ShantanuT01/DACTYL-Pretraining huggingface dataset:
It is well known that due to its divergence at large impact parameters, the Boltzmann collision integral in the kinetic equation for 3D systems of particles interacting through a $1/r$ potential must be replaced by a Balescu-Lenard-like collision term. However, the latter diverges at small impact parameters. This comes from the fact that only weak interactions are considered while strong collisions between close particles are neglected in its derivation. We show that a solution to this dilemma exists in the framework of the BBGKY formulation of statistical mechanics. It is based on a separate treatment of the contribution of the strong interactions from that of the weak interactions. The strong interaction part leads to a new term that involves a fractional Laplacian operator in velocity space while the weak interaction component yields the Balescu-Lenard collision term with an explained lower cut-off at the Landau length. For spatially uniform initial conditions, the fractional Laplacian contribution leads to a long-tailed velocity distribution as long as the spatial inhomogeneity remains small. We present results from molecular dynamics simulations confirming the existence of such long tails.
We implement Grover's quantum search algorithm on a nuclear spin chain quantum computer, taking into Ising type interactions between nearest and second nearest neighbours into account. The performance of the realisation of the algorithm is studied by numerical simulations with four spins. We determine the temporal behaviour of the fidelity during the algorithm, and we compute the final fidelity as a function of the Rabi frequency. For the latter, we obtained pronounced maxima at frequencies which fulfil the condition of the (2\pi k)-method with respect to the second nearest neighbour interactions.
In this paper, we analyze the periodic factors of Sturmian words for the findings to lead to a linear-time algorithm for the computation of runs in this class of words which, to our best knowledge, is an open problem in literature.
Recent high-resolution observations of metal absorption lines in high-redshift damped Ly-alpha systems have shown that Al III, a tracer of moderately-ionized gas, very often has a velocity structure indistinguishable from that of low-ionization gas. Regions of ionized and neutral hydrogen in these systems are likely cospatial. The higher-ionization Si IV and C IV absorption shows a much weaker or non-existent correlation with the low ionization material, implying that the regions traced by Al III are photoionized by a soft (stellar) spectrum, by a hard (power law) spectrum with a very low ionization parameter, or a combination of both. We discuss the ionization of the damped Ly-alpha systems and use photoionization equilibrium models to make quantitative estimates of its effects on abundance studies in these systems. We show that ionization effects may be large enough to account for the observed dispersion in absolute metal abundances in damped Ly-alpha systems, causing systematically higher abundances in lower column density systems. The observed Si^+/Fe^+ and Zn^+/Cr^+ ratios may systematically overestimate the intrinsic Si/Fe and Zn/Cr ratios, respectively, if ionized gas is present in these systems, thereby mimicking the effects of alpha-element enrichment or dust depletion.
We have updated the Ba II model atom by taking into account the H I impact excitation with the rate coefficients from the quantum-mechanical calculations of Belyaev and Yakovleva (2018). Using high-resolution stellar spectra and the non-local thermodynamic equilibrium (non-LTE) line formation for Ba II, we have determined the fraction of barium isotopes with an odd mass number (fodd}) in four Galactic halo giants with well-known atmospheric parameters. We use a method based on the requirement that the abundances from the Ba II 4554 A resonance and Ba II 5853, 6496 A subordinate lines be equal. An accuracy of 0.04 dex in determining the barium abundance from individual lines has been achieved. In three stars (HD 2796, HD 108317, and HD 122563) fodd >= 0.4. This suggests that >= 80 % of the barium observed in these stars was synthesized in the r-process. In HD 128279 fodd = 0.27 exceeds the fraction of odd barium isotopes in the Solar system, but only slightly. The dominance of the r-process at the formation epoch of our sample stars is confirmed by the presence of a europium overabundance relative barium, with [Eu/Ba] > 0.3. We have calculated the non-LTE abundance corrections for five Ba II lines and investigated their dependence on atmospheric parameters in the ranges of effective temperatures from 4500 to 6500 K, surface gravities log g from 0.5 to 4.5, and metallicities [Fe/H] from 0 to -3.
