ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the effect of the fast rotation and vertical viscosity on the lifespan of solutions to the three-dimensional primitive equations (also known as the hydrostatic Navier-Stokes equations) with impermeable and stress-free boundary conditions. Firstly, for a short time interval, independent of the rate of rotation $|\Omega|$, we establish the local well-posedness of solutions with initial data that is analytic in the horizontal variables and only $L^2$ in the vertical variable. Moreover, it is shown that the solutions immediately become analytic in all the variables with increasing-in-time (at least linearly) radius of analyticity in the vertical variable for as long as the solutions exist. On the other hand, the radius of analyticity in the horizontal variables might decrease with time, but as long as it remains positive the solution exists. Secondly, with fast rotation, i.e., large $|\Omega|$, we show that the existence time of the solution can be prolonged, with "well-prepared" initial data. Finally, in the case of two spatial dimensions with $\Omega=0$, we establish the global well-posedness provided that the initial data is small enough. The smallness condition on the initial data depends on the vertical viscosity and the initial radius of analyticity in the horizontal variables.
We consider a system of two bosonic modes each subject to the dynamics induced by a thermal Markovian environment and we identify instantaneous, local symplectic controls that minimise the loss of entanglement in the Gaussian regime. By minimising the decrease of the logarithmic negativity at every instant in time, it will be shown that a non-trivial, finite amount of local squeezing helps to counter the effect of decoherence during the evolution. We also determine optimal control routines in the more restrictive scenario where the control operations are applied on only one of the two modes. We find that applying an instantaneous control only at the beginning of the dynamics, i.e. preparing an appropriate initial state, is the optimal strategy for states with symmetric correlations and when the dynamics is the same on both modes. More generally, even in asymmetric cases, the delayed decay of entanglement resulting from the optimal preparation of the initial state with no further action turns out to be always very close to the optimised control where multiple operations are applied during the evolution. Our study extends directly to mono-symmetric systems of any number of modes, i.e. to systems that are invariant under any local permutation of the modes within any one partition, as they are locally equivalent to two-mode systems.
We find that for large enough strange quark mass, $m_s^2/4 \mu \Delta>2/3(1-0.024),$ kaon condensed CFL phase of asymptotically dense 3 flavor quark matter is unstable with respect to spontaneous generation of currents of Nambu Goldstone bosons due to spontaneous breaking of baryon number symmetry and hypercharge symmetry in CFL$K^0$ ground state. The total baryon and hypercharge currents still vanish in the ground state. We find that CFL$K^0$ and the new state are separated by the first order phase transition.
The general sum-connectivity index of a graph $G$ is defined as $\chi_\alpha(G)=\sum\limits_{uv\in E(G)} {(d(u)+d(v))^{\alpha}}$, where $d(v)$ denotes the degree of the vertex $v$ in $G$ and $\alpha$ is a real number. In this paper it is deduced the maximum value for the general sum-connectivity index of $n$-vertex trees for $-1.7036\leq \alpha <0$ and of $n$-vertex unicyclic graphs for $-1\le \alpha <0$ respectively, with fixed maximum degree $\triangle $. The corresponding extremal graphs, as well as the $n$-vertex unicyclic graphs with the second maximum general sum-connectivity index for $n\ge 4$ are characterized. This extends the corresponding results by Du, Zhou and Trinajsti\' c [arXiv:1210.5043] about sum-connectivity index.
We compute the anomalous two-loop four-point amplitudes in N=4 pure supergravity, using unitarity and the double-copy construction. We also present all terms determined by four-dimensional cuts in two all-multiplicity two-loop anomalous superamplitudes. This result provides the first two-loop n-point gravity amplitude, up to a class of undetermined rational terms, which are absent at four points. We show that a recently proposed finite counterterm cancels these amplitudes to this order. We argue that the counterterm does not spoil the three-loop finiteness of anomalous amplitudes in the N=4 theory.
