ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the asymptotics of the $k$-regular self-similar fragmentation process. For $\alpha > 0$ and an integer $k \geq 2$, this is the Markov process $(I_t)_{t \geq 0}$ in which each $I_t$ is a union of open subsets of $[0,1)$, and independently each subinterval of $I_t$ of size $u$ breaks into $k$ equally sized pieces at rate $u^\alpha$. Let $k^{ - m_t}$ and $k^{ - M_t}$ be the respective sizes of the largest and smallest fragments in $I_t$. By relating $(I_t)_{t \geq 0}$ to a branching random walk, we find that there exist explicit deterministic functions $g(t)$ and $h(t)$ such that $|m_t - g(t)| \leq 1$ and $|M_t - h(t)| \leq 1$ for all sufficiently large $t$. Furthermore, for each $n$, we study the final time at which fragments of size $k^{-n}$ exist. In particular, by relating our branching random walk to a certain point process, we show that, after suitable rescaling, the laws of these times converge to a Gumbel distribution as $n \to \infty$.
We analyse the phenomenological implications of a light Higgs boson, $h$, within the CP-conserving 2-Higgs Doublet Model (2HDM) Type-I, for the detection prospects of the charged $H^\pm$ state at Run II of the Large Hadron Collider (LHC), assuming $\sqrt{s}=13$ TeV as energy and ${\cal O}(100~{\rm fb}^{-1})$ as luminosity. When sufficiently light, this $h$ state can open up the bosonic decay channel $H^\pm \to W^{\pm(*)}h$, which may have a branching ratio significantly exceeding those of the $H^\pm \to \tau\nu$ and $H^\pm \to cs$ channels. We perform a broad scan of the 2HDM Type-I parameter space, assuming the heavier of the two CP-even Higgs bosons, $H$, to be the observed SM-like state with a mass near 125 GeV. Through these scans we highlight regions in which $m_{H^\pm} < m_t +m_b$ that are still consistent with the most recent limits from experimental searches. We find in these regions that, when the $H^\pm \to W^{\pm(*)}h$ decay mode is the dominant one, the $h$ can be highly fermiophobic, with a considerably large decay rate in the $\gamma\gamma$ channel. This can result in the total cross section of the $\sigma(pp\to H^\pm h \to W^{\pm(*)} + 4\gamma)$ process reaching up to ${\cal O}(100~{\rm fb})$. We therefore investigate the possibility of observing this spectacular signal at the LHC Run II.
Magnetic Towers represent one of two fundamental forms of MHD outflows. Driven by magnetic pressure gradients, these flows have been less well studied than magneto-centrifugally launched jets even though magnetic towers may well be as common. Here we present new results exploring the behavior and evolution of magnetic tower outflows and demonstrate their connection with pulsed power experimental studies and purely hydrodynamic jets which might represent the asymptotic propagation regimes of magneto-centrifugally launched jets. High-resolution AMR MHD simulations (using the AstroBEAR code) provide insights into the underlying physics of magnetic towers and help us constrain models of their propagation. Our simulations have been designed to explore the effects of thermal energy losses and rotation on both tower flows and their hydro counterparts. We find these parameters have significant effects on the stability of magnetic towers, but mild effects on the stability of hydro jets. Current-driven perturbations in the Poynting Flux Dominated (PDF) towers are shown to be amplified in both the cooling and rotating cases. Our studies of the long term evolution of the towers show that the formation of weakly magnetized central jets within the tower are broken up by these instabilities becoming a series of collimated clumps which magnetization properties vary over time. In addition to discussing these results in light of laboratory experiments, we address their relevance to astrophysical observations of young star jets and outflow from highly evolved solar type stars.
