arXiv subjects
Publications and source records attributed to Tong Liu.
We determine reductions of 2-dimensional, irreducible, semi-stable, and non-crystalline representations of $\mathrm{Gal}(\overline{\mathbb Q}_p/\mathbb Q_p)$ with Hodge--Tate weights $0 < k-1$ and with $\mathcal L$-invariant whose $p$-adic norm is sufficiently large, depending on $k$. Our main result provides the first systematic examples of the reductions for $k \geq p$.
Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we unveil a different class of mobility edges, dubbed anomalous mobility edges, that separate bands of localized states from bands of critical states in diagonal and off-diagonal quasiperiodic models. We first introduce an exactly solvable quasi-periodic diagonal model and analytically demonstrate the existence of anomalous mobility edges. Moreover, numerical multifractal analysis of the corresponding wave functions confirms the emergence of a finite band of critical states. We then extend the sudy to a quasiperiodic off-diagonal Su-Schrieffer-Heeger model and show numerical evidence of anomalous mobility edges. We finally discuss possible experimental realizations of quasi-periodic models hosting anomalous mobility edges. These results shed new light on the localization and critical properties of low-dimensional systems with aperiodic order.
Reflecting light to a pre-determined non-specular direction is an important ability of metasurfaces, which is the basis for a wide range of applications (e.g., beam steering/splitting and imaging). However, anomalous reflection with 100% efficiency has not been achieved at optical frequencies in conventional metasurfaces, due to losses and/or insufficient nonlocal control of light waves. Here, we propose a new type of all-dielectric quasi-three-dimensional subwavelength structures, consisting of multilayer films and specifically designed meta-gratings, to achieve perfect anomalous reflections at optical frequencies. A complex multiple scattering process was stimulated by effectively coupling different Bloch waves and propagating waves in the proposed meta-system, thus offering the whole meta-system the desired nonlocal control on light waves required to achieve perfect anomalous reflections. Two perfect anomalous reflectors were designed to reflect normally incident 1550 nm light to the 40° and 75° directions with absolute efficiencies higher than 99%, and were subsequently fabricated and experimentally demonstrated to exhibit efficiencies 98% and 88%, respectively. Our results pave the way towards realizing optical meta-devices with desired high efficiencies in realistic applications.
A black hole (BH) hyperaccretion system might be born after the merger of a BH and a neutron star (NS) or a binary NS (BNS). In the case of a high mass accretion rate, the hyperaccretion disk is in a state of neutrino-dominated accretion flow (NDAF) and emits numerous anisotropic MeV neutrinos. Only a small fraction of these neutrinos annihilates in the space outside of the disk and then launch ultrarelativistic jets that break away from the merger ejecta to power gamma-ray bursts. Mergers and their remnants are generally considered sources of gravitational waves (GWs), neutrinos, and kilonovae. Anisotropic neutrino emission and anisotropic high-velocity material outflows from central BH-NDAF systems can also trigger strong GWs and luminous disk-outflow-driven (DOD) kilonovae, respectively. In this paper, the anisotropic multimessenger signals from NDAFs with outflows, including DOD kilonovae, MeV neutrinos, and GWs, are presented. As the results, the typical AB magnitude of the DOD kilonovae is lower than that of AT 2017gfo at the same distance, and it decreases with increasing viewing angles and its anisotropy is not sensitive to the outflow mass distribution but mainly determined by the velocity distribution. Since neutrinos with $\gtrsim 10~\rm MeV$ are mainly produced in the inner region of the disk, they will be dramatically deflected to a large viewing angle by relativity effects. Moreover, the strains of GWs induced by anisotropic neutrinos increase with increasing viewing angles. The accumulation of multimessenger detection of the BH-NS/BNS mergers with different viewing angles might further verify the existence of NDAFs with outflows.
Distinct X-ray plateau and flare phases have been observed in the afterglows of gamma-ray bursts (GRBs), and most of them should be related to central engine activities. In this paper, we collect 174 GRBs with X-ray plateau phases and 106 GRBs with X-ray flares. There are 51 GRBs that overlap in the two selected samples. We analyze the distributions of the proportions of the plateau energy $E_{\rm plateau}$ and the flare energy $E_{\rm flare}$ relative to the isotropic prompt emission energy $E_{\rm γ,iso}$. The results indicate that they well meet the Gaussian distributions and the medians of the logarithmic ratios are $\sim -0.96$ and $-1.39$ in the two cases. Moreover, strong positive correlations between $E_{\rm plateau}$ (or $E_{\rm flare}$) and $E_{\rm γ,iso}$ with slopes of $\sim 0.95$ (or $\sim0.80$) are presented. For the overlapping sample, the slope is $\sim 0.80$. We argue that most of X-ray plateaus and flares might have the same physical origin but appear with different features because of the different circumstances and radiation mechanisms. We also test the applicabilities of two models, i.e., black holes surrounded by fractured hyperaccretion disks and millisecond magnetars, on the origins of X-ray plateaus and flares.
