ShantanuT01/DACTYL-Pretraining huggingface dataset:
The structural, dielectric and ferroelectric properties of lead-free (Na0.5-xKxBi0.5-xLax)TiO3 powders synthesized by sol-gel self-combustion method were investigated. Rietveld refinement of Synchrotron x-ray diffraction data confirms pure single phase rhombohedral crystal structure with R3c space group for all the compositions and anti-phase octahedral tilting angle decreased with increase in composition x. Homogeneity and elemental proportions were confirmed by Energy dispersive x-ray spectrometry. The temperature-dependent dielectric study has shown two diffuse type of dielectric anomaly for all the samples, due to A-site disorder in the lattice, which has been assigned to two-has transitions: ferroelectric to anti-ferroelectric and anti-ferroelectric to the paraelectric phase transition. The transition temperature of these phase transitions is found to decrease as a function of composition. Thermal stability range of dielectric constant increases from ~100C to 220C as a function of composition. Stable dielectric constant first increases, from 1557 10 % for parent compound, with the composition, highest for 6 % composition with emid ~ 2508 10 % for the temperature range ~180 C to 340C and after that decreases to 1608 10 % for 12 % but remain higher than the parent compound Na0.5Bi0.5TiO3. Ferroelectric measurements have shown monotonously decreasing coercive field as a function of the composition due to a decrease in grain size, confirmed by microstructural studies using Field Emission Scanning Electron Microscope. Exponential increases in the energy storage efficiency from ~ 17 % to 87 % as a function of composition have also observed. These types of materials, with stable high dielectric constant and low tan delta, have a vast scope in the field of the thermally stable dielectric constant materials and energy storage applications.
The effect of nuclear superfluidity on antimagnetic rotation bands in $^{105}$Cd and $^{106}$Cd are investigated by the cranked shell model with the pairing correlations and the blocking effects treated by a particle-number conserving method. The experimental moments of inertia and the reduced $B(E2)$ transition values are excellently reproduced. The nuclear superfluidity is essential to reproduce the experimental moments of inertia. The two-shears-like mechanism for the antimagnetic rotation is investigated by examining the shears angle, i.e., the closing of the two proton hole angular momenta, and its sensitive dependence on the nuclear superfluidity is revealed.
We use inverse methods of statistical mechanics and computer simulations to investigate whether an isotropic interaction designed to stabilize a given two-dimensional (2D) lattice will also favor an analogous three-dimensional (3D) structure, and vice versa. Specifically, we determine the 3D ordered lattices favored by isotropic potentials optimized to exhibit stable 2D honeycomb (or square) periodic structures, as well as the 2D ordered structures favored by isotropic interactions designed to stabilize 3D diamond (or simple cubic) lattices. We find a remarkable `transferability' of isotropic potentials designed to stabilize analogous morphologies in 2D and 3D, irrespective of the exact interaction form, and we discuss the basis of this cross-dimensional behavior. Our results suggest that the discovery of interactions that drive assembly into certain 3D periodic structures of interest can be assisted by less computationally intensive optimizations targeting the analogous 2D lattices.
With a prescribed Coulomb-type energy-momentum tensor, an exact solution of the Einstein field equations over a nonsimply-connected manifold is presented. This spherically symmetric solution has neither curvature singularities nor closed timelike curves. It can be considered to be a regularization of the singular Reissner-Nordstrom solution over a simply-connected manifold.
Let $X$ be an Abelian threefold. We prove a formula, conjectured by the first author, expressing the Euler characteristic of the generalized Kummer schemes $K^nX$ of $X$ in terms of the number of plane partitions. This computes the Donaldson-Thomas invariant of the moduli stack $[K^nX/X_n]$.