It is known from numerical simulations that thermal conduction along magnetic field lines plays an important role in the evolution of the kink instability in coronal loops. This study presents the observational signatures of the kink instability in long coronal loops when parallel thermal conduction is included. The 3D nonlinear magnetohydrodynamic equations are solved numerically to simulate the evolution of a coronal loop that is initially in an unstable equilibrium. The loop has length 80 Mm, width 8 Mm and an initial maximum twist of Phi = 11.5 pi, where Phi is a function of the radius. The initial loop parameters are obtained from a highly twisted loop observed in the TRACE 171 A waveband. Synthetic observables are generated from the data. These observables include spatial and temporal averaging to account for the resolution and exposure times of TRACE images. Parallel thermal conduction reduces the maximum local temperature by up to an order of magnitude. This means that different spectral lines are formed and different internal loop structures are visible with or without the inclusion of thermal conduction. However, the response functions sample a broad range of temperatures. The result is that the inclusion of parallel thermal conductivity does not have as large an impact on observational signatures as the order of magnitude reduction in the maximum temperature would suggest; the net effect is a blurring of internal features of the loop structure.
An open problem about finite geometric progressions in syndetic sets leads to a family of diophantine equations related to the commutativity of translation and multiplication by squares.
Observations of afterglows of gamma-ray bursts suggest (GRBs) that post-shock magnetic fields are strongly amplified to about 100 times the shock-compressed value. The Weibel instability appears to play an important role in generating of the magnetic field. However, recent simulations of collisionless shocks in homogeneous plasmas show that the magnetic field generated by the Weibel instability rapidly decays. There must be some density fluctuations in interstellar and circumstellar media. The density fluctuations are anisotropically compressed in the downstream region of relativistic shocks. In this paper, we study the Weibel instability in electron--positron plasmas with the spatially anisotropic density distributions by means of two-dimensional particle-in-cell simulations. We find that large magnetic fields are maintained for a longer time by the Weibel instability driven by the spatially anisotropic density structure. Particles anisotropically escape from the high density region, so that the temperature anisotropy is generated and the Weibel instability becomes unstable. Our simulation results suggest that the Weibel instability driven by an anisotropic density structure can generate sufficiently large magnetic fields and they can cover sufficiently large regions to explain the afterglow emission of GRBs.
We explore the stellar population of M31 in a Spitzer Space Telescope survey utilizing IRAC and MIPS observations. Red supergiants are the brightest objects seen in the infrared; they are a prominent evolutionary phase. Due to their circumstellar envelopes, many of these radiate the bulk of their luminosity at IRAC wavelengths and do not stand out in the near infrared or optically. Going fainter, we see large numbers of luminous asymptotic giant branch (AGB) stars, many of which are known long period variables. Relative to M33, the AGB carbon star population of M31 appears sparse, but this needs to be spectroscopically confirmed.
We used a combination of optical and near-UV Hubble Space Telescope photometry and FLAMES/ESO-VLT high-resolution spectroscopy to characterize the stellar content of the old and massive globular cluster (GC) NGC121 in the Small Magellanic Cloud (SMC). We report on the detection of multiple stellar populations, the first case in the SMC stellar cluster system. This result enforces the emerging scenario in which the presence of multiple stellar populations is a distinctive-feature of old and massive GCs regardless of the environment, as far as the light element distribution is concerned. We find that second population (SG) stars are more centrally concentrated than first (FG) ones. More interestingly, at odds with what typically observed in Galactic GCs, we find that NGC121 is the only cluster so far to be dominated by FG stars that account for more than 65% of the total cluster mass. In the framework where GCs were born with a 90-95% of FG stars, this observational finding would suggest that either NGC121 experienced a milder stellar mass-loss with respect to Galactic GCs or it formed a smaller fraction of SG stars.
Many different cosmological models have been proposed to address the cosmological constant problem and the coincidence problem. We compare here four different models that can be used to describe an effective (time-dependent) cosmological constant $\Lambda(z)$. A numerical analysis of the $\Lambda(z)$ evolution obtained for each model shows that it can be used for distinguishing between all four models. We calculate next the $\omega(\Lambda)$ frequencies for quasinormal modes of gravitational perturbations of Schwarzschild-de Sitter black holes at different redshifts. Considering that the variation of $\Lambda$ happens on cosmological timescales, the combined $\omega(\Lambda(z))$ could be used in principle to track the evolution of the cosmological constant. We quantify the resulting minute frequency shift in the quasinormal mode frequencies and show that the relative frequency shift grows as $M^2$. However, even in a most optimistic scenario with an extremely high mass supermassive black hole there is no prospect for the detection of this effect.