We present a series of numerical simulations that explore how the `X-factor', $X_{CO}$ -- the conversion factor between the observed integrated CO emission and the column density of molecular hydrogen -- varies with the environmental conditions in which a molecular cloud is placed. Our investigation is centred around two environmental conditions in particular: the cosmic ray ionisation rate (CRIR) and the strength of the interstellar radiation field (ISRF). Since both these properties of the interstellar medium have their origins in massive stars, we make the assumption in this paper that both the strength of the ISRF and the CRIR scale linearly with the local star formation rate (SFR). The cloud modelling in this study first involves running numerical simulations that capture the cloud dynamics, as well as the time-dependent chemistry, and ISM heating and cooling. These simulations are then post-processed with a line radiative transfer code to create synthetic 12CO (1-0) emission maps from which $X_{CO}$ can be calculated. We find that for 1e4 solar mass virialised clouds with mean density 100 cm$^{-3}$, $X_{CO}$ is only weakly dependent on the local SFR, varying by a factor of a few over two orders of magnitude in SFR. In contrast, we find that for similar clouds but with masses of 1e5 solar masses, the X-factor will vary by an order of magnitude over the same range in SFR, implying that extra-galactic star formation laws should be viewed with caution. However, for denser ($10^4$ cm$^{-3}$), super-virial clouds such as those found at the centre of the Milky Way, the X-factor is once again independent of the local SFR.
In recent years, distinctive-dictionary construction has gained importance due to his usefulness in data processing. Usually, one or more dictionaries are constructed from a training data and then they are used to classify signals that did not participate in the training process. A new dictionary construction algorithm is introduced. It is based on a low-rank matrix factorization being achieved by the application of the randomized LU decomposition to a training data. This method is fast, scalable, parallelizable, consumes low memory, outperforms SVD in these categories and works also extremely well on large sparse matrices. In contrast to existing methods, the randomized LU decomposition constructs an under-complete dictionary, which simplifies both the construction and the classification processes of newly arrived signals. The dictionary construction is generic and general that fits different applications. We demonstrate the capabilities of this algorithm for file type identification, which is a fundamental task in digital security arena, performed nowadays for example by sandboxing mechanism, deep packet inspection, firewalls and anti-virus systems. We propose a content-based method that detects file types that neither depend on file extension nor on metadata. Such approach is harder to deceive and we show that only a few file fragments from a whole file are needed for a successful classification. Based on the constructed dictionaries, we show that the proposed method can effectively identify execution code fragments in PDF files.   $\textbf{Keywords.}$ Dictionary construction, classification, LU decomposition, randomized LU decomposition, content-based file detection, computer security.
We revisit the regular black hole found by Hayward in $4-$dimensional static, spherically symmetric spacetime. To find a possible source for such a spacetime we resort to the non-linear electrodynamics in general relativity. It is found that a magnetic field within this context gives rise to the regular Hayward black hole. By employing such a regular black hole we construct a thin-shell wormhole for the case of various equations of state on the shell. We abbreviate a general equation of state by $p=\psi \left( \sigma \right) $ where $p$ is the surface pressure which is the function of the mass density ($\sigma $). In particular, a linear, logarithmic, Chaplygin, etc. forms of equations of state are considered. In each case we study the stability of the thin-shell against linear perturbations. We plot the stability regions by tuning the parameters of the theory. It is observed that the role of the Hayward parameter is to make the TSW more stable. Perturbations of the throat with small velocity condition is also studied. The matter of our TSWs, however, remains to be exotic.
We have shown that a longitudinal wave emerges as a result of general transformations similar to gauge transformations of electrodynamics. The time derivative and the gradient of the gauge function and their alike yield the longitudinal wave. The de Broglie wave associated with the particle motion is a longitudinal one. This wave accompanied the motion of all massive objects. It has a zero magnetic field (or vorticity). The invariance of Dirac equation under these transformations makes the electron to behave as a massless particle while having a mass.