A new 5D thick brane solution is presented. We conjecture that the deduced thick brane is a plane defect in a bulk gauge condensate.
Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in a linearized sense. The method is implemented as a nonlinear evolution code which satisfies convergence tests in the nonlinear regime and is robustly stable in the weak field regime. A linearized version has been stably matched to a characteristic code to compute the gravitational waveform radiated to infinity.
We study the pullback of the stable and augmented base locus under a finite surjective morphism between normal varieties over a perfect field.
The simplest observables used to probe the interaction of hard partons with a QCD medium in ultrarelativistic heavy ion collisions measure disappearance, such as the nuclear modification factor R_AA. The information content of such observables is however limited. More differential information is obtained from triggered correlation observables where a trigger condition ensures that a hard event has taken place and the correlation of other objects in the event with the trigger contains information about the nature of parton-medium interaction. By construction, triggered correlation observables are conditional probabilities, i.e. they measure events biased by the trigger condition. The presence of this bias makes the interpretation of observables non-intuitive, but at the same time represents an opportunity to design future measurements to selectively probe particular physics. In this work, an overview over the four types of biases occuring in triggered hard correlation observables is given, followed by a study of current jet correlation phenomenology in the light of the preceding discussion.
A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition at the face $x=0$ is studied with the aim of finding explicit solutions. It is not a standard heat conduction problem because a heat source $-\Phi(x)F(V(t),t)$ is considered, where $V$ represents the heat flux at $x=0$. Explicit solutions independents of the space or temporal variables are given. Solutions with separated variables when the data functions are defined from the solution $X=X(x)$ of a linear initial value problem of second order and the solution $T=T(t)$ of a non-linear (in general) initial value problem of first order which involves the function $F$, are also given and explicit solutions corresponding to different definitions of $F$ are obtained. A solution by an integral representation depending on the heat flux at $x=0$ for the case in which $F=F(V,t)=\nu V$, $\nu>0$, is obtained and explicit expressions for the heat flux at $x=0$ and for its corresponding solution are calculated when $h=h(x)$ is a potential function and $\Phi=\Phi(x)$ is given by $\Phi(x)=\lambda x$, $\Phi(x)=-\mu\sinh{(\lambda x)}$ or $\Phi(x)=-\mu\sin{(\lambda x)}$, $\lambda>0$ and $\mu>0$. The limit when the temporal variable $t$ tends to $+\infty$ of each explicit solution obtained in this paper is studied and the "controlling" effects of the source term $-\Phi F$ are analysed by comparing the asymptotic behavior of each solution with the asymptotic behavior of the solution to the same problem but in absence of source term. Finally, a relationship between this problem with another non-classical initial and boundary value problem for the heat equation is established and explicit solutions for this second problem are also obtained.
In recent years, several Radio-Loud Narrow-Line Seyfert 1 galaxies (RL-NLS1) possessing relativistic jets have come into attention with their detections in Very Large Baseline Array (VLBA) and in $\gamma$-ray observations. In this paper we attempt to understand the nature of radio-jets in NLS1s by examining the kpc-scale radio properties of, hitherto, the largest sample of 11101 optically-selected NLS1s. Using 1.4 GHz FIRST, 1.4 GHz NVSS, 327 MHz WENNS, and 150 MHz TGSS catalogues we find the radio-detection of merely $\sim$ 4.5 per cent (498/11101) NLS1s, with majority (407/498 $\sim$ 81.7 per cent) of them being RL-NLS1s. Our study yields the highest number of RL-NLS1s and it can only be a lower limit. We find that the most of our radio-detected NLS1s are compact ($<$ 30 kpc), exhibit both flat as well as steep radio spectra, and are distributed across a wide range of 1.4 GHz radio luminosities (10$^{22}$ $-$ 10$^{27}$ W Hz$^{-1}$). At the high end of radio luminosity our NLS1s often tend to show blazar-like properties such as compact radio-size, flat/inverted radio spectrum, radio variability and polarization. The diagnostic plots based on the mid-IR colours suggest that the radio emission in NLS1s is mostly powered by AGN, while nuclear star-formation may have a significant contribution in NLS1s of low radio luminosities. The radio luminosity versus radio-size plot infers that the radio-jets in NLS1s are either in the early evolutionary phase or possibly remain confined within the nuclear region due to low-power or intermittent AGN activity.