Wherever one talks of dark matter, one does so where there is an observable matter and an associated unsolved dynamical issue to be settled. We promote this observation to the status of an axiom and conjecture that there is a dark companion to every baryonic matter, subject to certain rules as regards its size, distribution. To pursue the proposition in a systematic way we resort to the rotation curves of spiral galaxies. They have non classical features. First, we design a spacetime metric around the galaxy to accommodate these features. Next we calculate the density and pressure of a hypothetical dark matter that could generate such a spacetime. In the weak field regime and for a spherical distribution of mass $M$, we are able to assign a dark perfect gas companion, whose density is almost proportional to $M^{1/2}$ and fades away almost as $r^{-2}$. However, in view of this orderly relation between the observable mass and its dark companion, one may choose to interpret the whole scenario as an alternative theory of gravitation.
The parameter A+, defined as the area enclosed between the cumulative radial distribution of blue straggler stars (BSSs) and that of a reference population, is a powerful indicator of the level of BSS central segregation. As part of the Hubble Space Telescope UV Legacy Survey of Galactic globular clusters (GCs), here we present the BSS population and the determination of A+ in 27 GCs observed out to about one half-mass radius. In combination with 21 additional clusters discussed in a previous paper this provides us with a global sample of 48 systems (corresponding to \sim 32\% of the Milky Way GC population), for which we find a strong correlation between A+ and the ratio of cluster age to the current central relaxation time. Tight relations have been found also with the core radius and the central luminosity density, which are expected to change with the long-term cluster dynamical evolution. An interesting relation is emerging between A+ and the ratio of the BSS velocity dispersion relative to that of main sequence turn-off stars, which measures the degree of energy equipartition experienced by BSSs in the cluster. These results provide further confirmation that BSSs are invaluable probes of GC internal dynamics and A+ is a powerful dynamical clock.
Employing electrons for direct control of nanoscale reaction is highly desirable since it provides fabrication of nanostructures with different properties at atomic resolution and with flexibility of dimension and location. Here, applying in situ transmission electron microscopy, we show the reversible oxidation and reduction kinetics in Ag, well controlled by changing the dose rate of electron beam. Aberration-corrected high-resolution transmission electron microscopy observation reveals that O atoms are preferably inserted and extracted along the {111} close-packed planes of Ag, leading to the nucleation and decomposition of nanoscale Ag2O islands on the Ag substrate. By controlling electron beam size and dose rate, we demonstrated fabrication of an array of 3 nm Ag2O nanodots in an Ag matrix. Our results open up a new pathway to manipulate atomistic reaction with electron beam towards the precise fabrication of nanostructures for device applications.
The fast evolution and widespread of deepfake techniques in real-world scenarios require stronger generalization abilities of face forgery detectors. Some works capture the features that are unrelated to method-specific artifacts, such as clues of blending boundary, accumulated up-sampling, to strengthen the generalization ability. However, the effectiveness of these methods can be easily corrupted by post-processing operations such as compression. Inspired by transfer learning, neural networks pre-trained on other large-scale face-related tasks may provide useful features for deepfake detection. For example, lip movement has been proved to be a kind of robust and good-transferring highlevel semantic feature, which can be learned from the lipreading task. However, the existing method pre-trains the lip feature extraction model in a supervised manner, which requires plenty of human resources in data annotation and increases the difficulty of obtaining training data. In this paper, we propose a self-supervised transformer based audio-visual contrastive learning method. The proposed method learns mouth motion representations by encouraging the paired video and audio representations to be close while unpaired ones to be diverse. After pre-training with our method, the model will then be partially fine-tuned for deepfake detection task. Extensive experiments show that our self-supervised method performs comparably or even better than the supervised pre-training counterpart.