A strong coupling between the electron spin and its motion is one of the prerequisites of spin-based data storage and electronics. A major obstacle is to find spin-orbit coupled materials where the electron spin can be probed and manipulated on macroscopic length scales, for instance across the gate channel of a spin-transistor. Here, we report on millimeter-scale edge channels with a conductance quantized at a single quantum 1 $\times$ $e^2/h$ at zero magnetic field. The quantum transport is found at the lateral edges of three-dimensional topological insulators made of bismuth chalcogenides. The data are explained by a lateral, one-dimensional quantum confinement of non-topological surface states with a strong Rashba spin-orbit coupling. This edge transport can be switched on and off by an electrostatic field-effect. Our results are fundamentally different from an edge transport in quantum spin Hall insulators and quantum anomalous Hall insula-tors.
We have studied theoretically the possibility of ultra-fast manipulation of a single electron spin in 2D semiconductor quantum dots, by means of high-frequency time-dependent electric fields. The electron spin degree of freedom is excited through spin-orbit coupling, and the procedure may be enhanced by the presence of a static magnetic field. We use quantum optimal control theory to tailor the temporal profile of the electric field in order to achieve the most effective manipulation. The scheme predicts significant control over spin operations in times of the order of picoseconds -- an ultrafast time scale that permits to avoid the effects of decoherence if this scheme is to be used as a tool for quantum information processing.
We study the relation between the type of a double point of a plane curve and the curvilinear 0-dimensional subschemes of the curve at the point. An Algorithm related to a classical procedure for the study of double points via osculating curves is described and proved. Eventually we look for a way to create examples of rational plane curves with given singularities $A_s$.
This is a survey on the intermittent behavior of the parabolic {Anderson} model, which is the Cauchy problem for the heat equation with random potential on the lattice $\Z^d$. We first introduce the model and give heuristic explanations of the long-time behavior of the solution, both in the annealed and the quenched setting for time-independent potentials. We thereby consider examples of potentials studied in the literature. In the particularly important case of an i.i.d. potential with double-exponential tails we formulate the asymptotic results in detail. Furthermore, we explain that, under mild regularity assumptions, there are only four different universality classes of asymptotic behaviors. Finally, we study the moment Lyapunov exponents for space-time homogeneous catalytic potentials generated by a {Poisson} field of random walks.
A palintiple is a natural number which is an integer multiple of its digit reversal. A previous paper partitions all palintiples into three distinct classes according to patterns in the carries and then determines all palintiples belonging to the shifted-symmetric class. In this paper we consider a strategy for finding all symmetric palintiples based upon recent work. We also discuss the last case of asymmetric palintiples and consider bases for which asymmetric palintiples do not exist.
The Fermi gamma-ray space telescope has revolutionized our view of the gamma-ray sky and the high energy processes in the Universe. While the number of known gamma-ray emitters has increased by orders of magnitude since the launch of Fermi, there is an ever increasing number of, now more than a thousand, detected point sources whose low-energy counterpart is to this day unknown. To address this problem, we combined optical polarization measurements from the RoboPol survey as well as other discriminants of blazars from publicly available all-sky surveys in machine learning (random forest and logistic regression) frameworks that could be used to identify blazars in the Fermi unidentified fields with an accuracy of >95%. Out of the potential observational biases considered, blazar variability seems to have the most significant effect reducing the predictive power of the frameworks to ~80-85%. We apply our machine learning framework to six unidentified Fermi fields observed using the RoboPol polarimeter. We identified the same candidate source proposed by Mandarakas et al. for 3FGL J0221.2+2518.
