ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a new approach for predicting stable equilibrium shapes of crystalline islands on flat substrates, as commonly occur through solid-state dewetting of thin films. The new theory is a generalization of the widely used Winterbottom construction i.e., an extension of the Wulff construction for particles on substrates). This approach is equally applicable to cases where the crystal surface energy is isotropic, weakly anisotropic, strongly anisotropic and "cusped". We demonstrate that, unlike in the classical Winterbottom approach, multiple equilibrium island shapes may be possible when the surface energy is strongly anisotropic. We analyze these shapes through perturbation analysis, by calculating the first and second variations of the total free energy functional with respect to contact locations and island shape. Based on this analysis, we find the necessary conditions for stable equilibria and exploit this through a generalization of the Winterbottom construction to identify all possible stable equilibrium shapes. Finally, we propose a dynamical evolution method based on surface diffusion mass transport to determine whether all of the stable equilibrium shapes are dynamically accessible. Applying this approach, we demonstrate that islands with different initial shapes may evolve into different stationary shapes and show that these dynamically-determined stationary states correspond to the predicted stable equilibrium shapes, as obtained from the generalized Winterbottom construction.
We report a theoretical investigation on the conductance and its fluctuation of three-dimensional topological insulators (3D TI) in $Bi_2Se_3$ and $Sb_2Te_3$ in the presence of disorders. Extensive numerical simulations are carried out. We find that in the diffusive regime the conductance is quantized with fractional value. Importantly, the conductance fluctuation is also quantized with a universal value. For 3D TI connected by two terminals, three independent conductances $G_{zz}$, $G_{xx}$ and $G_{zx}$ are identified where z is the normal direction of quintuple layer of 3D TI (see inset of Fig.1). The quantized conductance are found to be $<G_{zz}>=1$, $<G_{xx}>=4/3$ and $<G_{zx}>=6/5$ with corresponding quantized conductance fluctuation 0.54, 0.47, and 0.50. The quantization of average conductance and its fluctuation can be understood by theory of mode mixing. The experimental realization that can observe the quantization of average conductance is discussed.
We provide a new construction of $[n,9,n-9]_q$ near-MDS codes arising from elliptic curves with $n$ ${\mathbb F}_q$-rational points. Furthermore we show that in some cases these codes cannot be extended to longer near-MDS codes.
Stellar companion of a black hole orbiting in an eccentric orbit will experience modulating tidal force with a periodicity same as that of the orbital period. This, in turn, would modulate accretion rates, and the seed photon flux which are inverse Comptonized to produce harder X-rays. By analyzing complete all sky monitor (ASM) data (1.5-12 keV) of RXTE and all sky survey data (15-50 keV) of Swift/BAT we discover this periodicity in several objects. We also estimate eccentricities from the RMS power of the peak around quasi-orbital periods (QOP). Our method provides an independent way to obtain time periods and eccentricities of such compact binaries.
We present the detection of a rare case of dramatic strengthening in the UV absorption profiles in the spectrum of the quasar J115122.14+020426.3 between observations ~2.86 years apart in the quasar rest-frame. A 2001 spectrum from the Sloan Digital Sky Survey (SDSS) shows a CIV "mini-broad" absorption line (FWHM=1,220 km/s) with a maximum blueshift velocity ~9,520 km/s, while a later spectrum from the Very Large Telescope (VLT) shows significantly broader and stronger absorption line, with a maximum blueshift velocity of ~12,240 km/s, that qualifies as a broad absorption line. A similar variability pattern is observed in two additional systems at lower blueshifted velocities and in the Lya and NV transitions as well. One of the absorption systems appears to be resolved and shows evidence for partial covering of the quasar continuum source (Cf~0.65), indicating a transverse absorber size of, at least, ~6 x 10^(16) cm. In contrast, a cluster of narrower CIV lines appears to originate in gas that fully covers the continuum and broad emission line sources. There is no evidence for changes in the centroid velocity of the absorption troughs. This case suggests that, at least some of the absorbers that produce "mini-broad" and broad absorption lines in quasar spectra do not belong to intrinsically separate classes. Here, the "mini-broad" absorption line is most likely interpreted as an intermediate phase before the appearance of a broad absorption line due to their similar velocity. While the current observations do not provide enough constraints to discern among the possible causes for this variability, future monitoring of multiple transitions at high resolution will help achieve this goal.
