ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $p_n$ be the number of partitions of an integer $n$. For each of the partition statistics of counting their parts, ranks, or cranks, there is a natural family of integer polynomials. We investigate their asymptotics and the limiting behavior of their zeros as sets and densities.
The exact numerical diagonalization of the Hamiltonian of a 2D circular quantum dot is performed for 2, 3, and 4 electrons.The results are compared with those of the perturbation theory.Our numerical results agree reasonably well for small values of the dimensionles coupling constant \lambda=a\over a_B where a is the dot radius and a_B is the effective Bohr radius.Exact diagonalization results are compared with the classical predictions, and they are found to be almost coincident for large \lambda values. PACS Numbers: 73.20.Dx, 73.61.-r
The search for Dark Matter (DM) has great potential to reveal physics beyond the Standard Model. As such, searches for evidence of DM particles are being carried out using a wide range of techniques, such as direct searches for DM particles, searches for DM produced with colliders, and indirect searches for the Standard Model annihilation products of DM. Dwarf spheroidal galaxies (dSphs) are excellent targets for indirect Dark Matter searches due to their relatively high DM content and negligible expected astrophysical background. A collaboration was formed to maximise the sensitivity of DM searches towards dSphs by combining for the first time dSph data from three imaging air Cherenkov telescope (IACT) arrays: HESS, MAGIC, and VERITAS; the Fermi-LAT satellite, and the water Cherenkov detector HAWC. Due to the diverse nature of the instruments involved, each experiment will analyse their individual datasets from multiple targets and then the results will be combined at the likelihood level. For consistency of the likelihoods across the five experiments, a common approach is used to treat the astrophysical factor (J-Factor) for each target and an agreed set of annihilation channels are considered. We also agree on a common statistical approach and treatment of instrumental systematic uncertainties. The results are presented in terms of constraints on the velocity-weighted cross section for DM self-annihilation as a function of the DM particle mass.
Using a set of high resolution simulations, we quantify the effect of species specific initial transfer functions on probes of the IGM via the Lyman-$\alpha$ forest. We focus on redshifts $2-6$, after H~{\sc i} reionization. We explore the effect of these initial conditions on measures of the thermal state of the low density IGM: the curvature, Doppler width cutoff, and Doppler width distribution. We also examine the matter and flux power spectrum, and potential consequences for constraints on warm dark matter models. We find that the curvature statistic is at most affected at the $\approx2\%$ level at $z=6$. The Doppler width cutoff parameters are affected by $\approx5\%$ for the intercept, and $\approx8\%$ for the fit slope, though this is subdominant to sample variation. The Doppler width distribution shows a $\approx30\%$ effect at $z=3$, however the distribution is not fully converged with simulation box size and resolution. The flux power spectrum is at most affected by $\approx5\%$ at high redshift and small scales. We discuss numerical convergence with simulation parameters.
We present a catalogue of photometric and structural properties of 228 nuclear star clusters (NSCs) in nearby late-type disk galaxies. These new measurements are derived from a homogeneous analysis of all suitable WFPC2 images in the $HST$ archive. The luminosity and size of each NSC is derived from an iterative PSF-fitting technique, which adapts the fitting area to the effective radius ($r_{\rm eff}$) of the NSC, and uses a WFPC2-specific PSF model tailored to the position of each NSC on the detector. The luminosities of NSCs are $\leq\!10^8L_{\rm V,\odot}$, and their integrated optical colours suggest a wide spread in age. We confirm that most NSCs have sizes similar to Globular Clusters (GCs), but find that the largest and brightest NSCs occupy the regime between Ultra Compact Dwarf (UCD) and the nuclei of early-type galaxies in the size-luminosity plane. The overlap in size, mass, and colour between the different incarnations of compact stellar systems provides a support for the notion that at least some UCDs and the most massive Galactic GCs, may be remnant nuclei of disrupted disk galaxies. We find tentative evidence for the NSCs' $r_{\rm eff}$ to be smaller when measured in bluer filters, and discuss possible implications of this result. We also highlight a few examples of complex nuclear morphologies, including double nuclei, extended stellar structures, and nuclear $F606W$ excess from either recent (circum-)nuclear star formation and/or a weak AGN. Such examples may serve as case studies for ongoing NSC evolution via the two main suggested mechanisms, namely cluster merging and $in\ situ$ star formation.