We present extended modeling of the strong lens system RXJ1131-1231 with archival data in two HST bands in combination with existing line-of-sight contribution and velocity dispersion estimates. Our focus is on source size and its influence on time-delay cosmography. We therefore examine the impact of mass-sheet degeneracy and especially the degeneracy pointed out by Schneider & Sluse (2013) using the source reconstruction scale. We also extend on previous work by further exploring the effects of priors on the kinematics of the lens and the external convergence in the environment of the lensing system. Our results coming from RXJ1131-1231 are given in a simple analytic form so that they can be easily combined with constraints coming from other cosmological probes. We find that the choice of priors on lens model parameters and source size are subdominant for the statistical errors for $H_0$ measurements of this systems. The choice of prior for the source is sub-dominant at present (2% uncertainty on $H_0$) but may be relevant for future studies. More importantly, we find that the priors on the kinematic anisotropy of the lens galaxy have a significant impact on our cosmological inference. When incorporating all the above modeling uncertainties, we find $H_0 = 86.6^{+6.8}_{-6.9}$ km s$^{-1}$Mpc$^{-1}$, when using kinematic priors similar to other studies. When we use a different kinematic prior motivated by Barnab\`e et al. (2012) but covering the same anisotropic range, we find $H_0 = 74.5^{+8.0}_{-7.8}$ km s$^{-1}$Mpc$^{-1}$. This means that the choice of kinematic modeling and priors have a significant impact on cosmographic inferences. The way forward is either to get better velocity dispersion measures which would down weight the impact of the priors or to construct physically motivated priors for the velocity dispersion model.
Problems in applying random-matrix theory (RMT) to nuclear reactions arise in two domains. To justify the approach, statistical properties of isolated resonances observed experimentally must agree with RMT predictions. That agreement is less striking than would be desirable. In the implementation of the approach, the range of theoretically predicted observables is too narrow.
The electronic structure of the cleaved perovskite (CH3NH3PbBr3) single crystal was studied in an ultra-high vacuum (UHV) system by angle-resolved photoemission spectroscopy (ARPES) and inverse photoelectron spectroscopy (IPES). Highly reproducible dispersive features of the valence bands were observed with nice symmetry about the Brillouin zone center and boundaries. The largest dispersion width was found to be ~0.73 eV and ~0.98 eV along the {\Gamma}X and {\Gamma}M directions, respectively. The effective mass of the holes was estimated to be ~0.59 m0. The quality of the surface was verified by atomic force microscopy (AFM) and scanning electron microscope (SEM). The elemental composition was investigated by high resolution x-ray photoelectron spectroscopy (XPS). The experimental electronic structure shows a good agreement with the theoretical calculation.
The goal of the present text is to state and prove a generalization of Raynaud localization theorem in the setting of derived geometry. More explicitly, we show that the $\infty$-category of quasi-paracompact and quasi-separated derived $k$-analytic spaces can be realized as a localization of the $\infty$-category of admissible derived formal schemes. We construct a derived rigidification functor generalizing Raynaud rigidification functor. In order to construct the latter we will need to formalize derived formal $\mathcal{O}_k$-adic formal geometry via a structured spaces approach. We prove that $\mathcal{O}_k$-adic Postnikov towers of derived $\mathcal{O}_k$-adic Deligne-Mumford stacks decompose and we relate these to Postnikov towers of derived $k$-analytic spaces. This is possible by a precise comparison between the $\mathcal{O}_k$-adic cotangent complex and the $k$-analytic cotangent complex.
The proton emission induced by polarized photons is studied in the energy range above the giant resonance region and below the pion emission threshold. Results for the 12C, 16O and 40Ca nuclei are presented. The sensitivity of various observables to final state interaction, meson exchange currents and short range correlations is analyzed. We found relevant effects due to the virtual excitation of the $\Delta$ resonance.
A nonlinear Fokker-Planck equation is obtained in the continuous limit of a one-dimensional lattice with an energy landscape of wells and barriers. Interaction is possible among particles in the same energy well. A parameter $\gamma$, related to the barrier's heights, is introduced. Its value is determinant for the functional dependence of the mobility and diffusion coefficient on particle concentration, but has no influence on the equilibrium solution. A relation between the mean field potential and the microscopic interaction energy is derived. The results are illustrated with classical particles with interactions that reproduce fermion and boson statistics.
