ShantanuT01/DACTYL-Pretraining huggingface dataset:
Co-sputtered Au-Ni thin films having thickness of 30 nm were deposited on Si(100) substrates and irradiated with 160 keV ^{40}Ar^{+} under ambient condition at a number of fluences and analyzed using Rutherford backscattering spectrometry (RBS). The variation of Au signal counts in the RBS spectra with ion dose has been investigated. The distribution of Au, Ni and Si atoms over various depths within the as deposited and irradiated samples have been computed using the backscattering data by means of a direct analytical method. Au and Si profiles have been fitted with error function and the relative changes in variance for various ion fluences compared to that of as deposited profiles have been studied. The spreading rates of different constituents across the interface due to Ar ion impact have also been discussed.
Globular clusters are compact, gravitationally bound systems of up to a million stars. The GCs in the Milky Way contain some of the oldest stars known, and provide important clues to the early formation and continuing evolution of our Galaxy. More generally, GCs are associated with galaxies of all types and masses, from low-mass dwarf galaxies to the most massive early-type galaxies which lie in the centres of massive galaxy clusters. GC systems show several properties which connect tightly with properties of their host galaxies. For example, the total mass of GCs in a system scales linearly with the dark matter halo mass of its host galaxy. Numerical simulations are at the point of being able to resolve globular cluster formation within a cosmological framework. Therefore, GCs link a range of scales, from the physics of star formation in turbulent gas clouds, to the large-scale properties of galaxies and their dark matter. In this Chapter we review some of the basic observational approaches for GC systems, some of their key observational properties, and describe how GCs provide important clues to the formation of their parent galaxies.
We present an optimized seeded chemical vapor transport method for the growth of Cu$_{2}$OSeO$_{3}$ that allows for chemical control in a system with many stable phases to selectively produce large phase pure single crystals. This method is shown to consistently produce single crystals in the range of 120 to 180 mg. A Wulff construction model of a representative crystal shows that the minimum energy surface is {1 1 0}, followed by {1 0 0}. Analysis of the lowest index planes revealed that cleavage of Se-O bonds has a large energy cost, leading to an overall high surface energy. The seeded chemical vapor transport demonstrated here shows promise for large single crystal growth of other functional materials such as Weyl semimetals, frustrated magnets, and superconductors.
We show that under reasonable conditions, a random $n\times (2+\epsilon) n$ integer matrix is surjective on $\mathbb{Z}^{n}$ with probability $1-O(e^{-cn})$. We also conjecture that this should hold for $n\times (1+\epsilon)n$, and provide a counterexample to show that our "reasonableness" conditions are necessary.
We construct a fake exponential Brownian motion, a continuous martingale different from classical exponential Brownian motion but with the same marginal distributions, thus extending results of Albin and Oleszkiewicz for fake Brownian motions. The ideas extend to other diffusions.
We study sandpile models as closed systems, with conserved energy density $\zeta$ playing the role of an external parameter. The critical energy density, $\zeta_c$, marks a nonequilibrium phase transition between active and absorbing states. Several fixed-energy sandpiles are studied in extensive simulations of stationary and transient properties, as well as the dynamics of roughening in an interface-height representation. Our primary goal is to identify the universality classes of such models, in hopes of assessing the validity of two recently proposed approaches to sandpiles: a phenomenological continuum Langevin description with absorbing states, and a mapping to driven interface dynamics in random media. Our results strongly suggest that there are at least three distinct universality classes for sandpiles.
The evolution with energy scale of the partonic logarithmic scaled energy spectra is investigated in the framework of the modified leading logarithmic approximation (MLLA). The behaviour of the higher order moments is compared to a number of analytic predictions and $\rm e^+e^-$ data.