The present work proposes a new formalism for the inner regions of a neutrino-dominated accretion flows (NDAFs) by considering the self-gravity, where the neutrino opacity is high enough to make neutrinos trapped becoming a dominant factor in the transportation of energy and angular momentum over the magneto rotational instability. We investigate the possibility of gravitational instability and fragmentation to model the highly variable structure of the prompt emission in gamma-ray bursts (GRBs). The results lead us to introduce the gravitational instability, in these inner regions, as a source of a new viscosity which is of the same functional form as that of the $β$-prescription of viscosity. Such a consideration brings about fragmentation in the unstable inner disk. In addition, we find the consequent clumpy structure of this area capable to account for the temporal variability of GRB's light curve, especially for the lower choices of the parameter $β$, $\sim 10^{-5}$. Finally, we predict the formation of gravitational waves through the migration of fragments before being tidally disrupted. These waves appear to be detectable via a range of current and future detectors from LIGO to Cosmic Explorer.
SUNNY is an Algorithm Selection (AS) technique originally tailored for Constraint Programming (CP). SUNNY enables to schedule, from a portfolio of solvers, a subset of solvers to be run on a given CP problem. This approach has proved to be effective for CP problems, and its parallel version won many gold medals in the Open category of the MiniZinc Challenge -- the yearly international competition for CP solvers. In 2015, the ASlib benchmarks were released for comparing AS systems coming from disparate fields (e.g., ASP, QBF, and SAT) and SUNNY was extended to deal with generic AS problems. This led to the development of sunny-as2, an algorithm selector based on SUNNY for ASlib scenarios. A preliminary version of sunny-as2 was submitted to the Open Algorithm Selection Challenge (OASC) in 2017, where it turned out to be the best approach for the runtime minimization of decision problems. In this work, we present the technical advancements of sunny-as2, including: (i) wrapper-based feature selection; (ii) a training approach combining feature selection and neighbourhood size configuration; (iii) the application of nested cross-validation. We show how sunny-as2 performance varies depending on the considered AS scenarios, and we discuss its strengths and weaknesses. Finally, we also show how sunny-as2 improves on its preliminary version submitted to OASC.
The central engine of gamma-ray bursts (GRBs) remains an open and forefront topic in the era of multimessenger astrophysics. The X-ray plateaus appear in some GRB afterglows, which are widely considered to originate from the spindown of magnetars. According to the stable magnetar scenario of GRBs, an X-ray plateau and a decay phase as $\sim t^{-2}$ should appear in X-ray afterglows. Meanwhile, the ``normal'' X-ray afterglow is produced by the external shock from GRB fireball. We analyze the Neil Gehrels \emph{Swift} GRB data, then find three gold samples, which have an X-ray plateau and a decay phase as $\sim t^{-2}$ superimposed on the jet-driven normal component. Based on these features of the lightcurves, we argue that the magnetars should be the central engines of these three GRBs. Future joint multimessenger observations might further test this possibility, then which can be beneficial to constrain GRB physics.
Time series forecasting (TSF) is fundamentally required in many real-world applications, such as electricity consumption planning and sales forecasting. In e-commerce, accurate time-series sales forecasting (TSSF) can significantly increase economic benefits. TSSF in e-commerce aims to predict future sales of millions of products. The trend and seasonality of products vary a lot, and the promotion activity heavily influences sales. Besides the above difficulties, we can know some future knowledge in advance except for the historical statistics. Such future knowledge may reflect the influence of the future promotion activity on current sales and help achieve better accuracy. However, most existing TSF methods only predict the future based on historical information. In this work, we make up for the omissions of future knowledge. Except for introducing future knowledge for prediction, we propose Aliformer based on the bidirectional Transformer, which can utilize the historical information, current factor, and future knowledge to predict future sales. Specifically, we design a knowledge-guided self-attention layer that uses known knowledge's consistency to guide the transmission of timing information. And the future-emphasized training strategy is proposed to make the model focus more on the utilization of future knowledge. Extensive experiments on four public benchmark datasets and one proposed large-scale industrial dataset from Tmall demonstrate that Aliformer can perform much better than state-of-the-art TSF methods. Aliformer has been deployed for goods selection on Tmall Industry Tablework, and the dataset will be released upon approval.
Existing system dealing with online complaint provides a final decision without explanations. We propose to analyse the complaint text of internet fraud in a fine-grained manner. Considering the complaint text includes multiple clauses with various functions, we propose to identify the role of each clause and classify them into different types of fraud element. We construct a large labeled dataset originated from a real finance service platform. We build an element identification model on top of BERT and propose additional two modules to utilize the context of complaint text for better element label classification, namely, global context encoder and label refiner. Experimental results show the effectiveness of our model.
