ShantanuT01/DACTYL-Pretraining huggingface dataset:
The kinetic and interaction energies of a three-dimensional dilute ground-state Bose gas confined in a trap are calculated beyond a mean-field treatment. They are found to depend on the pairwise interaction trough two characteristic lengths: the first, a, is the well-known scattering length and the second, b, is related to the latter by b=a-\lambda d a/d\lambda with \lambda being the coupling constant. Numerical estimations show that the pairwise interaction energy of a dilute gas of alkali atoms in a trap is negative (in spite of the positive scattering length); its absolute value is found by about the order of magnitude larger than that of the mean-field interaction energy that corresponds to the last term in the Gross-Pitaevskii functional.
In this article, we investigate sparse subsets of the natural numbers and study the sparseness of some sets associated with the Euler's totient function $\phi$ via the property of `Banach Density'. These sets related to the totient function are defined as follows: $V:=\phi(\mathbb{N})$ and $N_i:=\{N_i(m)\colon m\in V \}$ for $i = 1, 2, 3,$ where $N_1(m)=\max\{x\in \mathbb{N}\colon \phi(x)\leq m\}$, $N_2(m)=\max(\phi^{-1}(m))$ and $N_3(m)=\min(\phi^{-1}(m))$ for $ m\in V$. Masser and Shiu call the elements of $N_1$ as `sparsely totient numbers' and construct an infinite family of these numbers. Here we construct several infinite families of numbers in $N_2\setminus N_1$ and an infinite family of composite numbers in $N_3$. We also study (i) the ratio $\frac{N_2(m)}{N_3(m)}$, which is linked to the Carmichael's conjecture, namely, $|\phi^{-1}(m)|\geq 2 ~\forall ~ m\in V$, and (ii) arithmetic and geometric progressions in $N_2$ and $N_3$.   Finally, using the above sets associated to the totient function, we generate an infinite class of subsets of $\mathbb{N}$, each with asymptotic density zero and containing arbitrarily long arithmetic progressions.
We present ground-based observations of the nu_1 and nu_3 fundamental bands of H2O toward the massive protostar AFGL 2136 IRS 1, identifying absorption features due to 47 different ro-vibrational transitions between 2.468 micron and 2.561 micron. Analysis of these features indicates the absorption arises in warm (T=506+-25 K), very dense (n(H2)>5*10^9 cm^-3) gas, suggesting an origin close to the central protostar. The total column density of warm water is estimated to be N(H2O)=(1.02+-0.02)*10^19 cm^-2, giving a relative abundance of N(H2O)/N(H2)~10^-4. Our study represents the first extensive use of water vapor absorption lines in the near infrared, and demonstrates the utility of such observations in deriving physical parameters.
We present an analysis of archival RXTE and BeppoSAX data of the X-ray source 4U2206+54 . For the first time, high energy data (> 30 kev) are analyzed for this source. The data are well described by comptonization models (CompTT and BMC) in which seed photons with temperatures between 1.1 kev and 1.5 kev are comptonized by a hot plasma at 50 kev thereby producing a hard tail which extends up to, at least, 100 kev. We offer a new method of identification of neutron star systems using a temperature - luminosity relation. If a given X-ray source is characterized by a low bolometric luminosity and a relatively high color blackbody temperature (>1 kev) it has necessarily to be a neutron star rather than a black hole. From these arguments it is shown that the area of the soft photon source must be small (r ~ 1 km) and that the accretion disk, if present, must be truncated very far from the compact object. Here we report on the possible existence of a cyclotron line around 30 kev. The presence of a neutron star in the system is strongly favored by the available data.