Quantum fluctuations become particularly relevant in highly frustrated quantum magnets and can lead to new states of matter. We provide a simple and robust scenario for inducing magnetic vortex crystals in frustrated Mott insulators. By considering a quantum paramagnet that has a gapped spectrum with six-fold degenerate low energy modes, we study the magnetic field induced condensation of these modes. We use a dilute gas approximation to demonstrate that a plethora of multi-$\mathbf{Q}$ condensates are stabilized for different combinations of exchange interactions. This rich quantum phase diagram includes magnetic vortex crystals, which are further stabilized by symmetric exchange anisotropies. Because magnetic skyrmion and domain wall crystals have already been predicted and experimentally observed, this novel vortex phase completes the picture of emergent crystals of topologically nontrivial spin configurations.
The Coronal Multi-channel Polarimeter (CoMP) has previously demonstrated the presence of Doppler velocity fluctuations in the solar corona. The observed fluctuations are thought to be transverse waves, i.e. highly incompressible motions whose restoring force is dominated by the magnetic tension, some of which demonstrate clear periodicity. We aim to exploit CoMP's ability to provide high cadence observations of the off-limb corona to investigate the properties of velocity fluctuations in a range of coronal features, providing insight into how(if) the properties of the waves are influenced by the varying magnetic topology in active regions, quiet Sun and open fields regions. An analysis of Doppler velocity time-series of the solar corona from the $10,747$~{\AA} Iron XIII line is performed, determining the velocity power spectra and using it as a tool to probe wave behaviour. Further, the average phase speed and density for each region are estimated and used to compute the spectra for energy density and energy flux. In addition, we assess the noise levels associated with the CoMP data, deriving analytic formulae for the uncertainty on Doppler velocity measurements and providing a comparison by estimating the noise from the data. It is found that the entire corona is replete with transverse wave behaviour. The corresponding power spectra indicates that the observed velocity fluctuations are predominately generated by stochastic processes, with the spectral slope of the power varying between the different magnetic regions. Most strikingly, all power spectra reveal the presence of enhanced power occurring at $ \sim3$~mHz, potentially implying that the excitation of coronal transverse waves by $p$-modes is a global phenomenon.
Minkowski functionals have recently been introduced into cosmology as novel tools for studying the large-scale distribution of matter in the Universe. We present a brief overview of the method, including its mathematical foundations as well as some completed and upcoming applications.
We calculate the relaxational dynamical critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the minimal subtraction scheme in two loop order. The three different bicritical static universality classes previously found for such systems correspond to three different dynamical universality classes within the static borderlines. The Heisenberg and the biconical fixed point lead to strong dynamic scaling whereas in the region of stability of the decoupled fixed point weak dynamic scaling holds. Due to the neighborhood of the stability border between the strong and the weak scaling dynamic fixed point corresponding to the static biconical and the decoupled fixed point a very small dynamic transient exponent, of $\omega_v^{{\cal B}}=0.0044$, is present in the dynamics for the physically important case $n_\|=1$ and $n_\perp=2$ in $d=3$.
We have compiled from the available literature a large set of radio measurements of black hole binaries in the hard X-ray state for which measurements of the gigahertz frequency radio spectral index are possible. We separate the sample into `radio loud' and `radio quiet' subsets based upon their distribution in the radio -- X-ray plane, and investigate the distribution of radio spectral indices within each subset. The distribution of spectral indices of the `radio loud' subset is well described by a Gaussian distribution with mean spectral index $\alpha = +0.2$ and standard deviation $0.2$ (here spectral index is defined such that a positive spectral index means more flux at higher frequencies). The sparser sample for the `radio quiet' subset can be approximated, less well, by a Gaussian with mean $\alpha = -0.2$ and standard deviation $0.3$; alternatively the simple mean of the distribution of the radio quiet subset is $-0.3$. The two spectral index distributions are different at high statistical significance. Confirming previous work in the literature, we test to see if the differences in observed spectra could result from different distributions of jet viewing angles, but find no evidence for this. We conclude therefore that the jets in the two groups are physically different in some way, and briefly discuss possible origins and further possible diagnostics. Finally we note that extrapolating to lower frequencies the two subsets move closer together in the radio -- X-ray plane, and approximately merge into a single distribution at around 400 MHz.
