ShantanuT01/DACTYL-Pretraining huggingface dataset:
We find that the observed log N - log S relation of X-ray clusters can be reproduced remarkably well with a certain range of values for the fluctuation amplitude $\sigma_8$ and the cosmological density parameter $\Omega_0$ in cold dark matter (CDM) universes. The $1\sigma$ confidence limits on $\sigma_8$ in the CDM models with $n=1$ and $h = 0.7$ are expressed as $(0.54 \pm 0.02) \Omega_0^{-0.35-0.82\Omega_0+0.55\Omega_0^2}$ ($\lambda_0=1-\Omega_0$) and $(0.54 \pm 0.02) \Omega_0^{-0.28-0.91\Omega_0+0.68\Omega_0^2}$ ($\lambda_0=0$), where $n$ is the primordial spectral index, and $h$ and $\lambda_0$ are the dimensionless Hubble and cosmological constants. The errors quoted above indicate the statistical ones from the observed log N - log S only, and the systematic uncertainty from our theoretical modelling of X-ray flux in the best-fit value of $\sigma_8$ is about 15%. In the case of $n=1$, we find that the CDM models with $(\Omega_0,\lambda_0,h,\sigma_8) \simeq (0.3,0.7,0.7,1)$ and $(0.45, 0, 0.7, 0.8)$ simultaneously account for the cluster log N - log$S$, X-ray temperature functions, and the normalization from the COBE 4 year data. The derived values assume the observations are without systematic errors, and we discuss in details other theoretical uncertainties which may change the limits on $\Omega_0$ and $\sigma_8$ from the log N - log S relation. We have shown the power of this new approach which will become a strong tool as the observations attain more precision.
Based on theoretical argument and experimental evidence, we conjecture that structure functions of turbulent times series exhibit log-periodic modulations decorating their power law dependence. In order to provide ironclad experimental evidence, we stress the need for novel methods of averaging and propose a novel ``canonical'' averaging scheme for the analysis of structure factors of turbulent flows. The strategy is to determine the scale $r_c$ at which the dissipation rate is the largest in a given turn-over time series. This specific scale $r_c$ translates into a specific ``phase'' in the logarithm of the scale which, when used as the origin, allows one to phase up the different measurements of a structure factor $S_p(r) = A_p (\bar\epsilon r)^{p/3}$ in different turn-over time realizations. We expect, as in Laplacian growth and in rupture, that the log-periodic oscillations will be reinforced by this canonical averaging. Demonstrating unambiguously the presence of log-periodicity and thus of discrete scale invariance (DSI) in turbulent time-series would provide an important step towards a direct demonstration of the Kolmogorov cascade or at least of its hierarchical imprint.
We present a general method for constructing stochastic processes with prescribed local form. Such processes include variable amplitude multifractional Brownian motion, multifractional $\alpha$-stable processes, and multistable processes, that is processes that are locally $\alpha(t)$-stable but where the stability index $\alpha(t)$ varies with $t$. In particular we construct multifractional multistable processes where both the local self-similarity and stability indices vary.
A plane drawing of a graph is {\em cylindrical} if there exist two concentric circles that contain all the vertices of the graph, and no edge intersects (other than at its endpoints) any of these circles. The {\em cylindrical crossing number} of a graph \(G\) is the minimum number of crossings in a cylindrical drawing of \(G\). In his influential survey on the variants of the definition of the crossing number of a graph, Schaefer lists the complexity of computing the cylindrical crossing number of a graph as an open question. In this paper we settle this by showing that this problem is NP-complete. Moreover, we show an analogous result for the natural generalization of the cylindrical crossing number, namely the \(t\)-{\em circle crossing number}.
There still exists the possibility that the phenomenon of gamma-ray bursts (GRBs) is a mixture of events of different nature, even within the class of long (>2 s) bursts. We try to put statistical constraints on a possible non-cosmological component using the uniform GRB catalog of Stern & Tikhomirova obtained from an overall scan of the full 9.1 year BATSE 1024 ms data. The sample consists of 3906 GRBs and includes non-triggered bursts with peak fluxes down to 0.1 photons cm$^{-2}$ s$^{-1}$. We find no significant deviations from isotropy. The constraints on a non-cosmological population are still weak. The allowed contribution of a GRB subpopulation originating from an extended galactic halo is about 60% and the upper limit on an Eucledian component (e.g., nearby galactic or non-cosmological extragalactic GRBs) is 23%. The results concern mainly the class of long GRBs.
