ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study approximation properties of sequences of centered additive random fields $Y_d$, $d\in\mathbb{N}$. The average case approximation complexity $n^{Y_d}(\varepsilon)$ is defined as the minimal number of evaluations of arbitrary linear functionals that is needed to approximate $Y_d$ with relative $2$-average error not exceeding a given threshold $\varepsilon\in(0,1)$. We investigate the growth of $n^{Y_d}(\varepsilon)$ for arbitrary fixed $\varepsilon\in(0,1)$ and $d\to\infty$. Under natural assumptions we obtain general results concerning asymptotics of $n^{Y_d}(\varepsilon)$. We apply our results to additive random fields with marginal random processes corresponding to the Korobov kernels.
The isothermal magnetic entropy changes are studied in Ni80Fe20/Ni67Cu33/Co90Cu10/Mn80Ir20 stacks at temperatures near the Curie point of the Ni67Cu33 spacer by applying magnetic fields in a few tens of Oersted. Such low fields were sufficient for toggling magnetic moments in the soft ferromagnetic (FM) layer (Ni80Fe20). It is found out that this switching provides the magnetic entropy change, which is up to 20 times larger than that achievable in a single Ni67Cu33 film subjected to such low fields. Our finding holds promise to be utilized in the magnetocaloric devices that would be based on FM/PM/FM heterostructures and would operate with moderate magnetic fields.
Silicon thin films for coverages ($\theta$) between 0.3 and 3 monolayers have been grown on rutile \ce{TiO2}(110)-(1x1) at room temperature and studied by x-ray and ultra-violet photoelectron spectroscopies, Auger electron spectroscopy, and low energy electron diffraction (LEED). A clear evidence of a strong \ce{Si}/\ce{TiO2} interaction consistent with the high affinity of O for Si has been found. The Ti cations on the substrate are reduced, while the Si film is oxidized, yielding \ce{SiO2} and a mixture of silicon suboxides. Neutral Si atoms are observed at a coverage of 3 monolayers. At the interface region we observe the formation of cross-linking Ti-O-Si bonds. The thin Si overlayer strongly attenuates the $(1 \times 1)$ LEED pattern from the substrate. Finally, thermal annealing results in the improvement of the \ce{SiO2} stoichiometry, but the surface order is not recovered. Using ab-initio density functional theory we have obtained optimum geometrical configurations and corresponding density of states for 1/3 \le \theta \le 1$ monolayers of Si adsorbed on the $1 \times 1$ two-dimensional unit cell.
We introduce nine further local facets of the classical Problem of Time, and underlying Background Independence aspects, the previous two Articles having covered one further facet-and-aspect each for a total of eleven. I.e. 1) Constraint Closure, 2) Assignment of Observables, 3) Space Construction from Less Structured Space, A) Spacetime Construction from Space, 0') Spacetime Relationalism, 1') Spacetime Generator Closure, 2') Assignment of Spacetime Observables, 3') Spacetime Construction from Less Structured Spacetime, and B) Foliation Independence. These are classically implemented piecemeal by the Dirac Algorithm for 1) and the Lie Algorithm for 1'). Taking Function Spaces Thereover: over phase space for 2) and over the space of spacetimes for 2'). Feeding Deformed Families into the Dirac Algorithm for A) and into the Lie Algorithm for 3) and 3'), working out whenever Rigidity is encountered. Spacetime's diffeomorphism-invariance and perturbative Lie derivative for 0'). Finally, Refoliation Invariance following from the Dirac algebroid of the GR constraints for B). Each of these approaches is moreover grounded in Lie's Mathematics in accord with this Series' claim. The generalizations required to extend these resolutions to solve combined rather than just piecemeal facets is the main subject of Articles V to XIII. We include novel work on, firstly, Closure, including a blockwise breakdown into more specific Closure Problems. Secondly, on a coordinate-free Multi-tensor Calculus suitable for joint treatment of Background Independence aspects, presenting in particular the Dirac Algorithm, and ensuing theory of observables and of deformations. Finally, aspect 3') is new to the current Article.
