ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study discontinuous percolation transitions (PT) in the diffusion-limited cluster aggregation model of the sol-gel transition as an example of real physical systems, in which the number of aggregation events is regarded as the number of bonds occupied in the system. When particles are Brownian, in which cluster velocity depends on cluster size as $v_s \sim s^{\eta}$ with $\eta=-0.5$, a larger cluster has less probability to collide with other clusters because of its smaller mobility. Thus, the cluster is effectively more suppressed in growth of its size. Then the giant cluster size increases drastically by merging those suppressed clusters near the percolation threshold, exhibiting a discontinuous PT. We also study the tricritical behavior by controlling the parameter $\eta$, and the tricritical point is determined by introducing an asymmetric Smoluchowski equation.
Conditional on a strong form of the Goldbach conjecture, we determine all finite connected components of the aliquot graph containing a number less than $10^9$, as well as those containing an amicable pair below $10^{14}$ or one of the known perfect or sociable cycles below $10^{17}$. Along the way we develop a fast algorithm for computing the inverse image of an even number under the sum-of-proper-divisors function.
The disentangling effect of repeated applications of the bit flip channel (I\otimes\sigma_x) on bipartite qubit systems is analyzed. It is found that the rate of loss of entanglement is not uniform over all states. The distillable entanglement of maximally entangled states decreases faster than that of less entangled states. The analysis is also generalized to noise channels of the form n.sigma.
Let $g$ be a primitive holomorphic or Maass newform for $\Gamma_0(D)$. In this paper, by studying the Bessel integrals associated to $g$, we prove an asymptotic Bessel $\delta$-identity associated to $g$. Among other applications, we prove the following hybrid subconvexity bound $$ L\left(1/2+it,g\otimes \chi\right)\ll_{g,\varepsilon} (q(1+|t|))^{\varepsilon}q^{3/8}(1+|t|)^{1/3} $$ for any $\varepsilon>0$, where $\chi \bmod q$ is a primitive Dirichlet character with $(q, D)=1$. This improves the previous known result.
I discuss two aspects of top-quark physics: V_tb and the top-quark mass. The similarities and differences with bottom and charm physics are emphasized.
Intermediate and high velocity HI clouds rain onto the plane of our Galaxy. They are observed at heights of between 500 and 1500 pc, falling onto the Galactic plane at velocities from 50 to 140 km s$^{-1}$. To explain the origin of these clouds, we present a galactic fountain model, driven by the wind from a super stellar cluster (SSC). We solve the equations for a steady, radiative de Laval nozzle flow. We consider two effects not considered previously in astrophysical nozzle flow models: cooling functions for different metallicities, and the direct action of the galactic gravitational field on the gas flowing along the nozzle. For an adiabatic nozzle flow, the gravity acting directly on the gas within the nozzle "stalls" the nozzle flow for initial wind velocities lower than the escape velocity from the Galaxy. For the same wind velocity, a radiative nozzle flow stalls at lower altitudes above the galactic plane. We find that SSC winds with velocities of $v_w=500 - 800$ km s$^{-1}$ produce nozzles stall at heights of $x_m=1 - 15$ kpc. The stalled nozzle flow then rains back onto the galactic plane at velocities in the range observed in intermediate and high velocity HI clouds. We study a nozzle flow driven by a wind from a SSC close to the Galactic centre. We find that for velocities within the range expected for a SSC wind, we can produce nozzle flows that stall above the galactic plane. These stalled flows produce cool, infalling clouds with velocities similar to those of intermediate and high velocity HI clouds.
Graphene epoxide, with oxygen atoms lining up on pristine graphene sheets, is investigated theoretically in this Letter. Two distinct phases: metastable clamped and unzipped structures are unveiled in consistence with experiments. In the stable (unzipped) phase, epoxy group breaks underneath sp2 bond and modifies the mechanical and electronic properties of graphene remarkably. The foldable epoxy ring structure reduces its Young's modulus by 42.4%, while leaves the tensile strength almost unchanged. Epoxidation also perturbs the pi state and opens semiconducting gap for both phases, with dependence on the density of epoxidation. In the unzipped structures, localized states revealed near the Fermi level resembles the edge states in graphene nanoribbons. The study reported here paves the way for oxidation-based functionalization of graphene-related materials.