Recently the small value of the cosmological constant and its ability to accelerate the expansion of the Universe is of great interest. We discuss the possibility of forming of anisotropic compact stars from this cosmological constant as one of the competent candidates of dark energy. For this purpose we consider the analytical solution of Krori and Barua metric. We take the radial dependence of cosmological constant and check all the regularity conditions, TOV equations, stability and surface redshift of the compact stars. It has been shown as conclusion that this model is valid for any compact star and we have cited $4U 1820-30$ as a specific example of that kind of star.
We present results of the spectral and timing analysis of the X-ray pulsar LMC X-4 with the NuSTAR observatory in the broad energy range 3-79 keV. Along with the detailed analysis of the averaged source spectrum, the high-precision pulse phased-resolved spectra were obtained for the first time. It has been shown that the comptonization model gives the best approximation of the obtained spectra. The evolution of its parameters was traced depending on the pulse phase as well. The search for the possible cyclotron absorption line was performed for all energy spectra in the 5-55 keV energy range. The obtained upper limit for the depth of the cyclotron absorption line $\tau\simeq0.15$ ($3\sigma$) indicates no cyclotron absorption line in this energy range, which provides an estimate of the magnitude of the magnetic field on the surface of the neutron star: $B < 3 \times 10^{11}$ G or $B > 6.5 \times 10^{12}$ G. The latter one is agree with the estimate of the magnetic field obtained from the analysis of the power spectrum of the pulsar: $B \sim 3 \times 10^{13}$ G. Based on results of the pulse phase-resolved spectroscopy we revealed a delay between maxima of the source emission and the equivalent width of the fluorescent iron line. This delay can be apparently associated with the travel time of photons between the emitting regions in the vicinity of the neutron star and the relatively cold regions where this emission is reflected (presumably, at the inflowing stream or at the place of an interaction of the stream and the outer edge of the accretion disk).
Changing the morphology of the growing surface and the nature of residual impurities in (Ge,Mn) layers - by using different substrates - dramatically changes the morphology of the ferromagnetic Mn-rich inclusions and the magnetotransport properties. We obtained p-type layers with nanocolumns, either parallel or entangled, and n-type layers with spherical clusters. Holes exhibit an anomalous Hall effect, and electrons exhibit a tunneling magnetoresistance, both with a clear dependence on the magnetization of the Mn-rich inclusions; holes exhibit orbital MR, and electrons show only the normal Hall effect, and an additional component of magnetoresistance due to weak localization, all three being independent of the magnetic state of the Mn rich inclusions. Identified mechanisms point to the position of the Fermi level of the Mn-rich material with respect to the valence band of germanium as a crucial parameter in such hybrid layers.
We look at the equilibrium of a Brownian particle in an inhomogeneous space following the alternative approach proposed in ref.[1]. We consider a coordinate dependent damping that makes the stochastic dynamics the one with multiplicative noise. Here we show that the mapping to an additive noise gives the equilibrium distribution of the generalized Langevin dynamics of a particle with mass. The procedure does not need inclusion of any ad hoc current cancelling term in the Langevin dynamics. The result shows a modified Maxwell-Boltzmann distribution with a damping dependent amplitude.
In this paper, we study rank-1 projector solutions to the completely integrable Euclidean $CP^{N-1}$ sigma model in two dimension and their associated surfaces immersed in the $su(N)$ Lie algebra. We reinterpret and generalize the proof of A.M. Din and W.J. Zakzrewski [1980] that any solution for the $CP^{N-1}$$ sigma model defined on the Riemann sphere with finite action can be written as a raising operator acting on a holomorphic one, or a lowering operator acting on a antiholomorphic one. Our proof is formulated in terms of rank-1 Hermitian projectors so it is explicitly gauge invariant and gives new results on the structure of the corresponding sequence of rank-1 projectors. Next, we analyze surfaces associated with the $CP^{N-1}$ models defined using the Generalized Weierstrass Formula for immersion, introduced by B. Konopelchenko [1996]. We show that the surfaces are conformally parameterized by the Lagrangian density with finite area equal to the action of the model and express several other geometrical characteristics of the surface in terms of the Lagrangian density and topological charge density of the model. We demonstrate that any such surface must be orthogonal to the sequence of projectors defined by repeated application of the raising and lowering operators. Finally, we provide necessary and sufficient conditions that a surface be related to a $CP^{N-1}$ sigma model.