We introduce spin projection methods in the shell model Monte Carlo approach and apply them to calculate the spin distribution of level densities for iron-region nuclei using the complete $(pf+g_{9/2})$-shell. We compare the calculated distributions with the spin-cutoff model and extract an energy-dependent moment of inertia. For even-even nuclei and at low excitation energies, we observe a significant suppression of the moment of inertia and odd-even staggering in the spin dependence of level densities.
Understanding the distribution of digits in the expansions of perfect powers in different bases is difficult. Rather than consider the asymptotic digit distributions, we consider the base-10 digits of a restricted sequence of powers of two. We apply elementary methods to show that this sequence of powers of two can be constructed to preserve trailing digits while locally maximizing the number of zeroes between nonzero digits. We also provide a heuristic description of the trailing digits of these powers of two.
Atomically controlled crystal growth of thin films has established foundations of nanotechnology aimed at the development of advanced functional devices. Crystallization under non-equilibrium conditions allows engineering of new materials with their atomically-flat interfaces in the heterostructures exhibiting novel physical properties. From a fundamental point of view, knowledge of the electronic structures of thin films and their interfaces is indispensable to understand the origins of their functionality which further evolves into realistic device application. In view of extreme surface sensitivity of the conventional vacuum-ultraviolet (VUV) angle-resolved photoemission spectroscopy (ARPES), with a probing depth of several angstroms, experiments on thin films have to use sophisticated in-situ sample transfer systems to avoid surface contamination. In this Letter, we put forward a method to circumvent these difficulties using soft X-ray (SX) ARPES. A GaAs:Be thin film in our samples was protected by an amorphous As layer with an thickness of $\sim 1$ nm exceeding the probing depth of the VUV photoemission with photon energy $h\nu$ around 100 eV. The increase of the probing depth with increasing $h\nu$ towards the SX region has clearly exposed the bulk band dispersion without any surface treatment. Any contributions from potential interface states between the thin film and the amorphous capping layer has been below the detection limit. Our results demonstrate that SX-ARPES enables the observation of coherent three-dimensional band dispersion of buried heterostructure layers through an amorphous capping layer, breaking through the necessity of surface cleaning of thin film samples. Thereby, this opens new frontiers in diagnostics of authentic momentum-resolved electronic structure of protected thin-film heterostructures.
(X/peanut)-shaped features observed in a significant fraction of disk galaxies are thought to have formed from vertically buckled bars. Despite being three dimensional structures, they are preferentially detected in near edge-on projection. Only a few galaxies are found to have displayed such structures when their disks are relatively face-on - suggesting that either they are generally weak in face-on projection or many may be hidden by the light of their galaxy's face-on disk.   Here we report on three (collisionless) simulated galaxies displaying peanut-shaped structures when their disks are seen both face-on and edge-on - resembling a three-dimensional peanut or dumbbell. Furthermore, these structures are accompanied by ansae and an outer ring at the end of the bar --- as seen in real galaxies such as IC~5240.   The same set of quantitative parameters used to measure peanut structures in real galaxies have been determined for the simulated galaxies, and a broad agreement is found. In addition, the peanut length grows in tandem with the bar, and is a maximum at half the length of the bar. Beyond the cutoff of these peanut structures, towards the end of the bar, we discover a new positive/negative feature in the $B_6$ radial profile associated with the isophotes of the ansae/ring.   Our simulated, self-gravitating, three-dimensional peanut structures display cylindrical rotation even in the near-face-on disk projection. In addition, we report on a kinematic pinch in the velocity map along the bar minor-axis, matching that seen in the surface density map.
Inspired by the recent measurement of the B(E2;$0_{2}^{+} \to 2_{1}^+$) and B(E0;$0_{2}^{+} \to 0_{1}^+$) values in $^{12}$Be, we give an interpretation of available spectroscopic data on both $^{12}$Be and $^{11}$Be, using a simple model which contains the essential feature of these two nuclei; the presence of weakly-bound neutron(s) in deformed potentials. The agreement of the calculated results with observed data is surprisingly good, including well-known strong E1 transitions in both nuclei.