The Candidate Cluster and Protocluster Catalog (CCPC) is a list of objects at redshifts z > 2 composed of galaxies with spectroscopically confirmed redshifts that are coincident on the sky and in redshift. These protoclusters are identified by searching for groups in volumes corresponding to the expected size of the most massive protoclusters at these redshifts. In CCPC1 we identified 43 candidate protoclusters among 14,000 galaxies between 2.74 < z < 3.71. Here we expand our search to more than 40,000 galaxies with spectroscopic redshifts z > 2.00, resulting in an additional 173 candidate structures. The most significant of these are 36 protoclusters with overdensities {\delta} > 7. We also identify three large proto-supercluster candidates containing multiple protoclusters at z = 2.3, 3.5 and z = 6.56. Eight candidates with N > 10 or more galaxies are found at redshifts z > 4.0. The last system in the catalog is the most distant spectroscopic protocluster candidate known to date at z = 6.56.
In this paper, we consider nonnegative solutions of spatially heterogeneous Fisher-KPP type reaction-diffusion equations in the whole space. Under some assumptions on the initial conditions, including in particular the case of compactly supported initial conditions, we show that, above any arbitrary positive value, the solution is increasing in time at large times. Furthermore, in the one-dimensional case, we prove that, if the equation is homogeneous outside a bounded interval and the reaction is linear around the zero state, then the solution is time-increasing in the whole line at large times. The question of the monotonicity in time is motivated by a medical imagery issue.
We present a method to investigate the radial stability of a spherical anisotropic system that hosts a central supermassive black hole (SBH). Such systems have never been tested before for stability, although high anisotropies have been considered in the dynamical models that were used to estimate the masses of the central putative supermassive black holes. A family of analytical anisotropic spherical Hernquist models with and without a black hole were investigated by means of N-body simulations. A clear trend emerges that the supermassive black hole has a significant effect on the overall stability of the system, i.e. an SBH with a mass of a few percent of the total mass of the galaxy can prevent or reduce the bar instabilities in anisotropic systems. Its mass not only determines the strength of the instability reduction, but also the time in which this occurs. These effects are most significant for models with strong radial anisotropies. Furthermore, our analysis shows that unstable systems with similar SBH but with different anisotropy radii evolve differently: highly radial systems become oblate, while more isotropic models tend to form into prolate structures. In addition to this study, we also present a Monte-Carlo algorithm to generate particles in spherical anisotropic systems.
We report the discovery of the optical counterpart to GRB 980326. Its rapid optical decay can be characterized by a power law with exponent -2.10 +/- 0.13 and a constant underlying source at R_c=25.5 +/- 0.5. Its optical colours 2.1 days after the burst imply a spectral slope of -0.66 +/- 0.70. The gamma-ray spectrum as observed with BATSE shows that it is among the 4% softest bursts ever recorded. We argue that the rapid optical decay may be a reason for the non-detection of some low-energy afterglows of GRBs.
Functional determinants for a single scalar field with negative mass squared are evaluated on homogeneous lens spaces. For example, on even order spaces, the Hartle--Hawking wave function oscillates about its zeros with increasing amplitude as the (imaginary) mass increases. I also present results for the binary tetrahedral, octahedral and icosahedral factors of the three--sphere. The final answer is given as a quadrature and some graphs are drawn. In the technical evaluation of the infinite sums, the explicit form of the degeneracies is not needed.
The exchange interactions of Cr4N, Mn4N, Fe4N, Co4N, and Ni4N compounds with perovskite structure were calculated to obtain the Curie temperatures for these compounds from Monte Carlo calculations. Contrary to naive expectation, the exchange interactions vary markedly among these five compounds. In Fe4N, the intra-sublattice interaction of the Fe 3c atoms is strongly negative, leading to a significant reduction of the Curie temperature. The calculated Curie temperatures are 291K (Cr4N), 710K (Mn4N), 668K (Fe4N), 827K (Co4N), and 121K (Ni4N), in good agreement with experimental observations where available. The much lower Curie temperature of Ni4N compared to fcc Ni is explained on the basis of the exchange interactions.
We present numerical simulations of orbiting black holes for around twelve cycles, using a high-order multipatch approach. Unlike some other approaches, the computational speed scales almost perfectly for thousands of processors. Multipatch methods are an alternative to AMR (adaptive mesh refinement), with benefits of simplicity and better scaling for improving the resolution in the wave zone. The results presented here pave the way for multipatch evolutions of black hole-neutron star and neutron star-neutron star binaries, where high resolution grids are needed to resolve details of the matter flow.