The rotation of horizontal branch stars places important constraints on angular momentum evolution in evolved stars and therefore rotational mixing on the giant branch. Prompted by new observations of rotation rates of horizontal branch stars, we calculate simple models for the angular momentum evolution of a globular cluster giant star from the base of the giant branch to the star's appearance on the horizontal branch. We include mass loss, and infer the accompanied loss of angular momentum for each of four assumptions about the internal angular momentum profile. These models are compared to observations of horizontal branch rotation rates in M13. We find that rapid rotation on the horizontal branch can be reconciled with slow solid body main sequence rotation if giant branch stars have differential rotation in their convective envelopes and a rapidly rotating core, which is then followed by a redistribution of angular momentum on the horizontal branch. We discuss the physical reasons why these very different properties relative to the solar case may exist in giants. Rapid rotation in the core of the main sequence precursors of the rapidly rotating horizontal branch star, or an angular momentum source on the giant branch is required for all cases if the rotational velocity of turnoff stars is less than 4 km s$^{-1}$. We suggest that the observed range in rotation rates on the horizontal branch is caused by internal angular momentum redistribution which occurs on a timescale comparable to the evolution of the stars on the horizontal branch. The apparent lack of rapid horizontal branch rotators hotter than 12 000 K in M13 could be a consequence of gravitational settling, which inhibits internal angular momentum transport. Alternative explanations and observational tests are discussed.
In this paper, electrical and electronic properties of strained mono-layer InTe for two structures, $\alpha$, and $\beta$ phases, is investigated. The band structure is obtained using density functional theory (DFT). The minimum energy and effective mass of the conduction band and second conduction band for different strains are calculated. A FET with using InTe as the channel material is investigated. Voltage-current characteristics of InTe FET is calculated and I$_{ON}$/I$_{OFF}$ ratio is obtained with respect to biaxial strain.
One method to overcome the notorious problem of time in the quantisation of gravity is the identification of a physically preferred time parameter, a promising candidate being so-called `York time'. The dynamical equations for matter and spatial geometry in York time may be obtained via Hamiltonian reduction, that is, by solving the Hamiltonian constraint for the physical, non-vanishing Hamiltonian density identified as the variable conjugate to the chosen time parameter. Yet in general this equation cannot be solved algebraically. Here we show how in a cosmological scenario, where one may treat geometric and matter inhomogeneities as small perturbations, one is able to obtain the physical Hamiltonian density by solving the constraint equation perturbatively. By construction the Hamiltonian density is quadratic in the perturbation variables, which makes it easily quantisable, although subtleties arise due to the non-canonical form of the Poisson brackets and the time-dependent coefficients. The latter are determined by the evolution of the background variables.
We study the diffraction of atoms and weakly-bound three-atomic molecules from a transmission grating at non-normal incidence. Due to the thickness of the grating bars the slits are partially shadowed. Therefore, the projected slit width decreases more strongly with the angle of incidence than the projected period, increasing, in principle, the experimental resolution. The shadowing, however, requires a revision of the theory of atom diffraction. We derive an expression in the style of the Kirchhoff integral of optics and show that the diffraction pattern exhibits a characteristic asymmetry which must be accounted for when comparing with experimental data. We then analyze the diffraction of weakly bound trimers and show that their finite size manifests itself in a further reduction of the slit width by (3/4)<r> where <r> is the average bond length. The improved resolution at non-normal incidence may in particular allow to discern, by means of their bond lengths, between the small ground state of the helium trimer (<r>=1 nm, Barletta and Kievsky, Phys. Rev. A 64, 042514 (2001)) and its predicted Efimov-type excited state (<r>=8 nm, ibid.), and in this way to experimentally prove the existence of this long-sought Efimov state.
Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the application of nontrivial logical gate operations to the encoded qubits. Here, we present examples of such operations by implementing, in addition to the identity operation, the NOT and the Hadamard gate to a logical qubit encoded in a five qubit system that allows correction of arbitrary single qubit errors. We perform quantum process tomography of the encoded gate operations, demonstrate the successful correction of all possible single qubit errors and measure the fidelity of the encoded logical gate operations.
In recent years, the task of segmenting foreground objects from background in a video, i.e. video object segmentation (VOS), has received considerable attention. In this paper, we propose a single end-to-end trainable deep neural network, convolutional gated recurrent Mask-RCNN, for tackling the semi-supervised VOS task. We take advantage of both the instance segmentation network (Mask-RCNN) and the visual memory module (Conv-GRU) to tackle the VOS task. The instance segmentation network predicts masks for instances, while the visual memory module learns to selectively propagate information for multiple instances simultaneously, which handles the appearance change, the variation of scale and pose and the occlusions between objects. After offline and online training under purely instance segmentation losses, our approach is able to achieve satisfactory results without any post-processing or synthetic video data augmentation. Experimental results on DAVIS 2016 dataset and DAVIS 2017 dataset have demonstrated the effectiveness of our method for video object segmentation task.
Mancala is a generic name for a family of sowing games that are popular all over the world. There are many two-player mancala games in which a player may move again if their move ends in their own store. In this work, we study a simple solitaire mancala game called Tchoukaillon that facilitates the analysis of "sweep" moves, in which all of the stones on a portion of the board can be collected into the store. We include a self-contained account of prior research on Tchoukaillon, as well as a new description of all winning Tchoukaillon boards with a given length. We also prove an analogue of the Chinese Remainder Theorem for Tchoukaillon boards, and give an algorithm to reconstruct a complete winning Tchoukaillon board from partial information. Finally, we propose a graph-theoretic generalization of Tchoukaillon for further study.
Organic thermoelectric (TE) materials create a brand new perspective to search for high-efficiency TE materials, due to their small thermal conductivity. The overlap of pz orbitals, commonly existing in organic {\pi}-stacking semiconductors, can potentially result in high electronic mobility comparable to inorganic electronics. Here we propose a strategy to utilize the overlap of pz orbitals to increase the TE efficiency of layered polymeric carbon nitride (PCN). Through first-principles calculations and classical molecular dynamics simulations, we find that A-A stacked PCN has unexpectedly high cross-plane ZT up to 0.52 at 300 K, which can contribute to n-type TE groups. The high ZT originates from its one-dimensional charge transport and small thermal conductivity. The thermal contribution of the overlap of pz orbitals is investigated, which noticeably enhances the thermal transport when compared with the thermal conductivity without considering the overlap effect. For a better understanding of its TE advantages, we find that the low-dimensional charge transport results from strong pz-overlap interactions and the in-plane electronic confinement, by comparing {\pi}-stacking carbon nitride derivatives and graphite. This study can provide a guidance to search for high cross-plane TE performance in layered materials.