In this paper we present a detailed study of the giant radio halo in the galaxy cluster Abell 697, with the aim to constrain its origin and connection with the cluster dynamics. We performed high sensitivity GMRT observations at 325 MHz, which showed that the radio halo is much brighter and larger at this frequency, compared to previous 610 MHz observations. In order to derive the integrated spectrum in the frequency range 325 MHz--1.4 GHz, we re--analysed archival VLA data at 1.4 GHz and made use of proprietary GMRT data at 610 MHz. {Our multifrequency analysis shows that the total radio spectrum of the giant radio halo in A\,697 is very steep, with $\alpha_{\rm~325 MHz}^{\rm~1.4 GHz} \approx 1.7-1.8$. %\pm0.1$. Due to energy arguments, a hadronic origin of the halo is disfavoured by such steep spectrum. Very steep spectrum halos in merging clusters are predicted in the case that the emitting electrons are accelerated by turbulence, observations with the upcoming low frequency arrays will be able to test these expectations.}
Spin accumulation is a crucial but imprecise concept in spintronics. In metal-based spintronics it is characterized in terms of semiclassical distribution functions. In semiconductors with a strong spin-orbit coupling the spin accumulation is interpreted as a superposition of coherent eigenstates. Both views can be reconciled by taking into account the electron-electron interaction: a sufficiently strong self-consistent exchange field reduces a spin accumulation to a chemical potential difference between the two spin bands even in the presence of spin-orbit coupling. We demonstrate the idea on a clean two-dimensional electron gas (2DEG) by showing how the exchange field protects a spin accumulation from dephasing and introduces an easy-plane anisotropy.
The ratio of transverse momentum distribution of thermal photons to dilepton has been evaluated. It is observed that this ratio reaches a plateau beyond a certain value of transverse momentum. We argue that this ratio can be used to estimate the initial temperature of the system by selecting the transverse momentum and invariance mass windows judiciously. It is demonstrated that if the radial flow is large then the plateau disappear and hence a deviation from the plateau can be used as an indicator of large radial flow. The sensitivity of the results on various input parameters has been studied.
We examine the frequencies of the fundamental ($f$-) and the gravity ($g_i$-) mode in gravitational waves from accreting protoneutron stars (PNSs) toward black hole formation. For this purpose, we analyze numerical results of gravitational collapse of massive stars for two different progenitors with three equations of state. We adopt profiles of central objects obtained from the numerical simulations by solving general relativistic neutrino-radiation hydrodynamics under the spherical symmetry. Using a series of snapshots as a static configuration at each time step, we solve the eigenvalue problem to determine the specific frequencies of gravitational waves from the evolving PNSs with accretion from core bounce to black hole formation by the relativistic Cowling approximation. We find that the frequency of the $f$-mode gravitational waves can be expressed as a function of the average density of the PNS at each time step almost independently of the progenitor models in accord with the previous studies on ordinary PNSs. We also find that the ratio of the $g_1$-mode frequency to the $f$-mode frequency is insensitive to the progenitor, but strongly depends on the compactness of the PNSs. Having a simultaneous observation of the $f$- and $g_1$-mode gravitational waves, it would provide the information of the average density and compactness of PNS, which can reconstruct the evolution of mass and radius of the PNSs as a constraint on the equation of state at high densities. Furthermore, we show that the highest average density of the PNS with the maximum mass can be estimated with the detection of the $f$-mode gravitational waves together with the help of the neutrino observations.
We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of the Catalan triangle.