Unambiguous evidence of coronal implosions during solar eruptions and flares

In the implosion conjecture, coronal loops contract as the result of magnetic energy release in solar eruptions and flares. However, after almost two decades, observations of this phenomenon are still rare and most previous reports are plagued by projection effects so that loop contraction could be either true implosion or just a change in loop inclination. In this paper, to demonstrate the reality of loop contractions in the global coronal dynamics, we present four events with the continuously contracting loops in an almost edge-on geometry from the perspective of SDO/AIA, which are free from the ambiguity caused by the projection effects, also supplemented by contemporary observations from STEREO for examination. In the wider context of observations, simulations and theories, we argue that the implosion conjecture is valid in interpreting these events. Furthermore, distinct properties of the events allow us to identify two physical categories of implosion. One type demonstrates a rapid contraction at the beginning of the flare impulsive phase, as magnetic free energy is removed rapidly by a filament eruption. The other type, which has no visible eruption, shows a continuous loop shrinkage during the entire flare impulsive phase, which we suggest shows the ongoing conversion of magnetic free energy in a coronal volume. Corresponding scenarios are described that can provide reasonable explanations for the observations. We also point out that implosions may be suppressed in cases when a heavily mass-loaded filament is involved, possibly serving as an alternative account for their observational rarity

Building topological device through emerging robust helical surface states

We propose a nonlocal manipulation method to build topological devices through emerging robust helical surface states in Z_2=0 topological systems. Specifically, in a ribbon of Z_2=0 Bernevig- Hughes-Zhang (BHZ) model with finite-size effect, if magnetic impurities are doped on the top (bottom) edge, the edge states on the bottom (top) edge can be altered according to the strengths and directions of these magnetic impurities. Consequently, the backscattering between the emerging robust helical edge states and gapped normal edge states due to finite-size confinement is also changed, which makes the system alternate between a perfect one-channel conductor and a perfect insulator. This effect allows us to fabricate topological devices with high on-off ratio. Moreover, it can also be generalized to 3D model and more realistic Cd3As2 type Dirac semimetals.Comment: 7 pages, 6 figure

Machine Learning on generalized Complete Intersection Calabi-Yau Manifolds

Generalized Complete Intersection Calabi-Yau Manifold (gCICY) is a new construction of Calabi-Yau manifolds established recently. However, the generation of new gCICYs using standard algebraic method is very laborious. Due to this complexity, the number of gCICYs and their classification still remain unknown. In this paper, we try to make some progress in this direction using neural network. The results showed that our trained models can have a high precision on the existing type $(1,1)$ and type $(2,1)$ gCICYs in the literature. Moreover, They can achieve a $97\%$ precision in predicting new gCICY which is generated differently from those used for training and testing. This shows that machine learning could be an effective method to classify and generate new gCICY.Comment: 20 pages, 4 figure

Cursed yet Satisfied Agents

In real life auctions, a widely observed phenomenon is the winner's curse -- the winner's high bid implies that the winner often over-estimates the value of the good for sale, resulting in an incurred negative utility. The seminal work of Eyster and Rabin [Econometrica'05] introduced a behavioral model aimed to explain this observed anomaly. We term agents who display this bias "cursed agents". We adopt their model in the interdependent value setting, and aim to devise mechanisms that prevent the cursed agents from obtaining negative utility. We design mechanisms that are cursed ex-post IC, that is, incentivize agents to bid their true signal even though they are cursed, while ensuring that the outcome is individually rational -- the price the agents pay is no more than the agents' true value. Since the agents might over-estimate the good's value, such mechanisms might require the seller to make positive transfers to the agents to prevent agents from over-paying. For revenue maximization, we give the optimal deterministic and anonymous mechanism. For welfare maximization, we require ex-post budget balance (EPBB), as positive transfers might lead to negative revenue. We propose a masking operation that takes any deterministic mechanism, and imposes that the seller would not make positive transfers, enforcing EPBB. We show that in typical settings, EPBB implies that the mechanism cannot make any positive transfers, implying that applying the masking operation on the fully efficient mechanism results in a socially optimal EPBB mechanism. This further implies that if the valuation function is the maximum of agents' signals, the optimal EPBB mechanism obtains zero welfare. In contrast, we show that for sum-concave valuations, which include weighted-sum valuations and l_p-norms, the welfare optimal EPBB mechanism obtains half of the optimal welfare as the number of agents grows large