Using the PACS and SPIRE spectrometers on-board Herschel, we obtained observations of the Taffy galaxies (UGC 12914/12915) and bridge. The Taffy system is believed to be the result of a face-on collision between two gas-rich galaxies, in which the stellar disks passed through each other, but the gas was dispersed into a massive H I and molecular bridge between them. Emission is detected and mapped in both galaxies and the bridge in the [C II]157.7 $\mu$m and [O I]63.2 $\mu$m fine-structure lines. Additionally, SPIRE FTS spectroscopy detects the [C I] $^3$P$_2$$\rightarrow$$^3$P$_1$(809.3 GHz) and [C I] $^3$P$_1$$\rightarrow$$3$P$_0$(492.2 GHz) neutral carbon lines, and weakly detects high-J CO transitions in the bridge. These results indicate that the bridge is composed of a warm multi-phase medium consistent with shock and turbulent heating. Despite low star formation rates in the bridge, the [C II] emission appears to be enhanced, reaching [C II]/FIR ratios of 3.3% in parts of the bridge. Both the [C II] and [O I] lines show broad intrinsic multi-component profiles, similar to those seen in previous CO 1-0 and H I observations. The [C II] emission shares similar line profiles with both the double-peaked H I profiles and shares a high-velocity component with single-peaked CO profiles in the bridge, suggesting that the [C II] emission originates in both the neutral and molecular phases. We show that it is feasible that a combination of turbulently heated H$_2$ and high column-density H I, resulting from the galaxy collision, is responsible for the enhanced [C II] emission.
We compute the instanton partition functions of $\mathcal{N}=1$ SCFTs in class $\mathcal{S}_k$. We obtain this result via orbifolding Dp/D(p-4) brane systems and calculating the partition function of the supersymmetric gauge theory on the worldvolume of $K$ D(p-4) branes. Starting with D5/D1 setups probing a $\mathbb{Z}_\ell\times \mathbb{Z}_k$ orbifold singularity we obtain the $K$ instanton partition functions of 6d $(1,0)$ theories on $\mathbb{R}^4 \times T^2$ in the presence of orbifold defects on $T^2$ via computing the 2d superconformal index of the worldvolume theory on $K$ D1 branes wrapping the $T^2$. We then reduce our results to the 5d and to the 4d instanton partition functions. For $k=1$ we check that we reproduce the known elliptic, trigonometric and rational Nekrasov partition functions. Finally, we show that the instanton partition functions of $SU(N)$ quivers in class $\mathcal{S}_k$ can be obtained from the class $\mathcal{S}$ mother theory partition functions with $SU(kN)$ gauge factors via imposing the `orbifold condition' $a_{\mathcal{A}} \rightarrow a_A e^{2\pi i j/k}$ with $\mathcal{A}=jA$ and $A=1,\dots, N$, $j=1,\dots, k$ on the Coulomb moduli and the mass parameters.
The analysis of some effects caused by the spin--dependent pomeron couplings is presented. It is shown that the structure of pomeron--proton and quark--pomeron couplings can be tested in future polarized experiments on elastic $pp$ reactions and diffractive $Q \bar Q$ production.
We make a detailed time resolved spectroscopy of bright long gamma ray bursts (GRBs) which show significant GeV emissions (GRB 080916C, GRB 090902B, and GRB 090926A). In addition to the standard Band model, we also use a model consisting of a blackbody and a power-law to fit the spectra. We find that for the latter model there are indications for an additional soft component in the spectra. While previous studies have shown that such models are required for GRB 090902B, here we find that a composite spectral model consisting of two black bodies and a power law adequately fit the data of all the three bright GRBs. We investigate the evolution of the spectral parameters and find several generic interesting features for all three GRBs, like a) temperatures of the black bodies are strongly correlated to each other, b) flux in the black body components are strongly correlated to each other, c) the temperatures of the black body trace the profile of the individual pulses of the GRBs, and d) the characteristics of the power law component like the spectral index and the delayed onset bear a close similarity to the emission characteristics in the GeV regions. We discuss the implications of these results to the possibility of identifying the radiation mechanisms during the prompt emission of GRBs.
We study the behavior of non-relativistic quantum particles interacting with different potentials in the space-times generated by a cosmic string and a global monopole. We find the energy spectra in the presence of these topological defects and show how they differ from their free space-time values.