The recent availability of fine grained high sensitivity data from the new generation low radio frequency instruments such as the Murchison Widefield Array (MWA) have opened up opportunities for using novel techniques for characterizing the nature of solar emission at these frequencies. Here we use this opportunity to look for evidence for the presence of weak non-thermal emissions in the 100-240 MHz band, at levels weaker than have usually been probed. The presence of such features is believed to be a necessary consequence of nanoflare-based coronal and chromospheric heating theories. We separate the calibrated MWA solar dynamic spectra into a slowly varying and an impulsive, and hence non-thermal, component. We demonstrate that Gaussian mixtures modeling can be used to robustly model the latter and we estimate the flux density distribution as well as the prevalence of impulsive non-thermal emission in the frequency-time plane. Evidence for presence of non-thermal emission at levels down to $\sim$0.2 SFU (1 SFU = 10$^4$ Jy) is reported, making them the weakest reported emissions of this nature. Our work shows the fractional occupancy of the non-thermal impulsive emission to lie in the 17--45\% range during a period of medium solar activity. We also find that the flux density radiated in the impulsive non-thermal emission is very similar in strength to that of the slowly varying component, dominated by the thermal bremsstrahlung. Such significant prevalence and strength of the weak impulsive non-thermal emission has not been appreciated earlier.
Proton decay is one of the most important predictions of the grand unified theory (GUT). In the supersymmetric (SUSY) GUT, proton decays via the dimension-five operators need to be suppressed. In the $SO(10)$ model where ${\bf 10}+\overline{\bf 126}$ Higgs fields couple to fermions, neutrino oscillation parameters including the CP-violating Pontecorvo-Maki-Nakagawa-Sakata (PMNS) phase can be related to the Yukawa couplings to generate the dimension-five operators in the unified framework. We show how the suppressed proton decay depends on the PMNS phase, and stress the importance of the precise measurements of the PMNS phase as well as the neutrino 23-mixing angle. These become especially important if the SUSY particles are found around less than a few TeV at LHC and proton decays are observed at Hyper-Kamiokande and DUNE experiments in the near future.
Carbon fibers, especially those constructed from carbon nanotubes (CNTs), have attracted intensive interests from both scientific and engineering communities due to their outstanding physical properties. In this workHere we report, we find that the recently synthesized recently synthesized ultrathin diamond nanothread (DNT) not only possesses excellent torsional deformation capability, but also has excellent interfacial load transfer efficiency. Comparing with the (10,10) carbon nanotube bundles, (1) By considering a seven strand fiber, the flattening of nanotubes as observed in (10,10) CNT bundles is not observed in DNTdiamond nanothread bundle, which . This endows the DNT bundle withleads to a high torsional elastic limit that is almost three times higherfour times as obtained from the (10,10) CNT bundle. Pull-out tests reveal that (2) Pull-out tests reveal that tthe DNT diamond nanothread bundle has has an interface transfer load of more than twice that of the CNT carbon naontube bundle, corresponding to an order of magnitude higher in terms of . (3) Tthe interfacial shear strength of the DNT bundle is an order of magnitude higher than that of the CNT bundle. Such high interface load transfer efficiency is attributed to the zigzag morphology of DNT, which introduces a strong mechanical interlocking effect at the interface through the stick-slip motion (totally different from the load transfer mechanism in CNT bundle). The aforementioned three aspects are commonly used to gauge the performance of fibers. Obviously,These intriguing features enable DNT diamond nanothread as exhibits excellent potential candidate for constructing next generation carbon fibers.