We review the current theoretical situation with regard to the anomalously large cross section for exclusive J/psi + eta_c production in e^+ e^- annihilation, as measured by BELLE Collaboration.
The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph $G$, is denoted by $q(G)$. Using other parameters related to $G$, bounds for $q(G)$ are proven and then applied to deduce further properties of $q(G)$. It is shown that there is a great number of graphs $G$ for which $q(G)=2$. For some families of graphs, such as the join of a graph with itself, complete bipartite graphs, and cycles, this minimum value is obtained. Moreover, examples of graphs $G$ are provided to show that adding and deleting edges or vertices can dramatically change the value of $q(G)$. Finally, the set of graphs $G$ with $q(G)$ near the number of vertices is shown to be a subset of known families of graphs with small maximum multiplicity.
The Jansky Very Large Array was used to observe 121 magnetic cataclysmic variables (MCVs). We report radio detections of 19 stars. Fourteen are new radio sources, increasing the number of MCVs that are radio sources by more than twofold, from 8 to 22. Most detections are at 8.7 GHz (X-band) with a lesser number at 5.4 and 21.1 GHz (C- and K-bands). Most flux density limits are in the range of 47-470 uJy. With the exception of AE Aqr, the maximum flux detected is 818 uJy. Fourteen of the detections show approximately 100% circularly polarized emission, which is characteristic of electron-cyclotron maser emission. The data suggest that MCVs might be divided into two classes of radio emitters: those dominated by weakly polarized gyro-synchrotron emission and those by highly polarized electron-cyclotron maser emission.
Recent developments in solar, reactor, and accelerator neutrino physics are reviewed. Implications for neutrino physics, solar physics, nuclear two-body physics, and r-process nucleosynthesis are briefly discussed.
Density functional theory (DFT) calculations are used to investigate the electronic and magnetic structures of a two-dimensional (2D) monolayer Li$_{2}$N. It is shown that bulk Li$_{3}$N is a non-magnetic semiconductor. The non-spinpolarized DFT calculations show that $p$ electrons of N in 2D Li$_{2}$N form a narrow band at the Fermi energy $E_{\rm{F}}$ due to a low coordination number, and the density of states at the Fermi energy ($g(E_{\rm{F}}$)) is increased as compared with bulk Li$_{3}$N. The large $g(E_{\rm{F}}$) shows instability towards magnetism in Stoner's mean field model. The spin-polarized calculations reveal that 2D Li$_{2}$N is magnetic without intrinsic or impurity defects. The magnetic moment of 1.0\,$\mu_{\rm{B}}$ in 2D Li$_{2}$N is mainly contributed by the $p_{z}$ electrons of N, and the band structure shows half-metallic behavior. {Dynamic instability in planar Li$_{2}$N monolayer is observed, but a buckled Li$_{2}$N monolayer is found to be dynamically stable.} The ferromagnetic (FM) and antiferromagnetic (AFM) coupling between the N atoms is also investigated to access the exchange field strength. {We found that planar (buckled) 2D Li$_{2}$N is a ferromagnetic material with Curie temperature $T_{c}$ of 161 (572) K.}
We report molecular line observations in the CO J=3$\rightarrow$2, 6$\rightarrow$5 and 7$\rightarrow$6 transitions, made using the Atacama Pathfinder Experiment Telescope (APEX), toward the massive and dense core IRAS 16562$-$3959. This core harbors a string of radio sources thought to be powered by a central collimated jet of ionized gas. The molecular observations show the presence of high velocity gas exhibiting a quadrupolar morphology, most likely produced by the presence of two collimated outflows. The southeast-northwest molecular outflow is aligned with the string of radio continuum sources, suggesting it is driven by the jet. We find that the excitation temperature of the gas in the SE-NW outflow is high, with values of 145 and 120 K for the blueshifted and redshifted lobes, respectively. This outflow has a total mass of 1.92 \Msun, a total momentum of $\sim 89$ \Msun \kms and an averaged momentum rate of $\sim 3.0\times10^{-2}$ \Msun \kms yr$^{-1}$, values characteristics of flows driven by young massive stellar objects with high luminosities ($L_{\rm bol} \sim 2\times10^4$ \Lsun). Complementary data taken with the Atacama Submillimeter Telescope Experiment (ASTE) in high density and shock tracers support the picture that IRAS 16562$-$3959 is an accreting young massive star associated with an ionized jet, which is the energy source of a molecular outflow.