This paper studies the sharp interface limit for a mass conserving Allen-Cahn equation added an external noise and derives a stochastically perturbed mass conserving mean curvature flow in the limit. The stochastic term destroys the precise conservation law, instead the total mass changes like a Brownian motion in time. For our equation, the comparison argument does not work, so that to study the limit we adopt the asymptotic expansion method, which extends that for deterministic equations used in Chen et al. [3]. Differently from the deterministic case, each term except the leading term appearing in the expansion of the solution in a small parameter $\epsilon$ diverges as $\epsilon$ tends to $0$, since our equation contains the noise which converges to a white noise and the products or the powers of the white noise diverge. To derive the error estimate for our asymptotic expansion, we need to establish the Schauder estimate for a diffusion operator with coefficients determined from higher order derivatives of the noise and their powers. We show that one can choose the noise sufficiently mild in such a manner that it converges to the white noise and at the same time its diverging speed is slow enough for establishing a necessary error estimate.
In this work, we consider the one dimensional very singular fourth-order equation for solid-on-solid model in attachment-detachment-limit regime with exponential nonlinearity $$h_t = \nabla \cdot (\frac{1}{|\nabla h|} \nabla e^{\frac{\delta E}{\delta h}}) =\nabla \cdot (\frac{1}{|\nabla h|}\nabla e^{- \nabla \cdot (\frac{\nabla h}{|\nabla h|})})$$ where total energy $E=\int |\nabla h|$ is the total variation of $h$. Using a logarithmic correction $E=\int |\nabla h|\ln|\nabla h| d x$ and gradient flow structure with a suitable defined functional, we prove the evolution variational inequality solution preserves a positive gradient $h_x$ which has upper and lower bounds but in BV space. We also obtain the global strong solution to the solid-on-solid model which allows an asymmetric singularity $h_{xx}^+$ happens.
The multiperipheral ladder structure of the Pomeron leads to the quite natural conclusion that the elastic slope Bel is not simple linear function of the colliding particles energy logarithm. The existing experimental data on the diffraction cone shrinkage points to such "complicated" dependence indeed. The shrinkage diffraction cone speed up with the beam energy is directly connected with an extreme rise of total cross-section (Froissart limit).
Results of the time variability monitoring of the two classical T Tauri stars, RU Lup and IM Lup, are presented. Three photometric data sets were utilised: (1) simultaneous (same field) MOST satellite observations over four weeks in each of the years 2012 and 2013, (2) multicolour observations at the SAAO in April - May of 2013, (3) archival V-filter ASAS data for nine seasons, 2001 - 2009. They were augmented by an analysis of high-resolution, public-domain VLT-UT2 UVES spectra from the years 2000 to 2012. From the MOST observations, we infer that irregular light variations of RU Lup are caused by stochastic variability of hot spots induced by unstable accretion. In contrast, the MOST light curves of IM Lup are fairly regular and modulated with a period of about 7.19 - 7.58 d, which is in accord with ASAS observations showing a well defined 7.247+/-0.026 d periodicity. We propose that this is the rotational period of IM Lup and is due to the changing visibility of two antipodal hot spots created near the stellar magnetic poles during the stable process of accretion. Re-analysis of RU Lup high-resolution spectra with the Broadening Function approach reveals signs of a large polar cold spot, which is fairly stable over 13 years. As the star rotates, the spot-induced depression of intensity in the Broadening Function profiles changes cyclically with period 3.71058 d, which was previously found by the spectral cross-correlation method.
By using the $q$-analogue of van der Corput's method we study the divisor function in an arithmetic progression to modulus $q$. We show that the expected asymptotic formula holds for a larger range of $q$ than was previously known, provided that $q$ has a certain factorisation.
We discuss the equation of state of neutron stars in the dense interior considering hyperons and the possible onset of kaon condensation within the relativistic mean field model. We find that hyperons are favoured in dense matter and that their appearance make the existence of a kaon condensed phase quite unlikely. Implications for the recent measurements of kaons in heavy ion collisions at subthreshold energy are also given.