The study of electron-phonon interaction as a prominent inelastic effect is of great importance. In the present work, we have studied the inelastic effects due to the first order electron-phonon interactions on electronic properties of mono-atomic periodic chain, using the exact diagonalization technique. Hence, only acoustic modes are considered. To avoid the approximate results arising from Keldysh formalism and on-site electron-phonon interaction assumption, we have used the Green's function technique together with Fr\"{o}hlich Hamiltonian for the interaction part. Finally, as an example, we apply our method to the case of $N=6$ which could be considered as a Benzene-like molecule.
Tunneling rate is investigated in homogenous and anisotropic cosmologies. The calculations is done by two methods: Euclidean and Hamiltonian approaches. It is found that the probability decreases exponentialy as anisotropy is increased.
In this note we improve an algorithm from a recent paper by Bauer and Bennett for computing a function of Erd\"os that measures the minimal gap size $f(k)$ in the sequence of integers at least one of whose prime factors exceeds $k$. This allows us to compute values of $f(k)$ for larger $k$ and obtain new values of $f(k)$.
We study the electronic structure of the Re(0001) surface by means of ab-initio techniques based on the Fully Relativistic (FR) Density Functional Theory (DFT) and the Projector Augmented-Wave (PAW) method. We identify the main surface states and resonances and study in detail their energy dispersion along the main symmetry lines of the SBZ. Moreover, we discuss the effect of spin-orbit coupling on the energy splittings and the spin-polarization of the main surface states and resonances. Whenever possible, we compare the results with previously studied heavy metals surfaces. We find empty resonances, located below a gap similar to the L-gap of the (111) fcc surfaces, that have a downward dispersion and cross the Fermi level, similarly to the recently studied Os(0001) surface. Their spin polarization at the Fermi level is similar to that predicted by the Rashba model, but the usual level crossing at $\bar{\Gamma}$ is not found with our slab thickness. Moreover, for selected states, we follow the spin polarization along the high symmetry lines, discussing its behavior with respect to ${\bf k}_{\parallel}$, the wave-vector parallel to the surface.
We introduce a variation of interval graphs, called veto interval (VI) graphs. A VI graph is represented by a set of closed intervals, each containing a point called a veto mark. The edge $ab$ is in the graph if the intervals corresponding to the vertices $a$ and $b$ intersect, and neither contains the veto mark of the other. We find families of graphs which are VI graphs, and prove results towards characterizing the maximum chromatic number of a VI graph. We define and prove similar results about several related graph families, including unit VI graphs, midpoint unit VI (MUVI) graphs, and single and double approval graphs. We also highlight a relationship between approval graphs and a family of tolerance graphs.
For a transmission problem in a truncated two-dimensional cylinder located beneath the graph of a function u, the shape derivative of the Dirichlet energy (with respect to u) is shown to be well-defined and is computed. The main difficulties in this context arise from the weak regularity of the domain and the possible non-empty intersection of the graph of u and the transmission interface. The result is applied to establish the existence of a solution to a free boundary transmission problem for an electrostatic actuator.
We consider the defocusing nonlinear wave equations (NLW) on the two-dimensional torus. In particular, we construct invariant Gibbs measures for the renormalized so-called Wick ordered NLW. We then prove weak universality of the Wick ordered NLW, showing that the Wick ordered NLW naturally appears as a suitable scaling limit of non-renormalized NLW with Gaussian random initial data.