Training convolutional networks for semantic segmentation requires per-pixel ground truth labels, which are very time consuming and hence costly to obtain. Therefore, in this work, we research and develop a hierarchical deep network architecture and the corresponding loss for semantic segmentation that can be trained from weak supervision, such as bounding boxes or image level labels, as well as from strong per-pixel supervision. We demonstrate that the hierarchical structure and the simultaneous training on strong (per-pixel) and weak (bounding boxes) labels, even from separate datasets, constantly increases the performance against per-pixel only training. Moreover, we explore the more challenging case of adding weak image-level labels. We collect street scene images and weak labels from the immense Open Images dataset to generate the OpenScapes dataset, and we use this novel dataset to increase segmentation performance on two established per-pixel labeled datasets, Cityscapes and Vistas. We report performance gains up to +13.2% mIoU on crucial street scene classes, and inference speed of 20 fps on a Titan V GPU for Cityscapes at 512 x 1024 resolution. Our network and OpenScapes dataset are shared with the research community.
We have estimated a metallicity map of the Large Magellanic Cloud (LMC) using the Magellanic Cloud Photometric Survey (MCPS) and Optical Gravitational Lensing Experiment (OGLE III) photometric data. This is a first of its kind map of metallicity up to a radius of 4 - 5 degrees, derived using photometric data and calibrated using spectroscopic data of Red Giant Branch (RGB) stars. We identify the RGB in the V, (V$-$I) colour magnitude diagrams of small subregions of varying sizes in both data sets. We use the slope of the RGB as an indicator of the average metallicity of a subregion, and calibrate the RGB slope to metallicity using spectroscopic data for field and cluster red giants in selected subregions. The average metallicity of the LMC is found to be [Fe/H] = $-$0.37 dex ($\sigma$[Fe/H] = 0.12) from MCPS data, and [Fe/H] = $-$0.39 dex ($\sigma$[Fe/H] = 0.10) from OGLE III data. The bar is found be the most metal-rich region of the LMC. Both the data sets suggest a shallow radial metallicity gradient up to a radius of 4 kpc ($-$0.049$\pm$0.002 dex kpc$^{-1}$ to $-$0.066$\pm$0.006 dex kpc$^{-1}$). Subregions in which the mean metallicity differs from the surrounding areas do not appear to correlate with previously known features; spectroscopic studies are required in order to assess their physical significance.
The nature of gravity is fundamental to our understanding of our own solar system, the galaxy and the structure and evolution of the Universe. Einstein's general theory of relativity is the standard model that is used for almost ninety years to describe gravitational phenomena on these various scales. We review the foundations of general relativity, discuss the recent progress in the tests of relativistic gravity, and present motivations for high-accuracy gravitational experiments in space. We also summarize the science objectives and technology needs for the laboratory experiments in space with laboratory being the entire solar system. We discuss the advances in our understanding of fundamental physics anticipated in the near future and evaluate discovery potential for the recently proposed gravitational experiments.
For $\gamma>-{1/2}$, we provide the Karhunen-Lo\`{e}ve expansion of the weighted mean-centered Wiener process, defined by \[W _{\gamma}(t)=\frac{1}{\sqrt{1+2\gamma}}\Big\{W\big(t^{1+2\gamma}\big)- \int_0^1W\big(u^{1+2\gamma}\big)du\Big\},\] for $t\in(0,1]$. We show that the orthogonal functions in these expansions have simple expressions in term of Bessel functions. Moreover, we obtain that the $L^2[0,1]$ norm of $W_{\gamma}$ is identical in distribution with the $L^2[0,1]$ norm of the weighted Brownian bridge $t^{\gamma}B(t)$.