To study how supernova feedback structures the turbulent interstellar medium, we construct 3D models of vertically stratified gas stirred by discrete supernova explosions, including vertical gravitational field and parametrized heating and cooling. The models reproduce many observed characteristics of the Galaxy such as global circulation of gas (i.e., galactic fountain) and the existence of cold dense clouds in the galactic disk. Global quantities of the model such as warm and hot gas filling factors in the midplane, mass fraction of thermally unstable gas, and the averaged vertical density profile are compared directly with existing observations, and shown to be broadly consistent. We find that energy injection occurs over a broad range of scales. There is no single effective driving scale, unlike the usual assumption for idealized models of incompressible turbulence. However, >90% of the total kinetic energy is contained in wavelengths shortward of 200 pc. The shape of the kinetic energy spectrum differs substantially from that of the velocity power spectrum, which implies that the velocity structure varies with the gas density. Velocity structure functions demonstrate that the phenomenological theory proposed by Boldyrev is applicable to the medium. We show that it can be misleading to predict physical properties such as the stellar initial mass function based on numerical simulations that do not include self-gravity of the gas. Even if all the gas in turbulently Jeans unstable regions in our simulation is assumed to collapse and form stars in local freefall times, the resulting total collapse rate is significantly lower than the value consistent with the input supernova rate. Supernova-driven turbulence inhibits star formation globally rather than triggering it.
The two Large Magellanic Cloud star clusters NGC 1805 and NGC 1818 are approximately the same chronological age (~30 Myr), but show different radial trends in binary frequency. The F-type stars (1.3 - 2.2 MSun) in NGC 1818 have a binary frequency that decreases towards the core, while the binary frequency for stars of similar mass in NGC 1805 is flat with radius, or perhaps bimodal (with a peak in the core). We show here, through detailed N-body modeling, that both clusters could have formed with the same primordial binary frequency and with binary orbital elements and masses drawn from the same distributions (defined from observations of open clusters and the field of our Galaxy). The observed radial trends in binary frequency for both clusters are best matched with models that have initial substructure. Furthermore, both clusters may be evolving along a very similar dynamical sequence, with the key difference that NGC 1805 is dynamically older than NGC 1818. The F-type binaries in NGC 1818 still show evidence of an initial period of rapid dynamical disruptions (which occur preferentially in the core), while NGC 1805 has already begun to recover a higher core binary frequency, owing to mass segregation (which will eventually produce a distribution in binary frequency that rises only towards the core, as is observed in old Milky Way star clusters). This recovery rate increases for higher-mass binaries, and therefore even at one age in one cluster, we predict a similar dynamical sequence in the radial distribution of the binary frequency as a function of binary primary mass.
Despite more than half a century of studies in heavy-fermion compounds, a full understanding of the various possible magnetic ordering phenomena is still far from complete. Some heavy-fermion materials show so-called hidden-order phases, which are invisible to conventional diffraction techniques. The multipolar moments of the $f$-electrons in their specific crystal field environment play a decisive role in the formation of these phases. Such hidden-order phases have been observed in a variety of compounds containing $4f$ and $5f$ elements, like URu$_2$Si$_2$, NpO$_2$, YbRu$_2$Ge$_2$, and CeB$_6$. The competition or coexistence of multipolar ordering with more conventional magnetic order parameters, such as ferro- or antiferromagnetism, gives rise to complex magnetic-field$-$temperature phase diagrams in these compounds that provide a rich playground for experimental and theoretical investigations. Here I examine the pure and La-doped $f$-electron system CeB$_6$, as well as Ce$_{3}$Pd$_{20}$Si$_{6}$, by means of neutron scattering. The magnetic field dependence of the zone center exciton mode in CeB$_6$ was studied in fields up to 14.5 T and compared with the existing theory. A long standing question of the applicability of the phenomenological temperature dependence $\Gamma=k_{\text B}T_{\text K}+A \sqrt{T}$, where $T_{\text K}$ is the Kondo temperature, for two limiting cases, the Kondo lattice and Kondo impurity, has been investigated on a set of samples diluted with lanthanum. In Ce$_{3}$Pd$_{20}$Si$_{6}$, the order parameter of the AFQ phase was uncovered, and its field dependence was studied in fields up to 9 T.
At the present time even the most sophisticated, multi-dimensional simulations of core-collapse supernovae do not (self-consistently) include neutrino flavor transformation. This physics is missing despite the importance of neutrinos in the core-collapse explosion paradigm. Because of this dependence, any flavor transformation that occurs in the region between the proto-neutron star and the shock could result in major effects upon the dynamics of the explosion. We present the first hydrodynamic core-collapse supernova simulation which simultaneously includes flavor transformation of the free-streaming neutrinos in the neutrino transport. These oscillation calculations are dynamically updated and evolve self-consistently alongside the hydrodynamics. Using a $M=20\;{\rm M_{\odot}}$ progenitor, we find that while the oscillations have an effect on the neutrino emission and the heating rates, flavor transformation alone does not lead to a successful explosion of this progenitor in spherical symmetry.