The Complete Calibration of the Color-Redshift Relation survey (C3R2) is a spectroscopic programme designed to empirically calibrate the galaxy color-redshift relation to the Euclid depth (I_E=24.5), a key ingredient for the success of Stage IV dark energy projects based on weak lensing cosmology. A spectroscopic calibration sample as representative as possible of the galaxies in the Euclid weak lensing sample is being collected, selecting galaxies from a self-organizing map (SOM) representation of the galaxy color space. Here, we present the results of a near-infrared H- and K-bands spectroscopic campaign carried out using the LUCI instruments at the LBT. For a total of 251 galaxies, we present new highly-reliable redshifts in the 1.3<= z <=1.7 and 2<= z<=2.7 ranges. The newly-determined redshifts populate 49 SOM cells which previously contained no spectroscopic measurements and almost double the occupation numbers of an additional 153 SOM cells. A final optical ground-based observational effort is needed to calibrate the missing cells in particular in the redshift range 1.7<= z<=2.7 that lack spectroscopic calibration. In the end, Euclid itself will deliver telluric-free NIR spectra that can complete the calibration.
We put forward a pressure-parametric model to study the tiny deviation from cosmological constant(CC) behavior of the dark sector accelerating the expansion of the Universe. Data from cosmic microwave background (CMB) anisotropies, baryonic acoustic oscillations (BAO), Type Ia supernovae (SN Ia) observation are applied to constrict the model parameters. The constraint results show that such model suffers with $H_0$ tension as well. To realize this model more physically, we reconstruct it with the quintessence and phantom scalar fields, and find out that although the model predicts a quintessence-induced acceleration of the Universe at past and present, at some moment of the future, dark energy's density have a disposition to increase.
We report on a very bright, long-duration gamma-ray burst (GRB), GRB~220426A, observed by \emph{Fermi} satellite. GRB~220426A with total duration of $T_{90}=6$~s is composed with two main pulses and some sub-peaks. The spectral analysis of this burst with Band function reveals that both the time-integrated and the time-resolved spectra are very narrow with high $\alpha \gtrsim 0.2$ and low $\beta\lesssim -3.1$. It is strong reminiscent of GRB~090902B, a special GRB with identification of the photospheric emission. Then, we perform the spectral analysis of this burst based on a non-dissipated photospheric emission, which can be well modelled as the multicolor-blackbody with a cutoff power-law distribution of the thermal temperature. The spectral fittings reveal that the photospheric emission can well describe the radiation spectrum of this burst. We conclude that this burst would be a second burst in the class of GRB~090902B observed by \emph{Fermi} satellite. We also discuss the physics of photosphere and the origin of the high-energy component in GRB~220426A .
We consider the open string tachyon action in a world-sheet sigma model approach. We present explicit calculations up to order 8 in derivatives for the bosonic string, and mimic these to order 6 for the superstring, including terms with multiple derivatives acting on the tachyon field. We reproduce lower derivative terms obtained elsewhere, and speculate on the role of the world-sheet contact terms regularizing the action for the superstring tachyon.
In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.