The hydrodynamic evolution of self-gravitating gaseous stars is governed by the Euler-Poisson equations. We study the structure of the linear approximation of barotropic perturbations around spherically symmetric equilibria based on functional analytic tools. In contrast to folklore, we show that the spectrum of the linearized operator for general perturbations is not of the Sturm-Liouville type unless the perturbations are restricted. In particular, we prove that it is of the Sturm-Liouville type for irrotational perturbations.
Gravitational waves from the inspiral and coalescence of supermassive black-hole (SMBH) binaries with masses ~10^6 Msun are likely to be among the strongest sources for the Laser Interferometer Space Antenna (LISA). We describe a three-stage data-analysis pipeline designed to search for and measure the parameters of SMBH binaries in LISA data. The first stage uses a time-frequency track-search method to search for inspiral signals and provide a coarse estimate of the black-hole masses m_1, m_2 and of the coalescence time of the binary t_c. The second stage uses a sequence of matched-filter template banks, seeded by the first stage, to improve the measurement accuracy of the masses and coalescence time. Finally, a Markov Chain Monte Carlo search is used to estimate all nine physical parameters of the binary. Using results from the second stage substantially shortens the Markov Chain burn-in time and allows us to determine the number of SMBH-binary signals in the data before starting parameter estimation. We demonstrate our analysis pipeline using simulated data from the first LISA Mock Data Challenge. We discuss our plan for improving this pipeline and the challenges that will be faced in real LISA data analysis.
The Lugiato-Lefever equation is a cubic nonlinear Schr\"odinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a four-dimensional reversible dynamical system in which the evolutionary variable is the space variable. Relying upon tools from bifurcation theory and normal forms theory, we discuss the codimension 1 bifurcations. We prove the existence of various types of steady solutions, including spatially localized, periodic, or quasi-periodic solutions.
The initial mass function (IMF) is a key ingredient in many studies of galaxy formation and evolution. Although the IMF is often assumed to be universal, there is continuing evidence that it is not universal. Spectroscopic studies that derive the IMF of the unresolved stellar populations of a galaxy often assume that this spectrum can be described by a single stellar population (SSP). To alleviate these limitations, in this paper we have developed a unique hierarchical Bayesian framework for modelling composite stellar populations (CSPs). Within this framework we use a parameterized IMF prior to regulate a direct inference of the IMF. We use this new framework to determine the number of SSPs that is required to fit a set of realistic CSP mock spectra. The CSP mock spectra that we use are based on semi-analytic models and have an IMF that varies as a function of stellar velocity dispersion of the galaxy. Our results suggest that using a single SSP biases the determination of the IMF slope to a higher value than the true slope, although the trend with stellar velocity dispersion is overall recovered. If we include more SSPs in the fit, the Bayesian evidence increases significantly and the inferred IMF slopes of our mock spectra converge, within the errors, to their true values. Most of the bias is already removed by using two SSPs instead of one. We show that we can reconstruct the variable IMF of our mock spectra for signal-to-noise ratios exceeding $\sim$75.
A quantum mean field theory of the pyrochlore lattice is presented. The starting point is not the individual magnetic ions, as in the usual Curie-Weiss mean field theory, but a set of interacting corner sharing tetrahedra. We check the consistency of the model against magnetic susceptibility data, and find a good agreement between the theoretical predictions and the experimental data. Implications of the model and future extensions are also discussed.
We investigate the formation of molecular clouds from atomic gas by using three-dimensional magnetohydrodynamical simulations,including non-equilibrium chemical reactions, heating/cooling processes, and self-gravity by changing the collision speed $V_0$ and the angle $\theta$ between the magnetic field and colliding flow. We found that the efficiency of the dense gas formation depends on $\theta$. For small $\theta$, anisotropic super-Alfv\'enic turbulence delays the formation of gravitationally unstable clumps. An increase in $\theta$ develops shock-amplified magnetic fields along which the gas is accumulated, making prominent filamentary structures. We further investigate the statistical properties of dense clumps identified with different density thresholds. The statistical properties of the dense clumps with lower densities depend on $V_0$ and $\theta$ because their properties are inherited from the global turbulence structure of the molecular clouds. By contrast, denser clumps appear to have asymptotic universal statistical properties, which do not depend on the properties of the colliding flow significantly. The internal velocity dispersions approach subsonic and plasma $\beta$ becomes order of unity. We develop an analytic formula of the virial parameter which reproduces the simulation results reasonably well. This property may be one of the reasons for the universality of the initial mass function of stars.