Coronal implosions in solar eruptions and flares

Coronal implosions - the convergence motion of plasmas and entrained magnetic field in the corona due to a reduction in magnetic pressure - can help to locate and track sites of magnetic energy release or redistribution during solar flares and eruptions. Although this conjecture was proposed almost two decades ago, observa- tions of such phenomena are still rare, and even our understanding of it is far from complete. In this thesis, following an introduction to the background and techniques used, we first generalise the implosion idea based on its spirit concerning about the relationship between magnetic energy release and field shrinkage, which allows us to unite and explain three different phenomena, that is, peripheral implosions, inflows and dipolarisations, using only one single principle. Previous observations of apparent contractions in the periphery of active regions are mainly in a face-on state, which cannot exclude the possibilty of field inclining instead of a real contraction as the cause. This then motivates us to study an excellent event observed near the solar disk center, and evidence from both observations and coronal magnetic field extrapolations is found to support the implosion idea. In a unification of three main concepts for active region magnetic evolution implied by the observation, namely the metastable eruption model, the implosion conjecture, and the standard “CSHKP” flare model, the contraction of the field is explained by the removal of the erupting filament originally underneath rather than local magnetic energy dissipation in a flare invoked by previous authors. However, the observation and extrapolation results in the work above are indirect and still not adequate, as the complex structure of the solar atmosphere, and the simplified assumption and preprocessing in the extrapolation may lead us to a wrong conclusion. Thus in the following four carefully seleted events with the continuously contracting loops in an almost edge-on geometry are for the first time investigated, demonstrating the reality of contraction of field lines in the global coronal dynamics unambiguously. Meanwhile, two categories of implosions, flare- and eruption-driven, are identified, which could be interpreted well in the framework of the implosion conjecture, disproving other authors’ proposal. We also revisit one of the original assumptions of the implosion conjecture which may fail when a heavily-mass-loaded filament is involved, and in this case implosions can be suppressed, possibly served as an alternative explanation for their observational rarity. In the end, we move on to one of the generalised implosion types, i.e., the inflow, and also study other reconnection flows associated with it. Intrinsic to the well- accepted reconnection picture of a solar eruptive event, particularly in the standard model for two-ribbon flares (“CSHKP” model), are an advective flow of magnetized plasma into the reconnection region, expansion of field above the reconnection region as a flux rope erupts, retraction of heated post-reconnection loops, and downflows of cooling plasma along those loops. However, the evidence of these flows is still circumstantial and rare. We report in this work on a unique set of SDO/AIA imaging and Hinode/EIS spectroscopic observations of a flare in which all four flows are present simultaneously. This also includes spectroscopic evidence for a plasma upflow at the edge of the active region claimed by previous authors, which we suggest decomposing into two components, one associated with open field at quasi- separatrix layers, the other with large-scale expanding closed arcade field. The reconnection inflows are symmetric, and consistent with fast reconnection, and the post-reconnection loops show a clear cooling and deceleration as they retract. Unlike previous events observed at the solar limb which are obscured by complex foregrounds and thus makes the relationship between the plasma flows, the flare ribbons, cusp field and arcades formed in the lower atmosphere difficult to interpret, the disk location and favorable perspective of this event studied here have removed these ambiguities giving a clear picture of the reconnection dynamics. We end with a brief chapter summarizing the thesis and suggesting some future work

Disorder and metal-insulator transitions in Weyl semimetals

The Weyl semimetal (WSM) is a newly proposed quantum state of matter. It has Weyl nodes in bulk excitations and Fermi arcs surface states. We study the effects of disorder and localization in WSMs and find three exotic phase transitions. (I) Two Weyl nodes near the Brillouin zone boundary can be annihilated pairwise by disorder scattering, resulting in the opening of a topologically nontrivial gap and a transition from a WSM to a three-dimensional (3D) quantum anomalous Hall state. (II) When the two Weyl nodes are well separated in momentum space, the emergent bulk extended states can give rise to a direct transition from a WSM to a 3D diffusive anomalous Hall metal. (III) Two Weyl nodes can emerge near the zone center when an insulating gap closes with increasing disorder, enabling a direct transition from a normal band insulator to a WSM. We determine the phase diagram by numerically computing the localization length and the Hall conductivity, and propose that the exotic phase transitions can be realized on a photonic lattice.Comment: 7 pages with appendix, 6 figure

Finite size effects on hinge states in three-dimensional second-order topological insulators

We investigate the finite size effects of a three-dimensional second-order topological insulator with fourfold rotational symmetry and time-reversal symmetry. Starting from the effective Hamiltonian of the three-dimensional second-order topological insulator, we derive the effective Hamiltonian of four two-dimensional surface states with gaps derived by perturbative methods. Then, the sign alternation of the mass term of the effective Hamiltonian on the adjacent surface leads to the hinge state. In addition, we obtain the effective Hamiltonian and its wave function of one-dimensional gapless hinge states with semi-infinite boundary conditions based on the effective Hamiltonian of two-dimensional surface states. In particular, we find that the hinge states on the two sides of the same surface can couple to produce a finite energy gap