Motivated by recent experiments on Bi$_3$Mn$_4$O$_{12}$(NO$_3$), and a broader interest arising from numerical work on the honeycomb lattice Hubbard model, we have studied the effect of a magnetic field on honeycomb lattice spin models with quantum paramagnetic ground states. For a model with frustrating second-neighbor exchange, $J_2$, we use a Lindemann-like criterion within spin wave theory to show that N\'eel order melts beyond a critical $J_2$. The critical $J_2$ increases with a magnetic field, implying the existence of a field-induced paramagnet-N\'eel transition over a range of $J_2$. We also study bilayer model using a spin-$S$ generalization of bond operator mean field theory. We show that there is a N\'eel-dimer transition for various spin values with increasing bilayer coupling, and that the resulting interlayer dimer state undergoes a field induced transition into a state with transverse N\'eel order. Finally, we study a spin-3/2 model which interpolates between the Heisenberg model and the Affleck-Kennedy-Lieb-Tasaki (AKLT) parent Hamiltonian. Using exact diagonalization, we compute the fidelity susceptibility to locate the Neel-AKLT quantum critical point, obtain the spin gap of the AKLT parent Hamiltonian, and argue that AKLT state also undergoes field-induced Neel ordering.
We study stochastic heat equations in the sense of Walsh defined by fractal Laplacians on Cantor-like sets. For this purpose, we first investigate the corresponding heat kernels. Then, we prove existence and uniqueness of mild solutions to stochastic heat equations provided some Lipschitz and linear growth conditions. We establish H\"older continuity in space and time and compute the H\"older exponents. Moreover, we address the question of weak intermittency.
[Abridged] Observations of molecular gas at all redshifts are critical for measuring the cosmic evolution in molecular gas density and understanding the star-formation history of the Universe. The 12CO molecule (J=1-0 transition = 115.27 GHz) is the best proxy for extragalactic H2, which is the gas reservoir from which star formation occurs, and has been detected out to z~6. Typically, redshifted high-J lines are observed at mm-wavelengths, the most commonly targeted systems exhibiting high SFRs (e.g. submm galaxies), and far-IR-bright QSOs. While the most luminous objects are the most readily observed, detections of more typical galaxies with modest SFRs are essential for completing the picture. ALMA will be revolutionary in terms of increasing the detection rate and pushing the sensitivity limit down to include such galaxies, however the limited FoV when observing at such high frequencies makes it difficult to use ALMA for studies of the large-scale structure traced out by molecular gas in galaxies. This article introduces a strategy for a systematic search for molecular gas during the EoR (z~7 and above), capitalizing on the fact that the J=1-0 transition of 12CO enters the upper bands of cm-wave instruments at high-z. The FoV advantage gained by observing at such frequencies, coupled with modern broadband correlators allows significant cosmological volumes to be probed on reasonable timescales. In this article we present an overview of our future observing programme which has been awarded 6,500 hours as one of the Large Survey Projects for MeerKAT, the forthcoming South African SKA pathfinder instrument. Its large FoV and correlator bandwidth, and high-sensitivity provide unprecedented survey speed for such work. An existing astrophysical simulation is coupled with instrumental considerations to demonstrate the feasibility of such observations and predict detection rates.
Automatic color enhancement is aimed to adaptively adjust photos to expected styles and tones. For current learned methods in this field, global harmonious perception and local details are hard to be well-considered in a single model simultaneously. To address this problem, we propose a coarse-to-fine framework with non-local attention for color enhancement in this paper. Within our framework, we propose to divide enhancement process into channel-wise enhancement and pixel-wise refinement performed by two cascaded Convolutional Neural Networks (CNNs). In channel-wise enhancement, our model predicts a global linear mapping for RGB channels of input images to perform global style adjustment. In pixel-wise refinement, we learn a refining mapping using residual learning for local adjustment. Further, we adopt a non-local attention block to capture the long-range dependencies from global information for subsequent fine-grained local refinement. We evaluate our proposed framework on the commonly using benchmark and conduct sufficient experiments to demonstrate each technical component within it.