We present a five dimensional supersymmetric SO(10) model compactified on an orbifold $S^{(1)}/Z_2\tm Z_2'$. The gauge symmetry $G_{422}\equiv SU(4)_c\tm SU(2)_L\tm SU(2)_R$, realized on one of the fixed points (branes), is spontaneously broken to the MSSM via the higgs mechanism. Employing a flavor ${\cal U}(1)$ symmetry and suitably extending the 'matter' sector enables us to understand large mixings in the neutrino sector via a democratic approach, versus the small CKM mixings. A residual ${\cal R}$-symmetry on $G_{422}$ brane helps eliminate the troublesome dimension five nucleon decay, while the ${\cal U}(1)$ symmetry plays an essential role in suppressing dimension six decay. For rare leptonic decays we expect ${\rm BR}(\mu \to e\ga)\sim {\rm BR}(\tau \to \mu \ga)\sim {\rm BR}(\tau \to e\ga)$.
In this paper, we derive a new computational algorithm for Barrett technique for modular polynomial multiplication, termed BA-P. BA-P is then applied to a new residue arithmetic based Barrett algorithm for modular polynomial multiplication (BA-MPM). The focus of the work is an algorithm that carries out the entire computation using only modular arithmetic without conversion to large degree polynomials. There are several parts to this work. First, we set up a new BA-P using polynomials other than u^alfa. Second, residue arithmetic based BA-MPM is described. A complete mathematical framework is described including proofs of the steps in the computations and the validity of results. Third, we present a computational procedure for BA-MPM. Fourth, the BA-MPM is used as a basis for algorithms for modular polynomial exponentiation (MPE). Applications are in areas of signal security and cryptography.
The three-loop QCD corrections to the $\rho$ parameter from top and bottom quark loops are calculated. The result differs from the one recently calculated by Avdeev et al. As function of the pole mass the numerical value is given by $\drho=\frac{3G_F M_t^2}{8\sqrt{2}\pi^2}(1- 2.8599 \api - 14.594 (\api)^2 )$.
This note is based on the original proof of the shuffle conjecture by Carlsson and Mellit (arXiv:1508.06239, version 2), which seems to be too concise for the combinatorial community. James Haglund spent a semester to check through the proof line by line and took explicit note. Guoce Xin was asked by Adriano Garsia to elaborate the proof. The whole paper is thoroughly checked and filled in with details. Section 1 and the abstract of the original paper is included. Section 2 is rewritten for clarity. Other sections are filled with detailed proof and computation. We hope this note is accessible to graduate students.
In this short note, we give a proof, conditional on the Generalized Riemann Hypothesis, that there exist numbers x which are normal with respect to the continued fraction expansion but not to any base b expansion. This partially answers a question of Bugeaud.
In this paper, we present an attention-guided deformable convolutional network for hand-held multi-frame high dynamic range (HDR) imaging, namely ADNet. This problem comprises two intractable challenges of how to handle saturation and noise properly and how to tackle misalignments caused by object motion or camera jittering. To address the former, we adopt a spatial attention module to adaptively select the most appropriate regions of various exposure low dynamic range (LDR) images for fusion. For the latter one, we propose to align the gamma-corrected images in the feature-level with a Pyramid, Cascading and Deformable (PCD) alignment module. The proposed ADNet shows state-of-the-art performance compared with previous methods, achieving a PSNR-$l$ of 39.4471 and a PSNR-$\mu$ of 37.6359 in NTIRE 2021 Multi-Frame HDR Challenge.
We consider closed free tensionless strings in $AdS_d$, calculate exactly the boundary/boundary string evolution kernel and find the string dynamics to be completely frozen. We interpret therefore the boundary configurations as Wilson loop operators in a confining phase. This is taken as an argument in favor to the dual weakly coupled abelian gauge theory being that of $(d-4)$-forms in the $(d-1)$ dimensional boundary Minkowski space.