The quasar Main Sequence (MS) appears to be an incredibly powerful tool to organize the diversity in large samples of type-1 quasars but the most important physical parameters governing it are still unclear. Here we investigate the origin of the broadening and of a defining feature of Population B sources: a strong redward asymmetry of the Balmer emission lines. We focus on a prototypical source, Fairall 9. Spectropolarimetric data of the Fairall 9 broad H$\beta$ and H$\alpha$ profiles allowed for a view of the geometric and dynamical complexity of the line emitting regions. Measurements (1) provided evidence of rotational motion; (2) were helpful to test the presence of polar and equatorial scatterers, and their association with non-virial motions.
We study the resonance spectroscopy of 7He in the 4He+n+n+n cluster model, where the motion of valence neutrons is described in the cluster orbital shell model. Many-body resonances are treated on the correct boundary condition as the Gamow states in the complex scaling method. We obtain five resonances and investigate their properties from the configurations. In particular, the 1/2- state is found in a low excitation energy of 1.1 MeV with a width of 2.2 MeV, while the experimental determination of the position of this state is not so clear. We also evaluate the spectroscopic factors of the 6He-n components in the obtained 7He resonances. The importance of the 6He(2+) state is shown in several states of 7He.
We have studied the magnetic configuration in ultrathin antiferromagnetic Mn films grown around monoatomic steps on an Fe(001) surface by spin-polarized scanning tunneling microscopy/spectroscopy and ab-initio-parametrized self-consistent real-space tight binding calculations in which the spin quantization axis is independent for each site thus allowing noncollinear magnetism. Mn grown on Fe(001) presents a layered antiferromagnetic structure. In the regions where the Mn films overgrows Fe steps the magnetization of the surface layer is reversed across the steps. Around these defects a frustration of the antiferromagnetic order occurs. Due to the weakened magnetic coupling at the central Mn layers, the amount of frustration is smaller than in Cr and the width of the wall induced by the step does not change with the thickness, at least for coverages up to seven monolayers.
Stars with B[e] phenomenon comprise a very diverse group of objects in a different evolutionary status. These objects show common spectral characteristics, including presence of Balmer lines in emission, forbidden lines, and strong infrared excess due to the dust. The observations of emission lines indicate the illumination by ultraviolet ionizing source, which is a key part to understand the elusive nature of these objects. We study the ultraviolet variability of many B[e] stars to specify the geometry of the circumstellar environment and its variability. We analyse massive hot B[e] stars from our Galaxy and from Magellanic Clouds. We study the ultraviolet broad-band variability derived from the flux-calibrated data. We determine variations of individual lines and its correlation with the total flux variability. We detected variability of the spectral energy distribution and of the line profiles. The variability has several sources of origin, including the light absorption by the disk, pulsations, LBV-type variations, and eclipses in the case of binaries. The stellar radiation of most of B[e] stars is heavily obscured by circumstellar material. This suggests that the circumstellar material is not present only in the disk but also above its plane. The flux and line variability is consistent with a two-component model of circumstellar environment composed of the dense disk and ionized envelope. The observations of B[e] supergiants show that many of these stars have nearly the same luminosity of about $1.9\times10^{5}\,L_\odot$ and similar effective temperature.
We construct a class of superprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching density is given by an arbitrary bounded non-negative Borel function, and the superprocess is characterized by a martingale problem as a diffusion process with state space $M(\IR)$, improving and extending considerably the construction of Wang (1997, 1998). It is then proved in a special case that a suitable rescaled process of the superprocess converges to the usual super Brownian motion. An extension to measure-valued branching catalysts is also discussed.
The main purpose of this paper is to investigate several further interesting properties of symmetry for the p-adic invariant integral on Z_p.