Spin-orbit and spin-spin effects in the gravitational interaction are treated in a close analogy with the fine and hyperfine interactions in atoms. The proper definition of the cener-of-mass coordinate is discussed. The technique developed is applied then to the gravitational radiation of compact binary stars. Our result for the spin-orbit correction differs from that obtained by other authors. New effects possible for the motion of a spinning particle in a gravitational field are pointed out. The corresponding corrections, nonlinear in spin, are in principle of the same order of magnitude as the ordinary spin-spin interaction.
Calculations from stellar evolutionary models of low- and intermediate-mass asymptotic giant branch (AGB) stars provide predictions of elemental abundances and yields for comparison to observations. However, there are many uncertainties that reduce the accuracy of these predictions. One such uncertainty involves the treatment of low-temperature molecular opacities that account for the surface abundance variations of C, N, and O. A number of prior calculations of intermediate-mass AGB stellar models that incorporate both efficient third dredge-up and hot bottom burning include a molecular opacity treatment which does not consider the depletion of C and O due to hot bottom burning. Here we update the molecular opacity treatment and investigate the effect of this improvement on calculations of intermediate-mass AGB stellar models. We perform tests on two masses, 5 M$_{\odot}$ and 6 M$_{\odot}$, and two metallicities, $Z~=~0.001$ and $Z~=~0.02$, to quantify the variations between two opacity treatments. We find that several evolutionary properties (e.g. radius, $T_{\rm eff}$ and $T_{\rm bce}$) are dependent on the opacity treatment. Larger structural differences occur for the $Z~=~0.001$ models compared to the $Z~=~0.02$ models indicating that the opacity treatment has a more significant effect at lower metallicity. As a consequence of the structural changes, the predictions of isotopic yields are slightly affected with most isotopes experiencing changes up to 60 per cent for the $Z~=~0.001$ models and 20 per cent for the $Z~=~0.02$ models. Despite this moderate effect, we conclude that it is more fitting to use variable molecular opacities for models undergoing hot bottom burning.
We consider propagation of influence on a Configuration Model, where each vertex can be influenced by any of its neighbours but in its turn, it can only influence a random subset of its neighbours. Our (enhanced) model is described by the total degree of the typical vertex, representing the total number of its neighbours and the transmitter degree, representing the number of neighbours it is able to influence. We give a condition involving the joint distribution of these two degrees, which if satisfied would allow with high probability the influence to reach a non-negligible fraction of the vertices, called a big (influenced) component, provided that the source vertex is chosen from a set of good pioneers. We show that asymptotically the big component is essentially the same, regardless of the good pioneer we choose, and we explicitly evaluate the asymptotic relative size of this component. Finally, under some additional technical assumption we calculate the relative size of the set of good pioneers. The main technical tool employed is the "fluid limit" analysis of the joint exploration of the configuration model and the propagation of the influence up to the time when a big influenced component is completed. This method was introduced in Janson & Luczak (2008) to study the giant component of the configuration model. Using this approach we study also a reverse dynamic, which traces all the possible sources of influence of a given vertex, and which by a new "duality" relation allows to characterise the set of good pioneers.
We analyze the structure of simply-connected Enriques surface in characteristic two whose K3-like covering is normal, building on the work of Ekedahl, Hyland and Shepherd-Barron. We develop general methods to construct such surfaces and the resulting twistor lines in the moduli stack of Enriques surfaces, including the case that the K3-like covering is a normal rational surface rather then a normal K3 surface. Among other things, we show that elliptic double points indeed do occur. In this case,there is only one singularity.The main idea is to apply flops to Frobenius pullbacks of rational elliptic surfaces, to get the desired K3-like covering. Our results hinge on Lang's classification of rational elliptic surfaces, the determination of their Mordell--Weil lattices by Shioda and Oguiso, and the behavior of unstable fibers under Frobenius pullback via Ogg's Formula. Along the way, we develop a general theory of Zariski singularities in arbitrary dimension, which is tightly interwoven with the theory of height-one group schemes actions and restricted Lie algebras. Furthermore, we determine under what conditions tangent sheaves are locally free, and introduce a theory of canonical coverings for arbitrary proper algebraic schemes.
