Conditions for electron-cyclotron maser emission in the solar corona

Context. The Sun is an active source of radio emission ranging from long duration radio bursts associated with solar flares and coronal mass ejections to more complex, short duration radio bursts such as solar S bursts, radio spikes and fibre bursts. While plasma emission is thought to be the dominant emission mechanism for most radio bursts, the electron-cyclotron maser (ECM) mechanism may be responsible for more complex, short-duration bursts as well as fine structures associated with long-duration bursts. Aims. We investigate the conditions for ECM in the solar corona by considering the ratio of the electron plasma frequency {\omega}p to the electron-cyclotron frequency {\Omega}e. The ECM is theoretically possible when {\omega}p/{\Omega}e < 1. Methods. Two-dimensional electron density, magnetic field, plasma frequency, and electron cyclotron frequency maps of the off- limb corona were created using observations from SDO/AIA and SOHO/LASCO, together with potential field extrapolations of the magnetic field. These maps were then used to calculate {\omega}p/{\Omega}e and Alfven velocity maps of the off-limb corona. Results. We found that the condition for ECM emission ({\omega}p/{\Omega}e < 1) is possible at heights < 1.07 R_sun in an active region near the limb; that is, where magnetic field strengths are > 40 G and electron densities are greater than 3x10^8 cm-3. In addition, we found comparatively high Alfv\'en velocities (> 0.02 c or > 6000 km s-1) at heights < 1.07 R_sun within the active region. Conclusions. This demonstrates that the condition for ECM emission is satisfied within areas of the corona containing large magnetic fields, such as the core of a large active region. Therefore, ECM could be a possible emission mechanism for high-frequency radio and microwave bursts.Comment: 4 pages, 3 figure

Magnetic field-induced quantum critical point in YbPtIn and YbPt0.98_{0.98}In single crystals

Detailed anisotropic (H$\parallel$ab and H$\parallel$c) resistivity and specific heat measurements were performed on online-grown YbPtIn and solution-grown YbPt$_{0.98}$In single crystals for temperatures down to 0.4 K, and fields up to 140 kG; H$\parallel$ab Hall resistivity was also measured on the YbPt$_{0.98}$In system for the same temperature and field ranges. All these measurements indicate that the small change in stoichiometry between the two compounds drastically affects their ordering temperatures (T$_{ord}\approx3.4$ K in YbPtIn, and $\sim2.2$ K in YbPt$_{0.98}$In). Furthermore, a field-induced quantum critical point is apparent in each of these heavy fermion systems, with the corresponding critical field values of YbPt$_{0.98}$In (H$^{ab}_c$ around 35-45 kG and H$^{c}_c\approx120$ kG) also reduced compared to the analogous values for YbPtIn (H$^{ab}_c\approx60$ kG and H$^{c}_c>140$ kG

Field-Dependent Hall Effect in Single Crystal Heavy Fermion YbAgGe below 1K

We report the results of a low temperature (T >= 50 mK) and high field (H <= 180 kOe) study of the Hall resistivity in single crystals of YbAgGe, a heavy fermion compound that demonstrates field-induced non-Fermi-liquid behavior near its field-induced quantum critical point. Distinct features in the anisotropic, field-dependent Hall resistivity sharpen on cooling down and at the base temperature are close to the respective critical fields for the field-induced quantum critical point. The field range of the non-Fermi-liquid region decreases on cooling but remains finite at the base temperature with no indication of its conversion to a point for T -> 0. At the base temperature, the functional form of the field-dependent Hall coefficient is field direction dependent and complex beyond existing simple models thus reflecting the multi-component Fermi surface of the material and its non-trivial modification at the quantum critical point

Angular dependent planar metamagnetism in the hexagonal compounds TbPtIn and TmAgGe

Detailed magnetization measurements, M(T,H,theta), were performed on single crystals of TbPtIn and TmAgGe (both members of the hexagonal Fe_2P/ZrNiAl structure type), for the magnetic field H applied perpendicular to the crystallographic c axis. These data allowed us to identify, for each compound, the easy-axes for the magnetization, which coincided with high symmetry directions ([120] for TbPtIn and [110] for TmAgGe). For fixed orientations of the field along each of the two six-fold symmetry axes, a number of magnetically ordered phases is being revealed by M(H,T) measurements below T_N. Moreover, T ~ 2 K, M(H)|_theta measurements for both compounds (with H applied parallel to the basal plane), as well as T = 20 K data for TbPtIn, reveal five metamagnetic transitions with simple angular dependencies: H_{ci,j} ~ 1/cos(theta +/- phi), where phi = 0^0 or 60^0. The high field magnetization state varies with theta like 2/3*mu_{sat}(R^{3+})*cos(theta), and corresponds to a crystal field limited saturated paramagnetic, CL-SPM, state. Analysis of these data allowed us to model the angular dependence of the locally saturated magnetizations M_{sat} and critical fields H_c with a three coplanar Ising-like model, in which the magnetic moments are assumed to be parallel to three adjacent easy axes. Furthermore, net distributions of moments were inferred based on the measured data and the proposed model

Conditional Hardness of Earth Mover Distance

The Earth Mover Distance (EMD) between two sets of points A, B subseteq R^d with |A| = |B| is the minimum total Euclidean distance of any perfect matching between A and B. One of its generalizations is asymmetric EMD, which is the minimum total Euclidean distance of any matching of size |A| between sets of points A,B subseteq R^d with |A| <= |B|. The problems of computing EMD and asymmetric EMD are well-studied and have many applications in computer science, some of which also ask for the EMD-optimal matching itself. Unfortunately, all known algorithms require at least quadratic time to compute EMD exactly. Approximation algorithms with nearly linear time complexity in n are known (even for finding approximately optimal matchings), but suffer from exponential dependence on the dimension. In this paper we show that significant improvements in exact and approximate algorithms for EMD would contradict conjectures in fine-grained complexity. In particular, we prove the following results: - Under the Orthogonal Vectors Conjecture, there is some c>0 such that EMD in Omega(c^{log^* n}) dimensions cannot be computed in truly subquadratic time. - Under the Hitting Set Conjecture, for every delta>0, no truly subquadratic time algorithm can find a (1 + 1/n^delta)-approximate EMD matching in omega(log n) dimensions. - Under the Hitting Set Conjecture, for every eta = 1/omega(log n), no truly subquadratic time algorithm can find a (1 + eta)-approximate asymmetric EMD matching in omega(log n) dimensions