Structural distortions in nano-materials can induce dramatic changes in their electronic properties. This situation is well manifested in graphene, a two-dimensional honeycomb structure of carbon atoms with only one atomic layer thickness. In particular, strained graphene can result in both charging effects and pseudo-magnetic fields, so that controlled strain on a perfect graphene lattice can be tailored to yield desirable electronic properties. Here we describe the theoretical foundation for strain-engineering of the electronic properties of graphene, and then provide experimental evidences for strain-induced pseudo-magnetic fields and charging effects in monolayer graphene. We further demonstrate the feasibility of nanoscale strain engineering for graphene-based devices by means of theoretical simulations and nano-fabrication technology.
The physical mechanism for metal ablation induced by femtosecond laser irradiation was investigated. Results of calculations based on finite-temperature density functional theory (FTDFT) indicate that condensed copper becomes unstable at high electron temperatures due to an increase of electronic entropy at large volume, where the local density of states near the Fermi energy increases. Based on these results, an electronic entropy-driven (EED) model is proposed to explain metal ablation with a femtosecond laser. In addition, a mathematical model is developed for simulation of the laser ablation, where the effect of the electronic entropy is included. This mathematical model can quantitatively describe the experimental data in the low-laser-fuence region, where the electronic entropy effect is determined to be especially important.
In this paper we present a new mechanism for rationalizing, explaining and predicting pulsar glitches. Our new mechanism is based upon the concepts of type II superconductivity and the Bradlow bound.
We present a simple functional form for the joint distribution of R-band luminosity and [OII] 3727 emission-line equivalent widths of galaxies, and show that this form is a good fit to the galaxies in the Las Campanas Redshift Survey. We find a relationship between [OII] equivalent width W and R-band luminosity L_R of the approximate form: <W> \approx (10 \AA) (L_R/L_{R,*})^{-1/2}, where L_{R,*} is the characteristic luminosity in the Schechter function. Because this joint distribution yields information about the relationship between stellar mass in a galaxy and its recent star-formation rate, it can be useful for testing theories of galaxy formation. Furthermore, understanding this joint distribution locally will make it easier to interpret the evolution of [OII] emission-line widths to higher redshifts.
Massive stars are the drivers of the chemical evolution of dwarf galaxies. We review here the basics of massive star evolution and the specificities of stellar evolution in low-Z environment. We discuss nucleosynthetic aspects and what observations could constrain our view on the first generations of stars.
The effective spin Hamiltonian of a triple quantum dot with odd electron occupation weakly connected in series with left ($l$) and right ($r$) metal leads is composed of two-channel exchange and co-tunneling terms. Renormalization group equations for the corresponding three exchange constants $J_{l}$, $J_{r}$ and $J_{lr}$ are solved (to third order). Since $J_{lr}$ is relevant, the system is mapped on an anisotropic two-channel Kondo problem. The structure of the conductance as function of temperature and gate voltage implies that in the weak and intermediate coupling regimes, two-channel Kondo physics persists at temperatures as low as several $T_{K}$. At even electron occupation, the number of channels equals twice the spin of the triple dot (hence it is a fully screened impurity).
We revisit the 't Hooft expansion of 1/2 BPS circular Wilson loop in N=4 SYM studied by Drukker and Gross in hep-th/0010274. We find an interesting recursion relation which relates different number of holes on the worldsheet. We also argue that we can turn on the string coupling by applying a certain integral transformation to the planar result.
In this note, we will prove that $\mathbold{\zeta}$ and $\mathbold{\Gamma}$ can not satisfy any differential equation generated through a family of functions continuous in $\mathbold{\zeta}$ with polynomials in $\mathbold{\Gamma}$.