Katz & Zingale (2019, KZ19) recently studied a one-dimensional test problem, intended to mimic the process of detonation ignition in head-on collisions of two carbon--oxygen (CO) white dwarfs. They do not obtain ignition of a detonation in pure CO compositions unless the temperature is artificially increased or 5% He is included. In both of these cases they obtain converged ignition only for spatial resolutions better than 0.1 km, which are beyond the capability of multidimensional simulations. This is in a contradiction with the claims of Kushnir et al. (2013, K13), that a convergence to $\sim10\%$ is achieved for a resolution of a few km. Using Eulerian and Lagrangian codes we show that a converged and resolved ignition is obtained for pure CO in this test problem without the need for He or increasing the temperature. The two codes agree to within 1% and convergence is obtained at resolutions of several km. We calculate the case that includes He and obtain a similar slow convergence, but find that it is due to a boundary numerical artifact that can (and should) be avoided. Correcting the boundary conditions allows convergence with resolution of $\sim10\,\textrm{km}$ in an agreement with the claims of K13. It is likely that the slow convergence obtained by KZ19 in this case is because of a similar boundary numerical artifact, but we are unable to verify this. KZ19 further recommended to avoid the use of the burning limiter introduced by K13. We show that their recommendation is not justified.
In relativity there is space-time out there. In quantum mechanics there is entanglement. Entanglement manifests itself by producing correlations between classical events (e.g. the firing of some detectors) at any two space-time locations. If the locations are time-like separated, i.e. one is in the future of the other, then there is no specific difficulty to understand the correlations. But if the two locations are space-like separated, the problem is different. How can the two space-time locations out there know about what happens in each other without any sort of communication? If space-time really exists, the locations must do something like communicating. Or it was all set up at the Beginning. But the correlations depend also on the free choice of the experimentalists, one in each space-time location. This allowed John Bell to derive his inequality and the experimentalists to violate it, thus refuting the assumption that it was all set up at the beginning: the Correlations can't be explained by common causes.
The Catalan number sequence is one of the most famous number sequences in combinatorics and is well studied in the literature. In this paper we further investigate its fundamental properties related to the moment problem and prove for the first time that it is an infinitely divisible Stieltjes moment sequence in the sense of S.-G. Tyan. Besides, any positive real power of the sequence is still a Stieltjes determinate sequence. Some more cases including (a) the central binomial coefficient sequence (related to the Catalan sequence), (b) a double factorial number sequence and (c) the generalized Catalan (or Fuss-Catalan) sequence are also investigated. Finally, we pose two conjectures including the determinacy equivalence between powers of nonnegative random variables and powers of their moment sequences, which is supported by some existing results.
Generally, there are three main factors that determine the practical usability of registration, i.e., accuracy, robustness, and efficiency. In real-time applications, efficiency and robustness are more important. To promote these two abilities, we cast the multi-view registration into a clustering task. All the centroids are uniformly sampled from the initially aligned point sets involved in the multi-view registration, which makes it rather efficient and effective for the clustering. Then, each point is assigned to a single cluster and each cluster centroid is updated accordingly. Subsequently, the shape comprised by all cluster centroids is used to sequentially estimate the rigid transformation for each point set. For accuracy and stability, clustering and transformation estimation are alternately and iteratively applied to all point sets. We tested our proposed approach on several benchmark datasets and compared it with state-of-the-art approaches. Experimental results validate its efficiency and robustness for the registration of multi-view point sets.
Given a compact Lie group $G$, in this paper we establish $L^p$-bounds for pseudo-differential operators in $L^p(G)$. The criteria here are given in terms of the concept of matrix symbols defined on the non-commutative analogue of the phase space $G\times\widehat{G}$, where $\widehat{G}$ is the unitary dual of $G$. We obtain two different types of $L^p$ bounds: first for finite regularity symbols and second for smooth symbols. The conditions for smooth symbols are formulated using $\mathscr{S}_{\rho,\delta}^m(G)$ classes which are a suitable extension of the well known $(\rho,\delta)$ ones on the Euclidean space. The results herein extend classical $L^p$ bounds established by C. Fefferman on $\mathbb R^n$. While Fefferman's results have immediate consequences on general manifolds for $\rho>\max\{\delta,1-\delta\}$, our results do not require the condition $\rho>1-\delta$. Moreover, one of our results also does not require $\rho>\delta$. Examples are given for the case of SU(2)$\cong\mathbb S^3$ and vector fields/sub-Laplacian operators when operators in the classes $\mathscr{S}_{0,0}^m$ and $\mathscr{S}_{\frac12,0}^m$ naturally appear, and where conditions $\rho>\delta$ and $\rho>1-\delta$ fail, respectively.