We examine the properties of spiral shocks from a steady, adiabatic, non-axisymmetric accretion disk around a compact star in binary. We first time incorporate all the possible influences from binary through adopting the Roche potential and Coriolis forces in the basic conservation equations. In this paper, we assume the spiral shocks to be point-wise self-similar, and the flow is in vertical hydrostatic equilibrium to simplify the study. We also investigate the mass outflow due to the shock compression and apply it to the accreting white dwarf in binary. We find that our model will be beneficial to overcome the ad hoc assumption of optically thick wind generally used in the studies of the progenitor of supernovae Ia.
We consider MCMC algorithms for certain particle systems which include both attractive and repulsive forces, making their convergence analysis challenging. We prove that a version of these algorithms on a bounded state space is uniformly ergodic with an explicit quantitative convergence rate. We also prove that a version on an unbounded state-space is still geometrically ergodic, and then use the method of shift-coupling to obtain an explicit quantitative bound on its convergence rate.
This review paper provides an introduction of Markov chains and their convergence rates which is an important and interesting mathematical topic which also has important applications for very widely used Markov chain Monte Carlo (MCMC) algorithm. We first discuss eigenvalue analysis for Markov chains on finite state spaces. Then, using the coupling construction, we prove two quantitative bounds based on minorization condition and drift conditions, and provide descriptive and intuitive examples to showcase how these theorems can be implemented in practice. This paper is meant to provide a general overview of the subject and spark interest in new Markov chain research areas.
We study a one-dimensional lattice model subject to non-Hermitian quasiperiodic potentials. Firstly, we strictly demonstrate that there exists an interesting dual mapping relation between $|a|<1$ and $|a|>1$ with regard to the potential tuning parameter $a$. The localization property of $|a|<1$ can be directly mapping to that of $|a|>1$, the analytical expression of the mobility edge of $|a|>1$ is therefore obtained through spectral properties of $|a|<1$. More impressive, we prove rigorously that even if the phase $θ\neq 0$ in quasiperiodic potentials, the model becomes non-$\mathcal{PT}$ symmetric, however, there still exists a new type of real-complex transition driven by non-Hermitian disorder, which is a new universality class beyond $\mathcal{PT}$ symmetric class.
A repeating fast radio burst (FRB), FRB 20180916B (hereafter FRB 180916), was reported to have a 16.35-day period. This period might be related to a precession period. In this paper, we investigate two precession models to explain the periodic activity of FRB 180916. In both models, the radio emission of FRB 180916 is produced by a precessing jet. For the first disk-driven jet precession model, an extremely low viscous parameter (i.e., the dimensionless viscosity parameter $α\lesssim 10^{-8}$) is required to explain the precession of FRB 180916, which implies its implausibility. For the second tidal force-driven jet precession model, we consider a compact binary consists of a neutron star/black hole and a white dwarf; the white dwarf fills its Roche lobe and mass transfer occurs. Due to the misalignment between the disk and orbital plane, the tidal force of the white dwarf can drive jet precession. We show that the relevant precession periods are several days to hundreds of days, depending on the specific accretion rates and component masses. The duration of FRB 180916 generation in the binary with extremely high accretion rate will be several thousand years.
Fallback in core-collapse supernovae (CCSNe) plays an important role in determining the properties of the central compact remnants, which might produce a black hole (BH) hyperaccretion system in the centre of a massive CCSN. When the accretion rate is extremely high and neutrino cooling is dominant, the hyperaccretion should be in the phase of the neutrino-dominated accretion flows (NDAFs), and thus a large number of anisotropic MeV neutrinos will be launched from the disc along with the strong gravitational waves (GWs). In this paper, we perform a series of one-dimensional CCSN simulations with the initial explosion energy in the range of $2-8$ B (1 B = $10^{51}$ erg) to investigate the fallback processes. By considering the evolution of the central BH mass and spin in the fallback accretion, we present the effects of the initial explosion energies, masses and metallicities of the massive progenitor stars on the spectra of anisotropic MeV neutrinos and the waveform of GWs from NDAFs. These neutrino or GW signals might be detected by operational or future detectors, and the multimessenger joint detections could constrain the properties of CCSNe and progenitor stars.
The China Fusion Engineering Test Reactor (CFETR) and the Huazhong Field Reversed Configuration (HFRC), currently both under intensive physical and engineering designs in China, are the two major projects representative of the low-density steady-state and high-density pulsed pathways to fusion. One of the primary tasks of the physics designs for both CFETR and HFRC is the assessment and analysis of the magnetohydrodynamic (MHD) stability of the proposed design schemes. Comprehensive efforts on the assessment of MHD stability of CFETR and HFRC baseline scenarios have led to preliminary progresses that may further benefit engineering designs.
We compute reduction $\bar ρ$ of 3-dimensional irreducible crystalline representations $ρ$ of $G_{\mathbb Q_p}$ with Hodge-Tate weights $\{0, r , s\}$ satisfying $2 \leq r \leq p-2, \ \ 2+p \leq s \leq r + p-2.$ If $\bar ρ$ is irreducible then we show that the generic fiber of crystalline universal deformation ring of $\bar ρ$ is connected.