We present Monte Carlo simulations on a lattice system that displays a first order phase transition between a disordered phase (liquid) and an ordered phase (crystal). The model is augmented by an interaction that simulates the effect of elasticity in continuum models. The temperature range of stability of the liquid phase is strongly increased in the presence of the elastic interaction. We discuss the consequences of this result for the existence of a kinetic spinodal in real systems.
We introduce a class of exactly solvable SO(n) symmetric Hamiltonians with matrix product ground states. For an odd $n\geq 3$ case, the ground state is a translational invariant Haldane gap spin liquid state; while for an even $n\geq 4$ case, the ground state is a spontaneously dimerized state with twofold degeneracy. In the matrix product ground states for both cases, we identify a hidden antiferromagnetic order, which is characterized by nonlocal string order parameters. The ground-state phase diagram of a generalized SO(n) symmetric bilinear-biquadratic model is discussed.
We propose a new systematic method of studying correlations between parameters that describe an astronomical (or any) physical system. We recall that behind Dimensionless scaling laws in complex, self-interacting physical objects lies a rigorous theorem of Dimensional analysis, known widely as the Buckingham theorem. Once a {\it catalogue} of properties and forces that define an object or physical system is established, the theorem allows one to select a complete set of Dimensionless quantities or {\it Numbers} on which structure must depend. The internal structure takes the form of a functionally defined manifold in the space of these Numbers. Simple and familiar examples are discussed by way of introduction. Correlations in properties of astronomical objects can be sought either through the constancy of these Numbers or between pairs of the Numbers. In either case, within errors, the functional dependences take on an absolute numerical character. As our principal application, we study a well defined sample of galaxies in order to reveal the implied Tully Fisher and Baryonic Tully Fisher relations. We find that $L\,\propto\,v_{rot}^4$ for the former and $M_b\,\propto\,v_{rot}^3$ for the latter, suggesting that these relations may have different causal origins.
About one third of the 3033 $\gamma$-ray sources in the Third Fermi-LAT Gamma-ray Source Catalogue (3FGL) are unidentified and do not have even a tentative association with a known object, hence they are defined as unassociated. Among Galactic $\gamma$-ray sources, pulsars represent the largest class, with over 200 identifications to date. About one third of them are milli-second pulsars (MSPs) in binary systems. Therefore, it is plausible that a sizeable fraction of the unassociated Galactic $\gamma$-ray sources belong to this class. We collected X-ray and optical observations of the fields of twelve unassociated Fermi sources that have been classified as likely MSPs according to statistical classification techniques. To find observational support for the proposed classification, we looked for periodic modulations of the X-ray and optical flux of these sources, which could be associated with the orbital period of a MSP in a tight binary system. Four of the observed sources were identified as binary MSPs, or proposed as high-confidence candidates, while this work was in progress. For these sources, we present the results of our follow-up investigations, whereas for the others we present possible evidence of new MSP identifications. In particular, we discuss the case of 3FGL J0744.1-2523 that we proposed as a possible binary MSP based upon the preliminary detection of a 0.115 d periodicity in the flux of its candidate optical counterpart. We also found very marginal evidence of periodicity in the candidate optical counterpart to 3FGL J0802.3-5610, at a period of 0.4159 d, which needs to be confirmed by further observations.
Tissot indicatrices have provided visual measures of local area and isotropy distortions. Here we show how large scale distortions of flexion (bending) and skewness (lopsidedness) can be measured. Area and isotropy distortions depend on the map projection metric, flexion and skewness, which manifest themselves on continental scales, depend on the first derivatives of the metric. We introduce new indicatrices that show not only area and isotropy distortions but flexion and skewness as well. We present a table showing error measures for area, isotropy, flexion, skewness, distances, and boundary cuts allowing us to compare different world map projections. We find that the Winkel-Tripel projection (already adopted for world maps by the National Geographic), has low distortion on most measures and excellent quality overall.