According to a recent suggestion [1], the energy--momentum tensor for gravitating fields can be computed through a suitable rearrangement of the matter field equations, without relying on the variational definition. We show that the property observed by Accioly et al. in [1] is the consequence of a general identity, which follows from the covariance of the matter Lagrangian in much the same way as (generalized) Bianchi identities follow from the covariance of the purely gravitational Lagrangian. However, we also show that only in particular cases can this identity be used to obtain the actual form of the stress-energy tensor, while in general the method leads to ambiguities and possibly to wrong results. Moreover, in nontrivial cases the computations turn out to be more difficult than the standard variational technique.
Artificial PbTiO$_{3}$/SrTiO$_{3}$ superlattices were constructed using off-axis RF magnetron sputtering. X-ray diffraction and piezoelectric atomic force microscopy were used to study the evolution of the ferroelectric polarization as the ratio of PbTiO$_{3}$ to SrTiO$_{3}$ was changed. For PbTiO$_{3}$ layer thicknesses larger than the 3-unit cells SrTiO$_{3}$ thickness used in the structure, the polarization is found to be reduced as the PbTiO$_{3}$ thickness is decreased. This observation confirms the primary role of the depolarization field in the polarization reduction in thin films. For the samples with ratios of PbTiO$_{3}$ to SrTiO$_{3}$ of less than one a surprising recovery of ferroelectricity that cannot be explained by electrostatic considerations was observed.
The aim of the present thesis is to review the Blanchet-Damour approach to analytical study of gravitational waves emitted by localized perfect fluid sources. It is assumed these perfect fluids are such that it is possible to define small parameters for asymptotic expansions. Asymptotic expansions in this approach are called post-Minkowskian and post-Newtonian expansions. By plugging these expansions into the Einstein field equation, post-Minkowskian and post-Newtonian equations are obtained. The usual methods for solving these equations are to use the retarded and Poisson integrals. However, they cannot provide solutions up to any arbitrary order in these cases because of their divergence. In fact, these divergences motivated Blanchet and Damour to employ a new approach to solve the post-Minkowskian and post-Newtonian equations. They obtained the general solutions by means of a specific process of analytic continuation. These solutions have some unknown terms that if one determines, the gravitational field is described everywhere in $\mathbb{R}^3$. A matching procedure, which depends deeply on analytic continuation, is used to determine these unknown terms.
The two-dimensional spin-gap system ${\rm SrCu_2(BO_3)_2}$ shows unique physical properties due to the low-dimensionality character and the strong quantum fluctuations. Experimentally, 1/8-, 1/4-, and 1/3-plateaus have been observed in the magnetization curve under magnetic fields up to 70 Tesla, and the 1/2-plateau is expected to be stabilized at higher magnetic fields. We argue that spin-lattice effects are necessary to describe the superstructures at the plateaus, and we propose a simple microscopic model of spins interacting adiabatically with the lattice to reproduce the main features of the recent experimental results by nuclear magnetic resonance.
Monolayer islands of molybdenum disulfide (MoS$_2$) on Au(111) form a characteristic moir\'e structure, leading to locally different stacking sequences at the S-Mo-S-Au interface. Using low-temperature scanning tunneling microscopy (STM) and atomic force microscopy (AFM), we find that the moir\'e islands exhibit a unique orientation with respect to the Au crystal structure. This indicates a clear preference of MoS$_2$ growth in a regular stacking fashion. We further probe the influence of the local atomic structure on the electronic properties. Differential conductance spectra show pronounced features of the valence band and conduction band, some of which undergo significant shifts depending on the local atomic structure. We also determine the tunneling decay constant as a function of the bias voltage by a height-modulated spectroscopy method. This allows for an increased sensitivity of states with non-negligible parallel momentum $k_\parallel$ and the identification of the origin of the states from different areas in the Brillouin zone.