Let $L$ be a positive definite self-adjoint operator on the $L^2$-space associated to a $\si$-finite measure space. Let $H$ be the dual space of the domain of $L^{1/2}$ w.r.t. $L^2(\mu)$. By using an It\^o type inequality for the $H$-norm and an integrability condition for the hyperbound of the semigroup $P_t:=\e^{-Lt}$, general extinction results are derived for a class of continuous adapted processes on $H$. Main applications include stochastic and deterministic fast diffusion equations with fractional Laplacians. Furthermore, we prove exponential integrability of the extinction time for all space dimensions in the singular diffusion version of the well-known Zhang-model for self-organized criticality, provided the noise is small enough. Thus we obtain that the system goes to the critical state in finite time in the deterministic and with probability one in finite time in the stochastic case.
In recent years, the Characteristic formulation of numerical relativity has found increasing use in the extraction of gravitational radiation from numerically generated spacetimes. In this paper, we formulate the Characteristic initial value problem for $f(R)$ gravity. We consider, in particular, the vacuum field equations of Metric $f(R)$ gravity in the Jordan frame, without utilising the dynamical equivalence with scalar-tensor theories. We present the full hierarchy of non-linear hypersurface and evolution equations necessary for numerical implementation in both tensorial and eth forms. Furthermore, we specialise the resulting equations to situations where the spacetime is almost Minkowski and almost Schwarszchild using standard linearization techniques. We obtain analytic solutions for the dominant $\ell=2$ mode and show that they satisfy the concomitant constraints. These results are ideally suited as testbed solutions for numerical codes. Finally, we point out that the Characteristic formulation can be used as a complementary analytic tool to the $1+1+2$ semi-tetrad formulation.
In this paper, we establish concentration inequalities both for functionals of the whole solution on an interval [0, T ] of an additive SDE driven by a fractional Brownian motion with Hurst parameter H $\in$ (0, 1) and for functionals of discrete-time observations of this process. Then, we apply this general result to specific functionals related to discrete and continuous-time occupation measures of the process.
We report metallicities and radial velocities derived from spectra at the near-infrared calcium triplet for 373 red giants in a 200 square arcminute area at the optical center of the LMC bar. These are the first spectroscopic abundance measurements of intermediate-age and old field stars in the high surface brightness heart of the LMC. The metallicity distribution is sharply peaked at the median value [Fe/H] = -0.40, with a small tail of stars extending down to [Fe/H] <= -2.1; 10% of the red giants are observed to have [Fe/H] <= -0.7. The relative lack of metal-poor stars indicates that the LMC has a "G dwarf" problem, similar to the Milky Way. The abundance distribution can be closely approximated by two Gaussians containing 89% and 11% of the stars, respectively: the first component is centered at [Fe/H] = -0.37 with standard deviation = 0.15, and the second at [Fe/H] = -1.08 with standard deviation = 0.46. Because of the central location of our field, kinematic constraints are not strong, but there is no evidence that the bar deviates from the general motion of the LMC disk. The velocity dispersion of the whole sample is 24.7 +/- 0.4 km/sec. The most metal-poor 5% of stars ([Fe/H] < -1.15) show a dispersion of 40.8 +/- 1.7 km/sec, more than twice the value for the most metal-rich 5%. The age-metallicity relation (AMR) is almost flat during the period from 5-10 Gyr ago, with an apparent scatter of +/-0.15 dex about the mean metallicity for a given age. (abstract abridged)
Recent measurements of the parameters of the Concordance Cosmology Model ($\Lambda$CDM) done in the low-redshift Universe with Supernovae Ia/Cepheids, and in the distant Universe done with Cosmic Microwave Background (CMB) imply different values for the Hubble constant (67.4 $\pm$ 0.5 km s$^{-1}$ Mpc$^{-1}$ from Planck vs 74.03 $\pm$ 1.42 km s$^{-1}$ Mpc$^{-1}$, Riess et al. 2019). This Hubble constant tension implies that either the systematic errors are underestimated, or the $\Lambda$CDM does not represent well the observed expansion of the Universe. Since quasars - active galactic nuclei - can be observed in the nearby Universe up to redshift z $\sim$ 7.5, they are suitable to estimate the cosmological properties in a large redshift range. Our group develops two methods based on the observations of quasars in the late Universe up to redshift z$\sim $4.5, with the objective to determine the expansion rate of the Universe. These methods do not yet provide an independent measurement of the Hubble constant since they do not have firm absolute calibration but they allow to test the $\Lambda$CDM model, and so far no departures from this model were found.