A celebrated conjecture of Zs. Tuza says that in any (finite) graph, the minimum size of a cover of triangles by edges is at most twice the maximum size of a set of edge-disjoint triangles. Resolving a recent question of Bennett, Dudek, and Zerbib, we show that this is true for random graphs; more precisely:   \[ \mbox{for any $p=p(n)$, $\mathbb P(\mbox{$G_{n,p}$ satisfies Tuza's Conjecture})\rightarrow 1 $ (as $n\rightarrow\infty$).} \]
We consider a freely movable solid that separates a long tube into two regions, each of which is filled with a dilute gas. The gases in each region are initially prepared at the same pressure but different temperatures. Under the assumption that the pressure and temperatures of gas particles before colliding with the solid are kept constant over time, we show that temperature gaps appearing on the solid surface generate a force. We provide a quantitative estimation of the force, which turns out to be large enough to be observed by a macroscopic measurement.
In this paper a family of non-singular cylindrical perfect fluid cosmologies is derived. The equation of state corresponds to a stiff fluid. The family depends on two independent functions under very simple conditions. A sufficient condition for geodesic completeness is provided.
Spatially homogeneous cosmological models reduce to Hamiltonian systems in a low dimensional Minkowskian space moving on the total energy shell $H=0$. Close to the initial singularity some models (those of Bianchi type VIII and IX) can be reduced further, in a certain approximation, to a non-compact triangular billiard on a 2-dimensional space of constant negative curvature with a separately conserved positive kinetic energy. This type of billiard has long been known as a prototype chaotic dynamical system. These facts are reviewed here together with some recent results on the energy level statistics of the quantized billiard and with direct explicit semi-classical solutions of the Hamiltonian cosmological model to which the billiard is an approximation. In the case of Bianchi type IX models the latter solutions correspond to the special boundary conditions of a `no-boundary state' as proposed by Hartle and Hawking and of a `wormhole' state.
Conventional unsupervised domain adaptation (UDA) studies the knowledge transfer between a limited number of domains. This neglects the more practical scenario where data are distributed in numerous different domains in the real world. The domain similarity between those domains is critical for domain adaptation performance. To describe and learn relations between different domains, we propose a novel Domain2Vec model to provide vectorial representations of visual domains based on joint learning of feature disentanglement and Gram matrix. To evaluate the effectiveness of our Domain2Vec model, we create two large-scale cross-domain benchmarks. The first one is TinyDA, which contains 54 domains and about one million MNIST-style images. The second benchmark is DomainBank, which is collected from 56 existing vision datasets. We demonstrate that our embedding is capable of predicting domain similarities that match our intuition about visual relations between different domains. Extensive experiments are conducted to demonstrate the power of our new datasets in benchmarking state-of-the-art multi-source domain adaptation methods, as well as the advantage of our proposed model.
In this work we prove that the initial value problem (IVP) associated to the two-dimensional Benjamin-Ono equation $$\left. \begin{array}{rl} u_t+\mathcal H \Delta u +uu_x &\hspace{-2mm}=0,\qquad\qquad (x,y)\in\mathbb T^2,\; t\in\mathbb R,\\ u(x,y,0)&\hspace{-2mm}=u_0(x,y), \end{array} \right\}\,,$$ where $\mathcal H$ denotes the Hilbert transform with respect to the variable $x$ and $\Delta$ is the Laplacian with respect to the spatial variables $x$ and $y$, is locally well-posed in the periodic Sobolev space $H^s(\mathbb T^2)$, with $s>7/4$.