The Talmi-Moshinsky transformation is applied to the strong decay and production of mesons. Amplitudes for conventional mesons are obtained in a simple way and are generalised to encompass the production and decay of hybrid states. The selection rule disfavouring hybrid decay into pairs of identical S-wave mesons has a natural explanation and a new class of selection rules is uncovered with implications for production of the exotic $1^{-+}$ hybrid in $e^+e^-$ experiments, charmonia decays and the lattice.
In this work we introduce Relativistic Quantum Geometry (RQG) on a Modern Kaluza-Klein theory by studying the boundary conditions on a extended Einstein-Hilbert action for a 5D vacuum defined on a 5D (background) Riemannian manifold. We introduce a connection which describes a displacement from the background manifold to the extended one, on which the 5D vacuum Einstein equations with cosmological constant included, describes the dynamics of the scalar field $\sigma$, which is responsible of describing the mentioned displacement and complies with a relativistic quantum algebra that depends on the relativistic observers. In our formalism the extra dimension is considered as space-like, and therefore is a noncompact one. After considering a static foliation on the extra dimension, we obtain the dynamics for the gravitational waves that propagates on a 4D (curved) background, defined on the 4D induced curved Riemannian manifold. Finally, an example, in which we study a pre-inflationary model of the early universe is developed. We obtain some constraints from Planck2018 observations.
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are discussed and it has been shown that the results are consistent with the results of quantum mechanics.
The analysis of the terminating bands has been performed in the relativistic mean field framework. It was shown that nuclear magnetism provides an additional binding to the energies of the specific configuration and this additional binding increases with spin and has its {\it maximum} exactly at the terminating state. This suggests that the terminating states can be an interesting probe of the time-odd mean fields {\it provided that other effects can be reliably isolated.} Unfortunately, a reliable isolation of these effects is not that simple: many terms of the density functional theories contribute into the energies of the terminating states and the deficiencies in the description of those terms affect the result. The recent suggestion \cite{ZSW.05} that the relative energies of the terminating states in the $N \neq Z, A\sim 44$ mass region given by $\Delta E$ {\it provide unique and reliable constraints on time-odd mean fields and the strength of spin-orbit interaction} in density functional theories has been reanalyzed. The current investigation shows that the $\Delta E$ value is affected also by the relative placement of the states with different orbital angular momentum ${\it l}$, namely, the placement of the $d$ (${\it l}=2$) and $f$ (${\it l}=3$) states. This indicates the dependence of the $\Delta E$ value on the properties of the central potential.
We study theoretically two effects related to impurity depinning that are common for 1D Luttinger liquid (LL) and linear-chain CDW conductors. First, we consider the electron transport through a single impurity in a 1D conducting channel and study a new regime of conduction related to LL sliding at voltage above a threshold one. The DC current in this regime is accompanied by oscillations with frequency $f =I/e$. This resembles the CDW depinning in linear-chain conductors, the Josephson effect, and the Coulomb blockade. Second, we found that strong pinning of the LL by impurities leads to a magnetic field dependence of the low-temperature specific heat similar to that observed experimentally in CDW compounds. We interpret this in favor of possibility of formation of the LL in linear-chain compounds.
Recent observations suggest that many old pulsar wind nebulae (PWNe) are bright TeV gamma-ray sources without a strong X-ray counterpart. In this paper, we study the spectral evolution of PWNe taking into account the energy which was injected when they were young for old PWNe. We model the evolution of the magnetic field and solve for the particle distribution inside a uniformly expanding PWN. The model is calibrated by fitting the calculated spectrum to the observations of the Crab Nebula at an age of a thousand years. We find that only a small fraction of the injected energy from the Crab Pulsar goes to the magnetic field, consistent with previous studies. The spectral evolution model of the Crab Nebula shows that the flux ratio of TeV gamma-rays to X-rays increases with time, which implies that old PWNe are faint at X-rays, but not at TeV gamma-rays. The increase of this ratio is primarily because the magnetic field decreases with time and is not because the X-ray emitting particles are cooled more rapidly than the TeV gamma-ray emitting particles. Our spectral evolution model matches the observed rate of the radio flux decrease of the Crab Nebula.