Dark matter halos of sub-solar mass are the first bound objects to form in cold dark matter theories. In this article, I discuss the present understanding of "microhalos'', their role in structure formation, and the implications of their potential presence, in the interpretation of dark matter experiments.
Using our new photometric and spectroscopic observations as well as all available published data, we present a new interpretation of the properties of the peculiar emission-line binary UX Mon. We conclude that this binary is in a rare phase of fast mass transfer between the binary components prior to the mass ratio reversal. We firmly establish that the orbital period is secularly decreasing at a rate of $\dot{P}=-0.260$ seconds per year. From several lines of reasoning, we show that the mass ratio of the component losing mass to the mass-gaining component $q$ must be larger than 1 and find our most probable value to be $q=1.15\pm0.1$. The BINSYN suite of programs and the steepest descent method were used to perform the final modeling. We modeled the star as a W Ser star with a thick disk around its primary. Although the remaining uncertainties in some of the basic physical elements describing the system in our model are not negligible, the model is in fair agreement with available observations. Only the nature of the light variations outside the primary eclipse remains unexplained.
Every positive integer may be written uniquely as a base-$\beta$ decomposition--that is a legal sum of powers of $\beta$--where $\beta$ is the dominating root of a non-increasing positive linear recurrence sequence. Guided by earlier work on a two-player game which produces the Zeckendorf Decomposition of an integer (see [Bai+19]), we define a broad class of two-player games played on an infinite tuple of non-negative integers which decompose a positive integer into its base-$\beta$ expansion. We call this game the Generalized Bergman Game. We prove that the longest possible Generalized Bergman game on an initial state $S$ with $n$ summands terminates in $\Theta(n^2)$ time, and we also prove that the shortest possible Generalized Bergman game on an initial state terminates between $\Omega(n)$ and $O(n^2)$ time. We also show a linear bound on the maximum length of the tuple used throughout the game.
Motivated by health care systems with repeated services that have both personnel (nurse and physician) and space (beds) constraints, we study a restricted version of the Erlang-R model. The space restriction policies we consider are blocking or holding in a pre-entrant queue. We develop many-server approximations for the system performance measures when either policy applies, and explore the connection between them. We show that capacity allocation of both resources should be determined simultaneously, and derive the methodology to determine it explicitly. We show that the system dynamics is captured by the fraction of needy time in the network, and that returning customers should be accounted for both in steady-state and time-varying conditions. We demonstrate the application of our policies in two case studies of resource allocation in hospitals.
The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in ${\mathbb R}^3$, one of them is a bounded Lipschitz domain $\Omega $ with connected boundary, and another one is the exterior Lipschitz domain ${\mathbb R}^3\setminus \overline{\Omega }$. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces.
We construct infinite dimensional symmetries of a complex, free scalar field on curved space-times generated by isometries of the space-time. We use the Anti de-Sitter backgrounds as an example and check that the boundary terms appearing in the Noether current satisfy the requirement of Noether's theorem that they vanish at the boundary.
A seemingly obvious extension of the weak equivalence principle, in which all matter must respond to Post-Newtonian gravitational fields, such as Lense-Thirring and radiation fields, in a composition-independent way, is considered in light of the Kramers-Kronig dispersion relations for the linear response of any material medium to these fields. It is argued that known observational facts lead to violations of this extended form of the equivalence principle. (PACS numbers: 04.80.Cc, 04.80.Nn, 03.65.Ud, 67.40.Bz)