Doping a semiconductor quantum dot with just a single impurity atom can completely transform its physical properties. Here, we report and analyze the magnetic circular dichroism (MCD) spectra of colloidal CdSe quantum dot samples containing on average fewer than one Mn2+ per quantum dot. Even at this sub-single-dopant level, the low-temperature low-field data are dominated by impurity-induced Zeeman splittings caused by dopant-carrier sp-d exchange. Unlike in more heavily doped quantum dots, however, the MCD intensity at the first CdSe exciton shows a field-induced sign flip as the field strength is increased, reflecting competition between sp-d exchange and the intrinsic Zeeman splittings of comparable magnitude. Most unusually, the competition between these two effects leads to a large apparent shift in the first MCD peak maximum, which we show is attributable to a difference in sign of the intrinsic excitonic g factor between the first and second excitons. Finally, the sp-d and intrinsic contributions to the excitonic Zeeman splittings each exhibit unique magnetic-field and temperature dependencies, allowing the MCD spectra of undoped, singly doped, and bi-doped quantum dot sub-ensembles to be analyzed.
Phase transitions are investigated in the Bose-Fermi-Hubbard model in the mean field and hard-core boson approximations for the case of infinitely small fermion transfer and repulsive on-site boson-fermion interaction. The behavior of the Bose-Einstein condensate order parameter and grand canonical potential is analyzed as functions of the chemical potential of bosons at zero temperature. The possibility of change of order of the phase transition to the superfluid phase in the regime of fixed values of the chemical potentials of Bose- and Fermi-particles is established. The relevant phase diagrams are built.
In a Bayesian context, theoretical parameters are correlated random variables. Then, the constraints on one parameter can be improved by either measuring this parameter more precisely - or by measuring the other parameters more precisely. Especially in the case of many parameters, a lengthy process of guesswork is then needed to determine the most efficient way to improve one parameter's constraints. In this short article, we highlight an extremely simple analytical expression that replaces the guesswork and that facilitates a deeper understanding of optimization with interdependent parameters.
Although a nuclear spin is weakly coupled to its environment, due to its small gyromagnetic ratio, its coherence time is limited by the hyperfine coupling to a nearby noisy electron. Here, we propose to utilize continuous dynamical decoupling to refocus the coupling to the electron. If the random phase accumulated by the nuclear spin through the reduced coupling terms is sufficient small, we can increase the nuclear coherence time. Initially, we demonstrate this on a simple case with a two-level electron spin, while taking all relevant hyperfine coupling terms and noise terms into account. We then extend the analysis to a nitrogen-vacancy center in diamond having a three level structure.
In the context of equation-free computation, we devise and implement a procedure for using short-time direct simulations of a KPZ type equation to calculate the self-similar solution for its ensemble averaged correlation function. The method involves "lifting" from candidate pair-correlation functions to consistent realization ensembles, short bursts of KPZ-type evolution, and appropriate rescaling of the resulting averaged pair correlation functions. Both the self-similar shapes and their similarity exponents are obtained at a computational cost significantly reduced to that required to reach saturation in such systems.
We present and discuss the properties of a complete and well defined sample of X-ray selected type 1 AGNs including 26 Narrow-Line Seyfert 1 and 129 Broad-Line Seyfert 1 galaxies derived from the XMM-Newton Bright Serendipitous Survey (XBS). We study the differences between the two classes of AGNs for what concerns the X-ray properties (the photon-index) and the main physical parameters, like the Black-Hole mass and the Eddington ratio. We then consider the two classes together and look for statistical correlations between observed and physical parameters. We find a significant dependence of the photon-index with the Eddington ratio and a weaker (possibly secondary) correlation between the photon index and the Black-Hole Mass.