Let $S$ be a K3 surface with primitive curve class $\beta$. We solve the relative Gromov-Witten theory of $S \times \mathbb{P}^1$ in classes $(\beta,1)$ and $(\beta,2)$. The generating series are quasi-Jacobi forms and equal to a corresponding series of genus $0$ Gromov-Witten invariants on the Hilbert scheme of points of $S$. This proves a special case of a conjecture of Pandharipande and the author. The new geometric input of the paper is a genus bound for hyperelliptic curves on K3 surfaces proven by Ciliberto and Knutsen. By exploiting various formal properties we find that a key generating series is determined by the very first few coefficients.   Let $E$ be an elliptic curve. As collorary of our computations we prove that Gromov-Witten invariants of $S \times E$ in classes $(\beta,1)$ and $(\beta,2)$ are coefficients of the reciprocal of the Igusa cusp form. We also calculate several linear Hodge integrals on the moduli space of stable maps to a K3 surface and the Gromov-Witten invariants of an abelian threefold in classes of type $(1,1,d)$.
We prove global completeness in the expanding direction of spacetimes satisfying the vacuum Einstein equations on a manifold of the form $\Sigma \times S^{1}\times R$ where $\Sigma $ is a compact surface of genus $G>1.$ The Cauchy data are supposed to be invariant with respect to the group $S^{1}$ and sufficiently small, but we do not impose a restrictive hypothesis made in gr-qc 0112049 on the lowest eigenvalue of a relevant Laplacian. The total energy decay still holds, but its rate depends of the asymptotic value of this eigenvalue.
We report a numerical evolution of axisymmetric Brill waves. The numerical algorithm has new features, including (i) a method for keeping the metric regular on the axis and (ii) the use of coordinates that bring spatial infinity to the edge of the computational grid. The dependence of the evolved metric on both the amplitude and shape of the initial data is found.
Binary population synthesis (BPS) modelling is a very effective tool to study the evolution and properties of close binary systems. The uncertainty in the parameters of the model and their effect on a population can be tested in a statistical way, which then leads to a deeper understanding of the underlying physical processes involved. To understand the predictive power of BPS codes, we study the similarities and differences in the predicted populations of four different BPS codes for low- and intermediate-mass binaries. We investigate whether the differences are caused by different assumptions made in the BPS codes or by numerical effects. To simplify the complex problem of comparing BPS codes, we equalise the inherent assumptions as much as possible. We find that the simulated populations are similar between the codes. Regarding the population of binaries with one WD, there is very good agreement between the physical characteristics, the evolutionary channels that lead to the birth of these systems, and their birthrates. Regarding the double WD population, there is a good agreement on which evolutionary channels exist to create double WDs and a rough agreement on the characteristics of the double WD population. Regarding which progenitor systems lead to a single and double WD system and which systems do not, the four codes agree well. Most importantly, we find that for these two populations, the differences in the predictions from the four codes are not due to numerical differences, but because of different inherent assumptions. We identify critical assumptions for BPS studies that need to be studied in more detail.
We say a lattice tetrahedron whose centroid is its only non-vertex lattice point is lattice barycentric. The notation T(a,b,c) describes the lattice tetrahedron with vertices {0, e_1, e_2, a e_1 + b e_2 + c e_3}. Our result is that all such T(a,b,c) are unimodularly equivalent to T(3,3,4) or T(7,11,20).