We report on simultaneous radio and X-ray observations of the repeating fast radio burst source FRB 180916.J0158+65 using the Canadian Hydrogen Intensity Mapping Experiment (CHIME), Effelsberg, and Deep Space Network (DSS-14 and DSS-63) radio telescopes and the Chandra X-ray Observatory. During 33 ks of Chandra observations, we detect no radio bursts in overlapping Effelsberg or Deep Space Network observations and a single radio burst during CHIME/FRB source transits. We detect no X-ray events in excess of the background during the Chandra observations. These non-detections imply a 5-$\sigma$ limit of $<5\times10^{-10}$ erg cm$^{-2}$ for the 0.5--10 keV fluence of prompt emission at the time of the radio burst and $1.3\times10^{-9}$ erg cm$^{-2}$ at any time during the Chandra observations at the position of FRB 180916.J0158+65. Given the host-galaxy redshift of FRB 180916.J0158+65 ($z\sim0.034$), these correspond to energy limits of $<1.6\times10^{45}$ erg and $<4\times10^{45}$ erg, respectively. We also place a 5-$\sigma$ limit of $<8\times10^{-15}$ erg s$^{-1}$ cm$^{-2}$ on the 0.5--10\,keV absorbed flux of a persistent source at the location of FRB 180916.J0158+65. This corresponds to a luminosity limit of $<2\times10^{40}$ erg s$^{-1}$. Using Fermi/GBM data we search for prompt gamma-ray emission at the time of radio bursts from FRB 180916.J0158+65 and find no significant bursts, placing a limit of $4\times10^{-9}$ erg cm$^{-2}$ on the 10--100 keV fluence. We also search Fermi/LAT data for periodic modulation of the gamma-ray brightness at the 16.35-day period of radio-burst activity and detect no significant modulation. We compare these deep limits to the predictions of various fast radio burst models, but conclude that similar X-ray constraints on a closer fast radio burst source would be needed to strongly constrain theory.
We generate ring class fields of imaginary quadratic fields in terms of the special values of certain eta-quotients, which are related to the relative norms of Siegel-Ramachandra invariants. These give us minimal polynomials with relatively small coefficients from which we are able to solve certain quadratic Diophantine equations concerning non-convenient numbers.
In [F. Jiang, S. Jiang, On instability and stability of three-dimensional gravity driven viscous flows in a bounded domain, Adv. Math., 264 (2014) 831--863], Jiang et.al. investigated the instability of Rayleigh--Taylor steady-state of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity in a bounded domain $\Omega$ of class $C^2$. In particular, they proved the steady-state is nonlinearly unstable under a restrictive condition of that the derivative function of steady density possesses a positive lower bound. In this article, by exploiting a standard energy functional and more-refined analysis of error estimates in the bootstrap argument, we can show the nonlinear instability result without the restrictive condition.
The protohalo patches from which halos form are defined by a number of constraints imposed on the Lagrangian dark matter density field. Each of these constraints contributes to biasing the spatial distribution of the protohalos relative to the matter. We show how measurements of this spatial distribution -- linear combinations of protohalo bias factors -- can be used to make inferences about the physics of halo formation. Our analysis exploits the fact that halo bias factors satisfy consistency relations which encode this physics, and that these relations are the same even for sub-populations in which assembly bias has played a role. We illustrate our methods using a model in which three parameters matter: a density threshold, the local slope and the curvature of the smoothed density field. The latter two are nearly degenerate; our approach naturally allows one to build an accurate effective two-parameter model for which the consistency relations still apply. This, with an accurate description of the smoothing window, allows one to describe the protohalo-matter cross-correlation very well, both in Fourier and configuration space. We then use our determination of the large scale bias parameters together with the consistency relations, to estimate the enclosed density and mean slope on the Lagrangian radius scale of the protohalos. Direct measurements of these quantities, made on smaller scales than those on which the bias parameters are typically measured, are in good agreement.
In this paper we derive a strong maximum principle for weak supersolutions of nonlocal equations of the form $Iu=c(x) u$ in $\Omega$, where $\Omega\subset \mathbb{R}^N$ is a domain, $c\in L^{\infty}(\Omega)$ and $I$ is an operator of the form $Iu(x)=P.V.\int_{\mathbb{R}^N}(u(x)-u(y))j(x-y)\ dy$ with a nonnegative kernel function $j$. We formulate minimal positivity assumptions on $j$ corresponding to a class of operators which includes highly anisotropic variants of the fractional Laplacian. Somewhat surprisingly, this problem leads to the study of general lattices in $\mathbb{R}^N$. Our results extend to the regional variant of the operator $I$ and, under weak additional assumptions, also to the case of $x$-dependent kernel functions.