We investigate methods to estimate the parameters of the gravitational-wave signal from a spinning neutron star using Fourier transformed segments of the strain response from an interferometric detector. Estimating the parameters from the power, we find generalizations of the PowerFlux method. Using simulated elliptically polarized signals injected into Gaussian noise, we apply the generalized methods to estimate the squared amplitudes of the plus and cross polarizations (and, in the most general case, the polarization angle), and test the relative detection efficiencies of the various methods.
V371 Per was found to be a double-mode Cepheid with a fundamental mode period of 1.738 days, the shortest among Galactic beat Cepheids, and an unusually high period ratio of 0.731, while the other Galactic beat Cepheids have period ratios between 0.697 and 0.713. The latter suggests that the star has a metallicity [Fe/H] between -1 and -0.7. The derived distance from the Galactic Plane places it in the Thick Disk or the Halo, while all other Galactic beat Cepheids belong to the Thin Disk. There are indications from historical data that both the fundamental and first overtone periods have lengthened.
We present study of a typical explosive event (EE) at sub-arcsecond scale witnessed by strong non-Gaussian profiles with blue- and red-shifted emission of up to 150 km/s seen in the transition-region Si IV 1402.8 \AA, and the chromospheric Mg II k 2796.4 \AA\ and C II 1334.5 \AA\ observed by the Interface Region Imaging Spectrograph at unprecedented spatial and spectral resolution. For the first time a EE is found to be associated with very small-scale ($\sim$120 km wide) plasma ejection followed by retraction in the chromosphere. These small-scale jets originate from a compact bright-point-like structure of $\sim$1.5" size as seen in the IRIS 1330 \AA\ images. SDO/AIA and SDO/HMI co-observations show that the EE lies in the footpoint of a complex loop-like brightening system. The EE is detected in the higher temperature channels of AIA 171 \AA, 193 \AA\ and 131 \AA\ suggesting that it reaches a higher temperature of log T$=5.36\pm0.06$ (K). Brightenings observed in the AIA channels with durations 90--120 seconds are probably caused by the plasma ejections seen in the chromosphere. The wings of the C II line behave in a similar manner as the Si IV's indicating close formation temperatures, while the Mg II k wings show additional Doppler-shifted emission. Magnetic convergence or emergence followed by cancellation at a rate of $5\times10^{14}$ Mx s$^{-1}$ is associated with the EE region. The combined changes of the locations and the flux of different magnetic patches suggest that magnetic reconnection must have taken place. Our results challenge several theories put forward in the past to explain non-Gaussian line profiles, i.e. EEs. Our case study on its own, however, cannot reject these theories, thus further in-depth studies on the phenomena producing EEs are required.
Bars are common galactic structures in the local universe that play an important role in the secular evolution of galaxies, including the Milky Way. In particular, the velocity distribution of individual stars in our galaxy is useful to shed light on stellar dynamics, and provides information complementary to that inferred from the integrated light of external galaxies. However, since a wide variety of models reproduce the distribution of velocity and the velocity dispersion observed in the Milky Way, we look for signatures of the bar on higher-order moments of the line-of-sight velocity ($V_{los}$) distribution. We make use of two different numerical simulations --one that has developed a bar and one that remains nearly axisymmetric-- to compare them with observations in the latest APOGEE data release (SDSS DR14). This comparison reveals three interesting structures that support the notion that the Milky Way is a barred galaxy. A high skewness region found at positive longitudes constrains the orientation angle of the bar, and is incompatible with the orientation of the bar at $\ell=0^\circ$ proposed in previous studies. We also analyse the $V_{los}$ distributions in three regions, and introduce the Hellinger distance to quantify the differences among them. Our results show a strong non-Gaussian distribution both in the data and in the barred model, confirming the qualitative conclusions drawn from the velocity maps. In contrast to earlier work, we conclude it is possible to infer the presence of the bar from the kurtosis distribution.
We describe procedures for generating all 2-cell embedded simple graphs with up to a fixed number of vertices on a given surface. We also modify these procedures to generate closed 2-cell embeddings and polyhedral embeddings. We give results of computer implementations of these procedures for seven surfaces: the sphere, the torus, the double torus, the projective plane, the Klein bottle, the triple cross surface, and the quadruple cross surface.