We investigate how the Kitaev spin liquid state described by Majorana fermions coupled with $Z_2$ gauge fields is affected by non-Kitaev interactions which exist in real candidate materials of the Kitaev magnet. It is found that the off-diagonal exchange interaction referred to as the $\Gamma'$ term dramatically changes the Majorana band structure in the case of the antiferromagnetic Kitaev interaction, and gives rise to a topological phase transition from a non-Abelian topological phase with the Chern number equal to $\pm 1$ to an Abelian phase with the Chern number equal to $\pm 2$, in which the $Z_{2}$ vortices behave as Abelian anyons. On the other hand, other non-Kitaev interactions such as the Heisenberg interaction and the $\Gamma$ term, only affect the bandwidth of the Majorana band as long as the spin liquid state is not destabilized.
It is usually assumed that we will need to wait until next-generation surveys like Euclid, LSST and SKA, in order to improve on the current best constraints on primordial non-Gaussianity from the Planck experiment. We show that two contemporary surveys, with the SKA precursor MeerKAT and the Dark Energy Survey (DES), can be combined using the multi-tracer technique to deliver an accuracy on measurement of $f_{\rm NL}$ that is up to three times better than Planck.
Context: Magnetic null points are associated with high-energy coronal phenomena such as solar flares and are often sites of reconnection and particle acceleration. Dynamic twisting of a magnetic null point can generate a Kelvin-Helmholtz instability (KHI) within its fan plane and, under continued twisting, can instigate spine-fan reconnection and an associated collapse of the null point.   Aim: This article aims to compare the effects of isotropic and anisotropic viscosity in simulations of the KHI and collapse in a dynamically twisted magnetic null point.   Methods: Simulations were performed using the 3D magnetohydrodynamics code Lare3d with a custom anisotropic viscosity module. A pair of high resolution simulations was performed, one using isotropic viscosity and another using anisotropic viscosity, keeping all other factors identical, and the results analysed in detail. A further parameter study was performed over a range of values for viscosity and resistivity.   Results: Both viscosity models permit the growth of the Kelvin-Helmholtz instability and the eventual collapse of the null point. Over all studied parameters, anisotropic viscosity allows a faster growing instability, while isotropic viscosity damps the instability to the extent of stabilisation in some cases. Although the viscous heating associated with anisotropic viscosity is generally smaller, the ohmic heating dominates and is enhanced by the current sheets generated by the instability, leading to a greater overall heating rate when using anisotropic viscosity. The collapse of the null point occurs significantly sooner when anisotropic viscosity is employed.
Calculations of the $^{6,8}$He + $^{28}$Si total reaction cross sections at intermediate energies are performed on the basis of the Glauber-Sitenko microscopic optical-limit model. The target-nucleus density distribution is taken from the electron-nucleus scattering data, and the $^{6,8}$He densities are used as they are derived in different models. The results of the calculations are compared with the existing experimental data. The effects of the density tails of the projectile nuclei as well as the role of shell admixtures and short-range correlations are analyzed.
The primordial matter power spectrum quantifies fluctuations in the distribution of dark matter immediately following inflation. Over cosmic time, over-dense regions of the primordial density field grow and collapse into dark matter halos, whose abundance and density profiles retain memory of the initial conditions. By analyzing the image magnifications in eleven strongly-lensed and quadruply-imaged quasars, we infer the abundance and concentrations of low-mass halos, and cast the measurement in terms of the amplitude of the primordial matter power spectrum. We anchor the power spectrum on large scales, isolating the effect of small-scale deviations from the $\Lambda$CDM prediction. Assuming an analytic model for the power spectrum and accounting for several sources of potential systematic uncertainty, including three different models for the halo mass function, we obtain correlated inferences of $\log_{10}\left(P / P_{\Lambda \rm{CDM}}\right)$, the power spectrum amplitude relative to the predictions of the concordance cosmological model, of $0.0_{-0.4}^{+0.5}$, $0.1_{-0.6}^{+0.7}$, and $0.2_{-0.9}^{+1.0}$ at k = 10, 25 and 50 $\rm{Mpc^{-1}}$ at $68 \%$ confidence, consistent with cold dark matter and single-field slow-roll inflation.