We present analytical and numerical calculations for some exited states of the frustrated J1-J2 spin-1/2 Heisenberg model for linear chains and square lattices. We consider the lowest eigenstates in the subspaces determined by the eigenvalue M of the spin operator S_total^z. Because of the reduced number of Ising basis states in the subspaces with higher M we are able to diagonalize systems with up to N=144 spins. We find evidence that the Marshall-Peierls sign rule survives for a relatively large frustration parameter J2.
In this work, phosphorous-doped single-walled carbon nanotubes have been synthesized by the thermal decomposition of trimethylphosphine using a high-vacuum chemical vapor deposition method. Furthermore, a modified density-gradient-ultracentrifugation process has been applied to carefully purify our doped material. The combined use of Raman and X-ray photoelectron spectroscopy allowed us to provide the first insight into the bonding environment of P incorporated into the carbon lattice, avoiding competing signals arising from synthesis byproducts. This study represents the first step toward the identification of the bonding configuration of P atoms when direct substitution takes place.
We consider the dynamical off-equilibrium behavior of the three-dimensional O$(N)$ vector model in the presence of a slowly-varying time-dependent spatially-uniform magnetic field ${\bm H}(t) = h(t)\,{\bm e}$, where ${\bm e}$ is a $N$-dimensional constant unit vector, $h(t)=t/t_s$, and $t_s$ is a time scale, at fixed temperature $T\le T_c$, where $T_c$ corresponds to the continuous order-disorder transition. The dynamic evolutions start from equilibrium configurations at $h_i < 0$, correspondingly $t_i < 0$, and end at time $t_f > 0$ with $h(t_f) > 0$, or vice versa. We show that the magnetization displays an off-equilibrium scaling behavior close to the transition line ${\bm H}(t)=0$. It arises from the interplay among the time $t$, the time scale $t_s$, and the finite size $L$. The scaling behavior can be parametrized in terms of the scaling variables $t_s^\kappa/L$ and $t/t_s^{\kappa_t}$, where $\kappa>0$ and $\kappa_t > 0$ are appropriate universal exponents, which differ at the critical point and for $T < T_c$. In the latter case, $\kappa$ and $\kappa_t$ also depend on the shape of the lattice and on the boundary conditions. We present numerical results for the Heisenberg ($N=3$) model under a purely relaxational dynamics. They confirm the predicted off-equilibrium scaling behaviors at and below $T_c$. We also discuss hysteresis phenomena in round-trip protocols for the time dependence of the external field. We define a scaling function for the hysteresis loop area of the magnetization that can be used to quantify how far the system is from equilibrium.
We present the Catalog of High REsolution Spectra of Obscured Sources (CHRESOS) from the XMM-Newton Science Archive. It comprises the emission-line luminosities of H- and He-like transitions from C to Si, and the Fe 3C and Fe 3G L-shell ones. Here, we concentrate on the soft X-ray OVII(f) and OVIII Ly_alpha emission lines to shed light onto the physical processes with which their formation can be related to: active galactic nucleus vs. star forming regions. We compare their luminosity with that of two other important oxygen key lines [OIII]5007A, in the optical, and [OIV]25.89mic, in the IR. We also test OVII(f) and OVIIILy_alpha luminosities against that of continuum bands in the IR and hard X-rays, which point to different ionization processes. We probe into those processes by analyzing photoionization and colisional ionization model predictions upon our lines. We show that both scenarios can explain the formation and observed intensities of OVII(f) and OVIII Ly_alpha. By analyzing the relationships between OVII(f) and OVIII Ly_alpha, and all other observables: [OIII]5007A, [OIV]25.89mic emission lines, and MIR-12mic, FIR-60mic, FIR-100mic, 2-10 keV and 14-195 keV continuum bands, we conclude that the AGN radiation field is mainly responsible of the soft X-ray oxygen excitation.