The typical two-dimensional semiconductors, group \uppercase\expandafter{\romannumeral3A} chalcogenides, have garnered tremendous interest for their outstanding electronic, mechanical, and chemical properties. However, so far, there have been almost no reports on boron monosulfides (BS) binary material. Here, four two-dimensional BS sheets, namely the $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-BS sheets, are proposed and discussed from $\emph{ab initio}$ calculations. State-of-the-art first-principles calculations reveal all these structures are thermally and dynamically stable, indicating the potential for successful experimental synthesis. Especially, for $\alpha$-BS, it has a calculated exfoliation energy of 0.96 J m$^{-2}$, suggesting the preparation of $\alpha$-BS is feasible by the exfoliation of bulk rhombohedral-BS. Our results show that $\alpha$-, $\beta$-, $\gamma$-BS are semiconductors, whereas $\delta$-BS is a metallic system. Remarkably, our calculations indicate that $\delta$-BS is a superconductor with a large electron-phonon coupling ($\lambda$ = 1.51) leading a high superconducting critical temperature ($T_c$ $\approx $ 21.56 K), which is the first report of intrinsic superconducting property among all two-dimensional group \uppercase\expandafter{\romannumeral3A} chalcogenides. The desired mechanical and electronic properties render the BS sheets as the promising two-dimensional materials for future applications in nanoelectronics.
In the present work we investigate temperature effects on the spinor and scalar effetive QED in the context of Thermo Field Dynamics. Following Weisskopf's zero-point energy method, the problem of charge renormalization is reexamined and high temperature contributions are extracted from the thermal correction for the Lagrangian densities.
Adding a second scalar doublet (eta^+,eta^0) and three neutral singlet fermions N_{1,2,3} to the Standard Model of particle interactions with a new Z_2 symmetry, it has been shown that Re(eta^0) or Im(eta^0) is a good dark-matter candidate and seesaw neutrino masses are generated radiatively. A supersymmetric U(1) gauge extension of this new idea is proposed, which enforces the usual R parity of the Minimal Supersymmetric Standard Model, and allows this new Z_2 symmetry to emerge as a discrete remnant.
We use H$\alpha$ imaging spectroscopy taken via the Swedish 1-m Solar Telescope (SST) to investigate the occurrence of fan-shaped jets at the solar limb. We show evidence for near-simultaneous photospheric reconnection at a sunspot edge leading to the jets appearance, with upward velocities of 30\ks, and extensions up to 8~Mm. The brightening at the base of the jets appears recurrent, with a periodicity matching that of the nearby sunspot penumbra, implying running penumbral waves could be the driver of the jets. The jets' constant extension velocity implies that a driver counteracting solar gravity exists, possibly as a result of the recurrent reconnection erupting material into the chromosphere. These jets also show signatures in higher temperature lines captured from the Solar Dynamics Observatory (SDO), indicating a very hot jet front, leaving behind optically thick cool plasma in its wake.
We calculate the power spectrum of curvature perturbations when the inflaton field is rolling over the top of a local maximum of a potential. We show that the evolution of the field can be decomposed into a late-time attractor, which is identified as the slow roll solution, plus a rapidly decaying non-slow roll solution, corresponding to the field rolling ``up the hill'' to the maximum of the potential. The exponentially decaying transient solution can map to an observationally relevant range of scales because the universe is also expanding exponentially. We consider the two branches separately and we find that they are related through a simple transformation of the slow roll parameter $\eta$ and they predict identical power spectra. We generalize this approach to the case where the inflaton field is described by both branches simultaneously and find that the mode equation can be solved exactly at all times. Even though the slow roll parameter $\eta$ is evolving rapidly during the transition from the transient solution to the late-time attractor solution, the resultant power spectrum is an exact power-law spectrum. Such solutions may be useful for model-building on the string landscape.