The theory for the formation of the first population of stars (Pop III) predicts a IMF composed predominantly of high-mass stars, in contrast to the present-day IMF, which tends to yield stars with masses less than 1 M_Solar. The leading theory for the transition in the characteristic stellar mass predicts that the cause is the extra cooling provided by increasing metallicity and in particular the cooling provided at high densities by dust. The aim of this work is to test whether dust cooling can lead to fragmentation and be responsible for this transition. To investigate this, we make use of high-resolution hydrodynamic simulations. We follow the thermodynamic evolution of the gas by solving the full thermal energy equation, and also track the evolution of the dust temperature and the chemical evolution of the gas. We model clouds with different metallicities, and determine the properties of the cloud at the point at which it undergoes gravitational fragmentation. We follow the further collapse to scales of an AU when we replace very dense, gravitationally bound, and collapsing regions by a simple and nongaseous object, a sink particle. Our results suggest that for metallicities as small as 10^{-5}Z_Solar, dust cooling produces low-mass fragments and hence can potentially enable the formation of low mass stars. We conclude that dust cooling affects the fragmentation of low-metallicity gas clouds and plays an important role in shaping the stellar IMF even at these very low metallicities. We find that the characteristic fragment mass increases with decreasing metallicity, but find no evidence for a sudden transition in the behaviour of the IMF within the range of metallicites examined in our present study.
The primary star in the young stellar object (YSO) binary CO Ori displays UX Ori-type variability: irregular, high amplitude optical and near-infrared photometric fluctuations where flux minima coincide with polarization maxima. This is attributed to changes in local opacity. In CO Ori A, these variations exhibit a 12.4 yr cycle. Here, we investigate the physical origin of the fluctuating opacity and its periodicity using interferometric observations of CO Ori obtained using VLTI/GRAVITY. Continuum K-band circum-primary and circum-secondary emission are marginally spatially resolved for the first time while Br$\gamma$ emission is detected in the spectrum of the secondary. We estimate a spectral type range for CO Ori B of K2-K5 assuming visual extinction, $A_{\rm{V}}=2$ and a distance of 430 pc. From geometric modelling of the continuum visibilities, the circum-primary emission is consistent with a central point source plus a Gaussian component with a full-width-half-maximum of 2.31$\pm$0.04 milliarcseconds (mas), inclined at 30.2$\pm$2.2$^{\circ}$ and with a major axis position angle of 40$\pm$6$^{\circ}$. This inclination is lower than that reported for the discs of other UX Ori-type stars, providing a first indication that the UX Ori phenomena may arise through fluctuations in circumstellar material exterior to a disc, e.g. in a dusty outflow. An additional wide, symmetric Gaussian component is required to fit the visibilities of CO Ori B, signifying a contribution from scattered light. Finally, closure phases of CO Ori A were used to investigate whether the 12.4 yr periodicity is associated with an undetected third component, as has been previously suggested. We rule out any additional companions contributing more than 3.6% to the K-band flux within ~7.3-20 mas of CO Ori A.
Let $C$ be an algebraic curve of genus $g$ and $L$ a line bundle over $C$. Let $\mathcal{MS}_C(n,L)$ and $\mathcal{MO}_C(n,L)$ be the moduli spaces of $L$-valued symplectic and orthogonal bundles respectively, over $C$ of rank $n$. We construct rational curves on these moduli spaces which generalize Hecke curves on the moduli space of vector bundles. As a main result, we show that these Hecke type curves have the minimal degree among the rational curves passing through a general point of the moduli spaces. As its byproducts, we show the non-abelian Torelli theorem and compute the automorphism group of moduli spaces.
We consider the effect of doping on the magnetic order in quasi one-dimensional (1D) antiferromagnets. First the detailed magnetic response of finite spin-1/2 chains in the presence of a staggered field is determined, which by itself shows an interesting crossover as function of length and field strength. We can then understand the ordering by including an effective coupling between the chains, which results in a Neel ordered phase at low temperatures, but with a broad distribution of magnetic moments that has to be determined self-consistently.
Why are there no fundamental scalar fields actually observed in physics today? Scalars are the simplest fields, but once we go beyond Galilean-Newtonian physics they appear only in speculations, as possible determinants of the gravitational constants in the so-called Scalar-Tensor theories in non-quantum physics, and as Higgs particles, dilatons, etc., in quantum physics. Actually, scalar fields have had a long and controversial life in gravity theories, with a history of deaths and resurrections. This paper presents a brief overview of this history.