further, we find that $f_c \propto f_p^2$, consistent with the dynamic ordering theory of Koshelev and Vinokur. The microscopic nature of the flow and the ordering phenomena will also be discussed.Comment: 10 pages, 7 figure, submitted to PRB. Discussion has been improved and a figure has been adde

Critical Currents and Vortex States at Fractional Matching Fields in Superconductors with Periodic Pinning

We study vortex states and dynamics in 2D superconductors with periodic pinning at fractional sub-matching fields using numerical simulations. For square pinning arrays we show that ordered states form at 1/1, 1/2, and 1/4 filling fractions while only partially ordered states form at other filling fractions, such as 1/3 and 1/5, in agreement with recent imaging experiments. For triangular pinning arrays we observe matching effects at filling fractions of 1/1, 6/7, 2/3, 1/3, 1/4, 1/6, and 1/7. For both square and triangular pinning arrays we also find that, for certian sub-matching fillings, vortex configurations depend on pinning strength. For weak pinning, ordering in which a portion of the vortices are positioned between pinning sites can occur. Depinning of the vortices at the matching fields, where the vortices are ordered, is elastic while at the incommensurate fields the motion is plastic. At the incommensurate fields, as the applied driving force is increased, there can be a transition to elastic flow where the vortices move along the pinning sites in 1D channels and a reordering transition to a triangular or distorted triangular lattice. We also discuss the current-voltage curves and how they relate to the vortex ordering at commensurate and incommensurate fields.Comment: 14 figure