We present results for prompt photon and inclusive $\pi^0$ production in p-p and A-A collisions at RHIC and LHC energies. We include the full next-to-leading order radiative corrections and nuclear effects, such as nuclear shadowing and parton energy loss. We find the next-to-leading order corrections to be large and $p_T$ dependent. We show how measurements of $\pi^0$ production at RHIC and LHC, at large $p_T$, can provide valuable information about the nature of parton energy loss.   We calculate the ratio of prompt photons to neutral pions and show that at RHIC energies this ratio increases with $p_T$ approaching one at $p_T \sim 10$ GeV, due to the large suppression of $\pi^0$ production. We show that at the LHC, this ratio has steep $p_T$ dependence and approaches 10% effect at $p_T \sim 20$ GeV.
In this paper, we aim at improving the tracking of road users in urban scenes. We present a constraint programming (CP) approach for the data association phase found in the tracking-by-detection paradigm of the multiple object tracking (MOT) problem. Such an approach can solve the data association problem more efficiently than graph-based methods and can handle better the combinatorial explosion occurring when multiple frames are analyzed. Because our focus is on the data association problem, our MOT method only uses simple image features, which are the center position and color of detections for each frame. Constraints are defined on these two features and on the general MOT problem. For example, we enforce color appearance preservation over trajectories and constrain the extent of motion between frames. Filtering layers are used in order to eliminate detection candidates before using CP and to remove dummy trajectories produced by the CP solver. Our proposed method was tested on a motorized vehicles tracking dataset and produces results that outperform the top methods of the UA-DETRAC benchmark.
Novel dynamic programming algorithms to count the set $D(n)$ of zero-free degree sequences of length $n$, the set $D_c(n)$ of degree sequences of connected graphs on $n$ vertices and the set $D_b(n)$ of degree sequences of biconnected graphs on $n$ vertices exactly are presented. They are all based on a recurrence of Barnes and Savage and shown to run in polynomial time and are asymptotically much faster than the previous best known algorithms for these problems. These appear to be the first polynomial time algorithms to compute $|D(n)|$, $|D_c(n)|$ and $|D_b(n)|$ to the author's knowledge and have enabled us to tabulate them up to $n=118$, the majority of which were unknown. The available numerical results of $|D(n)|$ tend to give more supporting evidence of a conjecture of Gordon F. Royle about the limit of $|D(n)|/|D(n-1)|$. The OEIS entries that can be computed by algorithms in this paper are A004251, A007721, A007722 and A095268.
Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space coordinates, in Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincar\'e-Weyl generators or $\mathfrak{gl}(n)$ generators, are constructed and R-matrix is discussed. Classification of linear realizations leading to vector-like deformed phase spaces is given. There are 3 types of spaces: $i)$ commutative spaces, $ii)$ $\kappa$-Minkowski spaces and $iii)$ $\kappa$-Snyder spaces. Corresponding star products are $i)$ associative and commutative (but non-local), $ii)$ associative and non-commutative and $iii)$ non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed.
We study the spectrum of scalar glueballs in SQCD-like theories whose gravity description is in terms of Nc D5 color branes wrapped on an S^2 inside a CY3-fold, and Nf backreacting D5 flavor branes wrapped on a non-compact two-cycle inside the same CY3-fold. We show that there exists a consistent truncation of the ten-dimensional Type IIB supergravity system to a five-dimensional non-linear sigma model consisting of four scalars coupled to gravity. Studying fluctuations of the scalars as well as the metric around particular backgrounds allows us to compute their spectra. A few different backgrounds share the same qualitative features, namely that the mass of the lightest scalar glueball increases as the number of flavors is increased, until one reaches the point Nf = 2 Nc after which the opposite behaviour is obtained. We show that the five-dimensional non-linear sigma model obeys Seiberg duality, and demonstrate this explicitly for the spectra of a class of backgrounds that are Seiberg dual to themselves.