We present an analysis of the MgII 2796, 2803 and FeII 2586, 2600 absorption line profiles in individual spectra of 105 galaxies at 0.3<z<1.4. The galaxies, drawn from redshift surveys of the GOODS fields and the Extended Groth Strip, fully sample the range in star formation rates (SFRs) occupied by the star-forming sequence with stellar masses log M_*/M_sun > 9.5 at 0.3<z<0.7. Using the Doppler shifts of the MgII and FeII absorption lines as tracers of cool gas kinematics, we detect large-scale winds in 66+/-5% of the galaxies. HST/ACS imaging and our spectral analysis indicate that the outflow detection rate depends primarily on galaxy orientation: winds are detected in ~89% of galaxies having inclinations (i) <30 degrees (face-on), while the wind detection rate is only ~45% in objects having i>50 degrees (edge-on). Combined with the comparatively weak dependence of the wind detection rate on intrinsic galaxy properties, this suggests that biconical outflows are ubiquitous in normal, star-forming galaxies at z~0.5. We find that the wind velocity is correlated with host galaxy M_* at 3.4-sigma significance, while the equivalent width of the flow is correlated with host galaxy SFR at 3.5-sigma significance, suggesting that hosts with higher SFR may launch more material into outflows and/or generate a larger velocity spread for the absorbing clouds. Assuming that the gas is launched into dark matter halos with simple, isothermal density profiles, the wind velocities measured for the bulk of the cool material (~200-400 km/s) are sufficient to enable escape from the halo potentials only for the lowest-M_* systems in the sample. However, the outflows typically carry sufficient energy to reach distances of >50 kpc, and may therefore be a viable source of cool material for the massive circumgalactic medium observed around bright galaxies at z~0. [abridged]
We formulate a theory of slow polaritons in atomic gases and apply it to the slowing down, storing, and redirecting of laser pulses in an EIT medium. The normal modes of the coupled matter and radiation are determined through a full diagonalization of the dissipationless Hamiltonian. Away from the EIT resonance where the polaritons acquire an excited-state contribution, lifetimes are introduced as a secondary step. With detuning included various four-wave mixing possibilities are analyzed. We investigate specifically the possibility of reverting a stopped polariton by reversing the control beam.
Tournaments are orientations of the complete graph, and the directed Ramsey number $R(k)$ is the minimum number of vertices a tournament must have to be guaranteed to contain a transitive subtournament of size $k$, which we denote by $TT_k$. We include a computer-assisted proof of a conjecture by Sanchez-Flores that all $TT_6$-free tournaments on 24 and 25 vertices are subtournaments of $ST_{27}$, the unique largest TT_6-free tournament. We also classify all $TT_6$-free tournaments on 23 vertices. We use these results, combined with assistance from SAT technology, to obtain the following improved bounds: $34 \leq R(7) \leq 47$.
Supernova 1604 is the last Galactic supernova for which historical records exist. Johannes Kepler's name is attached to it, as he published a detailed account of the observations made by himself and European colleagues. Supernova 1604 was very likely a Type Ia supernova, which exploded 350 pc to 750 pc above the Galactic plane. Its supernova remnant, known as Kepler's supernova remnant, shows clear evidence for interaction with nitrogen-rich material in the north/northwest part of the remnant, which, given the height above the Galactic plane, must find its origin in mass loss from the supernova progenitor system. The combination of a Type Ia supernova and the presence of circumstellar material makes Kepler's supernova remnant a unique object to study the origin of Type Ia supernovae. The evidence suggests that the progenitor binary system of supernova 1604 consisted of a carbon- oxygen white dwarf and an evolved companion star, which most likely was in the (post) asymptotic giant branch of its evolution. A problem with this scenario is that the companion star must have survived the explosion, but no trace of its existence has yet been found, despite a deep search.   1 Introduction; 2 The supernova remnant, its distance and multiwavelength properties; 2.1 Position, distance estimates and SN1604 as a runaway system; 2.2 X-ray imaging spectroscopy and SN1604 as a Type Ia supernova 2.3 The circumstellar medium as studied in the optical and infrared; 3 The dynamics of Kepler's SNR; 3.1 Velocity measurements; 3.2 Hydrodynamical simulations; 4 The progenitor system of SN 1604; 4.1 Elevated circumstellar nitrogen abundances, silicates and a single degenerate scenario for SN1604; 4.2 Problems with a single degenerate Type Ia scenario for SN 1604; 4.3 Was SN 1604 a core-degenerate Type Ia explosion?; 4.4 What can we learn from the historical light curve of SN 1604? ; 5 Conclusions